Statistical Mechanics Study Group
Time: Please see below and follow announcements.
Location: tba
General Idea: The aim of these meetings is to provide a forum to discuss both our own work and other recent (or notsorecent) developments in statistical mechanics. This is intended to be a "study group" not a "seminar"; speakers are asked to proceed slowly and audience participation is actively encouraged. After each talk there is also the opportunity for further informal discussions in more relaxed surroundings(link is external).
Schedule: The list below gives a provisional outline of talks planned for this semester. Please note, however, that our schedule is fairly flexible to allow for the evolving interests of the group.
Organizers: Vicenzo Nicosia; if you want to be on the group's mailing list, or perhaps want to give a talk yourself, please email us (v.nicosia@qmul.ac.uk).

DateRoomSpeakerTitle

15/10/2009 6:00 PMM513Rosemary Harris (QMUL)Current fluctuations in stochastic systems with longrange memorySeminar series:

29/10/2009 4:30 PMM513Paul Chleboun (University of Warwick)Finite size effects in a stochastic condensation modelSeminar series:

05/11/2009 5:00 PMM513Jan Naudts (University of Antwerp)joint with DSSP seminarMathematical Aspects of Generalized Entropies and their ApplicationsSeminar series:
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 BG distribution. 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.

19/11/2009 4:30 PMM513Owen Jepps (Griffith UniversityJust how anomalous is transport without the chaos?Seminar series:

10/12/2009 4:30 PMM513Igor Sokolov (Humboldt University, Berlin)Aging, ergodicity breaking and universal fluctuations in continuous time random walks: Theory and (possible) experimentaSeminar series:
We consider some peculiarities of subdiffusive transport within the continuous time random walk (CTRW) model as appearing in the meanfield description of particles' motion in random potentials (energetic disorder). The anomalous diffusion under CTRW is a process with nonstationary increments. This nonstationarity introduces explicit dependence of observables on the time elapsed from preparing the system in its present state, and corresponds to aging of the process. Aging leads to such unusual properties of the system's time evolution as death of linear response to an external stimulus or as intrinsic ergodicity breaking. The last can have different manifestations, like the explicit dependence of the moving time averages on the interval of averaging or like universal fluctuations in timeaveraged kinetic coefficients whose ensemble averages are sharp. These properties lead to several interesting effects, which are specific for energetic disorder and which can be used for distinguishing this mechanism of anomalous subdiffusion from other possible mechanisms (like the existence of slow modes or diffusion in geometrically disordered systems).

17/12/2009 4:30 PMM513Jörn Dunkel (University of Oxford)Nonlocal observables and lightconeaveraging in (special) relativistic thermodynamicsSeminar series:
The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional "isochronous" formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. I will discuss how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backwardlightcone of an observation event. This approach also allows for a straightforward extension of thermodynamics to general relativity. Theoretical considerations are illustrated through simple relativistic manybody simulations.

14/01/2010 4:30 PMM513Otto Pulkkinen (Universität des Saarlandes)Stateestimation of longrange correlated nonequilibrium systems: media estimationSeminar series:
Nonequilibrium systems have longranged spatial correlations even far away from critical points. These correlations have been observed experimentally, and recently it has been shown that they lead to nonlocal large deviation functionals in some models of heat and mass transport.
In this talk, we take a new point of view to nonequilibrium correlations. We discuss a functional level inverse problem, in which the state of a fluctuation field is estimated from a small amount of spatial information. In practice, this is accomplished by observing a dilute marker in a stationary flow. The particular problem we discuss is the estimation of the structure of an underlying medium, which determines the rate of transport. This system has the same kind of correlation structure as some driven diffusive systems, and which is observed in a RayleighBénard system. Thus the methods applied in media estimation could be useful in state estimation of timedependent fluctuation fields.

04/02/2010 5:00 PMM513Thomas Prellberg (QMUL)Lattice models of interacting polymers  a gentle introductionSeminar series:

18/02/2010 5:00 PMM513Wolfram Just (QMUL)The nature of sockeye salmon and Neimark Sacker bifurcationsSeminar series:
The fouryear oscillations of the number of spawning sockeye salmon that return to their native stream within the Fraser River basin in Canada are one of the most striking examples of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Different stocks can have their population maximum in different years. Various not fully convincing explanations for these oscillations have been attempted, ascribing this phenomenon either to transient effects or to stochastic influences, to depensatory predation or fishery, or to genetic effects. Here, we show that these oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the longterm persistence of these oscillations, but also reproduces correctly the sequence of one strong year followed by one intermediate year and two weak years. Furthermore, it explains the observations that these periodic oscillations occur only in large oligotrophic lakes, but not in ultraoligotrophic or mesotrophic lakes, and that they are usually not observed in salmon species that have a 5year generation time. 
04/03/2010 5:00 PMM513Friedrich Lenz (QMUL)Velocity distributions of foraging bumblebees in the presence of predatorsSeminar series:

25/03/2010 5:00 PMM513Arnaud Chéritat (Université Paul Sabatier, Toulouse)Siegel discsSeminar series:

30/03/2010 4:00 PMM103Hugo Touchette (QMUL)Brownian motion with dry frictionSeminar series:I will discuss the path integral solution of a Langevin equation with solidsolid (dry) friction, studied in part by PierreGilles de Gennes in 2005. I will show that the propagator of the Langevin equation is given by two types of optimal (most probable) paths, which correspond physically to a sliding motion, where the object moves with a nonzero velocity over the underlying surface, and a stickslip motion, where the object is stuck to the surface for a finite time. I will end the talk with some open questions related to this problem. This is joint work with Adrian Baule and Eddie G. D. Cohen (Rockefeller University), J. Phys. A: Math. Theor. 43, 025003, 2010.

19/04/2010 5:00 PMM103Tibor Antal (Harvard University)Stochastic 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.

27/05/2010 5:30 PMM513Ludger Santen (Universität des Saarlandes)Bidirectional stochastic transport on dynamic filamentsSeminar series:Intracellular transport along microtubules is bidirectional because molecular motors of different types may move in opposite directions on the filament. Models taking into account the mutual exclusion of particles turn out to be unrealistically inefficient on static networks due to jam formation. Different mechanisms will be discussed, which lead to a more efficient bidirectional transport. In particular we propose that the dynamics of the filaments is a crucial ingredient to understand how nature makes bidirectional transport efficient.

24/06/2010 5:30 PMM513Ian Ford (UCL)Particle coagulation kinetics beyond mean field theory using complex 'populations'

27/07/2010 5:15 PM203Bram Wynants (Katholieke Universiteit Leuven, Belgium)Response out of equilibriumSeminar series:

23/09/2010 5:30 PMM513Roberta Sinatra (Università di Catania)Optimal random walks in complex networksSeminar series:Designing diffusion processes which maximise the entropy rate on a given graph is an issue of utmost importance, with relevant applications in social, biological and technological systems. In order to perform a maximalentropy Markov walk on a graph, a walker needs to have, in principle, a global knowledge of the whole network at each time step. This information is in practice always unavailable in real systems. However, we demonstrate that this global knowledge is not necessary since in many realworld networks longrange interactions are weak and can be neglected. It is then possible to construct maximalentropy random walks with only local information on the graph structure. In particular, we show that an almost optimal random walk is obtained when the step probabilities are proportional to a power of the degree of the target node, with an exponent $\alpha$ that depends on the degreedegree correlations, and is equal to 1 in uncorrelated graphs.

30/09/2010 5:00 PMM513Wolfram Just (QMUL)A stochastic talk on a dry subjectSeminar series:A consistent theoretical description of friction is certainly one of the most challenging topics nature has still in stock. This talk won't contribute to this fundamental issue. We rather analyse a simple phenomenological model. In particular, we will focus on the impact of stochastic forcing on dry friction and the associated stickslip transition. Analytical solutions of the FokkerPlanck equation and of the corresponding eigenvalue problem will be presented, uncovering the dynamical phenomena in this piecewise smooth stochastic model.

14/10/2010 5:30 PMM513Boris Khoruzhenko (QMUL)How many eigenvalues of a truncated orthogonal matrix are real?Seminar series:

11/11/2010 4:30 PMM513Thomas Prellberg (QMUL)PERM and all that  a comparison of growth algorithmsSeminar series:Over the last few years, there have been a variety of growthlike algorithms
based on the Rosenbluth method, such as PERM, GARM, and GAS. Some of these have
been coupled with flathistogram techniques, resulting in multicanonical PERM,
flatPERM, flatGARM, and the like.
In this talk we will describe these various algorithms, point out their differences,
and discuss their respective strengths. 
25/11/2010 2:00 PMM513Jamie Wood (University of York)Bacterial respiration and the asymmetric exclusion processSeminar series:In this talk I will discuss some ongoing work related to mathematical modelling of the electron transport reactions that occur in gram negative bacteria. The particular bacteria of interest is Niesseria Meningitidis, a species of considerable medical interest. The details of the respiratory chain may have particular relevance to the nature of the pathogenicity of this organism, and so we have devoted time to developing two approaches to mathematical modelling of the respiratory behaviour. The first is Bayesian fitting of a simple differential equation model which I shall briefly discuss. The second is to use an asymmetric exclusion process linked by diffusable elements to model the movements of the electrons in detail. Note unusual time!

02/12/2010 4:30 PMM513David Chappell (University of NottinghamDynamical energy analysis for builtup acoustic systems at high frequenciesSeminar series:

09/12/2010 4:30 PMM513Benjamin Schlein (Hausdorff Center for Mathematics, Universität Bonn)Spectral Properties of Wigner MatricesSeminar series:Wigner matrices are hermitian (or real symmetric) NxN matrices whose entries are, up to the symmetry constraints, independent and identically distributed random variables. In this talk, I will discuss recent results concerning the statistical properties of the spectrum of Wigner matrices, in the limit of large N. In particular, I will present a proof of the universality of the local eigenvalue correlations.

13/01/2011 4:30 PMM513Hiroyasu Ando (RIKEN Brain Science Institute)Flexible parallel logic gates by synthetic gene networksSeminar series:
We show how a synthetic gene network can function, in an optimal window of noise, as a robust logic gate. Interestingly, noise enhances the reliability of the logic operation. Further, we consider a twodimensional model of a gene network, where we show how two complementary gate operations can be achieved simultaneously. We generalize this idea in two dimensional dynamical systems to achieve any two combinations of AND,OR, and XOR gates in parallel.

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).

10/02/2011 4:30 PMM513Richard Spinney (UCL)A Modern Treatment of Entropy Production for Simple Stochastic SystemsSeminar series:

24/03/2011 4:00 PMM513Philip Greulich (University of Edinburgh)Inhomogeneous driven lattice gasesSeminar series:

31/03/2011 5:30 PMM513Astrid S. de Wijn (Radboud University Nijmegen)From microscopic nonlinear dynamics to macroscopic friction: lowfriction sliding of nanocrystalsSeminar series:

19/05/2011 5:30 PMM513Rainer Klages (QMUL)Chaotic diffusion in randomly perturbed dynamical systemsSeminar series:The impact of spatial disorder [1] and timedependent noise [2] on diffusion in chaotic dynamical systems is studied. As an example, we consider deterministic random walks in a onedimensional periodic array of scatterers modeled by a parameterdependent coupled chaotic map. In computer simulations we find a crossover from deterministic to stochastic diffusion under variation of the perturbation strength related to different asymptotic laws for the diffusion coefficient. Typical signatures of this scenario are multiple suppression and enhancement of normal diffusion. These results are explained by simple theoretical approximations showing that the oscillations emerge as a direct consequence of the unperturbed deterministic diffusion coefficient, which is known to be a fractal function of control parameters [3].
[1] R.Klages, Phys. Rev. E 65, 055203(R) (2002)
[2] R.Klages, Europhys. Lett. 57, 796 (2002)
[3] R.Klages, Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics, Advanced Series in Nonlinear Dynamics Vol.24 (World Scientific, Singapore, 2007), Part 1. 
02/06/2011 5:30 PMM513Gabor Kiss (University of Exeter)Nonlinear oscillations of differential delay equationsSeminar series:The talk addresses the dynamics of differential delay equations. We shall report on coexistence of periodic solutions  proved with the aid of rigorous computations  to a particular equation with two delays. We use this result to try to understand some phenomena seen in applications.

28/06/2011 5:00 PMM513Aleksei Chechkin(Akhiezer Institute for Theoretical Physics, National Science Center "Kharkov Institute of Physics and Technology", Kharkov, Ukraine)Natural and Modified Forms of Distributed Order Fractional Diffusion EquationsSeminar series:
We consider diffusionlike equations with time and space fractional derivatives of distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose mean squared displacement does not change as a power law in time. Correspondingly, the underlying processes cannot be viewed as selfaffine random processes possessing a unique Hurst exponent. We show that different forms of distributedorder equations, which we call 'natural' and 'modified' ones, serve as a useful tool to describe the processes which become more anomalous with time (retarding subdiffusion and accelerated superdiffusion) or less anomalous demonstrating the transition from anomalous to normal diffusion (accelerated subdiffusion and truncated Lévy flights). Fractional diffusion equation with the distributedorder time derivative also accounts for the logarithmic diffusion (strong anomaly).

30/06/2011 5:30 PMM513Alexander Hartmann (Universität Oldenburg)Large deviation properties of random ensemblesSeminar series:
The largedeviation properties of different types of random graphs, are studied using numerical simulations. Also an application to the sequencealignment problem and to the ground state calculation of spin glasses is given.
First, distributions of the size of the largest component, in particular the largedeviation tail, are studied numerically for two graph ensembles, for ErdoesRenyi random graphs with finite connectivity and for twodimensional bond percolation. Probabilities as small as 10^180 are accessed using an artificial finitetemperature (Boltzmann) ensemble and applications of the WangLandau algorithm. The distributions for the ErdoesRenyi ensemble agree well with previously obtained analytical results. The results for the percolation problem, where no analytical results are available, are qualitatively similar, but the shapes of the distributions are somehow different and the finitesize corrections are sometimes much larger. Furthermore, for both problems, a firstorder phase transition at low temperatures T within the artificial ensemble is found in the percolating regime, respectively.
Second, the some recent results for distributions of the diameter are presented and compared to partial analytic results which are available from previous studies for ErdoesRenyi random graphs in the small connectivity region.
Finally, largedeviation properties of the distribution of sequence alignment scores of proteins (using the standard database parameters with (12,1) affine gap costs and BLOSUM score matrix) and the distribution of groundstate energies for the meanfield (SherringtonKirkpatrick) spin glass are presented. 
13/10/2011 5:30 PMM513Oscar Bandtlow (QMUL)Good vibrations and Long John's spectral approximation methodSeminar series:

27/10/2011 5:30 PMM531Geoffrey Sewell (QMUL)Macrostatistical treatment of fluctuating hydrodynamicsSeminar series:
I provide a macrostatistical treatment of hydrodynamical fluctuations about nonequilibrium steady states of reservoir driven manyparticle systems, which may be classical or quantal. The treatment is centred on the dynamics of locally conserved macroscopic observables, subject to very general assumptions of local equilibrium, chaoticity and an extension of Onsager's regression hypothesis to situations that may be far from global equilibrium. On this basis, I establish that the hydrodynamical fluctuations execute a classical Markov process, that is completely determined by the macroscopic properties of the system. Furthermore, the structure of this process carries generalisations of both Onsager's irreversible thermodynamics and Landau's fluctuating hydrodynamics to systems that may be far from thermal equilibrium.

10/11/2011 4:30 PMM513Adrian Baule (QMUL)Piecewisesmooth systems with noiseSeminar series:

24/11/2011 4:30 PMM513Michela Ottobre (Imperial College)Exponential convergence to equilibrium for open classical systems: hypoelliptic and hypocoercive techniquesSeminar series:
We will present the recently developed theory of hypocoercivity, which helps to prove exponential convergence to equilibrium in many cases of interest. Also, we will show how to find the exact rate of exponential convergence to equilibrium for (quadratic) hypoelliptic operators. As an example, we will apply these methods to one of the possible Markovian approximations of the nonMarkovian Langevin equation.

08/12/2011 4:30 PMM513Phil Howard (Centre for Ecology & Hydrology)Messing about on the river: an introduction to catchment hydrology & flood forecastingSeminar series:
When the weather is fine, then you know it's the time
For messing about on the river
(Tony Hatch)So goes the song, but how do we know? Catchment hydrology is the application of basic physical laws (such as mass conservation) and hydrodynamic theory, at the scale of river basins. It is of vital importance in water resources management and the forecasting and mitigation of floods, a natural hazard which costs the UK £2.5 billion every year: a figure which is likely to increase in the future due to greater urbanisation and climate change. It is inherently a multidisciplinary and applied subject, with active research ranging from the underlying mathematics to shaping government policy. I will present an overview of the work we do at CEH in this area, with emphasis on the various mathematical models employed and the extensive data resources we curate, many of which are publicly available through our online information gateway.

26/01/2012 4:30 PMM513Ines Weber (Universität des Saarlandes / University of Edinburgh)A model for nonequilibrium fluctuations of intracellular filamentsSeminar series:
Microtubules are highly dynamic biopolymer filaments involved in a wide variety of biological processes like cell division and intracellular transport. These filaments are semiflexible polymers, i.e. their bending energy is comparable to the thermal energy. Even though they form a rather stiff and highly crosslinked structural network, it has been shown that they typically exhibit significant bends on all length scales in the living cell.
Measurements of thermally driven microtubule fluctuations under laboratory conditions reveal a persistence length, which is several orders of magnitude larger than observed in living cells. Several studies investigated the interactions of motor proteins and mircotubules. Experiments and in vivo observations have shown microtubules to exhibit buckling instabilities induced by molecular motors, which compress the filament longitudinally. However, direct transversal motor activity on microtubules cannot be ruled out.
I will present a toy model for transversal deformations of a microtubule due to active processes. Simulations of motor proteins deforming a microtubule against a background network mimic the microtubule's behaviour under rapid steplike force fluctuations. The analysis of these fluctuations reveal interesting aspects of the apparent persistence length, motor cooperation as well as global filament displacement, which can be interpreted as a fractional random walk.

09/02/2012 4:30 PMM513David Arrowsmith (QMUL)Bose and Fermi walks on latticesSeminar series:

01/03/2012 4:30 PMM513Rodrigo VillavicencioSanchez (QMUL)Current fluctuations in the twodimensional ZeroRange ProcessSeminar series:

27/03/2012 5:30 PMM513Julia Slipantschuk (QMUL)Spectral properties of a realanalytic expanding circle mapSeminar series:
We construct a oneparameter family of real analytic uniformly expanding circle maps $f_{\lambda}, \lambda \in (0,1)$ for which the eigenvalues of the corresponding PerronFrobenius operator acting upon analytic functions are given by $\{\lambda^k\}_{k \in \mathbb{Z_+}}$

24/05/2012 5:30 PMM103Anton Klimovsky (Eurandom, Eindhoven University of Technology)Complex random energy model: Zeroes and fluctuations (NOTE CHANGE OF VENUE!)Seminar series:

05/07/2012 5:30 PMM203Andrea Cairoli (Padua/Imperial)Collective effects in the Tangled Nature Model of evolution: A deterministic approach to the study of the stability of the qESS states (NOTE CHANGE OF VENUE!)Seminar series:
Introduction:
The Tangled Nature Model of evolution is an individual based, stochastic model, which describes, with good agreement with actual observations, the evolution of a simple ecology. Its most remarkable feature is that its dynamics alternates between periods of metastable configurations and periods of hectic transitions, where the model does not show clear occupancy patterns and the population is spread randomly across the type space.
Hypothesis and methods:
The aim of this project is to analyze the stability of the stable configurations (qESS states) shown in the model by using a dynamical system approach. Indeed, we can derive a deterministic system of equations which approximates the dynamics of the model. Clearly, we can analyze the local stability of its fixed points by linearizing the equations about the equilibrium configurations. The idea in this work is to run simulations of the stochastic model to obtain specific configurations of the qESS states and use their averaged occupancy of these configurations to calculate the linearized dynamical matrix. The eigenvalues of this matrix are expected to be able to give useful information about the stability of the metastable states. In this presentation we will describe in details the ideas introduced and describe the results obtained. 
20/09/2012 5:30 PMM513Anita Mehta (S N Bose National Centre for Basic Sciences, Kolkata)Searching, fixating, storing, forgetting  the workings of memorySeminar series:
In this talk, I will present three different pieces of work, unified by a common theme, that of memory.
The first involves the modelling of eyetracking data – specifically, we have analysed the visual movements of sample populations subjected to simultaneous visual and aural inputs. We looked for correlations between these two forms of sensory stimuli via the analysis of the probability distributions of saccades and fixations. As our sample populations involved literate as well as illiterate people, we were able to investigate the effect of literacy on cognitive processing. This was particularly manifest in the case of fixations, where it appears that literacy leads to the presence of a characteristic (attentional) time scale in the appropriate probability distribution. On the other hand, scaleinvariance is observed in the saccadic distributions, independent of the literacy level of the subjects. We suggest that these are characterised by Levylike dynamics.
Another piece of work involves the role of synaptic metaplasticity to model the separate storage of long and shortterm memories in the human brain. We have presented and analysed two models of metaplastic synapses, whose main difference lies in the effect of a contrarian event on longterm memories. In one model, the effect is to build up an opposite memory of similar depth, while in the other, the effect is more shortterm. Although the transient properties of the models reflect this difference, their asymptotic behaviour is robustly the same – powerlaw forgetting with the same universal exponent, is manifested.
A third research area involves that of gametheoretic formulations of synaptic plasticity. The main motivation for this work is that competitive dynamics are thought to occur in many processes of learning involving synapses. We have shown that the competition between synapses in their weak and strong states gives rise to a natural framework of learning, with the prediction of memory inherent in a timescale for forgetting a learned signal. Among our main results is the prediction that memory is optimized if the weak synapses are really weak, and the strong synapses are really strong. We have also studied the dynamic responses of the effective system to various signal types, particularly with reference to an existing empirical motor adaptation model. The dependence of the systemlevel behaviour on the synaptic parameters and the signal strength has been analysed with a view to optimal performance, and illustrates the functional role of multiple timescales.

27/09/2012 5:30 PMM513Christoforos Hadjichrysanthou (City University)MOVED TO 25/09: Evolutionary dynamics on graphsSeminar series:
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.

11/10/2012 5:30 PMM513Hugo Touchette (QMUL)Sabbatical slide show followed by fluctuations in the AB modelSeminar series:

25/10/2012 5:30 PMM513Pádraig Mac Carron (Coventry University)Mythological NetworksSeminar series:

08/11/2012 4:30 PMM513Shihan Miah (QMUL)Statistics of Lagrangian quantum turbulenceSeminar series:

15/11/2012 4:30 PMM513Alexandre Lazarescu (CEA Saclay)Perturbative matrix Ansatz and exact current fluctuations in the open ASEPSeminar series:
The asymmetric simple exclusion process (ASEP) is one of the simplest, and yet one of the most studied models in nonequilibrium statistical physics. It is also related, more or less closely, to problems in biophysics (such as ribosomes moving on a mRNA, which is what it was originally meant to describe), growing interfaces, pedestrian and car traffic, quantum spin chains, and many more.
After a brief reminder on the theory of large deviations, I will show how, by using a method based on Derrida, Evans, Hakim and Pasquier's matrix Ansatz, one can obtain the exact fluctuation statistics of the current of particles that characterises the steady state of the ASEP, for any finite size and any values of the parameters. I will then analyze the behaviour of these fluctuations in the large size limit. Finally, if time allows, I will discuss what other quantities we might be able to access using this method.
Refs : J. Phys. A: Math. Theor. 44 (2011) 315001 , Phys. Rev. Lett. 109, 170601 (2012)

29/11/2012 4:30 PMM513Vincenzo Nicosia (University of Cambridge)Remote synchronisation and network symmetries (NOTE CHANGE OF DATE!)Seminar series:
The model proposed by Y. Kuramoto in 1975 has been widely used since then to study synchronous patterns in globallyconnected biological, technological and social systems, and has been recently extended to systems of oscillators coupled through heterogeneous topologies. It has been found that the emergence of synchronised states in networks of coupled oscillators crucially depends on the topological structure of the underlying coupling graph. We consider a frustrated Kuramoto model in which the oscillators are coupled through a complex networks and have identical natural frequencies, but only phaselock synchronisation is attainable. We show that the presence of symmetries in the coupling network has a central role on the synchronisation of the system. In particular we found that, at the stationary state, any two symmetric nodes of the graph end up having identical phases, i.e. they are perfectly synchronised, and this happens despite the distance of the two nodes in the graph. We prove that this remote synchronisation is induced solely by network symmetries, and we discuss an application to the human brain.

17/01/2013 4:30 PMM103Alessia Annibale (King's College London)Modeling Biological networks via tailored random graphs: a study of samplingSeminar series:
Determining the topology of a network is relevant for assessing network stability, dynamics and function. However, many surveyed networks that are reported in public data repositories, as protein interaction networks, are imperfect and often biased samples of the true underlying networks. This observation poses the interesting question of how representative a random subnet is for the global network and whether extrapolation of network topologies from partial network data to the whole network can be done. We use random graph ensembles tailored to real networks to compare network topologies macroscopically and quantify in a precise and practical way the effects of sampling on networks. We perform a systematic study of the effects of sampling on topological features of large protein interaction networks for a broad family of sampling protocols that include random and connectivity dependent node and/or link undersampling and oversampling, and derive exact formulae for degree distributions and degree correlation kernels of sampled networks, in terms of those of the underlying true network. Our formula suggest that inference on the topology of the true underlying network can be done accurately.

01/02/2013 2:30 PMG.O. Jones 602Freddy Bouchet(ENS Lyon)Statistical mechanics of Jupiter jets and vortices (joint with Astronomy, note unusual time and room)Seminar series:
We consider the formation of large scale structures (zonal jets and vortices), in planetary atmospheres. We will prove that modern statistical mechanics approaches predict the outcome of the very complex dynamics of geostrophic turbulence and predict jet and vortex structures and shapes.
Based on the equilibrium statistical mechanics of the quasigeostrophic dynamics, we will discuss a model of the Great Red Spot of Jupiter, and of other Jovian vortices. We will discuss the nonequilibrium statistical mechanics of Jupiter jets.
Large deviation theory is the basic mathematical tool on which those results are built. We will discuss the relations between large deviation and fluid mechanics at a basic level.

07/02/2013 4:30 PMM513Adnan Ali (University of Warwick)Scale invariant growth processes in expanding spaceSeminar series:
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by spacetime trajectories of interacting particles, and their large scale behaviour depends on the overall geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which depends only on the local scale invariance exponent and is independent of other properties such as the dimensionality. We illustrate our main result numerically in 1+1 dimensions for structures of coalescing L\'evy flights and fractional Brownian motions, including also branching, as well as for coalescencing finite size Brownian particles in 2+1 dimension. One of the main benefits is a full understanding of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations.

07/03/2013 4:30 PMM513Esa Räsänen (Tampere University of Technology)Fewparticle quantum dots: From chaos to controlSeminar series:
Semiconductor quantum dots have a variety of applications in, e.g., quantum transport, qubit design, and solarcell technology. In addition, they can be used as a computational playground to study complicated manybody quantum phenomena as well as chaotic effects. Here, the basics of quantum dots and their theoretical modeling are introduced. Then the attention is put to transport properties of stadiumshaped quantum dots that are shown to exhibit fractal conductance fluctuations in qualitative agreement with experiments. Finally, it is shown how quantum optimal control theory can be used to coherently control charge transfer and entanglement in quantumdot systems.

21/03/2013 4:30 PMM513Clare Dunning (University of Kent)Statistical lattice models and ordinary differential equationsSeminar series:

28/03/2013 4:30 PMM513Adam Nahum (University of Oxford)Loop models with crossingsSeminar series:
The universal behaviour of 2D loop models can change dramatically when loops are allowed to cross. I will describe new phase transitions in such models and argue that they are driven by unbinding of point defects in an appropriate replica sigma model. I will use the field theory for the loop models to explain the phase diagram of a related model for polymer collapse, and will briefly describe a connection between the loop models and Anderson metalinsulator transitions.

24/06/2013 5:00 PMM103Denis Evans (Australian National University)Dissipation and the foundations of statistical thermodynamicsSeminar series:
The argument of the Evans Searles Fluctuation Theorem [1], namely the dissipation function [2] is also the key quantity in all linear and nonlinear response theory [3]. It is also the key quantity in the proof of the newly discovered equilibrium relaxation theorems. For the first time we have, subject to certain simple assumptions, a proof of thermal relaxation to the canonical distribution function [4] postulated by J. Willard Gibbs.
REFERENCES
[1] D.J. Evans and D.J. Searles, Phys. Rev. E 50,1645(1994).
[2] D.J. Searles and D.J. Evans, J.Chem. Phys., 113,3503(2000).
[3] D.J. Evans, D.J. Searles and S.R. Williams, J. Chem. Phys., 128, 014504(2008), ibid, 128, 249901(2008).
[4] D.J. Evans, D.J. Searles and S.R. Williams, J. Stat Mech.,P07029(2009). 
25/06/2013 5:30 PMM513Fernando Rosas (Pontificia Universidad Catolica de Chile)Ideas about the dynamics of informationSeminar series:
Information theory provides a satisfactory theory for understanding stationary information sources. This theory, which was created to analyze communications between electronic devices, has found numerous applications in almost all branches of science.
A requirement to apply this theory is the existence of a fixed language, which is independent of the information that is shared. This makes this theory unsuitable for addressing fundamental questions of evolutionary biology, contemporary music cognition and many other disciplines. To the best of our knowledge, there exist no theory which is able to give account of evolving information sources and hence explain the dynamics of information.
There exist a deep link between information theory, which deals with stationary information sources, and equilibrium statistical mechanics. Thinking by analogy, we believe that nonequilibrium statistical mechanics holds the seeds for developing a theory which could explain the dynamics of information. The absence of the later may be related with the lack of a clear and general theory of nonequilibrium phenomena.
After reviewing the fundamentals concepts of information theory, the talk will present the limitations of the existent theory and explore the relationship between information dynamics and statistical physics.

11/07/2013 5:30 PMM103Yamir Moreno (University of Zaragoza)Diffusion processes on complex networked systemsSeminar series:
The study of complex networks sheds light on the relation between the structure and function of complex systems. In this talk, we thoroughly discuss two paradigmatic examples of diffusion dynamics that take place on complex architectures: the spreading of diseases and the socalled complex social contagion. For the first process, we revisit the main theoretical and computational results obtained in the last decade. Specifically, we discuss several relevant cases ranging from the spreading of single diseases in singlelayer networks, to the competitive dynamics of multistrain diseases on top of metapopulation systems. Secondly, we discuss a different class of theoretical and numerical approaches suited to describe the emergence of collective phenomena in largescale social systems. In particular, we show how this diffusion dynamics introduces different analytical and numerical challenges whose solution leads to a better understanding of the mechanisms at the root of the phenomena being analyzed.

10/10/2013 5:30 PMM513Pau Rabassa Sans (QMUL)Extreme Value Statistics and Dynamical SystemSeminar series:

24/10/2013 5:30 PMM513Yaming Chen (QMUL)Weaknoise limit of a piecewisesmooth stochastic differential equationSeminar series:

07/11/2013 4:30 PMM513Bhavin Khatri (MRC)Simple GenotypePhenotype Maps and the Stochastic Dynamics of Evolution and SpeciationSeminar series:

15/11/2013 4:00 PMM203Thanos Manos (CAMTP)Probing the role of accelerator modes on the dynamical localization properties of the quantum kicked rotator and on the anomalous diffusion of its classical analogueSeminar series:

28/11/2013 4:30 PMM513Tobias Reichenbach (Imperial)Processing of auditory signals: from the inner ear to neural networksSeminar series:

05/12/2013 4:30 PMM513Lucas Lacasa (QMUL)Irreversibility, time series, and networks
Seminar series:
Statistical Mechanics Study Group 
13/01/2014 4:00 PMM203Katy Rubin (King's College)Perturbations of protein interaction networks

31/01/2014 4:00 PMM203Trevor Graham (QMUL)Measuring and modelling clonal evolution in cancerSeminar series:

13/02/2014 4:30 PMM513Peter Schmelcher (Hamburg)Seminar cancelledSeminar series:

06/03/2014 4:30 PMM513Rainer Klages (QMUL)Irreversible transport from time reversible dissipative chaotic dynamicsSeminar series:

30/04/2014 5:00 PMM203Christian Van den Broeck (Hasselt)Stochastic thermodynamics: a very brief introductionSeminar series:
The main purpose of statistical mechanics is to give a microscopic derivation of macroscopic laws, including in particular the celebrated second law of thermodynamics. In recent years, there have been spectacular developments in this respect, including the integral and detailed work fluctuation theorems and the theory of stochastic thermodynamics. We give a brief introduction to these developments. In the first step, we derive the first and second law of thermodynamics for a Markovian stochastic process at the ensemble level, including two major advances: 1) the theory can be applied to smallscale systems including the effect of fluctuations, 2) the theory is not restricted to nearequilibrium dynamics. As an application, we evaluate the efficiency at maximum power of a twostate quan tum dot. We also briefly discuss the connection to informationtowork conversion (Landauer principle). In a second step we formulate stochastic thermodynamics at the trajectory level, introducing stochastic trajectorydependent quantities such as stochastic entropy, energy, heat, and work. Both the first and the second law can be formulated at this trajectory level. Concerning the second law, the crucial observation is that the stochastic entropy production can be written as the logarithm of the ratio of path probabilities. This in turn implies a detailed and integral work and fluctuation theorem, linking the probability to observe a given stochastic entropy production to that of observing minus this entropy change in a reverse experiment. The usual second law, stipulating the increase on average of the stochastic entropy production, follows as a subsidiary consequence.

06/08/2014 5:00 PMM103Peter Schmelcher (Hamburg)Nonequilibrium dynamics and transport in spatiotemporally driven latticesSeminar series:
The nonequilibrium classical dynamics and directed transport in lattices with
a spatiallydependent driving is explored. Prototype examples are phase, frequency
or amplitudemodulated lattices which, via a tuning of the parameters of the
driven unit cell, allow for an engineering of the classical phase space
and therefore of the magnitude and direction of the directed currents.
Several mechanisms for transient localization and trapping of particles
in different wells of the driven unit cell are presented and analyzed.
As a major first application we derive a mechanism for the patterned deposition
of particles in a spatiotemporally driven lattice. The working principle
is based on the breaking of the spatiotemporal translation symmetry, which is responsible
for the equivalence of all lattice sites. The patterned trapping of the particles occurs
in confined chaotic seas, created via the ramping of the height of the lattice potential.
Complex density profiles on the length scale of the complete lattice can be
obtained by a quasicontinuous, spatial deformation of the chaotic sea in a frequency modulated lattice.
In a second step we explore spatiotemporal superlattices consisting of
domains of differently timedriven spatial lattices. Here we demonstrate
a novel mechanisms for the conversion of ballistic to diffusive motion and vice versa.
This process takes place at the interfaces of domains subjected to different timedependent
forces. As a consequence a complex shorttime depletion dynamics at the interfaces followed
by longtime transient oscillations of the particle density are observed. The latter can
be converted to permanent density waves by an appropriate tuning
of the driving forces. The proposed mechanism opens the perspective of an
engineering of the nonequilibrium dynamics of particles in inhomogeneously driven lattices.
Finally we show the emergence of dynamical current reversals in longrange
interacting spatiotemporally driven lattices. 
10/12/2014 3:00 PMM513Jake TaylorKing (Oxford)Generalised velocity jump processesSeminar series:
There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long distance movement state and a resting or local movement state. Here a mathematical description of this process is formulated, adapted from Friedrich et. al. (2006). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of partial integrodifferential equations are tumultuous and therefore it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally a large time diffusive approximation is considered via a Cattaneo approximation (Hillen, 2004). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.

12/02/2015 5:00 PMM513Dmitry Kovrizhin (Cambridge)Nonequilibrium quantum matter: from quantum Hall edge states to quantum spinliquidsSeminar series:
I will talk about nonequilibrium quantum phenomena arising in the context of experimentally relevant condensed matter settings. Examples of the latter include quantum Hall (QHE) edge states driven out of equilibrium by applied bias voltage; and frustrated quantum magnets, where a sudden perturbation can result in an unusual nonequilibrium response. These systems show remarkable behaviour, such as emergence of nonequilibrium steady states, and a dynamical phase diagram, which arise as a result of fractionalization of electron/spin degrees of freedom into quasiparticles (e.g. Majorana fermions and fluxes of gauge field). I will present the theory of electron equilibration in QHE edge states, and discuss dynamical response in quantum spinliquids.
[1] D.L. Kovrizhin and J.T. Chalker, Phys. Rev. Lett. 109, 106403 (2012)
[2] J. Knolle, D.L. Kovrizhin, J.T. Chalker, and R. Moessner, Phys. Rev. Lett. 112, 207203 (2014) 
01/12/2016 5:00 PMM203Esa Raesaenen (Tampere, Finland)The physics of drumming: From fractals to superdiffusionIt has long been known that musicians do not keep time with the precision of a metronome. Here we show that in deviating from a perfectly precise beat, a professional drummer makes patterns in the timing and dynamics that have a particular mathematical form  a fractal [1]. These fractal, longrange correlated deviations make music sound distinctly human [2]. On the other hand, the series of cumulative fluctuations from the mean interbeat intervals, i.e., the musical drift or flow, has superdiffusive properties if there is no metronome present. We introduce our audio detection tools and time series analysis methods behind these findings. Our results on musical rhythms are brought to a more general context with other complex physiological signals such as the heartbeat. We also discuss the relevance of our results as a subtle element behind musical "groove"  among other better known elements such as rhythmic syncopation and musical interplay in the band.
[1] E. Räsänen et al., PLoS ONE 10(6): e0127902 (2015).
[2] H. Hennig et al., Phys. Today. 65, 64 (2012). 
08/12/2016 5:00 PMM203Uzy Smilansky (Weizmann Institute)The distribution of transit times through metric (quantum) graphsThis work is motivated by an experiment which is now being
carried out by Professor S Anlage in Maryland: A train of very short
electromagnetic pulses is fed to a network of coaxial transmission lines
through one vertex, and exit through another vertex. The times t it
takes to cross the network is the transit time of interest here. We
study the distribution of transit times and show that asymptotically it
falls off exponentially as Aexp(ct) and explain how the constants A and
c depend on the network connectivity and the lengths of its edges. 
07/10/2010 5:30 PMM513Oscar Bandtlow (QMUL)Bra Wars II: Return of the Resolvent  or: What every Physicist should know about OneParameter Semigroups
See below for a pdf of Oscar's smartboard scribblings...
Attachment Size SMSG_071010.pdf [PDF 1,177KB] 1.15 MB 
28/10/2010 5:30 PMM513Wolfram Just (QMUL)DP & DDESee below for a pdf of Wolfram's wondrous writings...
Attachment Size SMSG_281010.pdf [PDF 258KB] 258.81 KB 
10/03/2011 4:30 PMM513Wolfram Just (QMUL)Ignorant Control, or: Stochastic delay systems, random matrix theory for pedestrians, and a measurable function which can be written down without using the word "if"See the title.
At a technical level the talk shows how to compute the solution of a two dimensional linear map where one of the coefficients is a dichotomous random number (to be less imprecise: how to compute the exponential growth rate). Models of this type are the simplest, almost trivial, case of a dynamical system with random delay time. The results contribute at some superficial level to the understanding of time delayed feedback control.
FOOTNOTE: The scientific content of the talk has to be attributed to Günter Radons. He showed me the model and the computation of Lyapunov exponents (without this footnote I would certainly share the fate of the German Secretary of State for Defence).
See below for the smart scribblings from the seminar.Attachment Size smsg_100311.pdf [PDF 619KB] 619.99 KB 
22/09/2011 5:30 PMM513Dónal MacKernan (Atlantic Centre for Atomistic Modelling, University College Dublin)Multiscale Dynamical Stochastic Techniques in various Thermodynamics Ensembles, & the Adiabatic Approximation
See attachment for abstract.
Attachment Size tamdlondon.pdf [PDF 52KB] 52.62 KB