Complex Systems
Time: Tuesday at 16:00.
Location: Room W316, Queens building
Organizer: Vasso Anagnostopoulou

DateRoomSpeakerTitle

16/01/2018 4:00 PMW316, Queens' BuildingDavide Ravotti (Bristol)Quantitative mixing for areapreserving flows on compact surfaces
Given a compact surface, we consider the set of areapreserving flows with isolated fixed points. The study of these flows dates back to Novikov in the 80s and since then many properties have been investigated. Starting from an overview of the known results, we show that typical such flows admitting several minimal components are mixing when restricted to each minimal component and we provide an estimate on the decay of correlations for smooth observables.

23/01/2018 4:00 PMW316, Queens' BuildingPaul Geffert (QMUL)Nonequilibrium dynamics of a dry friction model subjected to coloured noise
We investigate the impact of noise on a twodimensional simple paradigmatic piecewisesmooth dynamical system. For that purpose, we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time of the noise provides an additional dimension in phase space, causes a nontrivial probability current, and establishes a proper nonequilibrium regime. Furthermore, the setup allows for the study of stickslip phenomena, which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified coloured noise approximation, developed by P. Jung and P. Hänggi. The analysis of probability currents and of power spectral densities underpins the observed stickslip transition, which is related with a critical value of the noise correlation time.

30/01/2018 4:00 PMW316, Queens' BuildingBenjamin Doyon (King's College)Emergent hydrodynamics in integrable systems out of equilibrium
The hydrodynamic approximation is an extremely powerful tool to describe the behavior of manybody systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large spacetime scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitelymany conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitelymany conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized onedimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived and its relation to quantum and classical integrable systems. If time permits I will touch on the geometry that lies at its core, how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and nonequilibrium currents.
This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, JeanSébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm. 
06/02/2018 4:00 PMW316, Queens' BuildingMark Pollicott (Warwick)Constructing Gibbs measures on hyperbolic attractors
Gibbs measures are a useful class of invariant measures for hyperbolic systems, of which the best known is the natural SinaiRuelleBowen measure. It is a standard fact that the volume measure on a small piece of unstable manifold can be pushed forward under the map (or flow) and in the limit converges to the SinaiRuelleBowen measure. Pesin asked the question: How can this construction be adapted to give other Gibbs measures? In this talk we will describe one solution.

13/02/2018 4:00 PMW316, Queens' BuildingCarlos PerezEspigares (Nottingham)Making rare events typical in Markovian open quantum systems
Large dynamical fluctuations  atypical realizations of the dynamics sustained over long periods of time  can play a fundamental role in determining the properties of collective behavior of both classical and quantum nonequilibrium systems. Rare dynamical fluctuations, however, occur with a probability that often decays exponentially in their time extent, thus making them difficult to be directly observed and exploited in experiments. In this talk I will explain, using methods from dynamical large deviations, how rare dynamics of a given (Markovian) open quantum system can always be obtained from the typical realizations of an alternative (also Markovian) system. The correspondence between these two sets of realizations can be used to engineer and control open quantum systems with a desired statistics “on demand”. I will illustrate these ideas by studying the photonemission behaviour of a threequbit system which displays a sharp dynamical crossover between active and inactive dynamical phases.

21/02/2018 1:00 PME303, Queens' BuildingPedro Miguel Duarte (Lisbon)Regularity of Lyapunov exponents of random linear cocycles (JOINT SEMINAR with Probability & Applications)
In [1] Émile Le Page established the Holder continuity of the top Lyapynov exponent for irreducible random linear cocycles with a gap between its first and second Lyapunov exponents. An example of B. Halperin (see Appendix 3 in [2]) suggests that in general, uniformly hyperbolic cocycles apart, this is the best regularity that one can hope for. We will survey on recent results and limitations on the regularity of the Lyapunov exponents for random GL(2)cocycles.
[1] Émile Le Page, Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications. Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), no. 2, 109–142.
[2] Barry Simon and Michael Taylor, Harmonic analysis on SL(2,R) and smoothness of the density of states in the onedimensional Anderson model. Comm. Math. Phys. 101 (1985), no. 1, 1–19. 
27/02/2018 4:00 PMW316, Queens' BuildingEvaMaria Graefe (Imperial College)TBA

15/09/2009 3:00 PM103LaiSang Young Courant Institute, New YorkNonequilibrium steady states for certain Hamiltonian models
Nonequilibrium steady states for two classes of Hamiltonian models with different local dynamics are discussed. Models in the first class have chaotic dynamics. An easytocompute algorithm that goes from microdynamics to macroprofiles such as energy is proposed, and issues such as memory, finitesize effects and their relation to geometry are discussed. Models in the second class have integrable dynamics. They become ergodic when driven at the boundary, but continue to exhibit anomolous behavior such as nonGibbsian local distributions. The results follow from a mixture of numerical and theoretical considerations, some of which are rigorous. They are in joint works with JP Eckmann, P Balint and K Lin.

28/03/2018 10:00 AMW316, Queens' BuildingAlex Arenas (Tarragona University)TBA

29/09/2009 3:01 PM103Hugo Touchette School of Mathematical Sciences, Queen Mary, University of LondonUnusual equilibrium properties of longrange systems
Manybody systems involving longrange interactions, such as selfgravitating particles or unscreened plasmas, give rise to equilibrium and nonequilibrium properties that are not seen in shortrange systems. One such property is that longrange systems can have a negative heat capacities, which implies that these systems cool down by absorbing energy. This talk will discuss the origin of this unusual property, as well as some of its connections with phase transitions, metastability, and the nonequivalence of statistical ensembles. It will be seen that the essential difference between long and shortrange systems is that the entropy can be nonconcave as a function of the energy for longrange systems. For shortrange systems, the entropy is always concave.

06/10/2009 3:04 PM103Murad Banaji Department of Medical Physics, University College LondonCombinatorial approaches to injectivity of functions with applications to multiple equilibria in dynamical systems
The question of deciding whether a given function is injective is important in a number of applications. For example, where the function defines a vector field, injectivity is sufficient to rule out multiple fixed points of the associated flow. One useful approach is to associate sets of matrices/ generalised graphs with a function, and make claims about injectivity based on (finite) computations on these matrices or graphs. For a large class of functions, a novel way of doing this will be presented. Wellknown results on functions with signed Jacobian, and more recent results in chemical reaction network theory, are both special cases of the approach presented. However the technique does not provide a unique way of associating matrices/graphs with functions, leading to some interesting open questions.

13/10/2010 3:06 PM103Ricardo CarreteroGonzales Department of Mathematics and Statistics, San Diego State University, USADynamics of soliton chains: From soliton interactions to homoclinic tangles
Nonlinear media host a wide variety of localized coherent structures (bright and dark solitons, vortices, aggregates, spirals, etc.) with complex intrinsic properties and interactions. In many situations such as optical communications, condensed matter waves and biochemical aggregates it is crucial to study the interaction dynamics of coherent structures arranged in periodic lattices. In this talk I will present results concerning chains and lattices of coherent structures and their dynamical reductions from PDEs to ODEs, and all the way down to discrete maps. Particular attention will be given to a) spatially localized vibrations (breathers) in 1D chains of coupled bright solitons and b) vortex lattices dynamics and their crystalline configurations.

20/10/2009 3:09 PM103Uchechukwu E. Vincent Department of Physics, Lancaster University and Olabisi Onabanjo University, NigeriaControlling Multiple CurrentReversals in Synchronized Ratchets
I will centre my talk mainly on the general theme of control and synchronization, and on how the problem of multiple currentreversals in ratchets could be translated into that of achieving asymptotic stability and tracking of its dynamical and transport properties. Currentreversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on the ratchet mechanism. Research in this domain is largely motivated by applications to a variety of systems such as asymmetric crystals, semiconductor surfaces under light radiation, vortices in Josephson junction arrays, microfluidic channels, transport of ion channels and muscle contraction. Here, by considering a system of two interacting ratchets, we will demonstrate how the interaction can be used to control the reversals. In particular, we will show that current reversal that exists in a single driven ratchet system can ultimately be eliminated in the presence of a second ratchet and then establish a connection between the underlying dynamics and reversalfree regime. The conditions for currentreversalfree transport will be given. Furthermore, we will discuss briefly some applications of our results, recent challenges and possible direction for future works.

28/10/2009 4:00 PM103Yan Fyodorov School of Mathematical Sciences, University of NothinghamExtreme value statistics of 1/f noises generated by Gaussian free fields: Statistical mechanics approach
We compute the distribution of the partition functions for a class of onedimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the twodimensional Gaussian Free Field (2dGFF) along various planar curves. The method is based on an analytical continuation of the Selberg integral from positive integers to the complex plane. In particular, we unveil a duality relation satisfied by the suitable generating function of free energy cumulants in the hightemperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the [0,1] interval and unit circle. If time permits, the relation to the velocity statistics in decaying Burgers turbulence and to the distribution of length of curves in Liouville quantum gravity will be shortly discussed. The results reported are obtained in collaboration with J.P. Bouchaud, P. Le Doussal, and A. Rosso.

03/11/2009 4:00 PM103Tobias Kuna Department of Mathematics, University of ReadingRealization of low order correlation functions
Correlation functions or factorial moments are important characteristics of spatial point process. The question under consideration is to what extend the first two correlation functions identify the point processes. This is a nonlinear infinite dimension version of the classical truncated moment problem. In collaboration with J. Lebowitz and E. Speer we derived general conditions, giving rise also to a new approach to moment problems and obtain more concrete results in particular situation.

05/11/2009 3:19 PM513Jan Naudts University of Antwerp(joint with Stat Mech study group)Mathematical Aspects of Generalized Entropies and their Applications
It is a rather common belief that the only probability distribution occurring in the statistical physics of manyparticle systems is that of Boltzmann and Gibbs (BG). This point of view is too limited. The BGdistribution, when seen as a function of parameters such as the inverse temperature and the chemical potential, is a member of the exponential family. This observation is important to understand the structure of statistical mechanics and its connection with thermodynamics. It also is the starting point of the generalizations discussed below. Recently, the notion of a generalized exponential family has been introduced, both in the mathematics and in the physics literature. A subclass of this generalized family is the qexponential family, where q is a real parameter describing the deformation of the exponential function. It is the intention of this talk to show the relevance for statistical physics of these generalizations of the BGdistribution. Particular attention will go to the configurational density of classical monoatomic gases in the micro canonical ensemble. These belong to the qexponential family, where q tends to 1 as the number of particles tends to infinity. Hence, in this limit the density converges to the BGdistribution.

10/11/2009 3:21 PM103Ralph Kenna Applied Mathematics Research Centre, Coventry UniversityCANCELLED  The sitedisordered Ising model in two and four dimensions
We review the Ising model with randomsite or randombond disorder, which has been controversial in both two and four dimensions. In the twodimensional case, the controversy is between the strong universality hypothesis which maintains that the leading critical exponents are the same as in the pure case and the weak universality hypothesis, which favours dilutiondependent leading critical exponents. Here the randomsite version of the model is subject to a finitesize scaling analysis, paying special attention to the implications for multiplicative logarithmic corrections. The analysis is supportive of the scaling relations for logarithmic corrections and of the strong scaling hypothesis in the 2D case. In the fourdimensional case unusual corrections to scaling characterize the model, and the precise nature of these corrections has been debated. Progress made in determining the correct 4D scenario is outlined.

22/01/2010 4:30 PMM103Robert Johnson and Mark WaltersGraphs as electrical networks, 1

29/01/2010 4:30 PMM103Robert Johnson and Mark WaltersGraphs as electrical networks, 2

05/02/2010 4:30 PMM103Peter CameronCombinatorics of inverse semigroups (after A. Umar)
Abdullahi Umar has discovered that many celebrated sequences of combinatorial numbers, including the factorials, binomial coefficients, Bell, Catalan, Schröder, Stirling and Lah numbers solve counting problems in certain naturally defined inverse semigroups of partial bijections on a finite set. I will give an account of some of these results, together with the beginning of a study of qanalogues where we consider linear bijections between subspaces of a finite vector space (and some very interesting open problems arise).

12/02/2010 4:30 PMM103John FabenReducing graphs by involutions
We are given a graph, now pick any involution and delete all of the vertices which are moved by this involution. Repeat with the new graph until your current graph is involutionfree. This involutionfree graph is uniquely defined (up to isomorphism) by the original, ie, it is independent of the choice of involution at each stage. This is proved using a lemma of Newman onthe confluence of reduction systems.

19/02/2010 9:58 AMM103Dan Hefetz (ETH Zürich)On two generalizations of the AlonTarsi polynomial method
Abstract: In a seminal paper, Alon and Tarsi have introduced an algebraic
technique for proving upper bounds on the choice number of graphs (and thus,
in particular, upper bounds on their chromatic number). The upper bound on
the choice number of G obtained via their method, was later coined the
AlonTarsi number of G and was denoted by AT(G). They
have provided a combinatorial interpretation of this parameter in terms of
the eulerian subdigraphs of an appropriate orientation of G.
Shortly afterwards, for the special case of line
graphs of dregular dedgecolorable graphs, Alon gave another
interpretation of AT(G), this time in terms of the signed dcolorings of
the line graph. In the talk I will generalize both results.
I will then use these results to prove some choosability results.
In the first part of the talk I will introduce chromatic, choice, and
AlonTarsi numbers of graphs.
In the second part I will state the two generalizations as well as
some applications. 
19/02/2010 5:00 PMM103Mohan Shrikhande (Central Michigan)Infinite families of nonembeddable quasiresidual Menon designs
The notion of residual and derived design of a symmetric design was introduced in a classic paper by R. C. Bose (1939). A quasiresidual (quasiderived) design is a 2design which has the parameters of a residual (derived) design. The embedding problem of a quasiresidual design into a symmetric design is an old and natural question. A Menon design of order h² is a symmetric (4h²,2h²h, h²h) design. Quasiresidual and quasiderived designs of a Menon design have parameters 2(2h²+h,h²,h²h) and 2(2h²h,h²h,h²h1), respectively.
We use regular Hadamard matrices to construct nonembeddable quasiresidual and quasiderived Menon designs. As applications, the first two new infinite families of nonembeddable quasiresidual and quasiderived Menon designs are constructed. This is a joint work with T. A. Alraqad.

26/02/2010 10:02 AMM103Derek PattersonGeneralising the Inequalities of Fisher and Bose

05/03/2010 4:30 PMM103Alex O'NeillSearching for optimal block designs using Cayley graphs

12/03/2010 4:30 PMM103Benny Sudakov (UCLA)Hypergraph Ramsey problem
The Ramsey number r_{k}(s,n) is the minimum N such that every redblue coloring of the ktuples of an Nelement set contains either a red set of size s or a blue set of size n, where a set is called red (blue) if all ktuples from this set are red (blue). Determining or estimating Ramsey numbers is one of the central problems in combinatorics. In this talk we discuss recent progress on several old and very basic hypergraph Ramsey problems.
Joint work with D. Conlon and J. Fox.

19/03/2010 4:30 PMM103Bill JacksonA zerofree interval for chromatic polynomials of 3connected graphs

30/04/2010 5:30 PMM103Richard MycroftA proof of Sumner's universal tournament conjecture for large n
A tournament is an orientation of a complete graph. Sumner conjectured in 1971 that any tournament G on 2n2 vertices contains any directed tree T on n vertices. Taking G to be a regular tournament on 2n3 vertices and T to be an outstar shows that this conjecture, if true, is best possible. Many partial results have been obtained towards this conjecture.
In this talk I shall outline how a randomised embedding algorithm can be used to prove an approximate version of Sumner's conjecture, by first proving a stronger result for the case when T has bounded maximum degree. Furthermore, I will briefly sketch how by considering the extremal cases of this proof we may deduce that Sumner's conjecture holds for all sufficiently large n.
This is joint work with Daniela Kühn and Deryk Osthus.

07/05/2010 5:30 PMM103Donald Keedwell (Surrey)Quasigroup laws which imply that the quasigroup is a loop or group
Abstract: Fiala has shown with computer aid that there are 35 laws of length at most six and involving the product operation only which have
the property of the title (discounting renaming, cancelling, mirroring and symmetry). However, he has not provided humanlycomprehensible proofs of these facts.We show that it is possible to give short understandable proofs of Fiala's results and to separate the loops and groups into classes.

14/05/2010 5:30 PMM103Bhalchandra D. Thatte (Oxford)Reconstructing population pedigrees and hypergraphs
I will introduce the problem of reconstructing population pedigrees from their subpedigrees (pedigrees of subpopulations) and present a construction of pairs of nonisomorphic pedigrees that have the same collection of subpedigrees. I will then show that reconstructing pedigrees is equivalent to reconstructing hypergraphs with isomorphisms from a suitably chosen group acting on the ground set. I will then discuss some ideas to characterize nonreconstructible pedigrees.

28/05/2010 5:30 PMM103Matt FayersCrystals and partitions
Crystals are certain labelled graphs which give a combinatorial understanding for certain representations of simple Lie algebras. Although crystals are known to exist for certain important representations, understanding what they look like is tricky, and an important theme in combinatorial representation theory is constructing models of crystals, where the vertices are given by simple combinatorial objects, with combinatorial rules for determining the edges.
I'll try to give a brief but comprehensible overview to motivate, and then concentrate on one particular crystal, for which there is a family of models based on partitions.

18/06/2010 5:30 PMM203Bill JacksonRigidity of direction/length frameworks

25/06/2010 4:30 PMM103Celia Glass (City)Minimizing the number of gapzeros in binary matrices
We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows. The problem is known to be NPhard. An analysis of the structure of an optimal solution, allows us to focus on a restricted solution space, and to use an implicit representation for searching the space. We develop an exact solution algorithm, which is polynomial if the number of columns is fixed, and two constructive heuristics to tackle instances with an arbitrary number of columns. The heuristics use a novel solution representation based upon column sequencing. In our computational study, all heuristic solutions are either optimal or close to an optimum. One of the heuristics is particularly effective, especially for problems with a large number of rows.

02/07/2010 5:30 PMM103Ian Wanless (Monash)Transversals and orthogonal Latin squares
A transversal of a latin square is a selection of entries that hits each row, column and symbol exactly once. We can construct latin
squares whose transversals are constrained in various ways. For orders that are not twice a prime, these constructions yield
2maxMOLS, that is, pairs of orthogonal latin squares that cannot be extended to a triple of MOLS. If only Euclid's theorem was false, we'd
have nearly solved the 2maxMOLS problem. 
09/07/2010 5:30 AMM103Koko KayibiRandom generation of graphs with prescribed degree sequence

01/10/2010 5:30 PMM103Ryan Martin (Iowa State University)Q_2free families in the Boolean lattice
For a family of subsets of {1,...,n}, ordered by inclusion, and a partiallyordered set P, we say that the family is Pfree if it does not contain a subposet isomorphic to P. We are interested in finding ex(n,P), the largest size of a Pfree family of subsets of [n]. It is conjectured that, for any fixed P, this quantity is (k+o(1))n(n1)/2 for some fixed integer k, depending only on P.
Recently, Boris Bukh has verified the conjecture for P which are in a "tree shape". There are some other small posets Pfor which the conjecture has been verified. The smallest for which it is unknown is Q_{2}, the Boolean lattice on two elements. We will discuss the bestknown upper bound for ex(n,Q_{2}) and an interesting open problem on graph theory that, if solved, would improve this bound. This is joint work with Maria Axenovich, Iowa State University and Jacob Manske, Texas State University.

08/10/2010 5:30 PMM103Sam TarziCartan triality and the 3coloured random graph

15/10/2010 5:30 PMM103Leonard SoicherNew optimal semiLatin squares coming from 2transitive groups

22/10/2010 5:30 PMM103Donald PreeceIf at first you don't succeed ...: a combinatorial breakthrough

29/10/2010 5:30 PMM103Peter CameronGenerating a group by coset representatives
Vivek Jain asked whether, when G is a finite group and H is a corefree subgroup of G, it is possible to generate G by a set of coset representatives of H in G. The answer is yes: the proof uses a result of Julius Whiston about the maximal size of an independent set in the symmetric group.
I will discuss the proof and some slight extensions, and will also talk about a parameter of a group conjecturally related to the maximum size of an independent set; this involves an open question about the subgroup lattices of finite groups.

05/11/2010 4:00 PMM103Rudolf Ahlswede (Bielefeld)Identification as a new concept of solution for probabilistic algorithms

05/11/2010 5:00 PMM103Robert Woodrow (Calgary)Intervals
The family of intervals of a binary structure on a set S satisfies well known properties:
 The empty set, the set S and every singleton is an interval.
 The intersection of a family of intervals is an interval.
 If X and Y are intervals with non empty intersection, the union is an interval.
 If X and Y are intervals and Y \ X is non empty then X \ Y is an interval.
 The union of an updirected family of intervals is an interval.
A family of subsets of S with these properties is called weakly partitive.
An interval X is called strong provided that for each interval Y, if the intersection of X and Y is nonempty then Y is a subset of X or Y contains X. Using the notion of strong interval, and a study of the characteristics of elements of a weakly partitive family, Pierre Ille and I gave a proof in [1] of his result that given a weakly partitive family I on a set Sthere is a binary structure on S whose intervals are exactly the elements of I.
[1] Weakly partitive families on infinite sets, Pierre Ille and Robert E. Woodrow, Contributions to Discrete Mathematics, Vol 4, Number 1, 2009 pp. 54–79.

12/11/2010 4:30 PMM103Mark JerrumThe Ising model on some classes of matroids
Classically, the Ising model in statistical physics is defined on a graph. But through the random cluster formulation we can make sense of the Ising partition function in the wider context of an arbitrary matroid. I expect most of the talk will be spent setting the scene. But eventually I'll come round to discussing the computational complexity of evaluating the partition function on various classes of matroids (graphic, regular and binary). I'm not a physicist nor a cardcarrying matroid theorist, so the talk should be pretty accessible.
This is joint work with Leslie Goldberg (Liverpool).

26/11/2016 4:30 PMM103Aylin CakirogluOn the optimality of truncations of projective spaces

10/12/2010 4:30 PMM103Mark WaltersEuclidean Ramsey Theory
A finite set X in some Euclidean space R^{n} is called Ramsey if for any k there is a d such that whenever R^{d} is kcoloured it contains a monochromatic set congruent to X. A long standing open problem is to characterise the Ramsey sets.
In this talk I will discuss the background to this problem, a new conjecture, and some group theoretic questions this new conjecture raises.

14/01/2011 4:30 PMM103Graham Farr (MonashTransforms, minors and generalised Tutte polynomials

21/01/2011 4:30 PMM103Charles Little (Massy University, NZ)A characterisation of PMcompact bipartite and nearbipartite graphs
The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. We characterise bipartite graphs and nearbipartite graphs whose perfect matching polytopes have diameter 1.

28/01/2011 4:30 PMM103Leonard SoicherConstructing semiLatin squares, exact comparison of their statistical efficiency measures, and a conjecture of R.A. Bai

04/02/2011 4:30 PMM103Dan HefetzHitting time results for MakerBreaker games
We prove that almost surely a random graph process becomes Maker's win in the MakerBreaker games ``kvertexconnectivity'', ``perfect matching'' and ``Hamiltonicity'' exactly when its minimum degree first becomes 2k, 2 and 4 respectively.

11/02/2011 4:30 PMM103Donald KeedwellConstructions of complete sets of orthogonal diagonal Sudoku latin squares

25/02/2011 4:30 PMM103Peter KeevashHypergraph packing, 1

04/03/2011 4:00 PMM103Richard MycroftHypergraph packing, 2

11/03/2011 4:30 PMM103Alan Sokal (NYU and UCL)Roots of a formal power series, with applications to graph enumeration and qseries, 1

18/03/2011 4:30 PMM103Alan Sokal (NYU and UCL)Roots of a formal power series, with applications to graph enumeration and qseries, 2

25/03/2011 4:30 PMM103Alan Sokal (NYU and UCL)Roots of a formal power series, with applications to graph enumeration and qseries, 3

01/04/2011 5:30 PMM103Dudley StarkThe asymptotic number of spanning forests of complete bipartite graphs

08/04/2011 5:30 PMM103Alan Sokal (NYU and UCL)Roots of a formal power series, with applications to graph enumeration and qseries, 4

13/05/2011 5:30 PMM103John McSorley (Southern Illinois)On (n,k,lambda)Ovals and (n,k,lambda)Cyclic Difference Sets, Ladders, Hadamard Ovals and Related Topics
See here [PDF 35KB].

20/05/2011 5:30 PMM103Max GadouleauCombinatorial representations
Combinatorial representations are generalisations of linear representations of matroids based on functions over an alphabet. In this talk, we define representations of a family of bases (rsets of an nset). We first show that any family is representable over some finite alphabet. We then link this topic with design theory, and especially Wilson's theory of PBDclosed sets. This allows us to show that all graphs (r=2) can be represented over all large enough alphabets. If time permits, we finally give a characterisation of families representable over a given alphabet as subgraphs of a determined hypergraph.

12/07/2011 5:30 PMM103Douglas StonesLatin squares and network motifs

07/10/2011 5:30 PMM103Peter CameronConference matrices
A conference matrix is an n×n matrix C with zeros on the diagonal and entries ±1 elsewhere which satisfies CC^{T}=(n1)I. Such a matrix has the maximum possible determinant given that its diagonal entries are zero and the other entries have modulus at most 1.
Conference matrices first arose in the 1950s in connection with conference telephony, and more recently have had applications in design of experiments in statistics. They have close connections with other kinds of combinatorial structure such as strongly regular graphs and Hadamard matrices.
It is known that the order of a conference matrix must be even, and that it is equivalent to a symmetric matrix if n is congruent to 2 (mod 4) or to a skewsymmetric matrix if n is congruent to 0 (mod 4). In the second case, they are conjectured to exist for all admissible n, but there are some restrictions in the first case (for example, there no conference matrices of order 22 or 34). Statisticians are interested to know what is the maximum possible determinant in cases where a conference matrix does not exist.
I will give a gentle introduction to the subject, and raise a recent open question by Dennis Lin.

14/10/2011 5:30 PMM103Geoff Whittle (LMS Aitken Lecturer)Wellquasiordering binary matroids
The Graph Minors Project of Robertson and Seymour is one of the highlights
of twentiethcentury mathematics. In a long series of mostly difficult papers
they prove theorems that give profound insight into the qualitative structure
of members of proper minorclosed classes of graphs. This insight enables
them to prove some remarkable banner theorems, one of which is that in
any innite set of graphs there is one that is a minor of the other; in other
words, graphs are wellquasiordered under the minor order.A canonical way to obtain a matroid is from a set of columns of a matrix over
a eld. If each column has at most two nonzero entries there is an obvious
graph associated with the matroid; thus it is not hard to see that matroids
generalise graphs. Robertson and Seymour always believed that their results
were special cases of more general theorems for matroids obtained from
matrices over nite elds. For over a decade, Jim Geelen, Bert Gerards and
I have been working towards achieving this generalisation. In this talk I will
discuss our success in achieving the generalisation for binary matroids, that
is, for matroids that can be obtained from matrices over the 2element eld.In this talk I will give a very general overview of my work with Geelen
and Gerards. I will not assume familiarity with matroids nor will I assume
familiarity with the results of the Graph Minors Project. 
21/10/2011 5:30 PMM103Emil VaughanAutomated proofs of Turán densities using Razborov's flag algebra method

28/10/2011 5:30 PMM103David EllisTriangleintersecting families of graphs
A family of graphs F on a fixed set of n vertices is said to be triangleintersecting if for any two graphs G,H in F, the intersection of G and H contains a triangle. Simonovits and Sos conjectured that such a family has size at most (1/8)2^{{n choose 2}}, and that equality holds only if F consists of all graphs containing some fixed triangle. Recently, the author, Yuval Filmus and Ehud Friedgut proved this conjecture, using discrete Fourier analysis, combined with an analysis of the properties of random cuts in graphs. We will give a sketch of our proof, and then discuss some related open questions.
All will be based on joint work with Yuval Filmus (University of Toronto) and Ehud Friedgut (Hebrew University of Jerusalem).

04/11/2011 4:30 PMM103Demetres ChristofidesDiameters of random Cayley graphs
See here [PDF 91KB].

10/11/2011 4:30 PMM103David Conlon (Cambridge)On two extensions of Ramsey's theorem

18/11/2011 4:30 PMM103Jessica Enright (Alberta)Listcolouring interval and permutation graphs

25/11/2011 4:30 PMM103Mark JerrumA graph polynomial, a Markov chain and a counterexample
Ge and Stefankovic recently introduced a novel twovariable graph polynomial. When specialised to a bipartite graphs G and evaluated at the point (1/2,1), the polynomial gives the number of independent sets in the graph. Inspired by this polynomial, they also introduced a Markov chain which, if rapidly mixing, would provide an efficient sampling procedure for independent sets in G. The proposed Markov chain is promising, in the sense that it overcomes the most obvious barrier to mixing. Unfortunately, by exhibiting a sequence of counterexamples, we can show that the mixing time of their Markov chain may be exponential in the size of the instance G.
I'll play down the complexitytheoretic motivation for this investigation, and concentrate on the combinatorial aspects, namely the graph polynomial and the construction of the counterexamples.
This is joint work with Leslie Ann Goldberg (Liverpool). A preprint is available as arXiv:1109.5242.

02/12/2011 4:30 PMM103Max GadouleauThe combinatorics of memoryless computation
An elementary problem when writing a computer program is how to swap the contents of two variables. Although the typical approach consists of using a buffer, this operation can actually be performed using XOR without memory. In this talk, we aim at generalising this approach to compute any function without memory.
We introduce a novel combinatorial framework for procedural programming languages, where programs are allowed to update only one variable at a time without the use of any additional memory. We first prove that any function of all the variables can be computed in this fashion. Furthermore, we prove that any bijection can be computed in a linear number of updates. We conclude the talk by going back to our seminal example and deriving the exact number of updates required to compute any manipulation of variables.

09/12/2011 4:30 PMM103Standa Zivny (Oxford)The complexity of conservativevalued CSPs

13/01/2012 4:30 PMM103Thomas MuumllerPresentations associated with group actions on sets

20/01/2012 4:30 PMM103Peter CameronSmall subsquares of Latin squares
I will talk about some work of Ian Wanless and his student Joshua Browning, and some further work that Ian and I did last month.
We are interested in the maximum number of subsquares of order m which a Latin square of order n can have, where we regard m as being fixed and n as varying and large. In many cases this maximum is (up to a constant) a power n^{r}, for some exponent r depending on m. However, we cannot prove that this always holds; the smallest value of m for which it is not known is m = 7.
A related problem concerns the maximum number of Latin squares isotopic to a fixed square of order m.

27/01/2012 4:30 PMM103Olof SisaskArithmetic progressions in sumsets via probability, geometry and analysis
We shall use a theorem of probability to prove a geometrical result, which when applied in an analytical context yields an interesting and surprisingly strong result in combinatorics on the existence of long arithmetic progressions in sums of two sets of integers. For the sake of exposition, we might focus on a version of the final result for vector spaces over finite fields: if A is a subset of F_{q}^{n} of some fixed size, then how large a subspace must A+A contain?
Joint work with Ernie Croot and Izabella Laba.

03/02/2012 4:30 PMM103Simeon Ball (UPC, Barcelona)Complete bipartite Turan numbers
Let H be a graph. The function ex(n,H) is the maximum number of edges that a graph with n vertices can have, which contains no subgraph isomorphic to H.
If H is not bipartite then the asymptotic behaviour of ex(n,H) is known, but if H is bipartite then in general this is not the case. This talk will focus on the case that H is a complete bipartite graph. I will review the previous constructions from a geometrical point of view and explain how this enables us to improve the lower bound of ex(n,K_{5,5}).

10/02/2012 4:30 PMM103R. A. BaileyThe Levi graph and the concurrence graph

24/02/2012 4:30 PMM103Robert JohnsonHamilton cycles and matchings with constraints on pairs of edges

09/03/2012 4:30 PMM103Catherine Greenhill (New South Wales)Making Markov chains less lazy
There are only a few methods for analysing the rate of convergence of an ergodic Markov chain to its stationary distribution. One is the canonical path method of Jerrum and Sinclair. This method applies to Markov chains which have no negative eigenvalues. Hence it has become standard practice for theoreticians to work with lazy Markov chains, which do absolutely nothing with probability 1/2 at each step. This must be frustrating for practitioners, who want to use the most efficient Markov chain possible.
I will discuss how laziness can be avoided by the use of a twentyyear old lemma of Diaconis and Stroock's, or my recent modification of that lemma. As an illustration, I will apply the new lemma to Jerrum and Sinclair's wellknown chain for sampling perfect matchings in a bipartite graph.

16/03/2012 4:30 PMM103Thomas PrellbergOn qdeformed algebraic and linear functional equations arising in lattice path enumeration

30/03/2012 5:30 PMM103Robert Schumacher (City)Acyclic orientations of graphs, 2

04/05/2012 3:00 PMM103Choongbum Lee (UCLA)Robustness of graphs  case study: Dirac's theorem
A typical result in graph theory can be read as following: under certain conditions, a given graph G has some property P. For example, a classical theorem of Dirac asserts that every nvertex graph G of minimum degree at least n/2 is Hamiltonian, where a graph is called Hamiltonian if it contains a cycle that passes through every vertex of the graph.
Recently, there has been a trend in extremal graph theory where one revisits such classical results, and attempts to see how strongly G possesses the property P. In other words, the goal is to measure the robustness of G with respect to P. In this talk, we discuss several measures that can be used to study robustness of graphs with respect to various properties. To illustrate these measures, we present three extensions of Dirac's theorem.

04/05/2012 4:00 PMM103Hao Huang (UCLA)Extremal problems in Eulerian digraphs
Graphs and digraphs behave quite differently, and many classical results for graphs are often trivially false when extended to general digraphs. Therefore it is usually necessary to restrict to a smaller family of digraphs to obtain meaningful results. One such very natural family is Eulerian digraphs, in which the indegree equals outdegree at every vertex.
In this talk, we discuss several natural parameters for Eulerian digraphs and study their connections. In particular, we show that for any Eulerian digraph G with n vertices and m arcs, the minimum feedback arc set (the smallest set of arcs whose removal makes G acyclic) has size at least m^{2}/2n^{2} + m/2n, and this bound is tight. Using this result, we show how to find subgraphs of high minimum degrees, and also long cycles in Eulerian digraphs. These results were motivated by a conjecture of Bollobas and Scott.
Joint work with Ma, Shapira, Sudakov and Yuster.

18/05/2012 5:30 PMM103Matt FayersGeneralised cores
This talk is on the combinatorics of partitions. Given a positive integer s, the set of scores is a highly structured subset of the set of all partitions, which is important in representation theory. I'll take two positive integers s,t, and define a set of partitions which includes both the set of scores and the set of tcores, and is somehow supposed to be the appropriate analogue of the union of these two sets.
This work is somewhat unfinished, and needs a new impetus. So I'll be hoping for some good questions!

08/06/2012 5:30 PMM103Bill JacksonRadically solvable graphs
A 2dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical extension of the field of rationals extended by the squared edge lengths. We show that the radical solvability of a generic framework depends only on its underlying graph and characterise which planar graphs give rise to radically solvable generic frameworks. We conjecture that our characterisation extends to all graphs. This is joint work with J. C. Owen (Siemens).

20/07/2012 5:30 PMM103Koko KayibiSampling ecological occurrence matrices
Ecological occurrence matrices, such as Darwin finches tables, are 0,1matrices whose rows are species of animals and colums are islands, and the (i,j) entry is 1 if animal i lives in island j, and is 0 otherwise. Moreover the row sums and columns sums are fixed by field observation of these islands. These occurence matrices are thus just bipartite graphs G with a fixed degree sequence and where V_{1}(G) is the set of animals and V_{2}(G) is the set of islands. The problem is, given an occurrence matrix, how to tell whether the distribution of animals is due to competition or to chance. Thus, researchers in Ecology are highly interested in sampling easily and uniformly ecological occurrence tables so that, by using Monte Carlo methods, they can approximate test statistics allowing them to prove or disprove some null hypothesis about competitions amongst animals.
Several algorithms are known to construct realizations on n vertices and m edges of a given degree sequence, and each one of them has its strengths and limitations. Most of these algorithms can be fitted in two categories: MonteCarlo Markov chains methods that are based on edgeswappings, and sequential sampling methods that are based on starting from an empty graph on n vertices and adding edges sequentially according to some probability scheme. We present a new algorithm that samples uniformly all simple bipartite realizations of a degree sequence and whose basic ideas may be seen as implementing a dual sequential method, as it inserts sequentially vertices instead of edges.
The running time of our algorithms is O(m) where m is the number od edges in any realization. The best algorithms that we know of are the one implicit in [1] that has a running time of O(ma_{max} where a_{max} is the maximum of the degrees, but is not uniform. Similarly, the algorithm presented by Chen et al. [3] does not sample uniformly, but nearly uniformly. Moreover the edgeswapping Markov Chains pionneered by Brualdi [2] and Kannan et al. [5], and much used by reseachers in Ecology, have just been proven in [4] to be fast mixing for semiregular degree sequences only.
 M. Bayati, J. H. Kim, and A. Saberi, A sequential algorithm for generating random graphs, Algorithmica 58 (2010), 860910.
 R. A. Brualdi, Matrices of zeroes and ones with fixed row and column sum vectors. Lin. Algebra Appl. 33 (1980), 159231.
 Y. Chen, P. Diaconis, S. Holmes, J. S. Liu, Sequential Monte Carlo methods for statistical analysis of tables, J. Am. Stat. Assoc. 100 (2005), 109120.
 P. L. Erdos, I. Miklós and Z. Toroczkai, A simple HavelHakimi type algorithm to realize graphical degree sequences of directed graphs, Electron. J. Combin. 17(1) (2010), #R66.
 R. Kannan, P. Tetali and S. Vempala, Simple Markovchain algorithms for generating bipartite graphs and tournaments, Random Struct. Algorithms 14(4) (1999), 293308.

24/08/2012 5:30 PMM103Mikkel Thorup (Bell Labs)The maximal block overhang problem

30/08/2012 5:30 PMM103Katarzyna RybarczykKrzywdzinskaComparison of random intersection graphs with ErdosRenyi graphs

05/10/2012 5:30 PMM103Peter CameronEntropy, partitions, groups and association schemes, 1
This is the first in a short series inspired by the talks by Terence Chan at our recent workshop on "Information flows and information bottlenecks". No familiarity with the talks will be assumed.
I will define the entropy function of a family of random variables on a finite probability space. I will prove Chan's theorem that it can be approximated (up to a scalar multiple) by the entropy function obtained when G is a finite group (carrying the uniform distribution) and the random variables are associated with a family of subgroups of G: the random variable associated with H takes a group element to the coset of H containing it.

12/10/2012 5:30 PMM103Rosemary BaileyEntropy, partitions, groups and association schemes, 2
This is the second in a short series inspired by the talks by Terence Chan at our recent workshop on "Information flows and information bottlenecks". No familiarity with the talks will be assumed.
A partition is uniform if all its parts have the same size. I will define orthogonality of partitions, and interpret orthogonality in terms of the entropy of the associated random variables. I will explain how a sublattice of the partition lattice consisting of mutually orthogonal uniform partitions gives rise to an association scheme.

26/10/2012 5:30 PMM103Dhruv MubayiQuasirandom hypergraphs
Since the foundational results of Thomason and ChungGrahamWilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this history, and then describe our recent results that provide such a generalization and unify much of the previous work. One key new aspect in the theory is a systematic study of hypergraph eigenvalues. If time permits I will show some applications to Sidorenko's conjecture and the certification problem for random kSAT. This is joint work with John Lenz.

02/11/2012 4:30 PMM103Sune JakobsenEntropy, partitions, groups and association schemes, 4
This talk will continue the discussion from previous talks in the series.

30/11/2012 1:29 PMM103Mark JerrumReducing graphs by automorphisms
Fix a prime p. Starting with any finite undirected graph G, pick an automorphism of G of order p and delete all the vertices that are moved by this automorphism. Apply the same procedure to the new graph, and repeat until a graph G* is reached that has no automorphisms of order p. Is the reduced graph G* uniquely defined (up to isomorphism) by G? I..e., is G* independent of the sequence of automorphisms chosen?
In a CSG in 2010 John Faben showed that the answer is "yes'' in the special case p = 2 (i.e., reduction by involutions) using Newman's Lemma on confluence of reduction systems. Later, he noticed that the general case can be handled using the socalled Lovász vector of a graph. I'll prove the general result and sketch some consequences to the extent that time allows.

07/12/2012 4:30 PMM103Fiachra KnoxPolynomialtime perfect matchings in dense hypergraphs

11/01/2013 4:30 PMM103Anthony HiltonHall's Theorem and extending latinized rectangles

25/01/2013 4:30 PMM103Peter CameronFinding a derangement
A derangement is a permutation with no fixed points.
An elementary theorem of Jordan asserts that a transitive permutation group of degree n>1 contains a derangement. Arjeh Cohen and I showed that in fact at least a fraction 1/n of the elements of the group are derangements. So there is a simple and efficient randomised algorithm to find one: just keep picking random elements until you succeed.
Bill Kantor improved Jordan's theorem to the statement that a transitive group contains a
derangement of prime power order. The theorem is constructive but requires the classification of finite simple groups. Emil Vaughan showed that Kantor's theorem yields a polynomialtime (but not at all straightforward) algorithm for finding one.This month, Vikraman Arvind from Chennai posted a paper on the arXiv giving a very simple deterministic polynomialtime algorithm to find a derangement in a transitive group. The proof is elementary and combinatorial.

01/02/2013 1:39 PMM103Murad Banaji (Portsmouth)Matrix stability from bipartite graphs
To what extent is the spectrum of a matrix determined by its "structure"? For example, what claims can be made simultaneously about all matrices in some qualitative class (i.e. with some fixed sign pattern)? Qualitative classes are naturally associated with signed digraphs or signed bipartite graphs, and some nice theory relates matrix spectra to structures in these graphs. But there are more exotic ways of associating matrixsets, not necessarily qualitative classes, with graphs (perhaps directed, signed, etc), and extracting information from the graphs. In applications, a quick graphcomputation may then suffice to make surprising claims about a family of systems. I'll talk about some recent results and open problems in this area, focussing in particular on the use of compound matrices.

08/02/2013 4:30 PMM103Leonard SoicherOptimal designs with minimum PVabberration

15/03/2013 4:00 PMM103Aylin CakirogluOptimal regulargraph designs

22/03/2013 4:00 PMM103Marcin KrzywkowskiTrees having many minimal dominating sets

19/04/2013 5:30 PMM103Tom Bohman (CarnegieMellon)Cube packing problems and zeroerror information theory

10/05/2013 5:30 PMM103Mikhail Klin (BGU)Some new infinite families of nonSchurian association schemes

17/05/2013 5:30 PMM103Daniel Kral' (Warwick)Algorithms for firstorder model checking
Metaalgorithms for deciding properties of combinatorial structures have recently attracted a significant amount of attention. For example, the famous theorem of Courcelle asserts that every property definable in monadic second order logic can be decided in linear time for graphs with bounded treewidth.
We focus on deciding simpler properties, those definable in first order (FO) logic. In the case of graphs, FO properties include the existence of a subgraph or a dominating set of a fixed size. Classical results include the almost linear time algorithm of Frick and Grohe which applies to graphs with locally bounded treewidth. In this talk, we first survey commonly applied techniques to design FPT algorithms for FO properties. We then focus on one class of graphs, intersection graphs of intervals with finitely many lengths, where these techniques do not seem to apply in a straightforward way, and we design an FPT algorithm for deciding FO properties for this class of graphs.
The talk contains results obtained during joint work with Ganian, Hlineny, Obdrzalek, Schwartz and Teska.

13/05/2013 5:30 PMM103Michelle KendallCombinatorial aspects of key predistribution schemes: designs, hypergraphs and expansion

27/09/2013 5:30 PMM103Chris Dowden (RHUL)Agreement protocols in the presence of a mobile adversary
Suppose various processors in a network wish to reach agreement on a particular decision. Unfortunately, some unknown subset of these may be under the control of a malicious adversary who desires to prevent such an agreement being possible.
To this end, the adversary will instruct his "faulty" processors to provide inaccurate information to the nonfaulty processors in an attempt to mislead them. The aim is to construct an "agreement protocol" that will always foil the adversary and enable the nonfaulty processors to reach agreement successfully (perhaps after several rounds of communication).
In traditional agreement problems, it is usually assumed that the set of faulty processors is "static", in the sense that it is chosen by the adversary at the start of the process and then remains fixed throughout all communication rounds. In this talk, we shall instead focus on a "mobile" version of the problem, providing results both for the case when the communications network forms a complete graph and also for the general case when the network is not complete.

04/10/2013 5:30 PMM103Peter CameronA graph covering problem
In 1983, Allan Schwenk posed a problem in the American Mathematical Monthly asking whether the edge set of the complete graph on ten vertices can be decomposed into three copies of the Petersen graph. He, and O. P. Lossers (the problemsolving group at Eindhoven University run by Jack van Lint – "oplossers" is Dutch for "solvers") gave a negative solution in 1987. This year, Sebastian Cioaba and I considered the question: for which m is it possible to find 3m copies of the Petersen graph which cover the complete graph m times. We were able to show that this is possible for all natural numbers m except for m = 1. I will discuss the proof, which involves three parts: one uses linear algebra, one uses group theory, and one is barehands.
Of course this problem can be generalised to an arbitrary graph G: Given a graph G on n vertices, for which integers mcan one cover the edges of K_{n} m times by copies of G? I will say a bit about what we can do, and pose some very specific problems.

11/10/2013 5:30 PMM103Stephen Tate (Warwick)Combinatorics in statistical mechanics
Combinatorial species of structure has been a subject which has had a great impact on Statistical Mechanics, especially through the use of generating functions. It has been described as a Rosetta stone for the key models of Statistical Mechanics (Faris 08) through the way in which it has the capacity to abstract and generalise many of the key features in Statistical Mechanical Models. The talk will focus on developing the main notions of these species of structure and the algebraic identity called LagrangeGood inversion, a method of finding the coefficients of an inverse power series. I will introduce some of the key concepts of Statistical Mechanics which indicate how they can be understood in the context of the combinatorial tools we have. These interpretations also indicate some interesting combinatorial identities. The final emphasis is on how the LagrangeGood inversion can help us to obtain a virial expansion for a gas comprising of many types of particle, as was used in a recent paper (Jansen, T. Tsagkarogiannis, Ueltschi).

18/10/2013 5:30 PMM103Alex FinkMatroid polytope valuations

01/11/2013 2:31 PMM103John SheehanEven orientations of graphs
We examine the structure of 1extendable graphs G which have no even Forientation where F is a fixed 1factor of G. In the case of regular graphs, graphs of connectivity at least four and of graphs of maximum degree three, a characterization is given.
Terminology A graph G is 1extendable if every edge belongs to at least one 1factor. An orientation of a graph G is an assignment of a "direction" to each edge of G. Now suppose that G has a 1factor F. Then an even Forientation of G is an orientation in which each Falternating cycle has exactly an even number of edges directed in the same fixed direction around the cycle.

22/11/2013 4:30 PMM103Francis Edward Su (Harvey Mudd College)Combinatorial fixed point theorems
The Brouwer fixed point theorem and the BorsukUlam theorem are beautiful and wellknown theorems of topology that admit combinatorial analogues: Sperner's lemma and Tucker's lemma. In this talk, I will trace recent connections and generalizations of these combinatorial theorems, including applications to the social sciences.

29/11/2013 4:30 PMM103Heiko GrossmannThe distance between two strict weak orders
Consider two strict weak orders (that is irreflexive, transitive, nontotal relations) on the same finite set. How similar are the two? This question is motivated by the statistical question of association between two rankings which contain ties. In order to assess the similarity of the orders I will present an approach where the lack of agreement is assessed by counting the number of certain operations that are needed to transform one weak order into the other. The resulting measure is a symmetric and positive definite function but does not satisfy the triangle inequality. Hence, technically, it is a distance but not a metric. So far the proposed distance can only be computed recursively. Input from the audience which would help me to derive a closed form solution and pointers to related "pure" literature I am not aware of will be greatly appreciated.

06/12/2013 4:30 PMM103Dang Nhat AnhGuessing game and fractional clique cover strategy
Guessing game is a variant of "guessing your own hat" game and can be played on any simple undirected graph. The aim of this game is to maximise the probability of the event that all players guess correctly their own value without any communication. The fractional clique cover strategy for playing the guessing game was developed by Christofides and Markstrom and was conjectured to be the optimal strategy. In this talk, we will construct some counterexamples to this conjecture.

13/12/2013 4:30 PMM103Peter Cameron, Robert SchumacherAcyclic orientations and polyBernoulli numbers
Acyclic orientations of a graph arise in various applications, including heuristics for colouring. The number of acyclic orientations is an evaluation of the chromatic polynomial. Stanley gave a formula for the average number of acyclic orientations of graphs with n vertices and m edges. Recently we have found the graphs with the minimum number of acyclic orientations, but the more interesting question about the maximum number is still open.
The regular complete bipartite graph (on an even number of vertices) is thought to maximise the number of acyclic orientations. Unexpectedly, the number turns out to be a polyBernoulli number, one of a family of numbers connected with polylogarithms. We will try to explain these connections.

17/01/2014 4:30 PMM103Leonard Soicher (QMUL)On cliques in edgeregular graphs
An edgeregular graph with parameters (v,k,t) is a regular graph of order v and valency k, such that every edge is in exactly t triangles, and a clique in a graph is a set of pairwise adjacent vertices. I will apply a certain quadratic "block intersection" polynomial to obtain information about cliques in an edgeregular graph with given parameters.

24/01/2014 4:30 PMM103Brett Stevens (Carleton University, Ottawa)Partition Graphs and characterization of designs by graph homomorphisms
Software testing makes use of combinatorial designs called covering arrays. These arrays are a generalization of Latin Squares and orthogonal arrays. Idealy we look to use the smallest possible array for the given parameters, but this is a hard problem. We define a family of graphs, partition graphs, which give a full characterization of optimal covering arrays using homomorphisms. We investigate these graphs and are able to determine the diameter, and for some subfamilies, the clique and chromatic number and homomorphic core of these graphs.
There are many open problems involving these graphs 
17/11/2009 4:00 PM103Erik Curiel Department of Philosophy, Logic and Scientific Method, London School of EconomicsCANCELLED  Classical mechanics is Lagrangian; it is not HamiltonianSeminar series:
One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems.

24/11/2009 4:00 PM103Amanda Turner Department of Mathematics and Statistics,Lancaster UniversityScaling limits of random growth modelsSeminar series:
In 1998 Hastings and Levitov proposed a model for planar random growth such as diffusionlimited aggregation (DLA) and the Eden model, in which clusters are represented as compositions of conformal mappings. I shall introduce an anisotropic version of this model, and discuss some of the natural scaling limits that arise. I shall show that very different behaviour can be seen in the isotropic case, and that here the model gives rise to a limit object known as the Brownian web.

27/01/2011 4:00 PMM513Debabrata Panja (Amsterdam)Anomalous polymer dynamics... anomalous? It is quite normalSeminar series:"Anomalous" refers to an anomaly, or, a situation out of the ordinary. In stochastic systems, anomalous dynamics is used to refer to sub or superdiffusive behavior, i.e, diffusive behavior is considered normal, or ordinary. In contrast, the dynamics of a tagged monomer of a polymer, for times less than the polymer's terminal relaxation time, is always subdiffusive. In polymeric systems this is considered normal. Standard examples of anomalous polymer dynamics are single polymeric systems such as phantom Rouse, selfavoiding Rouse, Zimm (both in good and theta solvents), reptation, adsorption and translocation; and manypolymeric systems such as polymer melts. In this talk I will argue that the trajectory description of tagged monomers in polymeric systems is robustly formulated by the Generalized Langevin Equation (GLE); the basis of which stems from the polymers' relaxation response to local strains, mediated by chain connectivity. The GLE formulation allows one to also describe polymer dynamics under weak forces. Further, I will demonstrate that the probabilistic description of tagged monomer trajectories in space is given by fractional Brownian Motion (fBM).

08/12/2009 4:00 PM103Neil O'Connell Mathematics Institute, University of WarwickDirected polymers and the quantum Toda latticeSeminar series:
I will present a result which gives a characterization of the law of the partition function of a Brownian directed polymer model in terms of the eigenfunctions of the quantum Toda lattice, and has close connections to random matrix theory.

15/12/2009 4:00 AM103Richard A. Watson School of Electronics and Computer Science, University of SouthamptonGlobal adaptation in systems of selfish components: A connectionist view of evolutionSeminar series:Darwin's 'tangled bank' passage depicts an intricate network of relationships between species in an ecosystem that is holistically unstructured. Each species may have numerous welladapted interdependencies with other species, but because each species is independently or 'selfishly' motivated by natural selection, and the ecosystem as a whole is not a unit of selection, ecosystem structure cannot be holistically adapted. The work we present challenges this doctrine. We show that evolved changes to interspecies relationships 'wire together' species the commonly cooccur. This simple observation has an intuitive explanation but significant consequences for ecosystem behaviour. This kind of change causes an ecosystem as a whole to develop an associative memory that can 'recall' past configurations, and under general conditions arrive at configurations of species that are globally adaptive even though each species is acting selfishly. We can understand how these results follow from this observation using associative learning theory from computational neuroscience. This implies that interspecies relationships are not merely tangled, but exhibit adaptive organisational principles in common with connectionist models of organismic learning. Whereas prior evolutionary theory treats ecological relationships and dynamics merely as the backdrop to the adaptation of the entities therein, we suggest a connectionist view of evolutionary adaptation where the relationships between entities and their dynamical interactions take the foreground. Understanding how systemlevel adaptation is possible in systems of selfish components, and how subsets of synergistic agents mutually reinforce conditions that are selfsustaining, sheds light on vital evolutionary questions such as the evolution of individuality, the major evolutionary transitions and the evolution of biological complexity.

15/01/2010 3:00 PM513Malte Henkel Groupe de Physique Statistique, Université de Nancy, FranceIntroduction to local scaleinvarianceSeminar series:Nonequilibrium critical phenomena are wellknown from a multitude of examples. I propose to generalise dynamical scaling to a local form of scaleinvariance. The present state of the art, and the main ingredients, will be presented and some tests of the theory, taken form ageing phenomena, will be outlined.

19/01/2010 4:00 PM103Vladimir Belitsky Instituto de Matemática e Estatística, Universidade de São Paulo, BrazilAnalytic results for a model of collective human behaviourSeminar series:We shall talk about several specific Heterogeneous Interacting Agent Models. Such models have been successfully used for explaining phenomena that arise from interaction of individuals that act by similar rules but may have different preferences and may react differently to the same social influence. Those exposed in our talk mirror the formation of the aggregate excess demand in a duopoly market and the price cycles in a stock market. The construction of Heterogeneous Interacting Agent Models is based on ideas from the Statistical Mechanics and the Interacting Particle Systems areas, however the technique used for analysis of the models is usually different from the traditional techniques of these areas. We shall explain carefully the basic of the construction and the approaches that may lead to analytic solution. Several open but maybe not too hard problems will be posed. They may be helpful for those who wish to enter the area of the Heterogeneous Interacting Agent Models and their applications.

26/01/2010 4:00 PM103Erik Curiel Department of Philosophy, Logic and Scientific Method, London School of EconomicsClassical mechanics is Lagrangian; it is not HamiltonianSeminar series:One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems.

02/02/2010 4:00 PM103Vivo Pierpaolo International Center for Theoretical Physics, Trieste, ItalyHow many eigenvalues of a Gaussian matrix are positive?Seminar series:The index of a random matrix (i.e. the number of positive or negative eigenvalues) is a random variable providing information about the stability of stationary points in highdimensional potential landscapes. For a Gaussian matrix model of large size N, typically half of the eigenvalues are positive and half negative (Wigner's semicircle law). However atypical fluctuations around the semicircle are quite interesting and surprisingly not well understood until very recent times. Using a Coulomb gas technique and functional methods, we find that the distribution of the index is not strictly Gaussian around the mean due to an unusual logarithmic singularity in the rate function. The variance of the index increases logarithmically with the matrix size, and such finding is compared with an exact finite N result based on the Andrejeff integration formula. The combinatorics behind this formula is still to be understood. Reference: Phys. Rev. Lett. 103, 220603, 2009.

19/02/2010 4:00 PM103Kim Christensen Condensed Matter Theory Group, Institute for Mathematical Sciences, Imperial College LondonAnt colonies as complex systems

16/02/2010 4:00 PM103Ralf Metzler Physik Department, Technical University of MunichSingle particle trajectory analysis in complex systems: Anomalous diffusion and violation of ergodicitySeminar series:Single particle trajectory analysis has become one of the standard tools to probe systems on smaller scales such as biological cells. If the particle motion follows the laws of regular Brownian motion the long time average equals the ensemble average, and thus a measured time series renders complete information on the systems. This is no longer necessarily fulfilled for systems in which deviations from the normal diffusive law \propto Kt occur. It will be shown in this talk how systems can be analysed when ergodicity is broken and thus the time average differens from the ensemble mean. From comparison to experiments it will be discussed that such problems are indeed relevant.

23/02/2010 4:00 PM103Matteo Colangeli School of Mathematical Sciences, Queen Mary, University of LondonFrom Boltzmann's equation to hydrodynamics: The art of model reductionSeminar series:I will survey in this talk two basic principles for reducing the description of nonequilibrium systems based on the quasiequilibrium approximation. The two principles are: i) coarsegraining of the entropy conserving microscopic dynamics and ii) construction of invariant manifolds for the dissipative microscopic dynamics. By applying the method of invariant manifolds, I will derive equations of generalized hydrodynamics from the linearized Boltzmann Equation and determine exact transport coefficients obeying GreenKubo formulas.

02/03/2010 4:00 PM103Andrew Curtis School of Mathematical Sciences, Queen Mary, University of LondonA perambulation around a parameter space of covering correspondencesSeminar series:Given a rational map $f:\hat{\mathbb{C}} \rightarrow \hat{\mathbb{C}}$, its associated covering correspondence $Cov^f$ is a multivalued function defined by the relation $f(w)  f(z) = 0$. The talk will consist of a tour of the parameter space of a particular family of dynamical systems involving such objects  those that invole the covering correspondence of $z \mapsto z^3  3z$ postcomposed with an involution.

09/03/2010 4:00 PM103Ralph Kenna Applied Mathematics Research Centre, Coventry UniversityPhase transitions in the growth of groupsSeminar series:Groups of interacting nodes (such as research groups of interacting scientists) are considered as manybody, complex systems and their cooperative behaviour is analysed from a statisticalphysics, meanfield viewpoint. Contrary to the naive expectation that group success is an accumulation of the strengths of its nodes, it is demonstrated that intragroup interactions play a dominant role. These drive the growth of groups and give rise to phenomena akin to phase transitions, where the relationship between group quality and size reduces. The hitherto intutitive notion of critical mass is quantified and measured for research groups in academia.

16/03/2010 4:00 PM103Roman V. Belavkin School of Engineering and Information Sciences, Middlesex UniversityGeometry and optimisation of learningSeminar series:Information states of a learning system can be represented by points on a statistical manifold  a subset of a vector space endowed with an information topology. Parametrisation of the optimal learning trajectory is obtained by solving the maximum information utility problem. Several results and their geometric interpretation are presented in general form for optimisation with an abstract information resource. Closed form expressions can be derived for specific examples, such as using the KLtype divergence. A range of applications is discussed including economics, machine learning and evolutionary systems.

23/03/2010 4:00 PM103Thomas Prellberg School of Mathematical Sciences, Queen Mary, University of LondonForcing adsorption of a tethered polymer by pullingSeminar series:We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition inbetween. In the absence of a pulling force this model has a secondorder thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a nonzero vertical component this transition becomes firstorder. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of vertical pulling.

30/03/2010 5:00 PM103Gunnar Pruessner Department of Mathematics, Imperial College LondonSelforganised criticality: Its history and recent developmentsSeminar series:Self Organised Criticality, for more than a decade one of the most popular subjects within Statistical Mechanics, was expected to be found everywhere, explaining not only earthquakes and forest fires, but hospital waiting times, wars and consciousness. Taking stock more than twenty years on, what are the core findings and what the open questions? I will attempt to give a fair assessment of the state of affairs. The understanding of Self Organised Criticality has advanced very far, not only on the basis of numerics, but also using technically more demanding methods. A few robust models have been identified and studied in detail, some even solved analytically. A number of puzzling phenomena and tempting problems remain, which I will try to highlight.

13/04/2010 5:00 PM103Lamberto Rondoni Dipartimento di Matematica, Politecnico di Torino, ItalyMemory effects in a Langevin equation for feedback cooling and the detection of gravitational wavesSeminar series:Consider a system in contact with a thermal reservoir described by a memoryless equilibrium Langevin dynamics of second order. The strength of the noise fluctuations is then set by the damping factor, in accordance with the FluctuationDissipation theorem. If some feedback mechanism is switched on, a new Langevin equation with memory must be considered. We show that, in the context of RLC circuits, and for stationary states, one can explicitly calculate the power spectrum of the current generated by the feedback, under two types of feeddback schemes. The first based on fixed time delays, the other based on lowpass frequency filtering. We highlight similarities and differences and explain why approaches relying directly on FluctuationsDissipation relations for the dissipative memory do not directly apply. The example of gravitational wave antennas, and the relevant nonequilibrium fluctuation relations is discussed in detail.

19/04/2010 5:00 PM103Tibor Antal Harvard University, USAStochastic Models of Tumor ProgressionSeminar series:Cancer is a genetic disease: it is caused by malignant (driver) mutations accumulating in somatic tissues. What are the fundamental laws of tumor progression and initiation? To address this question, I first consider cell kinetics in healthy tissues, then I discuss the arrival of the first driver mutation. To develop malignant cancer, however, several mutations are needed. Hence I turn to models of tumor progression through several stages from benign tumor to malignant cancer. I present experimental results on mice, clinical data on pancreatic and brain cancer, and compare them to various models with exact or approximate solutions.

27/04/2010 4:00 PM103Jacob Steel School of Mathematical Sciences, Queen Mary, University of LondonSPECIAL TALK: Majorisation ordering of invariant measures for transformations of the unit interval

27/04/2010 5:00 PM103Renaud Leplaideur Département de Mathématiques, Université de Brest, FranceSelection of maximizing measure at temperature zero in the shift

11/05/2010 3:00 PM103Alexander Plakhov Department of Mathematics, University of Aveiro, PortugalCANCELLED: Billiard scattering by rough bodies
The law of elastic reflection by a smooth mirror surface is well known: the angle of incidence is equal to the angle of reflection. In contrast, the law of elastic scattering by a rough surface is not unique, but depends on the shape of microscopic pits and groves forming the roughness. In the talk we will give the definition of a rough surface and provide a characterisation for laws of scattering by rough surfaces. We will also consider several problems of optimal resistance for rough bodies and discuss their relationship with MongeKantorovich optimal mass transfer. These problems can be naturally interpreted in terms of optimal roughening of the surface for artificial satellites on low Earth orbits.

18/05/2010 5:00 PM103David Chappell School of Mathematical Sciences, University of NottinghamCANCELLED

25/05/2010 5:00 PM103David Schwab Princeton UniversityHidden Markov models, statistical mechanics, and learning binding sites with finite data
Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a onedimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. This allows us to formulate a simple criteria for when it is possible to distinguish between binding sites of closely related TFs and derive a scaling relation relating the quantity of training data to the minimum energy (statistical) difference between TFs that one can resolve. We apply our formalism to the NF$\kappa$B TFfamily and find that it is composed of two related but statistically distinct subfamilies.

15/06/2010 5:00 PM103Andrew Ferguson University of WarwickEscape rates for Gibbs measures

31/08/2010 10:37 AM103Hiroyasu Ando RIKEN Brain Science Institute, JapanAdaptive delayed feedback control in onedimensional maps
Since the seminal work by Ott et al., the concept of controlling chaos have gathered much attention and several techniques have been proposed. Among those control methods, delayed feedback control is of interest for its applicability and tractability for analysis. In this talk, we propose a parametric delayed feedback control where delay time is adaptively changed by the state of the system. Unlike the conventional chaos control, we are able to obtain superstable periodic orbits. From the viewpoints of dynamical systems, the whole controlled system becomes a particular two dimensional system with multiple attractors in the sense of Milnor. Finally, I would like to mention a possible application of this control technique for a coding scheme.

28/09/2010 5:00 PM103Astero Provata AthensSynchronization and intermittent oscillations in coupled nonlinear stochastic networks

05/10/2010 5:00 PM103Henrik Jensen Imperial College LondonSelfsimilar behaviour in the brain: the correlations in reststate fMRI

12/10/2010 5:00 PM103Peter Sollich Kings College LondonLarge deviations and ensembles of trajectories in stochastic models
We consider ensembles of trajectories associated with large deviations of timeintegrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy relaxation, we show how they can be generated directly using auxiliary stochastic processes. We illustrate our results using the GlauberIsing chain, for which energybiased ensembles of trajectories can exhibit ferromagnetic ordering, and briefly discuss the relation between such biased ensembles and quantum phase transitions. The talk will conclude with a wish list of things we'd like to work out but so far haven't been able to.

19/10/2010 5:00 PM103Stefan Groote Tartu/MainzPerturbative methods for chaotic strings

26/10/2010 5:00 PM103Alexander Plakhov AveiroBilliard scattering by rough bodies

02/11/2010 4:00 PM103Renaud Lambiotte Imperial College LondonModules and hierarchies in complex networks

03/11/2010 1:30 PM203Special EventOne day ergodic theory meeting

09/11/2010 4:00 PM103Roland Zweimueller SurreyGlobally coupled chaotic systems with bistable thermodynamic limit

16/11/2010 4:00 PM103Siegfried Hess BerlinRegular and chaotic orientation behaviour and flow properties of nanorod fluids and liquid crystals

23/11/2010 4:00 PM103Jamie Wood YorkRecent results on the collective motion of fish, birds and insects  modelling speed distributions and their importance
Nature is rich with many different examples of the cohesive motion of animals. Individualbased models are a popular and promising approach to explain features of moving animal groups such as flocks of birds or shoals of fish. Previous models for collective motion have primarily focused on group behaviours of identical individuals, often moving at a constant speed. In contrast we put our emphasis on modelling the contributions of different individuallevel characteristics within such groups by using stochastic asynchronous updating of individual positions and orientations. Recent work has highlighted the importance of speed distributions, anisotropic interactions and noise in collective motion. We test and justify our modelling approach by comparing simulations to empirical data for fish, birds and insects. The techniques we use range from motion tracking to "equationfree" coarsegrained modelling. With the maturation of the field new exciting applications are possible for models such as ours.

30/11/2010 4:00 PM103James Robinson WarwickUniqueness of Lagrangian trajectories for weak solutions of the 2D and 3D NavierStokes equations

07/12/2010 4:00 PM103Juan ValienteKroon Queen MaryStability problems in mathematical General Relativity: conformal methods and geometric invariants

14/12/2010 4:00 PM103Joerg Neunhaeuserer ClausthalFrom number theory to dynamical systems via geometric measure theory

11/01/2011 4:00 PM103Dr. Erik Van der Straeten (QMUL)Stochastic differential equations with nonuniform temperatures

18/01/2011 4:00 PM103Dr. Valerio Lucarini (Reading)A statistical mechanical approach for the computation of the climatic response

25/01/2011 4:00 PM103Prof. Yuzuru Sato (Hokkaido)Noiseinduced phenomena in 1dimensional maps

01/02/2011 4:00 PM103Prof. John Cardy (Oxford)The ubiquitous 'c': From the StefanBoltzmann law to quantum information

08/02/2011 4:00 PM103Dr. Oleg Zaboronski (Warwick)Nonequilibrium phase transition in a model of clustercluster aggregation

05/02/2011 4:00 PM103Dr. Luca Giuggioli (Bristol)Animal movement and interaction and the emergence of territoriality

22/02/2011 4:00 PM103Prof. David Ruelle (IHES)Characterization of LeeYang polynomials

01/03/2011 4:00 PM103Dr. Hinke Osinga (Bristol)The role of global manifolds in the transition to chaos in the Lorenz model

08/03/2011 4:00 PMMLTNigel LesmoirGordon (Gordon Films UK)Benoit Mandelbrot and the colours of infinity (Movie)

15/03/2011 4:00 PM103Dr. Isaac Perez Castillo (KCL)Large deviations of the smallest eigenvalue of the WishartLaguerre ensemble

22/03/2011 4:00 PM103Dr. Hartmut Erzgraeber (Exeter)Symmetry reduction and shearinduced dynamics in coupledlaser models

29/03/2011 5:30 PMFogg LTProf. Dirk Helbing (Zurich)FuturICT

05/04/2011 5:00 PM103Dr. Adrian Baule (New York)Ensemble approaches in nonequilibrium statistical mechanics
In equilibrium statistical mechanics macroscopic observables are calculated as averages over statistical ensembles, which represent probability distributions of the microstates of the system under given constraints. Away from equilibrium ensemble theory breaks down due to the strongly dissipative nature of nonequilibrium steady states, where, for example, energy conservation no longer holds in general. Nevertheless, ensemble approaches can be useful in describing the statistical mechanics of nonequilibrium systems, as I discuss in this talk. Two different approaches are presented: (i) a theory of microscopic transition rates in sheared steady states of complex fluids and (ii) a statistical theory for jammed packings of nonspherical objects. In both cases the ensemble approach relies crucially on an assumption of ergodicity in the absence of equilibrium thermalization.

26/04/2011 5:00 PM103Prof. Richard Sharp (Manchester)Spectral triples and Gibbs measures on Cantor sets

17/05/2011 5:00 PM103Prof. Ian Melbourne (Surrey)Convergence of moments for Axiom A and nonuniformly hyperbolic flows

27/05/2011 11:28 AM103SPECIAL EVENT: CoSyDy meeting on Longrange correlations in space and time
Organisers: Rosemary J. Harris and Hugo Touchette
Much effort has focused recently on developing models of stochastic systems that are nonMarkovian or show longrange correlations in space or time, or both. The need for such models has come from many different fields, ranging from mathematical finance to biophysics, and from engineering to statistical mechanics.
This workshop will bring together a number of mathematicians and engineers interested in stochastic processes having longrange correlations, with a view to share ideas as to how we can define such correlations mathematically, as well as to how we can devise stochastic processes that go beyond the Markov model.
The meeting is part of the CoSyDy series, a London Mathematical Society Scheme 3 network bringing together UK mathematicians investigating Complex Systems Dynamics.
Schedule:
12:1513:05 Buffet lunch and welcome 13:0513:10 Welcome 13:1013:55 Thierry Bodineau, Departement de Mathematiques et Applications, ENS, Paris Long range correlations in nonequilibrium systems 14:0014:25 Robert Jack, Department of Physics, University of Bath Large deviations, glass transitions, and longranged correlations 14:3014:55 Robert Concannon, School of Physics & Astronomy, University of Edinburgh A nonMarkovian Asymmetric Simple Exclusion Process 15:0015:25 Tea and coffee 15:3016:15 Sergei Fedotov, School of Mathematics, The University of Manchester Longmemory effects in anomalous diffusion with reactions 16:2016:45 Raul Mondragon, Department of Electronic Engineering, Queen Mary, University of London Longrange correlations in queues See the full programme with abstracts in attachment.
All are welcome. Registration is not required, but for catering purposes we would appreciate if you could confirm your attendance to the organisers.
Attachment Size cosydyqmul2011plan.pdf [PDF 67KB] 67.79 KB 
04/10/2011 5:00 PMM103Carl Dettmann (Bristol)New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis

11/10/2011 5:00 PMM103Andrea Jimenez Dalmaroni (Imperial) CANCELLED 

18/10/2011 5:00 PMM103Wael Bahsoun (Loughborough)Metastability of intermittent and randomly perturbed maps
GonzalezTokman, Hunt and Wright studied a metastable expanding system which is described by a piecewise smooth and expanding interval map. It is assumed that the metastable map has two invariant subintervals and exactly two ergodic invariant densities. Due to small perturbations, the system starts to allow for infrequent leakage through subsets (called holes) of the initially invariant subintervals, forcing the two invariant subsystems to merge into one perturbed system which has exactly one invariant density. It is proved that the unique invariant density of the perturbed interval map can be approximated by a particular convex combination of the two invariant densities of the original interval map, with the weights in the combination depending on the sizes of the holes.
In this talk we will present analogous results in two cases: 1. intermittent interval maps; 2. Randomly perturbed expanding maps.

25/10/2011 5:00 PMM103Mark Holland (Exeter)Extreme value theory for physical observations
This talk is about recurrence time statistics for chaotic maps with strange attractors  focusing on the probability distributions that describe the typical recurrence statistics to certain subsets of the phase space. The limiting probability distributions depend on the geometry of the (chaotic) attractor, the dimension of the SRB measure on the attractor, and the observables on the system.

02/11/2011 2:00 PMM203One Day Ergodic Theory MeetingSpecial Event

02/11/2011 4:45 PMM203Alexander Gorodnik (Bristol) joint with One day Ergodic Theory MeetingQuantitative ergodic theorems and Diophantine approximation
We investigate the problem of Diophantine approximation on rational surfaces using ergodictheoretic techniques. It turns out that this problem is closely related to the asymptotic distribution of orbits for a suitably constructed dynamical system. Using this connection we establish analogues of Khinchin's and Jarnik's theorems in our setting.

08/11/2011 4:00 PM103Aleks Owczarek (Univ. Melbourne)Breaking crossover scaling in a model of polymer collapse

15/11/2011 4:00 PMM103Nikita Sidorov (Manchester)Growth of long matrix products, finiteness conjecture and maximizing sequences
The joint spectral radius (JSR) of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the finiteness property if there exists a periodic product which achieves this maximal rate of growth.
The purpose of this talk is to present the first completely explicit family of 2 × 2 matrices which do not possess the finiteness property. Time permitting, I will also mention recent advances concerning maximizing sequences (those which realize the JSR) of polynomial complexity.

29/11/2011 4:00 PMM103Franco Vivaldi (QMUL)Regular motions and anomalous transport in a piecewise isometric system

06/12/2011 4:00 PMM103Rui Carvalho (QMUL)Fair sharing of resources in a supply network with constraints
This talk investigates the effect of network topology on the fair allocation of network resources among a set of agents, an allimportant issue for the efficiency of transportation networks all around us. We analyse a generic mechanism that distributes network capacity fairly among existing flow demands, and describe some conditions under which the problem can be solved by semianalytical methods. We find that, for some regions of the parameter space, a fair allocation implies a decrease of at least 50% from maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a powerlaw with exponent 1. Our semianalytical framework suggests possible explanations for the wellknown reduction of throughput in fair allocations. It also suggests that the network topology can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers

13/12/2011 4:00 PMM103Vasso Anagnostopoulou (TU Dresden)Nonautonomous saddlenode bifurcations
We study the effect of external forcing on the saddlenode bifurcation pattern of interval maps. Replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both in a measuretheoretic and a topological setting. As an interesting new phenomenon, a dichotomy appears for the behaviour at the bifurcation point, which allows the bifurcation to be either "smooth" (as in the classical case) or "nonsmooth".

10/01/2012 4:00 PMM103Mike R Jeffrey (Bristol)From discontinuity to nondeterminism in dynamical systems
A recent study into the geometry underlying discontinuities in dynamics revealed some surprises. The problems of interest are fundamental, things like: frictional sticking, electronic switching, protein activation and neuron spiking. When a discontinuity occurs at some threshold value in a system of differential equations, the solutions that result might not be unique. Besides the myriad cute models from applications, we want to know what discontinuities really tell us about dynamics in the real world. Nonunique solutions are easily dismissed as unphysical, yet they tell us something about the extreme behaviour made possible in the limit as a sudden change becomes almost discontinuous. Initially unique solutions may become multivalued, revealing extreme sensitivity to initial conditions, a breakdown of determinism, yet the possible outcomes lie in a welldefined set: an "explosion". An intriguing connection between discontinuities and singularly perturbations is revealed by studying the socalled twofold singularities and canards, borrowing ideas from nonstandard analysis along the way. The outcomes have been seen in superconductor experiments, are possible in control circuits, they are hidden in plain sight in the dynamics of friction, impacts, and neuron spiking, and they lead to nondeterministic forms of chaos.

18/01/2012 4:00 PMM203Jens Starke (DTU/Lyngby)Traveling waves and oscillations in particle models
The macroscopic behaviour of microscopically defined particle models are investigated by equationfree techniques where no explicitly given equations are available for the macroscopic quantities of interest. We investigate situations with an intermediate number of particles where the number of particles is too large for microscopic investigations of all particles and too small for analytical investigations using manyparticle limits and density approximations. By developing and combining very robust numerical algorithms, it was possible to perform an equationfree numerical bifurcation analysis of macroscopic quantities describing the structure and pattern formation in particle models. The approach will be demonstrated for two examples from traffic and pedestrian flow. The presented traffic flow on a single lane highway shows besides uniform flow solutions also traveling waves of high density regions. Bifurcations and coexistence of these two solution types are investigated. The pedestrian flow shows the emergence of an oscillatory pattern of two crowds passing a narrow door in opposite directions. The oscillatory solutions appear due to a Hopf bifurcation. This is detected numerically by an equationfree continuation of a stationary state of the system. Furthermore, an equationfree twoparameter continuation of the Hopf point is performed to investigate the oscillatory behaviour in detail using the door width and relative velocity of the pedestrians in the two crowds as parameters.

24/01/2012 4:00 PMM103Mason A. Porter (Oxford)Synchronization of Cows
I discuss the synchronization of cows using both an agentbased model and then formulate a mechanistic model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise smooth dynamical system. I analyze the properties of this bovine dynamical system and develop an exact integrative form as a discretetime mapping. I then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. With this abstract approach, I not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, the model illustrates that it is possible for cows to synchronize less when the coupling is increased.

31/01/2012 4:00 PMM103Ian Morris (Surrey)A Devil's staircase associated to the joint spectral radii of a family pair of matrices
The joint spectral radius of a finite set of square matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. In joint work with Nikita Sidorov, Kevin Hare and Jacques Theys, we examine a certain oneparameter family of pairs of matrices in detail, showing that the matrix products which realise this optimal growth rate correspond to Sturmian sequences with a particular characteristic ratio. We investigate the dependence of this characteristic ratio on the parameter, and show that it takes the form of a Devil's staircase. We establish some fine properties of this Devil's staircase, answering a question posed by T. Bousch.

07/02/2012 4:00 PMM103Roberto Artuso (CNCS/Como)Weak decay of correlations: some new perspectives
The decay of classical temporal correlations represents a fundamental issue in dynamical systems theory, and, in the generic setting of systems with a mixed phase space, it still presents a remarkable amount of open problems. We will describe prototype systems where the main questions arise, and discuss some recent progress where polynomial mixing rates are linked to large deviations estimates.

21/02/2012 4:00 PMM103Anxo Sanchez (Madrid)The emergence of cooperation: the game theoretical and experimental approach
In this talk I will introduce the issue of the emergence of cooperation, identified by Science as one of the 25 most important problems for the 21st century. I will discuss the puzzle that cooperative behavior is in the light of evolution theory and the importance of cooperation in its major steps. Then I will present the main tool with which one can study this problem, namely game theory. I will review games played by two players and their classical and evolutionary versions. Finally, I will devote some time to recent experiments addressing the relevance of the structure of the evolving population for the emergence of cooperation.

28/02/2012 4:00 PMM103Peter Ashwin (Exeter)A stability index for nonasymptotically stable attractors
This talk will discuss a stability index that characterises the local geometry of the basin of attraction for a dynamical system. The index is of particular interest for attractors that are not asymptotically stable  such attractors are known to arise robustly, for example, as heteroclinic cycles in systems with symmetries.

29/02/2012 4:00 PMM203Rosario Mantegna (Palermo)Cooccurrence networks in social and economic systems
Heterogeneity is a ubiquitous aspect of many social and economic complex systems. The analysis and modeling of heterogeneous systems is quite difficult because each economic and social actor is characterized by different attributes and it is usually acting on a multiplicity of time scales. We use statistically validated networks [1], a recently introduced method to validate links in a bipartite system, to investigate heterogeneous social and economic systems. Specifically, we investigate the classic movieactor system [1] and the trading activity of individual investors of Nokia stock [2]. The method is unsupervised and allows constructing networks of social actors where the links indicate cooccurrence of events or decisions. Each link is statistically validated against a null hypothesis taking into account system heterogeneity. Community detection is performed on the statistically validated networks and the communities (partitions) obtained are investigated with respect to the overexpression or underexpression of the attributes characterizing the social actors and/or their activities [3].
[1] Michele Tumminello, Salvatore Miccichè, Fabrizio Lillo, Jyrki Piilo, Rosario N Mantegna (2011) Statistically Validated Networks in Bipartite Complex Systems. PLoS ONE 6(3): e17994.
[2] Michele Tumminello, Fabrizio Lillo, Jyrki Piilo, and Rosario N. Mantegna, Identification of clusters of investors from their real trading activity in a financial market (2012) New J. Phys. 14 013041
[3] Michele Tumminello , Salvatore Miccichè , Fabrizio Lillo , Jan Varho , Jyrki Piilo and Rosario N Mantegna, Community characterization of heterogeneous complex systems (2011) J. Stat. Mech. P01019

02/03/2012 4:00 PMM203HansHenrik Rugh (Orsay)Microcanonical thermodynamics: why does heat flow from hot to cold?

06/03/2012 4:00 PMM103Sergio Ciliberto (Lyon)Fluctuations, linear response and heat flux of a system coupled with an out of equilibrium bath
In this talk we will discuss the application of the Fluctuation Theorem (FT) on systems where the heat bath is out of equilibrium. We first recall the main properties of Fluctuation Theorem (FT) starting from experimental results. We then discuss the result of an experiment where we measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel, are interpreted, within the framework of (FT) , as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures. We finally show that the measured heat flux is related to the violation of the equilibrium Fluctuation Dissipation Theorem for the system.

13/03/2012 4:00 PMMLTMurray GellMann (Santa Fe)Generalized entropies

20/03/2012 4:00 PMM103Alberto Robledo (UNAM)The new faces of the Feigenbaum point
The new faces of the Feigenbaum point: Dynamical hierarchy, selfsimilar network, theoretical game and stationary distribution. In this talk we first show that the recently revealed features of the dynamics toward the Feigenbaum attractor form a hierarchical construction with modular organization that leads to a clearcut emergent property. Then we transcribe the wellknown Feigenbaum scenario into families of networks via the horizontal visibility algorithm, derive exact results for their degree distributions, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Next we study a discretetime version of the replicator equation for twostrategy theoretical games. Their stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replaces the usual fixedpoint population solutions. We observe the familiar perioddoubling and chaoticbandsplitting attractor cascades of unimodal maps. Finally, we look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group structure associated with the operation of increment of summands and rescaling. In this structure—where the only relevant variable is the difference in control parameter from its value at the transition to chaos—the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor.

15/05/2012 5:00 PMM103Peter Hazard (Warwick)Henonlike maps, Renormalisation and Invariants
I will discuss recent results concerning topological invariants for Henonlike maps in dimension two using the Renormalisation apparatus constructed by de Carvalho, Lyubich, Martens and myself.

23/05/2012 12:00 PMM103Annual Workshop of the London Dynamical Systems GroupSpecial Event
For details see the workshop webpage

18/09/2012 4:00 PM103Alexander Balanov (Loughborough University)Controlling collective electron dynamics via singleparticle complexity

25/09/2012 5:00 PM103Christoforos Hadjichrysanthou (City University)Evolutionary dynamics on graphs
Evolutionary dynamics have been traditionally studied in infinitely large homogeneous populations where each individual is equally likely to interact with every other individual. However, real populations are finite and characterised by complex interactions among individuals. Over the last few years there has been a growing interest in studying evolutionary dynamics in finite structured populations represented by graphs. An analytic approach of the evolutionary process is possible when the contact structure of the population can be represented by simple graphs with a lot of symmetry and lack of complexity. Such graphs are the complete graph, the circle and the star graph. Moreover, this is usually infeasible on complex graphs and the use of various assumptions and approximations is necessary for the exploration of the process. We propose a powerful method for the approximation of the evolutionary process in populations with a complex structure. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the process and the improved accuracy that it provides when compared to wellknown pair approximation methods.

02/10/2012 5:00 PM103Jan Sieber (University of Exeter)Tracking unstable periodic orbits in experiments with feedback control
I will explain how one can track unstable periodic orbits in experiments using noninvasive feedback control in the spirit of Pyragas' timedelayed feedback. In some (experimentally very common) situations one can achieve noninvasiveness of the control without subtracting a delayed term in the control and without having to apply Newton iterations. I will show some recent experimental results of David Barton, who was able to trace out a resonance surface of a mechanical nonlinear oscillator around a cusp in two parameters with high accuracy.

09/10/2012 5:00 PM103Elaine Chew (EECS, Queen Mary)Mathematical models, music structure and prosody
"Music exists in an infinity of sound. I think of all music as existing in the substance of the air itself. It is the composer's task to order and make sense of sound, in time and space, to communicate something about being alive through music." ~ Libby Larsen
It is the performer's task then to intuit this order, to make sense of the music  in ways that may augment or be different from the composer's own understanding  and to communicate the interpreted structure through prosodic cues to the listener. Just as physicists develop mathematical models to make sense of the world in which we live, music science researchers seek mathematical models to represent and manipulate music structures, both frozen in time (e.g. as mapped out in a score), or communicated in performance. Mathematics is also the glue that binds music to digital representations, allowing for largescale computations carried out by machines.
I shall begin by introducing some of my own work originating in music structure representation and analysis, then move on to more recent investigations into aspects of music prosody. A key element of this talk will be the posing of some open problems in the scientific study of music structure and expressive performance, in which I hope to solicit interest, and to which I shall invite responses. 
16/10/2012 5:00 PM103Jason Laurie (ENS Lyon)A large deviation approach to computing rare transitions in multistable stochastic turbulence flows
Many turbulent flows undergo sporadic random transitions after long periods of apparent statistical stationarity. A straightforward study of these transitions, through direct numerical simulation of the governing equations is nearly always impracticable. In this talk, we consider twodimensional and geostrophic turbulence models with stochastic forces in regimes where two or more attractors coexist. We propose a nonequilibrium statistical mechanics approach to the computation of rare transitions between two attractors. Our strategy is based on the large deviation theory for stochastic dynamical systems (FreidlinWentzell theory) derived from a path integral representation of the stochastic process.

23/10/2012 5:00 PM103Oleg Zaboronski (University of Warwick)Annihilating Brownian motions in one dimension and Ginibre ensemble of random matrices
It turns out that onedimensional probability distributions of annihilating Brownian motions on the real line is a Pfaffian point process. It also turns out that this Pfaffian point process describes the onedimensional statistics of real eigenvalues in Ginibre ensemble of random matrices. Is the real sector of Ginibre ensemble equivalent to annihilating Brownian motions as a stochastic process?

30/10/2012 4:00 PM103Sanju Velani (University of York)Diophantine approximation, fractal sets and lacunary sequences
The metric theory of Diophantine approximation on fractal sets is developed in which the denominators of the rational approximates are restricted to lacunary sequences. The case of the standard middle third Cantor set and the sequence {3^n : n \in N} is the starting point of our investigation. Our metric results for this simple setup answers a problem raised by Mahler. As with all 'good' problems  its solution opens up a can of worms.

06/11/2012 4:00 PM103Dragi Karevski (Nancy, France)Quantum NonEquilibrium Steady State Induced by Repeated Interactions
We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The twopoint correlations are calculated exactly and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady state current, proportional to the difference in the reservoirs' magnetizations, shows a nonmonotonous behavior with respect to the system reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.

13/11/2012 4:00 PM103Constantino Tsallis (CBPF, Brazil)News on statistical mechanics for complex systems
Strong thermodynamical arguments exist in the literature which show that the entropy S of say a manybody Hamiltonian system should be extensive (i.e., S(N)~N) independently from the range of the interactions between its elements. If the system has shortrange interactions, an additive entropy, namely the BoltzmannGibbs one, makes the job. For longrange interactions, nonergodicity and strong correlations are generically present, and nonadditive entropies become necessary to preserve the desired entropic extensivity. These and recently related points (qFourier transform, largedeviation theory, nonlinear quantum mechanics) will be briefly presented. BIBLIOGRAPHY: (i) J.S. Andrade Jr., G.F.T.da Silva, A.A. Moreira, F.D. Nobre and E.M.F. Curado, Phys. Rev. Lett. 105, 260601 (2010); (ii) F.D. Nobre, M.A. RegoMonteiro and C. Tsallis, Phys. Rev. Lett. 106, 140601 (2011); (iii) http://tsallis.cat.cbpf.br/biblio.htm

20/11/2012 4:00 PM103David Barton (Bristol)Bifurcation analysis in physical experiments: Open problems
Direct numerical continuation in physical experiments is made possible by the combination of ideas from control theory and nonlinear dynamics, resulting in a family of methods known as controlbased continuation. This family of methods allows both stable and unstable periodic orbits to be tracked through bifurcations such as a fold by varying suitable system parameters. As such, the intricate details of the bifurcation structure of a physical experiment can be investigated. In its original form controlbased continuation was based on the Pyragas' timedelayed feedback control strategy, suitably modified to overcome the stability issues that occur in the vicinity of a saddlenode bifurcation (fold). It has since become a much more general methodology.
There are a wide range of possible applications for such investigations across engineering and the applied sciences. Specifically, there is a great deal of promise in combining such methods with ideas such as numerical substructuring, whereby a numerical model is coupled to a physical experiment in realtime via actuators and sensors.
The basic scheme (known as controlbased continuation) works with standard numerical methods; however, the results are suboptimal due to the comparative expense of making an experimental observation and the inherent noise in the measurement. This talk will present the current stateoftheart and possibilities for future research in this area, from the development of numerical methods and controlstrategies to more fundamental dynamical systems research.

27/11/2012 4:00 PM103Raphael Chetrite (Nice, France)A hint of large deviations in statistical physics
The theory of large deviations is at the heart of recent progress in the field of statistical physics. I will discuss in this talk some developments that are interesting for nonequilibrium physics. In particular, I will insist on symmetries of large deviations and on analytical large deviation results.

04/12/2012 4:00 PM103Kavin Preethi Narasimhan (Computer Science, QMUL)Computer simulations of Fformations
The sociological notion of Fformations denote the spatial configurations that people assume in social interactions; and an Fformation system denotes all the behavioural aspects that go into establishing and sustaining an Fformation between people. Kendon (1990) identified some of the geometrical aspects of such Fformations that have to do with the spatial positions and orientations of interlocutors. In this talk, I will be presenting some of our twodimensional and threedimensional simulations that are based on Kendon's geometrical aspects of Fformations. Discussions will also extend to the evaluations carried out on the simulations by participants during a pilot study, their outcomes and implications.
Bibliography:
Kendon A. Conducting Interaction: Patterns of Behavior in Focused Encounters. Cambridge: Cambridge University Press, 1990.

11/12/2012 4:00 PM103Cesare Nardini (Florence and ENS Lyon)Energy landscape of classical spin models
Energy landscape methods make use of the stationary points of the energy function of a system to infer some of its collective properties. Recently this approach has been applied to equilibrium phase transitions, showing that a connection between some properties of the energy landscape and the occurrence of a phase transition exists, at least for certain simple models.
I will discuss the study of the energy landscape of classical O(n) models defined on regular lattices and with ferromagnetic interactions. This study suggests an approximate expression for the microcanonical density of states of the O(n) models in terms of the energy density of the Ising model. If correct, this would implies the equivalence of the critical values of the energy densities of a generic O(n) model and the n=1 case, i.e., a system of Ising spins with the same interactions. Numerical and analytical results are in good agreement with such prediction.

15/01/2013 4:00 PM103EvaMaria Graefe (Imperial College London)Complexified quantum theory and the semiclassical limit
The relation between quantum systems and their classical analogues is a subtle matter that has been investigated since the early days of quantum mechanics. Today, we have at our disposal powerful tools to formulate in a precise way the semiclassical limit. The understanding of quantum classical correspondence is of importance (a) for the interpretation and practical understanding of quantum effects, and (b) as a basis of a variety of simulation methods for quantum spectra and dynamics. Recently, there has been a growing interest in socalled nonHermitian or "complexified" quantum theories. Applications include (i) decay, (ii) transport and scattering phenomena, (iii) dissipative systems, and (iv) PTsymmetric theories. In this talk I will present an overview of some of the issues and novelties arising in the investigation of the classical analogues of such "complexified” quantum theories, with applications ranging from optics to cold atoms and BoseEinstein condensates.

22/01/2013 4:00 PM103Grigorios A. Pavliotis (Imperial College London)Convergence to equilibrium for nonreversible diffusions
The problem of convergence to equilibrium for diffusion processes is of theoretical as well as applied interest, for example in nonequilibrium statistical mechanics and in statistics, in particular in the study of Markov Chain Monte Carlo (MCMC) algorithms. Powerful techniques from analysis and PDEs, such as spectral theory and functional inequalities (e.g. logarithmic Sobolev inequalities) can be used in order to study convergence to equilibrium. Quite often, the diffusion processes that appear in applications are degenerate (in the sense that noise acts directly to only some of the degrees of freedom of the system) and/or nonreversible. The study of convergence to equilibrium for such systems requires the study of nonselfadjoint, possibly nonuniformly elliptic, second order differential operators. In this talk we will prove exponentially fast convergence to equilibrium for such diffusion processes using the recently developed theory of hypocoercivity. Furthermore, we will show how the addition of a nonreversible perturbation to a reversible diffusion can speed up convergence to equilibrium. This is joint work with M. Ottobre, K. PravdaStarov, T. Lelievre and F. Nier.

29/01/2013 4:00 PM103Ivette Fuentes (Nottingham)CANCELLED: Relativistic quantum information processing (Joint with the Relativity and Cosmology Seminar)
Research in the field of relativistic quantum information aims at finding ways to process information using quantum systems taking into account the relativistic nature of spacetime. Cutting edge experiments in quantum information are already reaching regimes where relativistic effects can no longer be neglected. Ultimately, we would like to be able to exploit relativistic effects to improve quantum information tasks. In this talk, we propose the use of moving cavities for relativistic quantum information processing. Using these systems, we will show that nonuniform motion can change entanglement affecting quantum information protocols such as teleportation between moving parties. Via the equivalence principle, our results also provide a model of entanglement generation by gravitational effects.

05/02/2013 4:00 PM103Ginestra Bianconi (QMUL)Entropy of network ensembles
The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of statistical mechanics and information theory to networks. In this talk we discuss recent works defining the Shannon entropy of a network ensemble and evaluating how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here play a crucial role for the formulation of null models of networks through maximumentropy arguments and contribute to inference problems emerging in the field of complex networks.

12/02/2013 4:00 PM103Charo I. Del Genio (Warwick)Degree based construction of directed networks
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of directed graphs with a given sequence of in and outdegrees. Previous algorithms used to generate such samples have either unknown mixing times, or lead often to unacceptably many rejections due to selfloops and multiple edges. I will present a method that can directly construct all possible directed realizations of a given degree sequence. This method is rejectionfree, guarantees the independence of the constructed samples, and allows the calculation of statistical averages of network observables according to a uniform or otherwise chosen distribution.

12/02/2013 4:00 PM103Charo I. Del Genio (Warwick)Degree based construction of directed networks
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of directed graphs with a given sequence of in and outdegrees. Previous algorithms used to generate such samples have either unknown mixing times, or lead often to unacceptably many rejections due to selfloops and multiple edges. I will present a method that can directly construct all possible directed realizations of a given degree sequence. This method is rejectionfree, guarantees the independence of the constructed samples, and allows the calculation of statistical averages of network observables according to a uniform or otherwise chosen distribution.

26/02/2013 4:00 PM103Martin Rasmussen (Imperial)Additive noise does not destroy a pitchfork bifurcation
It is wellknown from Crauel and Flandoli (Additive noise destroys a pitchfork bifurcation, J. Dyn. & Diff. Eqs 10 (1998), 259274) that adding noise to a system with a deterministic pitchfork bifurcation yields a unique random attracting fixed point with negative Lyapunov exponent for all parameters. Based on this observation, they conclude that the deterministic bifurcation is destroyed by the additive noise. However, we show that there is qualitative change in the random dynamics at the bifurcation point in the sense that, after the bifurcation, the Lyapunov exponent cannot be observed almost surely in finite time. We associate this bifurcation with a breakdown of both uniform attraction and equivalence under uniformly continuous topological conjugacies, and with nonhyperbolicity of the dichotomy spectrum at the bifurcation point. This is joint work with Mark Callaway, Jeroen Lamb and Doan Thai Son (all at Imperial College London).

05/03/2013 4:00 PM103Charles Walkden (Manchester)Stochastic stability for generalised iterated function systems
The talk will be about 'contractive Markov systems'  a generalisation of an iterated function system. Under a 'contractiononaverage' condition, such systems have a unique invariant measure. By studying how the spectral properties of a certain linear operator acting on an appropriate function space perturb, we will discuss the stochastic stability of this invariant measure and other probabilistic results.

12/03/2013 4:00 PM103Georg Ostrovski (Imperial)A Dynamical System Motivated by Games: Fictitious Play & Piecewise Affine Dynamics
In this talk I will present a dynamical system called Fictitious Play Dynamics. This is a basic learning algorithm from Game Theory, modelling learning behaviour of players repeatedly playing a game. Dynamically, it can be described as a nonsmooth (continuous and piecewise linear) flow on the threesphere, with global sections whose first return maps are continuous, piecewise affine and areapreserving. I will show how these systems give rise to very intricate behaviour and how they can be studied via a family of rather simple planar piecewise affine maps.

19/03/2013 4:00 PM103Satya Majumdar (Paris Sud)Random convex hulls: Applications to ecology and animal epidemicsConvex hull of a set of points in two dimensions roughly describes the shape of the set. In this talk, I will discuss the statistical properties of the convex hull for two stochastic processes in two dimensions: (i) a set of n independent planar Brownian paths (ii) a branching Brownian motion with death. We show how to compute exactly the mean perimter and the mean area of the convex hull in these two problems. The first problem has application in estimating the home range of an animal population of size n, while the second will be used to estimate the spatial extent of the outbreak of animal epidemics. Our result also makes an interesting connection between random geometry and extreme value statistics.

26/03/2013 4:00 PM103Thierry Platini (Coventry)Measure of violation of detailed balance criterion
Motivated by the classification of nonequilibrium steady states suggested by R. K. P. Zia and B. Schmittmann (J. Stat. Mech. 2007 P07012), I propose to measure the violation of the detailed balance criterion by the p norm of the matrix formed by the probability currents. Its asymptotic analysis for the totally asymmetric simple exclusion process motivates the definition of a 'distance' from equilibrium. In addition, I show that the latter quantity and the average activity are both related to the probability distribution of the entropy production. Finally, considering the open asymmetric simple exclusion process and open zerorange process, I show that the current of particles gives an exact measure of the violation of detailed balance.

24/09/2013 5:00 PM103Mike Field (Rice)Asynchronous Networks
A complex system in science and technology can often be represented as a network of interacting subsystems or subnetworks. If we follow a reductionist approach, it is natural (though not always wise!) to attempt to describe the dynamics of the network in terms of the dynamics of the subsystems of the network. Put another way, we often have a reasonable understanding of the "pieces", but how do they fit together, and what do they do collectively? In the simplest, and most studied cases, the subnetworks all run on the same clock (are updated simultaneously), and dynamics is governed by a fixed set of (usually analytic) dynamical equations: we say the network is synchronous (this is classical dynamics).
In biology, especially neuroscience, and technology, for example large distributed systems, these assumptions may not hold: components may run on different clocks, there may be switching between different dynamical equations, and most significantly, and quite unlike what happens in a classical synchronous network, component parts of the network may run independently of the rest of the network, and even stop, for periods of time. We say networks of this type are asynchronous.It is a major challenge to develop the mathematical theory of dynamics on asynchronous networks. In this talk, we describe examples of dynamics on synchronous and asynchronous networks and point out how properties such as switching are forced by an asynchronous structure. We also indicate relationships with random dynamical systems and problems related to "qualitative computing" .

01/10/2013 5:00 PM103Giovanni Diana (Luxembourg)The thermodynamic cost of information processing
We will present some recent results on the energetic cost of information processing in the framework of stochastic thermodynamics. This theory provides a consistent description of nonequilibrium processes governed by a Markovian dynamics. We shall discuss the physical role of the information exchange during measure, feedback and erasure for systems driven by an external controller. We will also address the issue of quantifying the thermodynamic cost of sensing for autonomous twocomponent systems and discuss the connection between dissipation and informationtheoretic correlation.

08/10/2013 5:00 PM103Peter Sollich (King's College)Gaussian process learning on random graphs
(Joint work with Matthew Urry)
We consider the problem of learning a function defined on the nodes of a graph, in a Bayesian framework with a Gaussian process prior. We show that the relevant covariance kernels have some surprising properties on large graphs, in particular as regards their approach to the limit of full correlation of the function values across all nodes.
Our main interest is in predicting the learning curves, i.e. the typical generalization error given a certain number of examples. We describe an approach for deriving these predictions that becomes exact in the limit of large random graphs. The validity of the method is broad and covers random graphs specified by arbitrary degree distributions, including the powerlaw distributions typical of social and other networks. We also discuss the effects of normalization of the covariance kernels. These are more intricate than for functions of real input variables, because of the variation in local connectivity structure on a graph. Time permitting, recent extensions to the case of learning with a mismatched prior will be covered.

22/10/2013 5:00 PM103Sebastian Ahnert (Cambridge)Compressible components reveal network architectures
We introduce a framework for compressing complex networks into powergraphs with overlapping powernodes. The most compressible components of a given network provide a highly informative sketch of its overall architecture. In addition this procedure also gives rise to a novel, linkbased definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. We show that this approach yields valuable insights into the largescale structure of transcription networks, food webs, and social networks, and allows for novel ways in which network architecture can be studied, defined and classified. Furthermore, when paired with enrichment analysis of node classification terms, this method can provide a concise overview of the dominant conceptual relationships that define the network.

29/10/2013 4:00 PM103Thilo Gross (Bristol)The Magical Red Arrow: Local Analysis and Global Phenomena in complex networks
Over the past decade complex networks have come be be recognized as powerful tools for the analysis of complex systems. The defining feature of complexity is emergence; complex systems exhibit phenomena that do not originate in the parts of the system, but rather in their interactions. The underlying structural and dynamical properties behind these phenomena are therefore, almost by definition, delocalized across the network. But, a major driving force of network theory is the hope that we can nevertheless trace these properties back to localized structures in the network. In other words, we study global networkwide phenomena but often search for the magical red arrow that points at a certain part of the network and says 'This causes it!'.
In this talk I focus on analytical investigation of network dynamics, where the network is considered as a large dynamical system. Combining approaches from dynamical systems theory and statistical physics with insights from network research analytical progress in the investigation of these systems can be made. I show that network dynamics is generally inherently nonlocal, but also point out a fundamental reason why many important real world phenomena can nevertheless be understood by a local dynamical analysis. 
05/11/2013 4:00 PM103Mason Porter (Oxford)Community Structure in Networks
Many networks have cohesive groups of nodes called "communities". The study of community structure borrows ideas from many
areas, and there exist myriad methods to detect comminities algorithmically. Community structure has also been insightful in many applications, as it can reveal social organization in friendship networks, groups of simultaneously active brain regions in functional brain networks, and more. My collaborators and I have been very active in studying community structure, and I will discuss some of our work on both methodological development and applications. I'll include examples from subjects like social networks, brain networks, granular materials, and more. 
12/11/2013 4:00 PM103Simone Severini (UCL)Graph Isomorphism: Quantum Ideas
Abstract (Short): I will review ideas to approach the Graph Isomorphism Problem with tools linked to Quantum Information.

19/11/2013 4:00 PM103Nick Jones (Imperial College)Structure in Networks and Signals
I this seminar I will discuss two distinct approaches to the structure of the world around us. In the first I'll discuss our implementation of a battery of thousands of signal processing tools as part of an attempt to organize our methods and to perform a skysurvey of types of dynamics. In the second I'll cover our work connecting topics in network analysis to parameterized complexity and outline how the complexity of some routing tasks on graphs scales with the number of communities rather than the number of nodes.

26/11/2013 4:00 PM103Ton Coolen (King's College London)Solvable model of an immune network on a finitely connected heterogeneous graph with extensively many short loops
The immune system can recall and execute a large number of memorized defense strategies in parallel. The explanation for this ability turns out to lie in the topology of immune networks. We studied a statistical mechanical immune network model with `coordinator branches' (Tcells) and `effector branches' (Bcells), and show how the finite connectivity enables the system to manage an extensive number of immune clones simultaneously, even above the percolation threshold. The model is solvable using replica techniques, in spite of the fact that the network has an extensive number of short loops.

03/12/2013 4:00 PM103Tim Rogers (Bath)Epidemics and elections: the importance of demographic noise in adaptive networks
Adaptive networks are models of complex systems in which the structure of the interaction network changes on the same timescale as the status of the nodes. For instance, consider the spread of a disease over a social network that is changing as people try to avoid the infection. In this talk I will try to persuade you that demographic noise (random fluctuations arising from the discrete nature of the components of the network) plays a major role in determining the behaviour of these models. These effects can be studied analytically by employing a reduceddimension Markov jump process as a proxy.

10/12/2013 4:00 PM103Stefan Grosskinsky (Warwick)Dynamics of condensation in inclusion processes and related models
The inclusion process is a driven diffusive system which exhibits a
condensation transition in certain scaling limits, where a fraction of
all particles condenses on a single lattice site. We study the dynamics
of this phenomenon, and identify all relevant dynamical regimes and
corresponding time scales as a function of the system size. This
includes a coarsening regime where clusters move on the lattice and
exchange particles, leading to a growing average cluster size. Suitable
observables exhibit a power law scaling in this regime before they
saturate to stationarity following an exponential decay depending on the
system size. For symmetric dynamics we have rigorous results on finite
lattices in the limit of infinitely many particles (joint work with
Frank Redig and Kiamars Vafayi). We have further heuristic results on
onedimensional periodic lattices in the thermodynamic limit, covering
totally asymmetric and symmetric dynamics (joint work with Jiarui Cao
and Paul Chleboun), and preliminary results for a generalized version of
the symmetric process that exhibits finite time blowup (joint work with
YuXi Chau). 
07/01/2014 4:30 PM103Sam Johnson (Imperial College)The role of trophic coherence in food webs: Diversity and stability reconciled?
Why are large, complex ecosystems stable? For decades it has been conjectured that they have some unidentified structural property. We show that trophic coherence  a hitherto ignored feature of food webs which current structural models fail to reproduce  is significantly correlated with stability, whereas size and complexity are not. Together with cannibalism, trophic coherence accounts for over 80% of the variance in stability observed in a 16foodweb dataset. We propose a simple model which, by correctly capturing the trophic coherence of food webs,
accurately reproduces their stability and other basic structural features. Most remarkably, our model shows that stability can increase with size and complexity. This suggests a key to May’s Paradox, and a range of opportunities and concerns for biodiversity conservation. 
14/01/2014 4:30 PM103Mark Broom (City University London)Evolution in structured populations: modelling the interactions of individuals and groups
Recently models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). We shall start by looking at some work on quite simple graphs. One limitation of this otherwise quite general framework, however, is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet many animal interactions can involve many players, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations with the focus on competition between territorial animals, where each animal or animal group has a "home range" which overlaps with a number of others, and interactions between various group sizes are possible. Depending upon the behaviour concerned we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the prisoner’s dilemma or the HawkDove game on graphs. We discuss some examples together with some important differences between this approach and evolutionary graph theory.

21/01/2014 4:30 PM103Dhagash Mehta (Univ. North Carolina)Computational Algebraic Geometry and Potential Energy Landscapes
The surface drawn by a potential energy function, which is usually a multivariate nonlinear function, is called the potential energy landscape (PEL) of the given Physical/Chemical system. The stationary points of the PEL, where the gradient of the potential vanishes, are used to explore many important Physical and Chemical properties of the system. Recently, we have employed the numerical algebraic geometry (NAG) method to study the stationary points of the PELs of various models arising from Physics and Chemistry and have discovered their many interesting characteristics. In this talk, I will mention some of these results after giving a very brief introduction to the NAG method. I will then go on discussing our latest adventure: exploring the PELs of random potentials with NAG, which will address not only one of a classic problems in Algebraic Geometry but will also find numerous applications in different areas such as String Theory, Statistical Physics, Neural Networks, etc.

28/01/2014 4:30 PM103Henrik Jensen (Imperial College)Music, the brain and the analysis of spatiotemporal correlations and information flow in and between brains of musician
First we discuss general fractal and critical aspects of the brain as indicated by recent fMRI analysis. We then turn to the analysis of EEG signals from the brain of musicians and listeners during performance of improvised and nonimprovised classical music. We are interested in differences between the response to the two different ways of playing music. We use measures of information flow to try to pin point differences in the structure of the network constituted by all the EEG electrodes of all musicians and listeners.

04/02/2014 4:30 PM103Thomas Prellberg (QMUL)The pressure of surfaceattached polymers and vesicles
A polymer grafted to a surface exerts pressure on the substrate. Similarly, a surfaceattached vesicle exerts pressure on the substrate. By using directed walk models, we compute the pressure exerted on the surface for grafted polymers and vesicles, and the effect of surface binding strength and osmotic pressure on this pressure.

11/02/2014 4:30 PM103Luca Dall 'Asta (Politecnico di Torino)Inverse problems for spreading dynamics on networks
Who are the most influential players in a social network? What's the origin of an epidemic outbreak? The answer to simple questions like these can hide incredibly difficult computational problems, that require powerful methods for the inference, optimization, and control of dynamical processes on large networks.
I will present a statistical mechanics approach to inverse dynamical problems in the idealized framework provided by simple models of irreversible contagion and diffusion on networks (linear threshold model, susceptibleinfectedremoved epidemic model). Using the cavity method (belief propagation), it is possible to explore the largedeviation properties of these dynamical processes, and develop efficient messagepassing algorithms to solve optimization and inference problems even on large networks. 
18/02/2014 4:30 PM103Geoff Rodgers (Brunel University)Network Growth Models with Intrinsic Vertex Fitness
An analytical solution for a network growth model of intrinsic vertex fitness is presented, along
with a proposal to a new paradigm in fitness based network growth models. This class of models
is classically characterised by a fitness linking mechanism that governs the attachment rate of new
links to existing nodes and a distribution of node fitness, that measures the attractiveness of a node.
It is argued in the present paper, that this distinction is unnecessary, instead linking propensity of
nodes can be expressed in terms of a ranking among existing nodes, which reduces the complexity
of the problem. At each timestep of this dynamical model either a new node joins the network and
is attached to one of the existing nodes or a new edge is added between two existing nodes with
probability proportional to the nodes attractiveness. The full analytic theory connecting the fitness
distribution, the linking function, and the degree distribution is constructed. Given any two of these
characteristics, the third one can be determined in closed form. Furthermore additional statistics
are computed to fully describe every aspect of this network model. One particularly interesting
finding is that for a factorisable, and not necessarily symmetric linking function, very restrictive
assumptions on the exact form of the linking function need to be imposed to find a powerlaw
degree distribution within this class of models. 
25/02/2014 4:30 PM103Iain Johnston (Imperial College London)Physical modelling and Bayesian inference elucidate the debated mechanism of the mtDNA bottleneck
Dangerous damage to mitochondrial DNA (mtDNA) between generations is ameliorated through a stochastic developmental process called the mtDNA bottleneck. The mechanism by which this process occurs is debated mechanistically and lacks quantitative understanding, limiting our ability to prevent the inheritance of mtDNA disease. We address this problem by producing a new, physically motivated, generalisable theoretical model for cellular mtDNA populations during development. This model facilitates, for the first time, a rigorous statistical treatment of experimental data on mtDNA during development, allowing us to resolve, with quantifiable confidence, the mechanistic question of the bottleneck. The mechanism with most statistical support involves random turnover of mtDNA with binomial partitioning at cell divisions and increased turnover during folliculogenesis. We analytically solve the equations describing this mechanism, obtaining closedform results for all mtDNA and heteroplasmy statistics throughout development, allowing us to explore the effects of potential sampling strategies and dynamic interventions for the bottleneck. We find that increasing mtDNA degradation during the bottleneck may provide a general therapeutic target to address mtDNA disease. Our theoretical advances thus allow the first rigorous statistical analysis of data on the bottleneck, resolving and obtaining analytic results for its debated mechanism and suggesting clinical strategies to assess and prevent the possibility of inherited mtDNA disease.

04/03/2014 4:30 PM103Anne Kandler (City University)How to analyse cultural change?
Cultural change is often quantified by changes in frequency of cultural traits over time. Based on those (observable) frequency patterns researchers aim to infer the nature of the underlying evolutionary processes and therefore to identify the (unobservable) causes of cultural change. Especially in archaeological and anthropological applications this inverse problem gains particular importance as occurrence or usage frequencies are often the only available information about past cultural traits or traditions and the forces affecting them. In this talk we start analyzing the described inference problem and discuss it in the context of the question of which learning strategies human populations should deploy to be welladapted to changing environmental conditions. To do so we develop a mathematical framework which establishes a causal relationship between changes in frequency of different cultural traits and the considered underlying evolutionary processes (in our case learning strategies). Besides gaining theoretical insights into the question of which learning strategies lead to efficient adaptation processes in changing environments we focus on ‘reverse engineering’ conclusions about the learning strategies deployed in current or past population, given knowledge of the frequency change dynamic over space and time. Using appropriate statistical techniques we investigate under which conditions populationlevel characteristics such as frequency distributions of cultural variants carry a signature of the underlying evolutionary processes and if this is the case how much information can be inferred from it. Importantly, we do not expect the existence of a unique relationship between observed frequency data and underlying evolutionary processes; to the contrary, we suspect that different processes can produce similar frequency pattern. However, our approach might help narrow down the range of possible processes that could have produced those observed frequency patterns, and thus still be instructive in the face of uncertainty. Rather than identifying a single evolutionary process that explains the data, we focus on excluding processes that cannot have produced the observed changes in frequencies. In the last part of the talk, we demonstrate the applicability of the developed framework to anthropological case studies.

11/03/2014 4:30 PM103Ole Peters (London Mathematical Laboratory)A discourse on decision theory
In April 2010 I gave a seminar at the Santa Fe Institute where I demonstrated that certain classic problems in economics can be resolved by revisiting basic tenets of the formalism of decision theory. Specifically, I noted that simple mathematical models of economic processes, such as the random walk or geometric Brownian motion, are nonergodic. Because of the nonstationarity of the processes, observables cannot be assumed to be ergodic, and this leads to a difference in important cases between time averages and ensemble averages. In the context of decision theory, the former tend to indicate how an individual will fare over time, while the latter may apply to collectives but are a priori meaningless for individuals. The effects of replacing expectation values by time averages are staggering  realistic predictions for risk aversion, market stability, and economic inequality follow directly. This observation led to a discourse with Murray GellMann and Kenneth Arrow about the history and development of decision theory, where the first studies of stochastic systems were carried out in the 17th century, and its relation to the development of statistical mechanics where refined concepts were introduced in the 19th century. I will summarize this discourse and present my current understanding of the problems.

18/03/2014 4:30 PM103Damien Foster (Coventry)Critical behaviour of Frustrated Walks on the Square Lattice
Interacting selfavoiding walks as models for polymer collapse in dilute solution have been studied for many years. The canonical model, also known as the Theta model, is rather well understood, and it was expected that all models with shortrange attractive interactions between “monomers” would give the same behaviour as the Theta model. In recent years a variety of models have been studied which do not conform to this expectation, and the observed behaviour depends on the specifics of the interaction and lattice.
In this talk I will review some of the known or conjectured results for these models, with particular attention to the selfavoiding trails and vertexinteracting selfavoiding walk models, and show how these models may be studied using extended transfer matrix methods (transfer matrices, DMRG and CTMRG methods). I will also present some results for the complex zeroes of the partition function as a method for finding critical points and estimates of the crossover exponents for walk models.

25/03/2014 4:30 PM103Davide Cellai (University of Limerick)Percolation models in multiplex networks
In the past few years, multilayer, interdependent and multiplex networks have quickly become a big avenue in mathematical modelling of networked complex systems, with applications in social sciences, largescale infrastructures, information and communications technology, neuroscience, etc. In particular, it has been shown that such networks can describe the resilience of large coupled infrastructures (power grids, Internet, water systems, …) to failures, by studying percolation properties under random damage.
Percolation is perhaps the simplest model of network resilience and can be defined or extended to multiplex networks (defined as a network with multiple edge types) in many different ways. In some cases, new analytical approaches must be introduced to include features that are intrinsic to multiplex networks. In other cases, extensions of classical models give origin to new critical phenomena and complex behaviours.
Regarding the first case, I will illustrate a new theoretical approach to include edge overlap in a simple percolation
model. Edge overlap, i.e. node pairs connected on different layers, is a feature common to many empirical cases,
such as in transportation networks, social networks and epidemiology. Our findings illustrate properties of
multiplex resilience to random damage and may give assistance in the design of largescale infrastructure.
Regarding the second aspect, I will present models of pruning and bootstrap percolation in multiplex networks. Bootstrap may be seen as a simple activation process and has applications in many areas of science. Our extension to multiplex networks can be solved analytically, has potential applications in network security, and provides a step in dealing with dynamical processes occurring on the network. 
31/03/2014 12:30 PMMLTSPECIAL EVENT: CoSyDy meeting on Complexity and Epidemic Dynamics
Organisers: Leon Danon and Rosemary J. Harris
Complex systems theory has played an increasingly important role in infectious disease epidemiology. From the fundamental basis of transmission between two interacting individuals, complexity can emerge at all scales, from small outbreaks to global pandemics. Traditional ODE models rely on simplistic characterisations of interactions and transmission, but as more and more data become available these are no longer necessary. The descriptive and predictive power of transmission models can be improved by statistical descriptions of behaviour and movement of individuals, and tools from complex systems contribute greatly to the discussion.
This workshop will cover advances in mathematical epidemiology that have been shaped by complex systems approaches. The workshop is intended to cover a broad spectrum of topics, from theoretical aspects of transmission on networks to current work shaping public policy on diseases of livestock and honey bees.
Attendance at this workshop is free and open to everyone. However, for catering purposes, please register your attendance via email to l.danon@qmul.ac.uk(link sends email) or rosemary.harris@qmul.ac.uk(link sends email) by 21st March.
The meeting is part of the CoSyDy series, a London Mathematical Society Scheme 3 network bringing together UK mathematicians investigating Complex Systems Dynamics. Travel support is available for participants from the member nodes.
Schedule:
11:3012:10 Vincent Jansen, Royal Holloway, University of London Rats, Fleas and the Tip of the Tongues: Modelling the Epidemiology of the Plague 12:1012:40 Jon Read, University of Liverpool Mobility, social encounter patterns and influenza exposure in Southern China 12:4013:30 Buffet Lunch 13:3014:10 Frank Ball, University of Nottingham Epidemics on random networks with tunable clustering, degree correlation and degree distribution [PDF 20KB] 14:1014:40 Kieran Sharkey, University of Liverpool Prevalence, invasion and duality for SIS dynamics on finite Networks 14:4015:10 Helen Johnson, London School of Hygiene and Tropical Medicine Keeping it Real: Calibration and Parametric Inference for Complex Epidemic Models [PDF 17KB] 15:1015:40 Tea and Coffee 15:4016:20 Rowland Kao, University of Glasgow Supersize me: how big data and whole genome sequencing are transforming epidemiology 16:2016:50 Mike Tildesley, University of Exeter Mathematical Modelling of Infectious Diseases in the Presence of Uncertainty 16:5017:20 Samik Datta, University of Warwick Modelling the spread of disease in honeybees 17:20 Drinks and Discussion All talks will now be in the Maths Lecture Theatre of the Mathematics Building. The full programme is also available as a pdf attachment below.
Attachment Size cosydyqmul2014plan.pdf [PDF 63KB] 63.24 KB 
06/05/2014 5:00 PM103Anita Kristine Ponsaing (Université de Genève)The Brauer loop model and algebraic geometry
The Brauer loop model is an integrable lattice model based on the Brauer
algebra, with crossings of loops allowed. The ground state of the
transfer matrix is calculable (with some caveats) via the quantum
KnizhnikZamolodchikov (qKZ) equation, a technique that expresses the
ground state components in terms of each other. This method has been
used frequently for lattice models of this type.In 2005 de Gier and Nienhuis noticed a connection between the ground
state of the periodic Brauer loop model and the degrees of the
irreducible components of a certain algebraic scheme as calculated by
Knutson in 2003. This connection was explored further by Di Francesco
and ZinnJustin in 2006, and proved shortly thereafter by Knutson and
ZinnJustin. The irreducible components can be labelled by the basis
elements of the ground state, and the final proof involves showing that
the multidegrees (an extension of the concept of polynomial degree) of
these irreducible components also satisfy the qKZ equation. This
connection seems similar in spirit to the connection between integrable
models and combinatorics, but is much less explored. 
04/06/2014 5:00 PM103Sitabhra Sinha (The Institute of Mathematical Sciences, Chennai, India)Using nonlinear dynamics and complex networks to understand the brain
Nonlinear dynamics of neuronneuron interaction via complex networks lie at the base of all brain activity. How such intercellular communication gives rise to behavior of the organism has been a longstanding question. In this talk, we first explore the evidence for the occurrence of such mesoscopic structures in the nervous system of the nematode C. elegans and in the macaque cortex. Next, we look at their possible functional role in the brain. We also consider the attractor network models of nervous system activity and investigate howmodular structures affect the dynamics of convergence to attractors. We conclude with a discussion of the general implications of our results for basin size of dynamical attractors in modular networks whose nodes have thresholdactivated dynamics. As such networks also appear in the context of intracellular signaling, our results may provide a glimpse of a universal (i.e., scaleinvariant) theory for information processing dynamics in biology.

08/07/2014 5:00 PM103Karim Essafi (Okinawa Institute of Science and Technology)Nonperturbative Renormalization Group Approach to Polymerized Membranes
Membranes or membranelike materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Membranes can be divided into two group : fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference etween fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid embranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. nonselfavoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, from the point of view of its mechanical properties, graphene identifies with the flat phase.

22/07/2014 5:00 PM103Pablo Hurtado Fernández (University of Granada)Scaling laws and local equilibrium in nonequilibrium fluids
When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple universal scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium (LE) and Fourier’s law hold. These results, that we prove for hard sphere fluids and more generally for systems with homogeneous potentials in arbitrary dimension, are likely to remain valid in the much broader family of strongly correlating fluids where excluded volume interactions are dominant. Extensive simulations of hard disk fluids confirm the universal scaling laws even under strong temperature gradients, suggesting that Fourier’s law remains valid in this highly nonlinear regime, with the expected corrections absorbed into a nonlinear conductivity functional. Our results also show that macroscopic LE is a very strong property, allowing us to measure the hard disks equation of state in simulations far from equilibrium with a surprising accuracy comparable to the best equilibrium simulations. Subtle corrections to LE are found in the fluctuations of the total energy which strongly point out to the nonlocality of the nonequilibrium potential governing the fluid’s macroscopic behavior out of equilibrium. Finally, our simulations show that both LE and the universal scaling laws are robust in the presence of strong finitesize effects, via a bulkboundary decoupling mechanism by which all sorts of spurious finitesize and boundary corrections sum up to renormalize the effective boundary conditions imposed on the bulk fluid, which behaves macroscopically.

23/09/2014 5:00 PMM103Oscar Bandtlow (QMUL)Continuity of the topological entropy for interval maps with holes
The topological entropy is a measure of the complexity
of a map. In this talk I will explain this notion in some detail and
report on a recent result with H.H. Rugh on the regularity of the
topological entropy of interval maps with holes as a function of the hole
position and size. 
30/09/2014 5:00 PM103Enzo Nicosia (QMUL)Reducibility of multiplex networks
Many complex systems are characterised by distinct types of
interactions among a set of elementary units, and their structure can
be thus better modelled by means of multilayer networks. A
fundamental open question is then how many layers are really necessary
to accurately represent a multilayered complex system. Drawing on the
formal analogy between quantum density operators and the normalised
Laplacian of a graph, we develop a simple framework to reduce the
dimensionality of a multiplex network while minimizing information
loss. We will show that the number of informative layers in some
natural, social and collaboration systems can be substantially
reduced, while multilayer engineered and transportation systems, for
which the redundancy is purposedly avoided in order to maximise their
efficiency, are essentially irreducible. 
07/10/2014 5:00 PMM103Christian Beck (QMUL)Axionic dark matter physics in Josephson junctions

14/10/2014 5:00 PM103Nicholas Moloney (London Mathematical Laboratory)Perils of thresholding
(Work in collaboration with F. FontClos, G. Pruessner, A. Deluca)
When analysing time series it is common to apply thresholds. For example, this could be to eliminate
noise coming from the resolution limitations of measuring devices, or to focus on extreme events in the case
of high thresholds. We analyse the effect of applying a threshold to the duration time of a birthdeath
process. This toy model allows us to work out the form of the duration time density in full detail. We find
that duration times decay with random walk exponent 3/2 for `short' times, and birthdeath exponent 2
for `long' times, where short and long are characterised by a thresholdimposed timescale. For sparse data
the ultimate 2 exponent of the underlying (multiplicative) process may never be observed. This may have
implications for realworld data in the interpretation of thresholdspecific decay exponents. 
21/10/2014 5:00 PMM103Colm Connaughton (Warwick)Oscillatory kinetics in clustercluster aggregation
I will discuss the mean field kinetics of irreversible coagulation in
the presence of a source of monomers and a sink at large cluster sizes
which removes large particles from the system. These kinetics are
described by the Smoluchowski coagulation equation supplemented with
source and sink terms. In common with many driven dissipative systems with
conservative interactions, one expects this system to reach a stationary
state at large times characterised by a constant flux of mass in the
space of cluster sizes from the smallscale source to the large scale sink.
While this is indeed the case for many systems, I will present here a
class of systems in which this stationary state is dynamically unstable.
The consequence of this instability is that the longtime kinetics are
oscillatory in time. This oscillatory behaviour is caused by the fact that
mass is transferred through the system in pulses rather than via a stationary
current in such a way that the mass flux is constant on average. The
implications of this unusual behaviour the nonequilibrium kinetics of
other systems will be discussed. 
28/10/2014 4:00 PM103Fabio Caccioli (UCL)A network model of financial contagion due to overlapping portfolios
Contemporary finance is characterized by a complex pattern of relations between financial institutions that can be conveniently modeled in terms of networks.
In stable market conditions, connections allow banks to diversify their investments and reduce their individual risk. The same networked structure may, however, become a source of contagion and stress amplification when some banks go bankrupt.
We consider a network model of financial contagion due to the combination of overlapping portfolios and marketimpact, and we show how it can be understood in terms of a generalized branching process. We estimate the circumstances under which systemic instabilities are likely to occur as a function of parameters such as leverage, market crowding and diversification.
The analysis shows that the probability of observing global cascades of bankruptcies is a nonmonotonic function of both the average diversification of financial institutions, and that there is a critical threshold for leverage below which the system is stable. Moreover the system exhibits "robust yet fragile'' behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. 
11/11/2014 4:00 PM103Patrick Wolfe (UCL)Understanding the Behavior of Large Networks
In this talk  which will be accessible to a general audience  we show how the asymptotic behavior of random networks gives rise to universal statistical summaries. These summaries are related to concepts that are well understood in the other contexts  such as stationarity and ergodicity  but whose extension to networks requires recent developments from the theory of graph limits and the corresponding analog of de Finetti's theorem. We introduce a new tool based on these summaries, which we call a network histogram, obtained by fitting a statistical model called a blockmodel to a large network. Blocks of edges play the role of histogram bins, and socalled network community sizes that of histogram bandwidths or bin sizes. For more details, see recent work in the Proceedings of the National Academy of Sciences (doi:10.1073/pnas.1400374111, with Sofia Olhede) and the Annals of Statistics (doi:10.1214/13AOS1173, with David Choi).

18/11/2014 4:00 PMM103Tomaso Aste (UCL)Unwinding Market Complexity: scaling laws and network filtering
Financial markets are complex systems with a large number of different factors contributing in an interrelated way. Complexity mainly manifests in two aspects: 1) changes in the statistical properties of financial signals when analyzed at different timescales; 2) dependency and causality structure dynamically evolving in time. These nonstationary changes are more significant during periods of market stress and crises.
In this talk I’ll discuss methods to study financial market complexity from a statistical perspective. Specifically, I’ll introduce two approaches: 1) multiscaling studies by means of novel scaling exponents and complexity measures; 2) network filtering techniques to make sense of big data.
I will discuss practical applications showing how a better understanding of market complexity can be used, in practice, to hedge risk and discover market inefficiencies.

20/11/2014 5:00 PMBR 3.02James Meiss (Colorado)Perturbing the Cat Map: Mixed Elliptic and Hyperbolic Dynamics
Arnold’s cat map is a prototypical dynamical system on the torus with uniformly hyperbolic dynamics. Since the famous picture of
a scrambled cat in the 1968 book by Arnold and Avez, it has become one of the icons of chaos. In 2010, Lev Lerman studied a family of maps homotopic to the cat map that has, in addition to a saddle, a parabolic fixed point. Lerman conjectured that this map could be a prototype for dynamics with a mixed phase space, having positive measure sets of nonuniformly hyperbolic and of elliptic orbits. We present some numerical evidence that supports Lerman’s conjecture. The elliptic orbits appear to be confined to a pair of channels bounded by invariant manifolds of the two fixed points. The complement of the channels appears to be a positive measure Cantor set. Computations show that orbits in the complement have positive Lyapunov exponents. 
21/11/2014 4:00 PM203Miguel Angel Muñoz (Universidad de Granada, Spain)Griffiths phases and criticality in brain networks
Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity, to the dynamic of gene expression or to flock dynamics. However, a wellfounded theory for understanding how and why living systems tune themselves to be poised in the vicinity of a critical point is lacking. In this talk I will review the concept of criticality with its associated scale invariance and powerlaw distributions. I will discuss mechanisms by which inanimate systems may selftune to critical points and compare such phenomenology with what observed in living systems. I will also introduce the concept of Griffiths phase an old acquaintance from the physics of disordered systems and show how it can be very naturally related to criticality in living structures such as the brain. In particular, taking into account the complex hierarchicalmodular architecture of cortical networks, the usual singular critical pointin the dynamics of neural activity propagation is replaced by an extended criticallike region with a fascinating dynamics which might justify the tradeoff between segregation and integration, needed to achieve complex cognitive functions.

25/11/2014 4:00 PM103Sergei Nechaev (LPTMS, Orsay, France)Lowdimensional topology and nonEuclidean geometry in Nature
In the talk I will demonstrate on specific examples the emergence of a new field, "statistical topology", which unifies topology, noncommutative geometry, probability theory and random walks. In particular, I plan to discuss the following interlinked questions: (i) how the ballistic growth ("Tetris" game) is related to random walks in symmetric spaces and quantum Toda chain, (ii) what is the optimal structure of the salad leaf in 3D and how it is related to modular functions and hyperbolic geometry, (iii) what is the fractal structure of unknotted long polymer chain confined in a bounding box and how this is related to Brownian bridges in spaces of constant negative curvature.

02/12/2014 4:00 PMM103Ferrucio Renzoni (UCL)Control of atomic motion with ac fields: from the ratchet effect to vibrational mechanics
The use of ac fields allows one to precisely control the motion of particles in periodic potentials. We demonstrate such a precise control with cold atoms in driven optical lattices, using two very different mechanism: the ratchet effect and vibrational mechanics. In the first one ac fields drive the system away from equilibrium and break relevant symmetries, in the second one ac fields lead to the renormalisation of the potential.

03/12/2014 1:30 PMM103Special eventOneday ergodic theory meeting
This is part of a series of collaborative meetings between Bristol, Leicester, Liverpool, Loughborough, Manchester, Queen Mary, Surrey, and Warwick, funded by a Scheme 3 grant from the London Mathematical Society.
For speakers, schedule, titles, and abstracts see the meeting webpage.

09/12/2014 4:00 PMM103Alain Joye (Institut Fourier, Universite de Grenoble)Spectral Transition for Random Quantum Walks on Trees
We consider random quantum walks on a homogeneous tree of degree 3 describing the discrete time evolution of a quantum particle with internal degree of freedom in C^3 hopping on the neighboring
sites of the tree in presence of static disorder. The one time step random unitary evolution operator of the particle depends on a unitary matrix C in U(3) which monitors the strength of the disorder.
We show the existence of open sets of matrices in U(3) for which the random evolution has either pure point spectrum almost surely or purely absolutely continuous spectrum.
We also establish properties of the spectral diagram which provide a description of the spectral transition driven by C in U(3). This is joint work with Eman Hamza. 
13/01/2015 2:00 PM203Jim Webber (chief scientist, Neo Technology)Neo Technology special lecture
In this special lecture, organized within our MSc Mathematics of Networks/Network Science, Dr. Jim Webber, chief scientist at Neo Technology, will talk about how Network Science is used in industry in a daily basis, within their software Neo4j.
Jim will introduce the notion of graph databases for storing and querying connected data structures. He will also look under the covers at Neo4j's design, and consider how the requirements for correctness and performance of connected data drive the architecture. Moving up the stack, he will explore Neo4j's Cypher query language and show how it can be used to tackle complex scenarios like recommendations in minutes (with live programming, naturally!). Finally he will discuss what it means to be a very large graph database and review the dependability requirements to make such a system viable.
Everybody is welcome, and we specially invite all our MSc and PhD students to attend, as it can be an excellent forum for discussion between academia and industry. 
13/01/2015 4:00 PM103Elsa Arcaute (UCL)City boundaries through percolation theory and fractals
In this talk we explore different ways to construct city boundaries and its relevance to current efforts towards a science of cities. We use percolation theory to understand the hierarchical organisation of the urban system, and look at the morphological characteristics of urban clusters for traces of optimization or universality.

20/01/2015 4:00 PM103Alex Arenas (Universidad Rovira i Virgili)Multilayer interconnected complex networks: an introduction
The constituents of a wide variety of realworld complex systems interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Recently, the interest of the research community increased towards such systems because accounting for the "multilayer" features of those systems is a challenge. In this lecture, we will discuss several realworld examples, put in evidence their multilayer information and review the most recent advance in this new field.

27/01/2015 4:00 PMM103Dmitry Turaev (Imperial)Fermi acceleration in nonergodic systems
We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads
to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this
process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase
after each period of the parameters variation. 
03/02/2015 4:00 PMM103Pierpaolo Vivo (KCL)Thirdorder phase transitions in Random Matrix models
The use of the socalled Coulomb gas technique in Random Matrix Theory goes back to the seminal works of Wigner and Dyson. I review some modern (and not so modern!) applications of this technique, which are linked via a quite intriguing unifying thread: the appearance of extremely weak (thirdorder) phase transitions separating the equilibrium phases of the fluid of "eigenvalues". A particular interesting example concerns the statistics of the largest eigenvalue of random matrices, and the probability of atypical fluctuations not described by the celebrated TracyWidom law. Recent occurrences of this type of phase transitions in condensed matter and statistical physics problems  which have apparently very little to do with each other  are also addressed, as well as some "exceptions" or "counterexamples".

05/02/2015 5:00 PMM513Jürgen Vollmer (Göttingen)Aggregate Growth, Size Distributions, and Corrections to Scaling Descriptions in Nanoparticle Synthesis, Dew and Rain Fo
Ripening in systems where the overall aggregate volume increases due to
chemical reactions or the drift of thermodynamic parameters is a problem
of pivotal importance in the material and environmental sciences. In
the former its better understanding provides insight into controlling
nanoparticle synthesis, annealing, and aging processes. In the latter
it is of fundamental importance to improve the parametrization of mist
and clouds in weather and climate models.I present the results of comprehensive laboratory experiments and
numerical studies addressing droplet growth and droplet size
distributions in systems where droplets grow due to sustained
supersaturation of their environment. Both, for classical theories
addressing droplets condensing on a substrate (like in dew and cooling
devices) and droplets entrained in an external flow (like in clouds and
nanoparticle synthesis) we identify severe shortcomings. I will show
that the quantitative modelling of rain formation in clouds on the one
hand and of the ageing and synthesis of nanoparticles on the other hand
face the same theoretical challenges, and that these challenges can be
addressed by adapting modern methods of nonequilibrium statistical
physics. 
10/02/2015 4:00 PMM103Radek Erban (Oxford)Mathematical Methods for Multiscale Modelling in Molecular, Cell and Population Biology
I will discuss methods for spatiotemporal modelling in molecular,
cell and population biology. Three classes of models will be considered:(i) microscopic (individualbased) models (molecular dynamics,
Brownian dynamics) which are based on the simulation of
trajectories of molecules (or individuals) and their localized
interactions (for example, reactions);(ii) mesoscopic (latticebased) models which divide the computational
domain into a finite number of compartments and simulate the time
evolution of the numbers of molecules (numbers of individuals)
in each compartment; and(iii) macroscopic (deterministic) models which are written in terms
of meanfield reactiondiffusionadvection partial differential
equations (PDEs) for spatially varying concentrations.In the first part of my talk, I will discuss connections between the
modelling frameworks (i)(iii). I will consider chemical reactions both at
a surface and in the bulk. In the second part of my talk, I will present
hybrid (multiscale) algorithms which use models with a different level
of detail in different parts of the computational domain.
The main goal of this multiscale methodology is to use a detailed
modelling approach in localized regions of particular interest
(in which accuracy and microscopic detail is important) and a less
detailed model in other regions in which accuracy may be traded
for simulation efficiency. I will also discuss hybrid modelling
of chemotaxis where an individualbased model of cells is coupled
with PDEs for extracellular chemical signals. 
17/02/2015 4:00 PMM103Carlo Barenghi (Newcastle)Quasiclassical wake in a quantum fluid
A famous problem of fluid dynamics is the flow around a cylindrical or spherical obstacle. At small flow velocity, a steady axisymmetric wake forms behind the obstacle; upon increasing the velocity the wake becomes longer, then asymmetric and time dependent (vortices of alternating signs are shed in the von Karman vortex street pattern), then turbulent. The question which we address is what happens if the fluid is a superfluid, such as liquid He, or an atomic BoseEinstein condensate: in the absence of viscosity, is there a quantum analog to the classical wake ?

03/03/2015 4:00 PM103Stefano Boccaletti (CNR Italy)Synchronization in multiplex networks
TBA

10/03/2015 4:00 PMM103Sergei Fedotov (Manchester)Anomalous random walk and nonlinear fractional subdiffusive equations: applications in physics and biology
Linear fractional equation involving a RiemannLiouville derivative
is the standard model for the description of anomalous subdiffusive
transport of particles. The question arises as to how to extend this fractional
equation for the nonlinear case involving particles interactions.
The talk will be concerned with the structural instability of fractional Fokker–Planck
equation, nonlinear fractional PDE's and aggregation phenomenon. 
17/03/2015 4:00 PM103Andrea Rapisarda (Catania)Micro and Macro Benefits of Random Investments in Financial Markets
In this talk, making use of statistical physics tools, we address the specific role of randomness in financial markets, both at micro and macro level. In particular, we will review some recent results obtained about the effectiveness of random strategies of investment, compared with some of the most used trading strategies for forecasting the behavior of real financial indexes. We also push forward our analysis by means of a SelfOrganized Criticality model, able to simulate financial avalanches in trading communities with different network topologies, where a Paretolike power law behavior of wealth spontaneously emerges. In this context we present new findings and suggestions for policies based on the effects that random strategies can have in terms of reduction of dangerous financial extreme events, i.e. bubbles and crashes.
References
A.E. Biondo, A. Pluchino, A. Rapisarda, Contemporary Physics 55 (2014) 318
A.E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, Phys Rev. E 88 (2013) 062814
A.E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, (2013) PLOS ONE 8(7): e68344.
A.E. Biondo, A. Pluchino, A. Rapisarda, Journal of Statistical Physics 151 (2013) 607. 
24/03/2015 4:00 PMM103Daphne Klotsa (Cambridge)*** Seminar cancelled ***

26/05/2015 4:01 PMM103Franco Vivaldi (QMUL)Mathematical Writing
Teaching mathematical writing gives you a vivid portrait of the students' struggle with exactness and abstraction, and new tools for dealing with it. This seminar intends to stimulate a discussion on how we introduce our
students to abstract mathematics; I also hope to give a positive twist to the soulsearching that normally accompanies exammarking. 
02/07/2015 5:00 PMM103Daphne Klotsa (Cambridge)Packing polyhedra: from ancient math to advanced materials
The densest way to pack objects in space, also known as the packing problem, has intrigued scientists and philosophers for millenia. Today, packing comes up in various systems over many length scales from batteries and catalysts to the selfassembly of nanoparticles, colloids and biomolecules. Despite the fact that so many systems' properties depend on the packing of differentlyshaped components, we still have no general understanding of how packing varies as a function of particle shape. Here, we carry out an exhaustive study of how packing depends on shape by investigating the packings of over 55,000 polyhedra. By combining simulations and analytic calculations, we study families of polyhedra interpolating between Platonic and Archimedean solids such as the tetrahedron, the cube, and the octahedron. Our resulting density surface plots can be used to guide experiments that utilize shape and packing in the same way that phase diagrams are essential to do chemistry. The properties of particle shape indeed are revealing why we can assemble certain crystals, transition between different ones, or get stuck in kinetic traps.
Links: http://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.011024(link is external),
http://www.newscientist.com/article/dn25163angryalieninpackingpuzzl...(link is external),
http://physicsworld.com/cws/article/news/2014/mar/03/findingbetterways...(link is external),
http://physics.aps.org/synopsisfor/10.1103/PhysRevX.4.011024(link is external)My website: http://wwwpersonal.umich.edu/~dklotsa/Daphne_Klotsas_Homepage/Home.html

16/06/2015 5:00 PMM103Gary Froyland (New South Wales)Transfer operators and dynamics
Transfer operators are global descriptors of ensemble evolution under nonlinear dynamics and form the basis of efficient methods of computing a variety of statistical quantities and geometric objects associated with the dynamics.
I will discuss two related methods of identifying and tracking coherent structures in timedependent fluid flow; one based on probabilistic ideas and the other on geometric ideas.
Applications to geophysical fluid flow will be presented. 
19/06/2015 5:00 PMM103Dorien Herremans (QMUL)Generating structured music using operations research methods
Many state of the art music generation/improvisation systems generate music that
sounds good on a notetonote level. However, these compositions often lack long term
structure or coherence. This problem is addressed in this research by generating music that
adheres to a structural template. A powerful variable neighbourhood search algorithm (VNS)
was developed, which is able to generate a range of musical styles based on it's
objective function, whilst constraining the music to a structural template. In the first
stage of the project, an objective function based on rules from music theory was used to
generate counterpoint. In this research, a machine learning approach is combined with the
VNS in order to generate structured music for the bagana, an Ethiopian lyre. Different
ways are explored in which a Markov model can be used to construct quality metrics that
represent how well a fragment fits the chosen style (e.g. music for bagana). This approach
allows us to combine the power of machine learning methods with optimization algorithms. 
24/06/2015 12:00 PMM103Tatjana Tchumatchenko (Max Planck for Brain Research)Nonlinear input summation in balanced networks can be controlled by activity dependent synapses
The synaptic inputs arriving in the cortex are under many circumstances
highly variable. As a consequence, the spiking activity of cortical
neurons is strongly irregular such that the coefficient of variation of
the interspike interval distribution of individual neurons is
approximately Poissonlike. To model this activity, balanced networks
have been put forward where a coordination between excitatory and strong
inhibitory input currents, which nearly cancel in individual neurons,
gives rise to this irregular spiking activity. However, balanced
networks of excitatory and inhibitory neurons are characterized by a
strictly linear relation between stimulus strength and network firing
rate. This linearity makes it hard to perform more complex computational
tasks like the generation of receptive fields, multiple stable activity
states or normalization, which have been measured in many sensory
cortices. Synapses displaying activity dependent shortterm plasticity
(STP) have been previously reported to give rise to a nonlinear network
response with potentially multiple stable states for a given stimulus.
In this seminar, I will discuss our recent analytical and numerical
analysis of computational properties of balanced networks which
incorporate shortterm plasticity. We demonstrate stimuli are normalized
by the network and that increasing the stimulus to one subnetwork,
suppresses the activity in the neighboring population. Thereby,
normalization and suppression are linear in stimulus strength when STP
is disabled and become nonlinear with activity dependent synapses. 
15/07/2015 2:00 PM410Jesus Gomez Gardenes (University of Zaragoza)Urban Mobility, Social Status and Contagion Processes
In this talk we study the impact that urban mobility patterns have on the onset of epidemics. We focus on two particular datasets from the cities of Medellín and Bogotá, both in Colombia. Although mobility patterns in these two cities are similar from those typically found for large cities, these datasets provide additional information about the socioeconomic status of the individuals. This information is particularly important when the level of inequality i a society is large, as it is the case in Colombia. Thus, taking advantage of this additional information we unveil the differences between the mobility patterns of these social stata to finally unveil the social hierarchy by analyzing the contagion patterns occurring during an epidemic outbreak.

29/09/2015 5:00 PMM103Kiyoshi Kanazawa (Tokyo Institute of Technology)Minimal Model of Stochastic Athermal Systems: Origin of NonGaussian Noise
Fluctuation in small systems has attracted wide interest because of the recent experimental development in biological, colloidal, and electrical systems. As accurate data on fluctuation have become accessible, the importance of mathematical modeling of fluctuation’s dynamics has been increasing. One of the minimal models for such systems is the Langevin equation, which is a simple model composed of the viscous friction and the white Gaussian noise. The validity of the Langevin model has been shown in terms of some microscopic theories [1], and this model has been used not only theoretically but also experimentally in describing thermal fluctuation.
On the other hand, nonGaussian properties of fluctuation are reported to emerge in athermal systems, such as biological, granular, and electrical systems. A natural question then would arises: When and how does the nonGaussian fluctuation emerge for athermal systems? In this seminar, we present a systematic method to derive a Langevinlike equation driven by nonGaussian noise for a wide class of stochastic athermal systems, starting from master equations and developing an asymptotic expansion [2, 3]. We found an explicit condition whereby the nonGaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. We also derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. Furthermore, we obtain the fullorder asymptotic formula of the steady distribution function for an arbitrary strong nonlinear friction, and show that the firstorder approximation corresponds to the independent kick model [4]. We apply our formulation to a granular motor under viscous and Coulombic frictions, and analytically obtain the angular velocity distribution functions. Our theory demonstrates that the nonGaussian Langevin equation is a minimal model of athermal systems.
[1] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, NorthHolland (2007).
[2] K. Kanazawa, T.G. Sano, T. Sagawa, and H. Hayakawa, Phys. Rev. Lett. 114, 090601 (2015).
[3] K. Kanazawa, T.G. Sano, T. Sagawa, and H. Hayakawa, J. Stat. Phys. 160, 1294 (2015).
[4] J. Talbot, R.D. Wildman, and P. Viot, Phys. Rev. Lett. 107, 138001 (2011). 
01/10/2015 4:00 PMM203Tomohiko Sano (Kyoto University)Nonequilibrium fluctuating motion of piston as a rectifier: From adiabatic piston to fluctuating engine
Rectification of work in nonequilibrium conditions has been one of the important topic of nonequilibrium statistical mechanics. Within the framework of equilibrium thermodynamics, it is well known that the works can be rectified from two thermal equilibrium baths. We address the question that how can we rectify work from Brownian object (piston) attached to multiple environments, including nonequilibrium baths? We focus on adiabatic piston problem under nonlinear friction, where the piston with sliding friction separates two gases of the same pressure, but different temperatures. Without sliding friction, the direction of piston motion is known to be determined from the difference of temperature of two gases [1,2]. However, if sliding friction exists, we report that the direction of motion depends on the amplitude of the friction, and nonlinearity of the friction [3]. If time allows, we also report the possibility of application to the problem of fluctuating heat engine, where the temperature of gas is changed, in a cyclic manner [4].
[1] E. H. Lieb, Physica A 263 491 (1999).
[2] Ch. Gruber and J. Piasecki, Physica A 268 412 (1999). A. Fruleux, R. Kawai and K. Sekimoto, Phys. Rev. Lett. 108 160601 (2012).
[3] T. G. Sano and H. Hayakawa, Phys. Rev. E 89 032104 (2014).
[4] T. G. Sano and H. Hayakawa, arXiv:1412.4468 (2014). 
06/10/2015 5:00 PMM103Istvan Kiss, University of SussexGeneralisation of Pairwise Models to nonMarkovian Epidemics on Networks
In this presentation, a generalisation of pairwise models to nonMarkovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new R_0like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integrodifferential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between nonMarkovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of nonMarkovian dynamics.

08/10/2015 3:00 PMM203Vladimir Kravtsov (ICTP)Multifractality of random eigenfunctions and work distribution in driven systems
Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wavefunction amplitudes in disordered systems close to the Anderson localization transition. In both cases, the probability distribution function is given by the largedeviation ansatz. Here we exploit the analogy between the statistics of work dissipated in a driven singleelectron box and that of random multifractal wavefunction amplitudes, and uncover new relations that generalize the Jarzynski equality. We checked the new relations theoretically using the rate equations for sequential tunnelling of electrons and experimentally by measuring the dissipated work in a driven singleelectron box and found a remarkable correspondence. The results represent an important universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localization.

13/10/2015 5:00 PMM103Rosemary J. Harris (QMUL)Memory effects in complex systems
I will give a gentle introduction to some recent work on the effects of longrange temporal correlations in stochastic particle models, focusing particularly on fluctuations about the typical behaviour. Specifically, in the first part of the talk, I will discuss how longrange memory dependence can modify the large deviation principle describing the probability of rare currents and lead, for example, to superdiffusive behaviour. In the second part of the talk, I will describe a more interdisciplinary project incorporating the psychological "peakend" heuristic for human memory into a simple discrete choice model from economics.
[Sun, sea and sand(pit): This is mainly work completed during my sabbatical and partially funded/inspired by the "sandpit" grant EP/J004715/1. There may be a few pictures!]

20/10/2014 5:00 PMM103Aleks Owczarek (University of Melbourne)Exact Solutions of Interacting Friendly Directed Walkers

21/10/2015 2:30 PMM203Special eventhttp://www.maths.qmul.ac.uk/seminars/onedayergodictheorymeeting4
This is part of a series of collaborative meetings between Bath, Bristol, Exeter, Leicester, Loughborough, Manchester, Queen Mary, Surrey, and Warwick, funded by a Scheme 3 grant from the London Mathematical Society.
For speakers, schedule, titles, and abstracts see the meeting webpage.

27/10/2015 4:00 PMM103Edwin Hancock, University of YorkVon Neumann Entropy, Complex Network Analysis and Machine Learning
The talk provides an overview recent work on the analysis of von Neumann entropy, which leads to new methods for network algorithms in both the machine learning and complex network domains. We commence by presenting simple approximations for the Von Neumann entropy of both directed and undirected networks in terms of edge degree statistics. In the machine learning domain, this leads to new description length methods for learning generative models of networkstructure, and new ways of computing information theoretic graph kernels. In the complex network domain, it provides a means of analysing the time evolution of networks, and making links with the thermodynamics of network evolution.

03/11/2015 4:00 PMM103EJ Janse van Rensburg (York University)Forces and Pressures in Models of Partially Directed Paths
The partially directed path is a classical model in lattice path combinatorics. In this talk I will review briefly the model and explain why it is a good model for quantifying polymer entropy. If the path is confined to the space between vertical walls in a halflattice, then it loses entropy. This loss of entropy induces an entropic force on the walls. I will show how to determine the generating and partition function of the model using the kernel method, and then compute entropic forces and pressures. In some cases the asymptotic behaviour of the entropic forces will be shown. This work was done in collaboration with Thomas Prellberg. See http://arxiv.org/abs/1509.07165

17/11/2015 4:00 PMM103Lucas Lacasa, QMULTime Series meet Network Science
In the last years, ideas and methods from network science have been
applied to study the structure of time series, thereby building a bridge
between dynamical systems, time series analysis and graph theory. In this
talk I will focus on a particular approach, namely the family of
visibility algorithms, and will give a friendly overview of the main
results that we have obtained recently. In particular, I will focus on
several canonical problems arising in different fields such as nonlinear
dynamics, stochastic processes, statistical physics and machine learning
as well as in applied fields such as finance, and will show how these can
be mapped, via visibility algorithms, to the study of certain topological
properties of visibility graphs. If time permits, I will also present a
diagrammatic theory that allows to find some exact results on the
properties of these graphs for general classes of Markovian dynamics. 
19/11/2015 4:30 PMM203Semyon Klevtsov (Cologne)Geometry and large N limits in Quantum Hall effect
Quantum Hall states are characterised by the precise quantization of Hall conductance, the phenomenon whose geometric origin was understood early on. One of the main goals of the theory is computing adiabatic phases corresponding to various geometric deformations (associated with the line bundle, metric and complex structure moduli), in the limit of a large number of particles. We consider QH states on Riemann surfaces, and give a complete characterisation of the problem for the integer QH states and for the Laughlin states in the fractional QHE, by computing the generating functional for these states. In the integer QH our method relies on the Bergman kernel expansion for high powers of holomorphic line bundle, and the answer is expressed in terms of energy functionals in Kahler geometry. We explain the relation of geometric phases to Quillen theory of determinant line bundles, using BismutGilletSoule anomaly formulas. On the sphere the generating functional is also related to the partition function for normal random matrix ensembles for a large class of potentials. For the Laughlin states we compute the generating functional using path integral in a 2d scalar field theory.

24/11/2015 4:00 PMM103Patrick Ilg (Reading)Some structural features underlying the dynamics of supercooled liquids

01/12/2015 4:00 PMM103Marina DiakonovaBeyond the Coevolving Voter Model
The binarystate voter model describes a system of agents who adopt the opinions of their neighbours. The coevolving voter model (CVM, [1]) extends its scope by giving the agents the option to sever the link instead of adopting a contrarian opinion. The resulting simultaneous evolution of the network and the configuration leads to a fragmentation transition typical of such adaptive systems. The CVM was our starting point for investigating coevolution in the context of multilayer networks, work that IFISC was tasked with under the scope of the LASAGNE Initiative. In this talk I will briefly review some of the outcomes and followup works. First we will see how coupling together of two CVM networks modifies the transitions and results in a new type of fragmentation [2]. I will then identify the latter with the behaviour of the singlenetwork CVM with select nodes constantly under the stress of noise [3]. Finally, I will relate our attempts to reproduce the effect of multiplexing on the voter model by studying behaviour of the standard aggregates; the negative outcome of which gives validity to considering the multiplex as a fundamentally novel, nonreducible structure [4].
[1] F. Vazquez, M. San Miguel and V. M. Eguiluz, Generic Absorbing Transition in Coevolution Dynamics, Physical Review Letters, 100, 108702 (2008)
[2] MD, M. San Miguel and V. E. Eguiluz, Absorbing and Shattered Fragmentation Transitions in Multilayer Coevolution, Physical Review E, 89, 062818, (2014)
[3] MD, V. M. Eguiluz and M. San Miguel, Noise in Coevolving Networks, Physical Review E, 92, 032803, (2015)
[4] MD, V. Nicosia, V. Latora and M. San Miguel, Irreducibility of Multilayer Network Dynamics: the Case of the Voter Model,arXiv:1507.08940 (2015) 
08/12/2015 4:00 PMM103Jarek Krawczyk (Durham)Elasticity dominated surface segregation of small molecules in polymer mixtures
We study the phenomenon of migration of the small molecular weight component of a binary
polymer mixture to the free surface using mean field and selfconsistent field theories. By proposing a free energy functional that incorporates polymermatrix elasticity explicitly, we compute the migrant volume fraction and show that it decreases significantly as the sample rigidity is increased. Estimated values of the bulk modulus suggest that the effect should be observable experimentally for rubberlike materials. This provides a simple way of controlling surface migration in polymer mixtures and can play an important role in industrial formulations, where surface migration often leads to decreased product functionality. 
12/01/2016 4:00 PM103Jens Starke (QMUL)Multiscale Analysis of Collective Behaviour in Particle Models  with Applications to Traffic and Pedestrian Flows

19/01/2016 4:00 PMM103Igor Smolyarenko (Brunel)Models of random growing networks
Network growth models with attachment rules governed by intrinsic node fitness are considered. Both direct and inverse problems of matching the growth rules to node degree distribution and correlation functions are given analytical solutions. It is found that the node degree distribution is generically broader than the distribution of fitness, saturating at power laws. The saturation mechanism is analysed using a feedback model with dynamically updated fitness distribution. The latter is shown to possess a nontrivial fixed point with a unique powerlaw degree distribution. Applications of fieldtheoretic methods to network growth models are also discussed.

26/01/2016 4:00 PMM103Sebino Stramaglia (Universita' di Bari)Network approach for bringing together brain structure and function
Understanding the relation between functional anatomy and structural substrates is a major challenge in neuroscience. To study at the aggregate level the interplay between structural brain networks and functional brain networks, a new method will be described; it provides an optimal brain partition —emerging out of a hierarchical clustering analysis— and maximizes the “crossmodularity” index, leading to large modularity for both networks as well as a large withinmodule similarity between them . The brain modules found by this approach will be compared with the classical Resting State Networks, as well as with anatomical parcellations in the Automated Anatomical Labeling atlas and with the Broadmann partition.

02/02/2016 4:00 PMM103Marian Boguna (University of Barcelona)Toward a cosmological theory of complex networks
Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that causal network representing the largescale structure of spacetime in our accelerating universe is a powerlaw graph with strong clustering, similar to many complex networks such as the Internet, social or biological networks. We prove that this strcutural similarity is a consequence of the asymptotic equivalence between the largescale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network
science and cosmology. However, our simple frameworks is unable to explain the emergence of community structure, a property that, along with scalefree degree distributions and strong clustering, is commonly found in real complex networks. Here we show how latent network geometry coupled with preferential attachment of the nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA) and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed. 
04/02/2016 5:00 PM203Jürgen F. Stilck (Fluminense Federal University)The nature of the polymer collapse transition
In a good solvent, a polymer chain assumes an extended configuration. As the solvent quality (or the temperature) is lowered, the configuration changes to globular, which is more compact. This collapse transition is also called coilglobule transition in the literature. Since the pioneering work by de Gennes, it is known that it corresponds to a tricritical point in a grandcanonical parameter space. In the most used lattice model to study it, the chain is represented by a selfavoiding walk on and the solvent is effectively taken into account by including attractive interactions between monomers on first neighbor sites which are not consecutive along a chain (SASAW's: selfattracting selfavoiding walks). We will review the model and show that small changes in it may lead to different phase diagrams, where the collapse transition is no longer a tricritial point. In particular, if the polymer is represented by a trail, which allows for multiple visits of sites but mantains the constraint of single visits of edges, we find two distinct polymerized phases besides the nonpolymerized phase and the collapse transition becomes a bicritical point.

09/02/2016 4:00 PM103Bartlomiej Waclaw (Edinburgh)Spatial models of cancer
Mathematical modelling of cancer has a long history, but all cancer models can be categorized into two classes. "Nonspatial" models treat cancerous tumours as wellstirred bags of cells. This approach leads to nice, often exactly solvable models. However, real tumours are not well mixed and different subpopulations of cancer cells reside in different spatial locations in the tumour. "Spatial" models that aim at reproducing this heterogeneity are often very complicated and can only be studied through computer simulations.
In this talk I will present spatial models of cancer that are analytically soluble. These models demonstrate how growth and genetic composition of tumours is affected by three processes: replication, death, and migration of cancer cells. I will show what predictions these models make regarding experimentally accessible quantities such as the growth rate or genetic heterogeneity of a tumour, and discuss how they compare to clinical data.

16/02/2016 4:00 PMM103Kim Christensen (Imperial)Simple Model for Atrial Fibrillation
Atrial fibrillation (AF) is the most common abnormal heart rhythm and the single biggest cause of stroke. Ablation, destroying regions of the atria, is applied largely empirically and can be curative but with a disappointing clinical success rate. We design a simple model of activation wave front propagation on an anisotropic structure mimicking the branching network of heart muscle cells. This integration of phenomenological dynamics and pertinent structure shows how AF emerges spontaneously when the transverse celltocell coupling decreases, as occurs with age, beyond a threshold value. We identify critical regions responsible for the initiation and maintenance of AF, the ablation of which terminates AF. The simplicity of the model allows us to calculate analytically the risk of arrhythmia and express the threshold value of transversal celltocell coupling as a function of the model parameters. This threshold value decreases with increasing refractory period by reducing the number of critical regions which can initiate and sustain microreentrant circuits. These biologically testable predictions might inform ablation therapies and arrhythmic risk assessment. Finally, the model is able to explain clinically observed patient variability w.r.t. the timecourse of AF.

17/02/2016 5:00 PM203Anna Cherubini (Salento)A study of the stochastic resonance as a periodic random dynamical system.
We study a standard model for the stochastic resonance from the point of view of dynamical systems. We present a framework for random dynamical systems with nonautonomous deterministic forcing and we prove the existence of an attracting random periodic orbit for a class of onedimensional systems with a timeperiodic component. In the case of the stochastic resonance, we use properties of the attractor to derive an indicator for the resonant regime.

23/02/2016 4:00 PMM103Janis Bajars (Nottingham Trent)Computing highfrequency wave energy distributions using Discrete Flow Mapping
Discrete Flow Mapping (DFM) was recently introduced as a meshbased high frequency method for modelling structureborne sound in complex structures comprised of twodimensional shell and plate subsystems. In DFM, the transport of vibrational energy between substructures is typically described via a local interface treatment where wave theory is employed to generate reflection/transmission and mode coupling coefficients. The method has now been extended to model threedimensional meshed structures, giving a wider range of applicability and also naturally leading to the question of how to couple the two and threedimensional substructures. In my talk I will present a brief overview of DFM, discuss numerical approaches and sketch ideas behind Discrete Flow Mapping in coupled two and three dimensional domains.

01/03/2016 4:00 PMM103Duccio Piovani (UCL)Forecasting Transitions in High Dimensional Complex Systems
There is a recognized need to build tools capable of anticipaticiting tipping points in complex systems. Most commonly this is done by describing a tipping point as a bifurcation and using the formalism coming from phase transitions. Here we try a different approach, applicable to systems with high dimensions. A metastable state is described as a highdimensional tipping point, a transition in this new optics is the escape of the system from such configuration, given by a rare perturbation parallel to un unstable direction.We will show our procedure by an application to two models: The Tangled Nature Model introduced by H. Jensen et al to mathematically explain the macroscopic intermittent dynamics of ecological systems, phenomenon known under the name of punctuated equilibrium. And high dimensional replicator systems with a stochastic element, first developed by J. Grujic. By describing the models' stochastic dynamics through a mean fied approximation we are able to gather information on the stability of the metastable configuration and predict the arrival of transitions.

08/03/2016 4:00 PMM103Fabrizio Lillo (Scuola Normale Superiore di Pisa)Statistical network models for financial systemic risk
Assessing systemic risk in financial markets and identifying systemically important financial institutions and assets is of great importance. In this talk I will consider two channels of propagation of financial systemic risk, (i) the common exposure to similar portfolios and fire sale spillovers and (ii) the liquidity cascades in the interbank networks. For each of them I will show how the use of statistical models of networks might be useful in systemic risk studies. In the first case, by applying the Maximum Entropy principle to the bipartite network of banks and assets, we propose a method to assess aggregated and single bank’s systemicness and vulnerability and to statistically test for a change in these variables when only the information on the size of each bank and the capitalization of the investment assets are available. In the second case, by inferring a stochastic block model from the eMID interbank network, we show that the extraordinary ECB intervention during the sovereign debt crisis changed completely the large scale organization of such market and we identify the banks that, changing their strategy in response to the intervention, contributed most to the architectural network mutation.

15/03/2016 4:00 PM103Fabien Paillusson (Lincoln)*** Seminar cancelled ***

22/03/2016 4:00 PM103Chiu Fan Lee (Imperial)Universality in Soft Active Matter
Biology systems operate in the far from equilibrium regime and one defining feature of living organisms is their motility. In the hydrodynamic limit, a system of motile organisms may be viewed as a form of active matter, which has been shown to exhibit behaviour analogous to that found in equilibrium systems, such as phase separation in the case of motilityinduced aggregation, and critical phase transition in incompressible active fluids. In this talk, I will use the concept of universality to categorise some of the emergent behaviour observed in active matter. Specifically, I will show that i) the coarsening kinetics of motilityinduced phase separation belongs to the LifshitzSlyozovWagner universality class [1]; ii) the orderdisorder phase transition in incompressible polar active fluids (IPAF) constitutes a novel universality class [2], and iii) the behaviour of IPAF in the ordered phase in 2D belongs to the KardarParisiZhang universality class [3].
References:
[1] C. F. Lee, “Interface stability, interface fluctuations, and the GibbsThomson relation in motilityinduced phase separations,” arXiv: 1503.08674, 2015.
[2] L. Chen, J. Toner, and C. F. Lee, “Critical phenomenon of the orderdisorder transition in incompressible active fluids,” New Journal of Phyics, 17, 042002, 2015.
[3] L. Chen, C. F. Lee, and J. Toner, “Birds, magnets, soap, and sandblasting: surprising connections to incompressible polar active fluids in 2D,” arXiv:1601.01924, 2016. 
29/03/2016 4:00 PMM103Ivan Tomasic (QMUL)Symbolic dynamics and difference algebra
We find a correspondence between certain difference algebras and subshifts of finite type (SFTs) as studied in symbolic dynamics. The known theory of SFTs from symbolic dynamics allows us to make significant advances in difference algebra. Conversely, a `Galois theory' point of view from difference algebra allows us to obtain new structure results for SFTs.

10/05/2016 4:00 PM103Marco Javarone (Cagliari)Evolutionary Game Theory and its Application to Optimization Tasks
Evolutionary Game Theory (EGT) represents the attempt to describe the evolution of populations by the formal frame of Game Theory, combined with principles and ideas of the Darwinian theory of evolution.
Nowadays, a long list of EGT applications spans from biology to socioeconomic systems, where the emergence of cooperation constitutes one of the topics of major interest.
Here statistical physics allows to investigate EGT dynamics, in order to understand the relations between microscopic and macroscopic behaviors in these systems.
Following this approach, during this talk a new application of EGT will be shown. In particular, a new heuristic for solving optimization tasks, like the Traveling Salesman Problem (TSP), will be introduced. Results of this work show that EGT can be a powerful framework for studying a wide range of problems. 
17/05/2016 4:00 PM103Yuri B. Gaididei (Bogolyubov Institute for Theoretical Physics, Kiev)Pattern formation in nonlinear systems with asymmetrically coupled elements: Peristaltic waves in pedestrian dynamics in
Many physical systems can be described by particle models. The interaction between these particles is often modeled by forces, which typ ically depend on the interparticle distance, e.g., gravitational attraction in celestial me chanics, Coulomb forces between charged par ticles or swarming models of selfpropelled par ticles. In most physical systems Newtons third law of actioreactio is valid. However, when considering a larger class of interacting par ticle models, it might be crucial to introduce an asymmetry into the interaction terms, such that the forces not only depend on the dis tance, but also on direction. Examples are found in pedestrian models, where pedestrians typically pay more attention to people in front than behind, or in traffic dynamics, where dri vers on highways are assumed to adjust their speed according to the distance to the preced ing car. Motivated by traffic and pedestrian models, it seems valuable to study particle sys tems with asymmetric interaction where New tons third law is invalid. Here general parti cle models with symmetric and asymmetric re pulsion are studied and investigated for finite range and exponential interaction in straight corridors and annulus. In the symmetric case transitions from oneto multilane (zigzag) be havior including multistability are observed for varying particle density and for a varying curvature with fixed density. When the asym metry of the interaction is taken into account a new “bubble”like pattern arises when the dis tance between lanes becomes spatially mod ulated and changes periodically in time, i.e. peristaltic motion emerges. We find the tran sition from the zigzag state to the peristaltic state to be characterized by a Hopf bifurcation.

31/05/2016 4:00 PM103Fabien Paillusson (Lincoln)Protocol dependent statistical properties of jammed granular matter
Granular matter is the prototypical example of systems that jam when subject to an external loading. Its athermal character, i.e. the fact that the motion of individual grains is insensitive to thermal fluctuations, makes its statistical properties a priori dependent on the protocol used to reach the jammed state. In this talk we will look at two distinct examples from different classes of such protocols: singlestep protocols and sequential protocols. Depending on the context, we will see how one can try to extend the definition of concepts borrowed from statistical thermodynamics such as entropy, ensembles and ergodicity so that they remain meaningful for jammed granular matter.

07/06/2016 4:00 PM103Gregory Berkolaiko, Texas A&MNodal count of eigenfunctions as index of instability
Zeros of vibrational modes have been fascinating physicists for
several centuries. Mathematical study of zeros of eigenfunctions goes
back at least to Sturm, who showed that, in dimension d=1, the nth
eigenfunction has n1 zeros. Courant showed that in higher dimensions
only half of this is true, namely zero curves of the nth eigenfunction of
the Laplace operator on a compact domain partition the domain into at
most n parts (which are called "nodal domains").It recently transpired that the difference between this upper bound
and the actual value can be interpreted as an index of instability of
a certain energy functional with respect to suitably chosen
perturbations. We will discuss two examples of this phenomenon: (1)
stability of the nodal partitions of a domain in R^d with respect to a
perturbation of the partition boundaries and (2) stability of a graph
eigenvalue with respect to a perturbation by magnetic field. In both
cases, the "nodal defect" of the eigenfunction coincides with the
Morse index of the energy functional at the corresponding critical
point. We will also discuss some applications of the above results.Based on arXiv:1103.1423, CMP'12 (with R.Band, H.Raz, U.Smilansky),
arXiv:1107.3489, GAFA'12 (with P.Kuchment, U.Smilansky),
arXiv:1110.5373, APDE'13
arXiv:1212.4475, PTRSA'13 to appear (with T.Weyand),
arXiv:1503.07245, JMP'15 to appear (with R.Band and T.Weyand) 
16/06/2016 4:00 PM103Alberto Antonioni (University Carlos III, Madrid)The role of costly information and unreliable reputation in networked cooperative interactions: experimental evidence
We all need to rely on cooperation with other individuals in many aspects of everyday life, such as teamwork and economic exchange in anonymous markets. In this seminar I will present two laboratory experiments which focus on the impact of information and reputation on human behavior when people engage cooperative interactions on dynamic networks. In the first study, we investigate whether and how the ability to make or break links in social networks fosters cooperation, paying particular attention to whether information on an individual’s actions is freely available to potential partners. Studying the role of information is relevant as complete knowledge on other people’s actions is often not available for free. In the second work, we focus our attention on the role of individual reputation, an indispensable tool to guide decisions about social and economic interactions with individuals otherwise unknown. Usually, information about prospective counterparts is incomplete, often being limited to an average success rate. Uncertainty on reputation is further increased by fraud, which is increasingly becoming a cause of concern. To address these issues, we have designed an experiment where participants could spend money to have their observable cooperativeness increased. Our findings point to the importance of ensuring the truthfulness of reputation for a more cooperative and fair society.

12/07/2016 4:00 PM103Shamik Gupta (MPI Dresden)Stochastic dynamics interrupted with big changes at random times
Consider a continuously evolving stochastic process that gets interrupted at random times with big changes. Examples are financial crashes due to a sudden fall in stock prices, a sudden decrease in population due to a natural catastrophe, etc. Question: How do these sudden interruptions affect the observable properties at long times?
As a first answer, we consider simple diffusion interrupted at random times by long jumps associated with resets to the initial state. We will discuss recent advances in characterizing the longtime properties of such a dynamics, thereby unveiling a host of rich observable properties. Time permitting, I will discuss the extension of these studies to manybody interacting systems.

06/09/2016 4:00 PM103Anthony Bonato (Ryerson University)Mining and modeling character networks
There has been emerging recent interest towards the study of the social
networks in cultural works such as novels and films. Such character networks
exhibit many of the properties of complex networks such as skewed degree
distribution and community structure, but may be of relatively small order
with a high multiplicity of edges. We present graph extraction,
visualization, and network statistics for three novels: Twilight by
Stephanie Meyer, Steven King's The Stand, and J.K. Rowling's Harry Potter
and the Goblet of Fire. Coupling with 800 character networks from films
found in the Moviegalaxies database, we compare the data sets to simulations
from various stochastic complex networks models including the ChungLu
model, the configuration model, and the preferential attachment model. We
describe our model selection experiments using machine learning techniques
based on motif (or small subgraph) counts. The ChungLu model best fits
character networks and we will discuss why this is the case. 
27/09/2016 4:00 PMM203Rainer Klages (QMUL)Statistical Physics and Anomalous Dynamics of Foraging
The title of my talk was the topic of an Advanced Study Group for which I was convenor last year [1]. In my talk I will give a brief outline about our respective research activities. It should be understandable to a rather general audience.
A question that attracted a lot of attention in the past two decades is whether biologically relevant search strategies can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy flight hypothesis. It states that under certain mathematical conditions Levy dynamics, which defines a key concept in the theory of anomalous stochastic processes, leads to an optimal search strategy for foraging organisms. This hypothesis is discussed very controversially in the current literature [2]. After briefly introducing the stochastic processes of Levy flights and Levy walks I will review examples and counterexamples of experimental data and their analyses confirming and refuting the Levy flight hypothesis. This debate motivated own work on deriving a fractional diffusion equation for an ndimensional correlated Levy walk [3], studying search reliability and search efficiency of combined LevyBrownian motion [4], and investigating stochastic first passage and first arrival problems [5].[1] www.mpipksdresden.mpg.de/~asg_2015(link is external)
[2] R.Klages, Search for food of birds, fish and insects, invited book chapter in: A.Bunde, J.Caro, J.Kaerger, G.Vogl (Eds.), Diffusive Spreading in Nature, Technology and Society. (Springer, Berlin, 2017).
[3] J.P.TaylorKing, R.Klages, S.Fedotov, R.A.Van Gorder, Phys.Rev.E 94, 012104 (2016).
[4] V.V.Palyulin, A.Chechkin, R.Klages, R.Metzler, J.Phys.A: Math.Theor. 49, 394002 (2016).
[5] G.Blackburn, A.V.Chechkin, V.V.Palyulin, N.W.Watkins, R.Klages, tbp. 
04/10/2016 4:00 PMM203Boris KhoruzhenkoHow many equilibria will a large complex system have?
In 1972 Robert May argued that (generic) complex systems become unstable to small displacements from equilibria as the system complexity increases. In search of a global signature of this instability transition, we consider a class of nonlinear dynamical systems whereby N degrees of freedom are coupled via a smooth homogeneous Gaussian vector field. Our analysis shows that with the increase in complexity, as measured by the number of degrees of freedom and the strength of interactions relative to the relaxation strength, such systems undergo an abrupt change from a simple set of equilibria (a single stable equilibrium for N large) to a complex set of equilibria. Typically, none of these equilibria are stable and their number is growing exponentially with N. This suggests that the loss of stability manifests itself on the global scale in an exponential explosion in the number of equilibria. [My talk is based on a joint paper with Yan Fyodorov and on an unpublished work with Gerard Ben Arous and Yan Fyodorov]

11/10/2016 4:00 PMM203Georgie Knight (Bristol)Spectral statistics of random geometric graphs
We study the spectrum of random geometric graphs using random matrix theory. We look at short range correlations in the level spacings via the nearest neighbour spacing distribution and long range correlations via the spectral rigidity. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find that the spectral statistics of random geometric graphs fits the universality of random matrix theory found in other random graph models.

18/10/2016 4:00 PMM203Sofia Olhede (UCL)Defining networks of tree species
I will discuss defining networks from observations of tree species. This talk will discuss how to quantify coassociations between multiple and inhomogeneous pointprocess patterns, and how to identify communities, or groups, in such observations. The work is motivated by the distribution of tree and shrub species from a 50 ha forest plot on Barro Colorado Island. We show that our method can be used to construct biologically meaningful subcommunities that are linked to the spatial structure of the plant community.
This is joint work with David Murrell and Anton Flugge.

25/10/2016 4:00 PMM203Etienne Fodor (Cambridge)Selfpropelled particles as an active matter system
Selfpropelled particles are able to extract energy from their environment to perform a directed motion. Such a dynamics lead to a rich phenomenology that cannot be accounted for by equilibrium physics arguments. A striking example is the possibility for repulsive particles to undergo a phase separation, as reported in both experimental and numerical realizations. On a specific model of selfpropulsion, we explore how far from equilibrium the dynamics operate. We quantify the breakdown of the time reversal symmetry, and we delineate a bona fide effective equilibrium regime. Our insight into this regime is based on the analysis of fluctuations and response of the particles. Finally, we discuss how the nonequilibrium properties of the dynamics can also be captured at a coarsegrained level, thus allowing a detailed examination of the spatial structure that underlies departures from equilibrium.

01/11/2016 4:00 PMM203George Bassel (Birmingham)Complex systems analysis of multicellularity
Life originated as single celled organisms, and multicellularity arose multiple times across evolutionary history. Increasingly more complex cellular arrangements were selected for, conferring organisms with an adaptive advantage. Uncovering the properties of these synergistic cellular configurations is central to identifying these optimized organizational principles, and to establish structurefunction relationships. We have developed methods to capture all cellular associations within plant organs using a combination of high resolution 3D microscopy and computational image analysis. These multicellular organs are abstracted into cellular connectivity networks and analysed using a complex system approach. This discretization of cellular organization enables the topological properties of global 3D cellular complexity in organs to be examined for the first time. We find that the organizing properties of global cellular interactions are tightly conserved both within and across species in diverse plant organs. Seemingly stochastic gene expression patterns can also be predicted based on the context of cells within organs. Finally, evidence for optimization in cellular configurations and transport processes have emerged as a result of natural selection. This provides a framework and insight to investigate the structurefunction relationship at the level of cell organization within complex multicellular organs.

15/11/2016 4:00 PMM203Enrico Scalas (Sussex)PseudoDifferential Relaxation Equations and SemiMarkov Processes
Recently, there has been a surge of interest in an old result discussed by Mainardi et al. [1] that relates pseudodifferential relaxation equations and semiMarkov processes. Meerschaert and Toaldo presented a rigorous theory [2] and I recently applied these ideas to semiMarkov graph dynamics [3]. In this talk, I will present several examples and argue that further work is needed to study the solutions of pseudodifferential relaxation equations and their properties.
References
[1] Mainardi, Francesco, Raberto, Marco, Gorenflo, Rudolf and Scalas, Enrico (2000) Fractional calculus and continuoustime finance II: the waitingtime distribution. Physica A Statistical Mechanics and its Applications, 287 (34). pp. 468481.
[2] Meerschaert, Mark M and Toaldo, Bruno (2015) Relaxation patterns and semiMarkov dynamics arXiv:1506.02951 [math.PR].
[3] Raberto, Marco, Rapallo, Fabio and Scalas, Enrico (2011) SemiMarkov graph dynamics. PLoS ONE, 6 (8). e23370. ISSN 19326203. Georgiou, Nicos, Kiss, Istvan and Scalas, Enrico (2015) Solvable non Markovian dynamic network. Physical Review E, 92 (4). 042801. ISSN 15393755. 
22/11/2016 4:00 PMM203Francesca Arrigo (Strathclyde)Preserving Sparsity in Dynamic Network Computations
Timedependency adds an extra dimension to network science computations, potentially causing a dramatic increase in both storage requirements and computation time. In the case of Katzstyle centrality measures, which are based on the solution of linear algebraic systems,allowing for the arrow of time leads naturally to full matrices that keep track of all possible routes for the flow of information. Such a buildup of intermediate data can make largescale computations infeasible. In this talk, we describe a sparsification technique that delivers accurate approximations to the fullmatrix centrality rankings, while retaining the level of sparsity present in the network timeslices. With the new algorithm, as we move forward in time the storage cost remains fixed and the computational cost scales linearly, so the overall task is equivalent to solving a single Katzstyle problem at each new time point.

29/11/2016 4:00 PMM203Nicola Perra (Greenwich)Networks and Time
Networks, virtually in any domain, are dynamical entities. Think for example
about social networks. New nodes join the system, others leave it, and links
describing their interactions are constantly changing. However, due to absence
of timeresolved data and mathematical challenges, the large majority of
research in the field neglects these features in favor of static
representations. While such approximation is useful and appropriate in some
systems and processes, it fails in many others. Indeed, in the case of sexual
transmitted diseases, ideas, and meme spreading, the cooccurrence, duration
and order of contacts are crucial ingredients.
During my talk, I will present a novel mathematical framework for the modeling
of highly timevarying networks and processes evolving on their fabric. In
particular, I will focus on epidemic spreading, random walks, and social
contagion processes on temporal networks. 
06/12/2016 10:57 AMM203Sergei Petrovskii (Leicester)Biological Invasion: Modeling Patchy Invasion of Alien Species
Biological invasion can be generically defined as the uncontrolled spread and proliferation of species to areas outside of their native range, hence called alien, usually following by their unintentional introduction by humans. A conventional view of the alien species spatial spread is that it occurs via the propagation of a travelling population front. In a realistic 2D system, such a front normally separates the invaded area behind the front from the uninvaded areas in front of the front. I will show that there is an alternative scenario called “patchy invasion” where the spread takes place via the spatial dynamics of separate patches of high population density with a very low density between them, and a continuous population front does not exist at any time. Patchy invasion has been studied theoretically in much detail using diffusionreaction models, e.g. see Chapter 12 in [1]. However, diffusionreaction models have many limitations; in particular, they almost completely ignore the socalled long distance dispersal (usually associated with stochastic processes known as Levy flights). Correspondingly, I will then present some recent results showing that patchy invasion can occur as well when long distance dispersal is taken into account [2]. In this case, the system is described by integraldifference equations with fattailed dispersal kernels. I will also show that apparently minor details of kernel parametrization may have a relatively strong effect on the rate of species spread.
[1] Malchow H, Petrovskii SV, Venturino E (2008) Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, Simulations. Chapman & Hall / CRC Press, 443p.
[2] Rodrigues LAD, Mistro DC, Cara ER, Petrovskaya N, Petrovskii SV (2015) Bull. Math. Biol. 77, 15831619.

07/12/2016 4:00 PMM203Special eventOne day ergodic theory meeting
This is part of a series of collaborative meetings between Bath, Bristol, Exeter, Leicester, Loughborough, Manchester, Queen Mary, St Andrews, Surrey and Warwick, funded by a Scheme 3 grant from the London Mathematical Society.
For speakers, abstracts and schedule, see the meeting web page.

13/12/2016 4:00 PMM203Rhoda J. Hawkins (Sheffield)Droplets of active matter: applications to biological cell movement and deformation
The cell cytoskeleton can be successfully modelled as an 'active gel'. This is gel that is driven out of equilibrium by the consumption of biochemical energy. In particular myosin molecular motors exert forces on actin filaments resulting in contraction. Theoretical studies of active matter over the past two decades have shown it to have rich dynamics and behaviour. Here I will discuss finite droplets or active matter in which interactions with the boundaries play an important role. Displacement of the whole droplet is generated by flows of the contractile active gel inside. I will show how this depends on the average direction of cytoskeleton filaments and the boundary conditions at the edge of the model cell, which are set by interactions with the external environment. I will consider the shape deformation and movement of such droplets. Inspired by applications to cell movement and deformation I will discuss the behaviour of a layer of active gel surrounding a passive solid object as a model for the cell nucleus.

10/01/2017 4:00 PMM203Chris Joyner (QMUL)GSE Statistics without spin
Abstract: The field of random matrix theory (RMT) was born out experimental observations of the scattering amplitudes of large atomic nuclei in the late 1950s. It led Wigner, Dyson and others to develop a theory comprising three standard random matrix ensembles, termed the Gaussian Orthogonal, Unitary and Symplectic Ensembles, which predicted the distribution of such resonances in various situations. Until recently it was a standard consensus that observing this third type of statistics (the GSE) required a quantum spin, however, together with S. Mueller and M. Sieber we proposed a quantum graph that would have such statistics, but without the spin requirement. Recently, this quantum graph has been realised in a laboratory setting, leading to the first experimental observation of GSE statistics, some 60 years after the conception of RMT. I will present the mathematical framework behind the construct of this system and the ideas which led to its conception.

17/01/2017 4:00 PMM203Nils Haug (QMUL)(Higherorder) multicritical points in twodimensional lattice polygon models
Twodimensional lattice paths and polygons such as selfavoiding walks and polygons and subclasses thereof are often used as models for biological vesicles and cell membranes. When tuning the pressure acting on the wall of the vesicle or the strength of the interactions between different parts of the chain, one often observes a phase transition between a deflated or crumpled towards an inflated or globulelike state. For models including selfavoiding polygons, staircase polygons, Dyck and Schröder paths, Bernoulli meanders and bridges, the phase transition between the different regimes is (conjectured to be) characterised by two critical exponents and a onevariable scaling function involving the Airy function. John Cardy conjectured that by turning on further interactions, one should be able to generate multicritical points of higher order, described by multivariate scaling functions involving generalised Airy integrals.

24/01/2017 4:00 PMM203Tiago Peixoto (Bath)Inferring the largescale structure of networks
Networks form the substrate of a wide variety of complex systems, ranging
from food webs, gene regulation, social networks, transportation and the
internet. Because of this, general network abstractions allow for the
characterization of these different systems under a unified mathematical
framework. However, due to the sheer size and complexity of many of theses
systems, it remains an open challenge to formulate general descriptions of
their structures, and to extract such information from data. In this talk, I
will describe a principled approach to this task, based on the elaboration
of probabilistic generative models, and their statistical inference from
data. In particular, I will present a general class of generative models
that describe the multilevel modular structure of network systems, as well
as efficient algorithms to infer their parameters. I will highlight the
common pitfalls present in more heuristic methods of capturing this type of
structure, and demonstrate the efficacy of more principled methods based on
Bayesian statistics. 
26/01/2017 3:00 PMM203Giovanni Petri (ISI Foundation, Torino)**SPECIAL SEMINAR** Topological brain ageing
Topology is one of the oldest and more relevant branches of mathematics, and it has provided an expressive and affordable language which is progressively pervading many areas of mathematics, computer science and physics.
Using examples taken from work drugaltered brain functional networks, I will illustrate the type of novel insights that algebraic topological tools are providing in the context of neuroimaging.I will then show how the comparison of homological features of structural and functional brain networks across a large age span highlights the presence of a globally conserved topological skeletons and of a compensation mechanism modulating the localization of functional homological features. Finally, with an eye to altered cognitive control in disease and early ageing, I will introduce preliminary theoretical results on the modelization of multitasking capacities from a statistical mechanical perspective and show that even a small overlap between tasks strongly limits overall parallel capacity to a degree that substantially outpaces gains by increasing network size.

31/01/2017 4:00 PMM203Jens Bolte (Royal Holloway)Spectra of interacting particles on quantum graphs
One reason for the success of oneparticle quantum graph models is that their spectra are determined by secular equations involving finitedimensional determinants. In general, one cannot expect this to extend to interacting manyparticle models. In this talk I will introduce some specific twoparticle quantum graph models with interactions that allow one to express eigenfunctions in terms of a Bethe ansatz. From this a secular equation will be determined, and eigenvalues can be calculated numerically. The talk is based on joint work with George Garforth.

07/02/2017 4:00 PMM203Naoki Masuda (Bristol)Dynamical switching of networks facilitates endemicity in the susceptibleinfectedsusceptible epidemic model
Epidemic processes on temporally varying networks are complicated by complexity
of both network structure and temporal dimensions. It is yet under debate what
factors make some temporal networks promote infection at a population level
whereas other temporal networks suppress it. We develop a theory to understand
the susceptibleinfectedsusceptible epidemic model on arbitrary temporal
networks, where each contact is used for a finite duration. We show that, under
certain conditions, temporality of networks lessens the epidemic threshold such
that infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times (precisely speaking, commutator's norm) is a useful
index to assess the impact of temporal networks on the epidemic threshold
value. 
14/02/2017 4:00 PMM203Oscar Bandtlow (QMUL)Ruelle transfer operators with explicit spectra
In a seminal paper Ruelle showed that the long time asymptotic behaviour of analytic hyperbolic systems can be understood in terms of the eigenvalues, also known as PollicottRuelle resonances, of the socalled Ruelle transfer operator, a compact operator acting on a suitable Banach space of holomorphic functions.
Until recently, there were no examples of Ruelle transfer operators arising from analytic hyperbolic circle or toral maps, with nontrivial spectra, that is, spectra different from {0,1}.
In this talk I will survey recent work with Wolfram Just and Julia Slipantschuk on how to construct analytic expanding circle maps or analytic Anosov diffeomorphisms on the torus with explicitly computable nontrivial PollicottRuelle resonances. I will also discuss applications of these results.

21/02/2017 4:00 PMQueens' W316Thierry Dauxois (CNRS & ENS de Lyon)Instabilities of Internal Gravity Wave Beams: insights from experimental and analytical approaches
Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most of the studies were focused on planewave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a locally confined profile are ubiquitous in the geophysical context.
We will discuss the reason for their ubiquity in stratified fluids, since they are solutions of the nonlinear governing equations. Moreover, in the light of the recent experimental and analytical studies of those internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams: the triadic resonant instability and the streaming instability.

07/03/2017 4:00 PMQueens' W316Maik Gröger (Jena)Amorphic complexity and nonsmooth saddlenode bifurcations
We start by giving a short introduction about quasiperiodically forced interval maps. To distinguish smooth and nonsmooth saddlenode bifurcations by means of a topological invariant, we introduce two new notions in the lowcomplexity regime, namely, asymptotic separation numbers and amorphic complexity. We present recent results with respect to these two novel concepts for additive and multiplicative forcing. This is joint work with G. Fuhrmann and T. Jäger.

14/03/2017 4:00 PMQueens'W316Jacopo Iacovacci (QMUL)Characterising complex network structures
Graphs can encode information from datasets that have a natural representation in terms of a network (for example datasets describing collaborations or social relations among individulas), as well as from data that can be mapped into graphs due to their intrinsic correlations, such as time series or images. Characterising the structure of complex networks at the micro and mesocale can thus be of fundamental importance to extract relevant information from our
data. We will present some algorithms useful to characterise the structure of particular classes of networks:i) multiplex networks, describing systems where interactions of different
nature are involved,and ii) visibility graphs, that can be extracted from time series.

21/03/2017 4:00 PMQueens'W316Johannes Zimmer (Bath)Particles and the geometry/thermodynamics of macroscopic evolution
One often aims to describe the collective behaviour of an infinite number of particles by the differential equation governing the evolution of their density. The theory of hydrodynamic limits addresses this problem. In this talk, the focus will be on linking the particles with the geometry of the macroscopic evolution. Zerorange processes will be used as guiding example. The geometry of the associated hydrodynamic limit, a nonlinear diffusion equation, will be derived. Large deviations serve as a tool of scalebridging to describe the manyparticle dynamics by partial differential equations (PDEs) revealing the geometry as well. Finally, time permitting we will discuss the nearminimum structure, studying the fluctuations around the minimum state described by the deterministic PDE.

13/06/2017 4:00 PMW316Gregory Berkoliako (Texas A&M)Local nodal surplus and nodal count distribution for graphs with disjoint loops.
The nodal surplus of the $n$th eigenfunction of a graph is defined as
the number of its zeros minus $(n1)$. When the graph is composed of
two or more blocks separated by bridges, we propose a way to define a
"local nodal surplus" of a given block. Since the eigenfunction index
$n$ has no local meaning, the local nodal surplus has to be defined in
an indirect way via the nodalmagnetic theorem of Berkolaiko and
Weyand.We will discuss the properties of the local nodal surplus and their
consequences. In particular, it also has a dynamical interpretation
as the number of zeros created inside the block (as opposed to those
who entered it from outside) and its symmetry properties allow us to
prove the longstanding conjecture that the nodal surplus distribution
for graphs with $\beta$ disjoint loops is binomial with parameters
$(\beta, 1/2)$. The talk is based on a work in progress with Lior Alon
and Ram Band. 
26/09/2017 4:00 PMW316Fabrizio Bianchi (Imperial College)Holomorphic motions of Julia sets
For a family of rational maps, results by Lyubich, ManéSadSullivan and DeMarco provide a fairly complete understanding of dynamical stability. I will review this onedimensional theory and present a recent generalisation to several complex variables. I will focus on the arguments that do not readily generalise to this setting, and introduce the tools and ideas that allow one to overcome these problems.

03/10/2017 4:00 PMW316Wolfram Just (QMUL)On synchronisation of oscillator networks with propagation delay
Kuramoto Sakaguchi type models are probably the simplest and most generic approach to investigate phase coupled
oscillators. Particular partially synchronised solutions, so called chimera states, have received recently a great deal of attention. Dynamical behaviour of this type will be discussed in the context of time delay dynamics caused by a finite propagation speed of signals. 
24/10/2017 4:00 PMW316Christian Bick (Oxford)Oscillator Networks: Collective Dynamics through Generalized Interactions
The function of many realworld systems that consist of interacting oscillatory units depends on their collective dynamics such as synchronization. The Kuramoto model, which has been widely used to study collective dynamics in oscillator networks, assumes that interactions between oscillators is determined by the sine of the differences between pairs of oscillator phases. We show that more general interactions between identical phase oscillators allow for a range of collective effects, ranging from chaotic fluctuations to localized frequency synchrony patterns.

31/10/2017 4:00 PMW316Selim Ghazouani (Warwick)Cascades in the dynamics of affine interval exchange transformations
We will present in this talk a 1parameter family of affine interval exchange transformations (AIET) which displays various dynamical behaviours. We will see that a fruitful viewpoint to study such a family is to associate to it what we call a dilation surface, which should be thought of as the analogue of a translation surface in this setting.
The study of this example is a good motivation to several conjectures on the dynamics of AIETs that we will try to expose.

14/11/2017 4:00 PMW316Rossano Schifanella (Turin)TBA

21/11/2017 4:00 PMW316Benjamin Schaefer (MPI Goettingen)Power Grids as Dynamical Systems: Recent Progress and a DataDriven Approach using Superstatistics
The Paris conference 2015 set a path to limit climate change to "well below 2°C". To reach this goal, integrating renewable energy sources into the electrical power grid is essential but poses an enormous challenge to the existing system, demanding new conceptional approaches. In this talk, I outline some pressing challenges to the power grid,
highlighting how methods from Mathematics and Physics can potentially support the energy transition.
In particular, I present our latest research on power grid fluctuations and how they threaten robust grid operation. For our analysis, we collected frequency recordings from power grids in North America, Europe and Japan, noticing significant deviations from Gaussianity. We develope a coarse framework to analytically characterize the impact of arbitrary noise distributions as well as a superstatistical approach. Overall, we identify energy trading as a significant contribution to today's frequency fluctuation and effective damping of the grid as a controlling factor to reduce fluctuation risks. 
28/11/2017 4:00 PMW316David Saad (Aston University)TBA

05/11/2017 4:00 PMW316Sofia Olhede (UCL)TBA

13/12/2017 1:00 PMQueens E303Dmitry Dolgopyat (Maryland) Dalia Terhesiu (Exeter) Tuomas Sahlsten (Manchester)One Day Ergodic Theory Meeting
This is part of a series of collaborative meetings between Bristol, Exeter, Leicester, Loughborough, Manchester, Queen Mary, St Andrews, Surrey and Warwick, funded by a Scheme 3 grant from the London Mathematical Society.
1:00pm  2:00pm: Dmitry Dolgopyat (Maryland), joint with the QMUL Probability and Applications Seminar
2:30pm  3:30pm: Dalia Terhesiu (Exeter)
4:00pm  5:00pm: Tuomas Sahlsten (Manchester)
For more information, visit the website:
http://www.maths.qmul.ac.uk/~ob/oneday_meeting/oneday17/onedaydynamics_q... 
27/09/2011 5:00 PMM103Henk Bruin (Surrey)Transience and Thermodynamics Formalism for (Induced) Interval Maps
Using inducing schemes (generalised first return maps) to obtain uniform expansion is a standard tool for (smooth) interval maps, in order to prove, among other things, the existence of invariant measures, their mixing rates and stochastic laws. In this talk I would like to present joint work with Mike Todd (St Andrews) on how this can be applied to maps on the brink of being dissipative. We discuss a family f_{λ} of Fibonacci maps for which Lebesguea.e. point is recurrent or transient depending on the parameter λ. The main tool is a specific induced Markov map F_{λ} with countably many branches whose lengths converge to zero. Avoiding the difficulties of distortion control by starting with a countably piecewise linear unimodal map, we can identify the transition from conservative to dissipative exactly, and also describe in great detail the impact of this transition on the thermodynamic formalism of the system (existence and uniqueness of equilibrium states, (non)analyticity of the pressure function and phase transitions).

15/10/2013 5:00 PM103Andrea Baronchelli (City University London)Lévy flights in human mental searches
Characterizing how we explore abstract spaces is key to understand our (ir)rational behaviour and decision making. While some light has been shed on the navigation of semantic networks, however, little is known about the mental exploration of metric spaces, such as the one dimensional line of numbers, prices, etc. Here we address this issue by investigating the behaviour of users exploring the “bid space” in online auctions. We find that they systematically perform Lévy flights, i.e., random walks whose step lengths follow a powerlaw distribution. Interestingly, this is the best strategy that can be adopted by a random searcher looking for a target in an unknown environment, and has been observed in the foraging patterns of many species. In the case of online auctions, we measure the powerlaw scaling over several decades, providing the neatest observation of Lévy ﬂights reported so far. We also show that the histogram describing single individual exponents is well peaked, pointing out the existence of an almost universal behaviour. Furthermore, a simple model reveals that the observed exponents are nearly optimal, and represent a Nash equilibrium. We rationalize these ﬁndings through a simple evolutionary process, showing that the observed behaviour is robust against invasion of alternative strategies. Our results show that humans share with the other animals universal patterns in general searching processes, and raise fundamental issues in cognitive, behavioural and evolutionary sciences.

03/07/2014 5:30 PM103Luna Lomonaco (USP, Sao Paolo)Paraboliclike mappings and correspondences
A polynomiallike mapping is a proper holomorphic map f : U′ → U, where U′, U ≈ D, and U′ ⊂⊂ U. This definition captures the behaviour of a polynomial in a neighbourhood of its filled Julia set. A polynomiallike map of degree d is determined up to holomorphic conjugacy by its internal and external classes, that is, the (conjugacy classes of) the restrictions to the filled Julia set and its complement. In particular the external class is a degree d realanalytic orientation preserving and strictly expanding selfcovering of the unit circle: the expansivity of such a circle map implies that all the periodic points are repelling, and in particular not parabolic.
We extended the polynomiallike theory to a class of parabolic mappings which we called paraboliclike mappings. In this talk we present the parabolic like mapping theory, and its uses in the family of degree 2 holomorphic correspondences in which matings between the quadratic family and the modular group lie. 
12/05/2016 5:00 PM103 , 3pm4pmYair Neuman (Ben Gurion University, BenGurion University of the Negev, Israel, Visiting Prof. Weizmann Institute of Science and University of OxfordComplex Psychological, Cognitive and Social System: Novel Approaches and Pressing Challenges
The study of complex human systems has become more important than ever as the risks facing human societies from the human and social factors are clearly increasing. However, disciplines, such as psychology and sociology, haven't made any significant scientific progress and they are immersed in theoretical approaches and empirical methodologies developed more than a 100 years ago. In this talk, I would like to point to the promise of applying ideas from complex systems and developing new computational tools for big data reservoirs in order to address the abovementioned challenge. I will provide several casestudies illustrating the benefits of the proposed approach and several open challenges that need to be addressed.
References (for illustration)
1. Neuman, Y. (2014). Introduction to computational cultural psychology. Cambridge University Press.
2. Neuman, Y., & Cohen, Y. (2014). A vectorial semantics approach to personality assessment. Scientific reports, 4.
3. Neuman, Y., Assaf, D., Cohen, Y., & Knoll, J. L. (2015). Profiling school shooters: automatic textbased analysis. Frontiers in psychiatry, 
10/10/2017 4:00 PMW316Nikos Karaliolios (Imperial College)Cohomological Rigidity and the AnosovKatok construction
Let f be a smooth volume preserving diffeomorphism of a compact manifold and φ a known smooth function of zero integral with respect to the volume. The linear cohomological equation over f is
ψ ○ f  ψ = φ
where the solution ψ is required to be smooth.Diffeomorphisms f for which a smooth solution ψ exists for every such smooth function φ are called Cohomologically Rigid. Herman and Katok have conjectured that the only such examples up to conjugation are Diophantine rotations in tori.
We study the relation between the solvability of this equation and the fast approximation method of AnosovKatok and prove that fast approximation cannot construct counterexamples to the conjecture.

11/07/2017 4:00 PMW316Andrea Cairoli (Imperial College)Microscopic Derivation of Coloured Lévy Flights in Active Swimmers' Suspensions
The motion of a tracer particle in a complex medium typically exhibits anomalous diffusive patterns, characterised, e.g, by a nonliner meansquared displacement and/or nonGaussian statistics. Modeling such fluctuating dynamics is in general a challenging task, that provides, despite all, a fundamental tool to probe the rheological properties of the environment. A prominent example is the dynamics of a tracer in a suspension of swimming microorganisms, like bacteria, which is driven by the hydrodynamic fields generated by the active swimmers. For dilute systems, several experiments confirmed the existence of nonGaussian fat tails in the displacement distribution of the probe particle, that has been recently shown to fit well a truncated Lévy distribution. This result was obtained by applying an argument first proposed by Holtsmark in the context of gravitation: the force acting on the tracer is the superposition of the hydrodynamic fields of spatially random distributed swimmers. This theory, however, does not clarify the stochastic dynamics of the tracer, nor it predicts the non monotonic behaviour of the nonGaussian parameter of the displacement distribution. Here we derive the Langevin description of the stochastic motion of the tracer from microscopic dynamics using tools from kinetic theory. The random driving force in the equation of motion is a coloured Lévy Poisson process, that induces powerlaw distributed position displacements. This theory predicts a novel transition of their characteristic exponents at different timescales. For short ones, the Holtzmarktype scaling exponent is recovered; for intermediate ones, it is larger. Consistently with previous works, for even longer ones the truncation appears and the distribution converge to a Gaussian. Our approach allows to employ well established functional methods to characterize the displacement statistics and correlations of the tracer. In particular, it qualitatively reproduces the non monotonic behaviour of the nonGaussian parameter measured in recent experiments.

14/11/2017 2:05 PMW316Rossano Schifanella (Turin)Combined effect of content quality and social ties on user engagement
The dynamics of attention in social media tend to obey power laws. Attention concentrates on a relatively small number of popular items neglecting the vast majority of content produced by the crowd. Although popularity can be an indication of the perceived value of an item within its community, previous research has highlighted the gap between success and intrinsic quality. As a result, high quality content that receives low attention remains invisible and relegated to the long tail of the popularity distribution. Moreover, the production and consumption of content is influenced by the underlying social network connecting users by means of friendship or followerfollowee relations. This talk will present a large scale study on the complex intertwinement between quality, popularity and social ties in an online photo sharing platform, proposing a methodology to democratize exposure and foster long term users engagement.

28/11/2017 4:00 PMW316Kay Brandner (Aalto, Finland)Thermodynamic Bounds on Precision in Ballistic MultiTerminal Transport
Is there a fundamental minimum to the thermodynamic cost of precision in nonequilibrium processes? Here, we investigate this question, which has recently triggered notable research efforts [1,2], for ballistic transport in a multiterminal geometry. For classical systems, we derive a universal tradeoff relation between total dissipation and the precision, at which particles are extracted from individual reservoirs [3]. Remarkably, this bound becomes significantly weaker in presence of a magnetic field breaking timereversal symmetry. By working out an explicit model for chiral transport enforced by a strong magnetic field, we show that our bounds are tight. Beyond the classical regime, we find that, in quantum systems far from equilibrium, correlated exchange of particles makes it possible to exponentially reduce the thermodynamic cost of precision [3]. Uniting aspects from statistical and mesoscopic physics, our work paves the way for the design of precise and efficient transport devices.
[1] A. C Barato, U. Seifert; Phys. Rev. Lett. 114, 158101 (2015).
[2] T. R. Gingrich, J. M. Horowitz, N. Perunov, J. L. England; Phys. Rev. Lett. 116, 120601 (2016).
[3] K. Brandner, T. Hanazato, K. Saito; arXiv:1710.04928 (2017).

05/12/2017 4:00 PMRoom: W316Sofia Olhede (UCL)Methods of network comparison
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path provides a notion of scale, which is vitally important in characterizing dominant modes of system behavior. Here, by combining topology with scale, we prove the existence of universal features which reveal the dominant scales of any network. We use these features to compare several canonical network types in the context of a social media discussion which evolves through the sharing of rumors, leaks and other news. Our analysis enables for the first time a universal understanding of the balance between loops and treelike structure across network scales, and an assessment of how this balance interacts with the spreading of information online. Crucially, our results allow networks to be quantified and compared in a purely modelfree way that is theoretically sound, fully automated, and inherently scalable. This work is joint with PierreAndre Maugis and Patrick Wolfe.

13/12/2017 4:00 PMQueens E303Dmitry Dolgopyat (Maryland) Dalia Terhesiu (Exeter) Sebastian van Strien (Imperial College)One Day Ergodic Theory Meeting
This is part of a series of collaborative meetings between Bristol, Exeter, Leicester, Loughborough, Manchester, Queen Mary, St Andrews, Surrey and Warwick, funded by a Scheme 3 grant from the London Mathematical Society.
1:00pm  2:00pm: Dmitry Dolgopyat (Maryland), joint with the QMUL Probability and Applications Seminar
Local Limit Theorem for Nonstationary Markov chains2:30pm  3:30pm: Dalia Terhesiu (Exeter)
The Pressure Function for Infinite Equilibrium Measures4:00pm  5:00pm: Sebastian van Strien (Imperial College)
Heterogeneously Coupled Maps. Coherent behaviour and reconstructing network from dataFor more information, visit the website:
http://www.maths.qmul.ac.uk/~ob/oneday_meeting/oneday17/onedaydynamics_q... 
15/05/2018 4:00 PMW316, Queens' BuildingDavid Saad (Aston University)

22/05/2018 4:00 PMW316, Queens' BuildingGiulia Campolo (Imperial College)TBA