# Statistical Mechanics Conference

## 109th Statistical Mechanics Conference

Sunday, May 12, 2013 at 08:00am -

May 2013
- 109th SMC Program

109th List of invited talks and abstracts

109th Short talk schedule

109 SMC presentation of invited talks

## LIST OF INVITED SPEAKERS AND THEIR TALK INFORMATION

109th STATISTICAL MECHANICS CONFERENCE

**Gyan Bhanot, Rutgers University**

Inferring The Evolution Of H5N1 And Estimating The Likelihood Of Pandemics

- Abstract: The H5N1 virus is highly pathogenic in birds, and occasionally infects humans with a high mortality rate. Although transmission between humans has been rare to date, recent studies have shown that as few as five acquired mutations makes the virus transmissible between mammals, suggesting its potential role as a pandemic agent. I will describe progress on four questions. Which viral loci are under selection? Does selection vary with geography? Is there human-specific selection? What is the likelihood of a pandemic strain emerging in the next few years?

**David Campbell, Boston University**

Global Phase Space Of Coherence And Entanglement In A Double-Well Bose-Einstein Condensate

- Abstract: Ultracold atoms provide ideal systems for the study of fundamental physical questions such as the emergence of decoherence and entanglement in quantum many-body systems. I will present results of a model study - using the Bose-Hubbard Hamiltonian - of the quantum dynamics of bosonic atoms in a double-well trap. I will show how, in the semi-classical limit, this problem reduces to an unusual integrable nonlinear dynamical system, the classical phase space of which provides considerable insight into the quantum system. I will discussion many-particle entanglement and spin-squeezing and show where true quantum features arise beyond the classical approximation.

**Eddie G.D. Cohen, Rockefeller University**

A Dynamical Derivation Of The Equilibrium Virial Expansion

- Abstract: TBA

**Joel Cohen, Rockefeller University**

Taylor's Law Of Fluctuation Scaling: From Bacteria To Humans And Beyond

- Abstract: L. R. Taylor (1961) and colleagues observed that, in many species, the logarithm of the variance of the density (individuals per area or volume) of a set of comparable populations was an approximately linear function of the logarithm of the mean density: for some a > 0, log(variance of population density) = log(a) + b Ã— log(mean population density). This relationship, equivalent to variance = a(mean)b, came to be known as Taylor's law (TL) of fluctuation scaling. TL has been verified in hundreds of species from bacteria to humans and beyond: in populations of stem cells, stock market trading, precipitation, packet switching on the Internet, measles cases, and the occurrence of single nucleotide polymorphisms. We will give some empirical examples of TL and some recent theoretical developments regarding the origins, interpretations, and consequences of TL.

**Peter Constantin, Princeton University**

Nonlocal Dissipation

- Abstract: TBA

**Frederick Cooper, Sante Fe Institute**

Improved Self Consistent Mean Field Tjheory for Dilute Bose Gases

- Abstract: By introducing composite fields related to both the normal and anomalous densities directly into the path integral, one can perform the Gaussian path integral over the original Bose fields and evaluate the remaining integrals by steepest descent. The self consistent mean-field theory obtained from the stationary phase solution allows one to remedy problems with previous mean-field theories. One obtains the Bogoliubov spectrum at weak coupling, obtains a second order phase transition to the BEC broken U(1) symmetry phase and a shift in the Bose condensation temperature close to the result of Monte-Carlo simulations. The composite field related to the anomalous density becomes the relevant order parameter for the onset of superfluidity.

**Susan Coppersmith, University of Wisonsin**

Investigation Of A Quantum Adiabatic Algorithm For Search Engine Ranking

- Abstract: An important method for search engine result ranking works by finding the principal eigenvector of the "Google matrix." Here, we show that a recently proposed quantum algorithm for preparing this eigenvector has a run-time that depends on features of the graphs other than the degree distribution. For a sample of graphs with degree distributions that more closely resemble the Web than in previous work, the proposed algorithm for eigenvector preparation does not appear to run exponentially faster than the classical case.

**Dmitry Dolgopyat, University of Maryland**

Piecewise Linear Fermi-Ulam Pingpongs

- Abstract: We consider a particle moving freely between two periodically moving infinitely heavy walls. We assume that one wall is fixed and the second one moves with piecewise linear velocities. We study the question about existence and abundance of accelerating orbits for that model. This is a joint work with Jacopo de Simoi.

**Emmanuel Fort, Langevin Institute, ESPCI - Paris**

Statistical Properties Of Path-Memory Driven Dual Objects

- Abstract: Transposable Elements (TEs) are the most widespread genetic parasites in eukaryotic genomes. Almost half of the human genome is explicitly derived from TE DNA. Many of these elements are remnants of past retroviral infections of the germ line that have kept intact important parts of their molecular replication machinery. Given the potential detrimental consequences of TE activity, host mechanisms of defense have evolved to identify and repress these transposons. For instance, recent progress has shed light on several molecular mechanisms that employ trans-acting repressors that recognize cis-acting sequences in a given TE, thereby blocking its expression. In this talk, I will present novel work regarding the evolution of these molecular mechanisms by which the host is able to learn to recognize and silence newly invading TEs. In particular, I will review basic aspects of the biology of piRNAs and show how these repressors evolve by means of new mutations that arise after their targets have invaded the host genome. Second, I will review the biology of the zinc finger/KAP1 transcriptional repressor complex, and show evidence that suggests that these repressors have been selected from existing genetic variation generated before their targets invaded the host genome. Finally, I will discuss some mathematical work motivated by the study of the dynamical processes by which the host population is able to produce and maintain a standing genetic variation of repressors.

**Alessandro Giuliani, Università di Roma Tre**

Striped States at the Ferromagnetic Transition

- Abstract: In this talk I will consider a 2D Ising model with nearest neighbor ferromagnetic interaction plus a long range antiferromagnetic interaction, decaying as (distance)^(-p), p>4. If the strength of the ferromagnetic coupling is larger than a critical value J_c, then the ground state is homoegeneous. If J is smaller than J_c and sufficiently close to it, it is believed that the ground state is periodic and consisting of stripes of constant width and alternating magnetization. In this talk I will present recent rigorous results confirming this picture: namely, the ratio of the exact ground state energy to the energy of the optimal periodic striped state tends to 1 as J-->J_c^-. Based on joint work with E. Lieb and J. Lebowitz, and with E. Lieb and R. Seiringer.

**Ramin Golestanian, University of Oxford**

Nonequilibrium Collective Behavior Of Thermally Active Colloids

- Abstract: Due to their force-free nature, phoretic transport mechanisms can be used to design self-propelled active colloids. In my talk, I will describe a particular class of such active colloids that self-propel and interact via temperature gradients that they generate. They exhibit interesting collective effects such as instabilities and emergent dynamical behaviors.

**Ilya Gruzberg, University of Chicago**

Quantum Hall Effects: A Theory Based On Conformal Restriction

- Abstract: TBA

**Gemunu Gunaratne, University of Houston**

Solution Surfaces Of Genetic Networks And Applications

- Abstract: Living systems maintain their physiological state under environmental changes and isolated genetic mutations through feedback within highly connected networks of genes, proteins, and other bio-molecules. Unfortunately, this robustness also makes it difficult to correct defects such as hereditary diseases, as evidenced by the surprising lack of efficacy of single target drugs that were designed to act on specific molecular targets. Side-affects from medications are another consequence of the connectivity in underlying networks. If accurate models of gene networks were available, they could be used to compute how effective therapies for diseases can be designed. Unfortunately, it is very difficult to construct sufficiently accurate models. We propose to use Â³solution surfacesÂ² of the gene network associated with a biological process. In principle, they can be obtained by sequencing many biologically perturbed mutants. However, studies of model networks and nonlinear electronic circuits show that the solutions surfaces are smooth; hence, good approximations can be obtained from triangulation. Furthermore, as we show through several examples, biologically relevant issues can be addressed in this approach. Specifically, we can compute how the state of a gene network can be moved to a pre-specified state. As an example, we have used the methodology to compute how the brain transcriptome of Drosophila can be altered in order to move the animal to a sleep-deprived like state. Experiments are being conducted to verify our predictions. Interestingly,this biologically motivated approach to study networks may have applications in other disciplines; some examples will be discussed.

**Anthony Guttmann, University of Melbourne**

Self-Avoiding Walks Absorbed at a Surface

- Abstract: In 2010 H. Duminil-Copin and S. Smirnov proved that the growth constant of self-avoiding walks (SAW) on a honeycomb lattice was $sqrt{2+sqrt{2}}, thereby proving a 30 year old conjecture of B. Nienhuis. In 1995 Batchelor and Yung conjectured that the critical fugacity of SAWs adsorbed on a surface of the honeycomb lattice is $1+sqrt{2}. We prove this result. An important byproduct is a proof that the bridge generating function, at criticality, for bridges crossing a strip of width $T$ vanishes as $T to infty. These results rely on a parafermionic identity that only holds for the hexagonal lattice. We argue that in the scaling limit the lattice is irrelevant, so that some such identity must hold for other lattices. We provide compelling evidence for this (but not a proof) by extensive numerical simulations. We obtain excellent estimates of the critical adsorption fugacity for other lattices. These are several orders of magnitude more accurate than pre-existing estimates in the case of the square lattice, and completely new in the case of the triangular lattice. (Joint work with N. Beaton, M. Bousquet-Melou, J. de Gier and H. Duminil-Copin and I. Jensen.)

**Hans-Rudolf Jauslin, Université de Bourgogne**

Wave Attraction and Singular Liouville-Arnold Tori

- Abstact: We consider the interaction of counter-propagating waves described by Hamiltonian wave equations, without dissipation. The geometry is a one-dimensional segment, with incoming boundary conditions at both ends. In these systems one observes, under quite general conditions a relaxation to a stationary state, which is selected among a set of stationary states that is compatible with the boundary conditions. We will discuss the relation between this selected state and singular Liouville-Arnold tori of the stationary equations, which are associated with resonances and a non- trivial Hamiltonian monodromy. We will illustrate these phenomena with several models, including the dynamics of the polarization of light in optical fibers and the massive Thirring model.

**Mogens Jensen, University of Copenhagen**

Arnold Tongues in Biology

- M.H. Jensen and S. Krishna, ""Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli"", FEBS Letters 586, 1664-1668 (2012).
- N. Mitarai, U. Alon and M.H. Jensen, ""Entrainment of linear and non-linear system under noise"", Chaos, to appear (2013)."

- Abstract: Oscillating genetic patterns have been observed in networks related to the transcription factors NFkB, p53 and Hes1. We identify the central feed-back loops and found oscillations when time delays due to saturated degradation are present. By applying an external periodic signal, it is sometimes possible to lock the internal oscillation to the external signal. For the NF-kB systems in single cells we have observed that the two signals lock when the ration between the two frequencies is close to basic rational numbers [1]. The resulting response of the cell can be mapped out as Arnold tongues. When the tongues start to overlap we observe a chaotic dynamics of the concentration in NF-kB [1]. Oscillations in some genetic systems can be triggered by noise, i.e. a linearly stable system might oscillate due to a noise induced instability. By applying an external oscillating signal to such systems we predict that it is possible to distinguish a noise induced linear system from a system which oscillates via a limit cycle. In the first case Arnold tongues will not appear, while in the second subharmonic mode-locking and Arnold tongues are likely [2].

**Yariv Kafri, Technion**

Non-Differentiable Large Deviation Functionals In Boundary Driven-Diffusive Systems

- Abstract: The talk will present recent work on the probability distribution of an arbitrary density profile in boundary driven diffusive systems (namely, the large deviation functional). It will be shown that the breaking of time-reversal symmetry can lead to a non-differentiable large deviation functional. The structure of some of these singularities will be discussed and shown to be well described by a Landau free energy. Connections with analogous results in systems with finite-dimensional phase spaces will be drawn.

**Elliott Lieb, Princeton University**

Statistical Properties Of Path-Memory Driven Dual Objects

- Abstract:In 1975 D. Bessis, P. Moussa and M. Villani in JMP 16, p.2318 noted that the Feynman-Kac integral representation for Trace exp(A - t B) (with A = a Schroedinger operator and B = a perturbing potential), when considered as a function of the coupling constant t, is the Laplace transform of a positive measure. This fact has several implications, one being that it leads to a sequence of upper and lower bounds to the free energy. This posivity property holds for a many-boson system but not obviously for a many-fermion system because of the "sign problem". Boldly, they conjectured that the positivity property would hold for *any* pair of self-adjoint operators, A and B, on *any* Hilbert space. For 36 years this conjecture was attacked by many people but no proof or counter-example was found, not even for 3x3 matrices! Finally, in 2011 H. Stahl found a proof (arXiv 1107.4875), which will appear in Acta Math. Some of the implications of the Stahl theorem will be discussed. It is hoped that more useful implications can be found by the listeners. (Joint work with R. Seiringer).

**Kirone Mallick, CEA Saclay**

Large Deviations Of The Current In The Open Exclusion Process

- Abstract: Non-equilibrium systems are often characterized by the transport of some quantity at a macroscopic scale, such as, for instance, a current of particles through a wire. This situation can be modeled by the asymmetric simple exclusion process, which is used as a template to study various aspects of non-equilibrium statistical physics. In this talk, we shall explain how to derive the full statistics of the current for the exclusion process with open boundaries and shall give combinatorial formulas valid for systems of all sizes and for all values of the parameters. Our exact analytical results coincide with the predictions of Macroscopic Fluctuation Theory and with numerical calculations using DMRG techniques.

**Vieri Mastropietro, University of Milan**

Universal Conductivity Properties In Many Body Physics

- Abstract: Several low dimensional interacting fermionic systems, including graphene and spin chains, exhibit remarkable universality properties in the conductivity. Universality in presence of many body interactions or disorder can be rigorously established under certain conditions by combining Renormalization Group methods with Ward Identities.

**Alexandre Morozov, Rutgers University**

Evolution of Novel Function in Proteins as a Stochastic Process: A Path-Based Approach

**Stefano Olla, Université Paris Dauphine**

Thermal Conductivity And Weak Coupling

- Abstract: We investigate thermal conductivity under weak coupling limits and energy conserving stochastic perturbations of the dynamics.

**Jacequeline Quintana, Universidad Nacional Autónoma de México**

Some Results For Over Simplified 2D Models: Molecular Simulations And Onsager Theory

- Abstract: Numerical simulations and Onsager theory of two-dimensional models of anisotropic and chiral molecules represented with over simplified systems reveal various types of assemblies. Our models can be easily modified in shape and symmetry, facilitating the understanding of the occurrence or suppression of phases, as well as their underlying competing structures.

**Anirvan Sengupta, Rutgers University**

Chromatin Architecture Dynamics and Long-Range Regulatory Control

- Abstract: Long distance regulatory interactions between enhancers and their target genes are commonplace in higher eukaryotes. Interposed boundaries or insulators are able to block these long distance regulatory interactions and provide specificity of gene regulation. The physical basis for insulator activity and how it relates to enhancer action at a distance remain unclear. We model the chromatin fiber as a semi-flexible polymer to explain how incorporating transient nonspecific and moderate attractive interactions between the chromatin fibers strongly enhances long distance regulatory interactions while maintaining a euchromatin-like state. Under these same conditions, the subdivision of a loop into two topologically independent loops by insulators inhibits inter-loop interactions. We finish by discussing how we could use the polymer model of chromatin to analyze data related to chromatin conformation and learn about regulatory contacts.

**Tatyana Shcherbina, Institite for Advanced Study**

Universality of the Second Mixed Moment of the Characteristic Polynomials of the 1D Gaussian Band Matrices

- Abstract: We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices. Assuming that the width of the band grows faster than $sqrt{N}$, where $N$ is a matrix size, we show that this asymptotic behavior in the bulk of the spectrum coincides with those for the Gaussian Unitary Ensemble.

**Yakov Sinai, Princeton University**

New Limiting Distributions for Square-Free Numbers

**Sara Solla, Northwestern University**

Generalized Linear Models of Spiking Neurons

- Abstract: Generalized Linear Models provide a framework for the systematic description of neural activity. The formulation of these models is based on the exponential family of probability distributions; the Bernoulli and Poisson distributions are relevant to the case of stochastic spiking. In this approach, the time-dependent mean firing rate of individual neurons is modeled in terms of experimentally accessible correlates of neural activity: patterns of activity of other neurons in the network, inputs provided through various sensory modalities or by other brain areas, and outputs such as muscle activity or motor actions. Model parameters are fit to maximize the likelihood of the observed firing statistics; smoothness and sparseness constraints can be incorporated via regularization techniques. When applied to neural data, this modeling approach provides a powerful tool for mapping the spatiotemporal receptive fields of individual neurons, characterizing network connectivity through pairwise interactions, and monitoring synaptic plasticity.

**Nikos Theodorakopoulos, NHRF Athens**

- Coauhors: Nikos Theodorakopoulos (NHRF Athens)* and Michel Peyrard (ENS-Lyon)

How Soft is DNA?

- N. Theodorakopoulos and M. Peyrard, Phys. Rev. Lett. 108, 078104 (2012)"

- The bending flexibility of DNA is essential in key biological processes, such as its packing in chromatin or in viruses. On the other hand, long, genomic sequences of double-stranded DNA in solution are known to be quite stiff on the nanoscale, with persistence lengths of the order of 50 nm. Openings of base pairs (""denaturation bubbles""), which are known to occur spontaneously near physiological temperatures, may provide a natural mechanism of local softening. Whereas the principle behind the mechanism (put forward by von Hippel in the 1960's) is clear, the existence of sufficient thermal bubble populations has been the subject of debate. I will present some recent results [1] which show, by studying the statistics of denaturation bubbles within the framework of the Peyrard-Bishop-Dauxois model of DNA melting, that such local softening is compatible with known macroscopic persistence lengths and can still account for the recently observed strong temperature dependence of bending stiffness in 200-base-pair-long sequences.

**David Vanderbilt, Rutgers University**

Quantum Anomalous Hall States On Decorated Magnetic Surfaces

- Abstract: Twenty-five years ago, Haldane [1] pointed out the possibility that a 2D crystalline insulator with broken time-reversal symmetry could exhibit a quantized Hall conductivity in the absence of an external magnetic field, potentially at room temperature. Despite the enormous recent interest in topological insulators of the non-magnetic type, we still have no good experimental realizations of Haldane's "quantum anomalous Hall" (QAH) or "Chern insulator" state. I shall report on our recent work [2] in which we propose that a fractional monolayer of heavy atoms (providing strong spin-orbit coupling) adsorbed on the surface of an insulating ferromagnet or antiferromagnet could realize the QAH state. As an outgrowth of this work, I will pose a problem regarding the statistics of the Chern numbers of the energy bands formed by random matrices wrapped on a torus. Numerical tests are roughly consistent with a normal distribution, but we are unaware of any underlying theory in connection with this problem.

**Benjamin Widom, Cornell University**

Thermodynamic Functions As Correlation-Function Integrals

- Abstract: TBA

Presentations of Talks Given at The 109th Statistical Mechanics Conference

Presentations of Talks Given at The 109th Statistical Mechanics Conference

**Amnon Aharony, Ben-Gurion University of the Negev**

Scale dependent competing interactions**Andrea Bertozzi, University of Californioa, Los Angeles**

Data clustering, modularity optimization, and total variation on graphs**Gyan Bhanot, Rutgers University**

Inferring The Evolution Of H5N1 And Estimating The Likelihood Of Pandemics**Curtis Callan, Princeton University**

Using sequence data to infer the mechanisms of T-cell receptor diversity generation**David Campbell, Boston University**

Global Phase Space Of Coherence And Entanglement In A Double-Well Bose-Einstein Condensate**Eddie G.D. Cohen, Rockefeller University**

A Dynamical Derivation Of The Equilibrium Virial Expansion**Joel Cohen, Rockefeller University**

Taylor's Law Of Fluctuation Scaling: From Bacteria To Humans And Beyond**Peter Constantin, Princeton University**

Nonlocal Dissipation**Frederick Cooper, Sante Fe Institute**

Improved Self Consistent Mean Field Theory for Dilute Bose Gases**Susan Coppersmith, University of Wisonsin**

Investigation Of A Quantum Adiabatic Algorithm For Search Engine Ranking**Predrag Cvitanovic, Georgia Tech**

Charting turbulence**Dmitry Dolgopyat, University of Maryland**

Piecewise Linear Fermi-Ulam Pingpongs**Emmanuel Fort, Langevin Institute, ESPCI - Paris**

Statistical Properties Of Path-Memory Driven Dual Objects**Alessandro Giuliani, Università di Roma Tre**

Striped States at the Ferromagnetic Transition**Ramin Golestanian, University of Oxford**

Nonequilibrium Collective Behavior Of Thermally Active Colloids**Ilya Gruzberg, University of Chicago**

Quantum Hall Effects: A Theory Based On Conformal Restriction**Gemunu Gunaratne, University of Houston**

Solution Surfaces Of Genetic Networks And Applications**Anthony Guttmann, University of Melbourne**

Self-Avoiding Walks Absorbed at a Surface**Hans-Rudolf Jauslin, Université de Bourgogne**

Wave Attraction and Singular Liouville-Arnold Tori**Mogens Jensen, University of Copenhagen**

Arnold Tongues in Biology**Yariv Kafri, Technion**

Non-Differentiable Large Deviation Functionals In Boundary Driven-Diffusive Systems**Elliott Lieb, Princeton University**

Statistical Properties Of Path-Memory Driven Dual Objects**Kirone Mallick, CEA Saclay**

Large Deviations Of The Current In The Open Exclusion Process**Vieri Mastropietro, University of Milan**

Universal Conductivity Properties In Many Body Physics**Alexandre Morozov, Rutgers University**

Evolution of Novel Function in Proteins as a Stochastic Process: A Path-Based Approach**Stefano Olla, Université Paris Dauphine**

Thermal Conductivity And Weak Coupling**Jacequeline Quintana, Universidad Nacional Autónoma de México**

Some Results For Over Simplified 2D Models: Molecular Simulations And Onsager Theory**Anirvan Sengupta, Rutgers University**

Chromatin Architecture Dynamics and Long-Range Regulatory Control**Tatyana Shcherbina, Institite for Advanced Study**

Universality of the Second Mixed Moment of the Characteristic Polynomials of the 1D Gaussian Band Matrices**Yakov Sinai, Princeton University**

New Limiting Distributions for Square-Free Numbers**Sara Solla, Northwestern University**

Generalized Linear Models of Spiking Neurons**Nikos Theodorakopoulos, NHRF Athens**

How Soft is DNA?**David Vanderbilt, Rutgers University**

Quantum Anomalous Hall States On Decorated Magnetic Surfaces**Benjamin Widom, Cornell University**

Thermodynamic Functions As Correlation-Function Integra