Statistical Mechanics Conference

107th Statistical Mechanics Conference

Sunday, May 06, 2012 at -

107th SMC Program
107th List of invited talks and abstracts
107th SMC short talk schedule
107 SMC presentation of talks

 

LIST OF INVITED SPEAKERS AND THEIR TALK INFORMATION
107th STATISTICAL MECHANICS CONFERENCE

  • Natan Andrei, Rutgers University
    Title: Quench Dynamics of Interacting Bosons
    Abstract: TBA

  • Mark Bowick, Syracuse University
    Title: Facets of Order
    Abstract: I will discuss the interplay between shape and order in block copolymer vesicles with internal liquid crystalline order including the realization of faceted liquid crystalline shells.

  • Yana Bromberg, Rutgers University
    Title: Differentiating SNP-mediated function disruption from disease
    Abstract: A major current effort in the scientific community focuses on evaluating individual predispositions to specific phenotypic traits/diseases given their genetic backgrounds. While the majority of disease causing mutants affect molecular function, the reverse is not necessarily true; i.e. functionally disruptive mutants do not always cause disease. The importance of a variant-affected site to specific molecular function or proper folding of the protein differentiates disease-causing variants from those with less severe phenotypes. Here we present a computational method for identification of protein functional sites via analysis of variant effects. We further relate the natural occurrence of mutations in these functional sites to the development of disease.

  • Eric Carlen, Rutgers University
    Title: Bounds for entanglement via an extension of strong subadditivity of entropy
    Abstract: We prove sharp lower bounds for the entanglement of formation and the squashed entanglement for bipartite states in terms of the conditional entropy,and give a new class of states for which both measures of entanglement can be exactly computed. We also derive upper bounds. This is joint work with Elliott Lieb.

  • Premi Chandra, Rutgers University
    Title: An Emergent Critical Phase in a 2D Frustrated Heisenberg Model
    Abstract: TBA

  • Michael Chertkov, Los Alamos National Laboratory
    Title: Statistical Physics for Smart (Power) Grids
    Abstract: We are asking modern power grids to serve under conditions for which they were not originally designed. We also expect the grids to be smart, in how they function, how they withstand contingencies, how they respond to fluctuations in generation and load, and how the grids are controlled. To meet these ever-increasing expectations requires extending power grid models beyond the scope of traditional power engineering. In this talk aimed at applied mathematicians and physicists I first review basics of power flows, and then outline a number of new problems in modeling power grids. In particular, I describe new approaches to study (a) voltage stability/collapse in distribution (low voltage) system; and if time permits, (b) probabilistic distance to failure in transmission (high voltage) system.

  • Philippe Choquard, ITP, EPF Lausanne CH
    Title: The 2D. Euler-Coriolis fluid: Theory and Illustration
    Abstract: We start with a canonical Hamiltonian, Clebsch like, formulation of inviscid, compressible and rotational,charged or neutral fluids, and their ensuing equations of motion including Euler equations for the velocity fields. We consider next the simplest example of a 2D perfect fluid in a rotating frame of reference, called the Euler-Coriolis fluid.Then,we take up the problem of describing the dynamics of a single cylindrical vortex immersed in an infinite compressible medium by means of the method of characteristics. An extension of the Hopf-Lax-Bellman variational principle is evoked to qualify the nature of the solutions, weak in general. Results of numerical analysis are lastly presented.

  • Sergio Ciliberto, CNRS
    Title: Experimental verification of Landauer's principle linking information and thermodynamics
    Abstract: TBA

  • James P. Crutchfield, University of California, Davis
    Title: The Past and the Future in the Present
    Abstract: We show why the amount of information communicated between the past and future---the excess entropy---is not in general the amount of information stored in the present---the statistical complexity. This is a puzzle, and a long-standing one, since the former describes observed behavior, while optimal prediction requires the latter. We present a closed-form expression for the excess entropy in terms of optimal causal predictors and retrodictors---both epsilon-machines of computational mechanics. This leads us to two new system properties: causal irreversibility---the temporal asymmetry between causal representations---and crypticity---the degree to which a process hides its state information. Joint work with Chris Ellison, Ryan James, and John Mahoney.

  • Freeman Dyson, Institute for Advanced Study
    Title: Partitions and the Grand Canonical Ensemble
    Abstract: Two disconnected remarks about partitions. First, a pedagogical remark connecting pure mathematics with statistical physics. The grand canonical ensemble of statistical mechanics is applied to the counting of partitions. This picture borrowed from physics gives a simple approximation to the exact calculation of the partition function by Hardy and Ramanujan.

  • Yves Elskens, CNRS/Aix-Marseilles University
    Title: Propagation of chaos in wave-particle interaction
    Abstract: The validity of quasilinear (QL) theory describing the paradigmatic weak warm beam instability has been controversial for decades. We prove that the velocities of N passive particles in a single one-dimensional wave field converge in law to a diffusion process, in the limit of a dense wave spectrum with independent amplitudes and random phases, when the power spectrum is uniform. The proof provides a full probabilistic foundation to the QL approximation and to the ensemble picture for a single realization of the stochastic environment. For the self-consistent Vlasov?wave dynamics, we prove analytically and nume- rically that in the strongly nonlinear regime where the particle distribution function has formed a plateau and wave intensities have settled, QL predictions remain valid thanks to the absence of mode coupling, and particles evolve in a quenched random wave field. We confirm numerically that the wave power spectrum at saturation agrees statistically with the prediction from the conservation law resulting from the locality in velocity of the wave-particle interaction. We also observe a nonlinear, non-QL stage in the development of the instability, before its saturation.
    1. Y. Elskens and E. Pardoux, Diffusion limit for many particles in a periodic stochastic acceleration field, Ann. Appl. Prob. 20 (2010) 2022-2039.
    2. N. Besse, Y. Elskens, D.F. Escande and P. Bertrand, Validity of quasilinear theory : refutations and new numerical confirmation, Plasma Phys. Control. Fusion 53 (2011) 025012.
  • Laszlo Erdoes, Universitat Muenchen
    Title: Localization length in random band matrices
    Abstract: TBA

  • Santo Fortunato, Aalto University
    Title: Characterizing and modeling citation dynamics
    Abstract: Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts for the presence of citation bursts as well.

  • Carl Franck, Cornell University
    Title: Experimentally Exploring the Limits and Consequences of Chemical Communication Between Cells
    Abstract: Statistical physicists have long enjoyed investigating the collective states that arise via interactions between molecules. Turning to unicellular microbes, we now contemplate the ``purposeful" cooperative behavior that results from the exchange of chemical messages in living matter. To begin, we will explain how our recent measurements of the sensitivity of the amoeba Dictyostelium discoideum (Dicty) to chemical gradients challenge contemporary theory based on intrinsic noise in chemical message detection. In the second part of the talk, we will argue that a familiar but unsolved problem for cell biologists, that a nutritious medium fails to ignite cell proliferation below a critical density of cells, present physicists with the chance to explore a transition to multicellular life. We will be especially focused on the experimental confirmation of the transition in dilute Dicty suspensions in the midst of biological variability.

  • Jochen Gemmer, Universitat Osnabruk
    Title: Emergence of Thermodynamcical Behavior in Closed Quantum Systems: A Small Spin System as an Example
    Abstract: "Thermodynamical behavior" implies a number of properties: Describability in terms of a few variables, approach of these variables to universal equilibrium values (relaxation), possibly an exponential form of the above relaxation, etc. Most of these properties appear to be absent in standard quantum mechanics. In order to cure this many approaches resort to some sort of bath. We deliberately try to avoid the standard notion of a bath here and look for the above properties in an isolated spin system. The considered observable is the spatial distribution of the magnetization. Key words are typicality, eigenstate thermalization hypothesis (ETH), Langevin-dynamics, etc.

  • Vojkan Jaksic, McGill University
    Title: Quantum entropic functionals, fluctuations symmetries, and Araki-Lieb-Thirring inequality
    Abstract: TBA

  • Konstantin Khanin, University of Toronto
    Title: Intermediate disorder for directed polymers
    Abstract: We discuss the scaling properties of directed polymers in the situation when inverse temperature is scaled with the size of the polymer. It turns out that in the critical case one can observe a new universal disorder regime.

  • Roberto Livi, INFN
    Title: Transport properties of the Discrete Nonlinear Schrodinger equation
    Abstract: We discuss how negative temperature metastable states may emerge in the DNLSE as a product of the spontaneous formation of nonlinear excitations (breathers). This phenomenon determines anomalous transport features that can be detected experimentally in BEC on optical lattices as well as in arrays of coupled optical fibers.

  • Natalia Komarova, University of California, Irvine
    Title: Cooperation as an engine of evolution
    Abstract: Cancer comes about by a sequence of mutations that change the cells' fitness and create advantageous phenotypes. These phenotypes displace other cells and spread, thus winning the evolutionary competition. It is possible that in order to create those advantageous mutants, several different mutations have to be accumulated in a cell, such that each individual mutation is disadvantageous, and together they comprise a fitness advantage. In the literature, this is often called "crossing a fitness valley". In this talk I will present a novel mechanism by which such fitness valleys can be crossed. It envolves the notion of cooperation among the cells, where shared benefits are received through "division of labor". I will show how in such context, cooperation can speed up the evolutionary process. Moreover, the emergence of cheaters that destroy cooperation dynamics can "unite" all mutations within one individual on a fast time scale. Paradoxically, the presence of such cheaters happens to accelerate evolution even more.

  • Mariano Lopez, University of Mexico
    Coauthors: A. Santos [1],S. B. Yuste[1] and M. Lopez de Haro*[2]
    Title: Structural properties of fluids interacting via piece-wise constant potentials with a hard core
    Abstract: The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived by using a (semi-analytical) rational-function approximation method. The results are illustrated for the cases of a square-shoulder plus square-well potential and a shifted square-well and compared both with simulation data and with those that follow from the (numerical) solutions of the Percus-Yevick integral equation.
    [1] Departamento de Fisica, Universidad de Extremadura, Badajoz 06071, Spain
    [2] Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico, Temixco, Mor. 62580, Mexico.

  • Juan Maldacena, Institute for Advanced Study
    Title: Solving a four dimensional gauge theory using integrability
    Abstract: We will review progress on exact solutions for the planar limit of the most supersymmetric version of four dimensional quantum chromodynamics. In the large N limit, this theory contains some strings. One can solve the theory on these strings by the ideas of integrability. This uses methods that have been developed to solve integrable spin chains in condensed matter, with some suitable modifications. These exact solutions smoothly interpolate between almost free gluons in four dimensions at weak coupling and strings in ten dimensions at strong coupling.

  • Robert McCann, University of Toronto
    Title: Higher-order time asymptotics of fast diffusion in Euclidean space: a dynamical systems approach
    Abstract: With Jochen Denzler (UT Knoxville) and Herbert Koch (Bonn), we quantify the speed of convergence and higher asymptotics of fast diffusion dynamics on Euclidean space to the Barenblatt (self similar) profile. The degeneracy in the parabolicity of the equation is cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution semigroup becomes differentiable with respect to Hoelder initial data on the cigar. The linearization of the dynamics is given by Laplace-Beltrami operator plus a drift term (which can be suppressed by the introduction of appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. We provide a detailed study of the linear and nonlinear problems in Hoelder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional analytic spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.

  • Clement Mouhot, University of Cambridge
    Title: A new approach to the hydrodynamic limit of interacting particle systems: the zero range process
    Abstract: TBA

  • Bruno Nachtergaele, University of California, Davis
    Title: Five generalizations of the AKLT model
    Abstract: The spin-1 antiferromagnetic quantum spin chain introduced by Affleck, Kennedy, Lieb, and Tasaki in 1987 (now known as the AKLT model) was the starting point of and continues to be the inspiration for a great number of significant advances in our understanding of quantum spin models. In this talk I will give an overview of some of these developments guided by five generalizations of the AKLT model.

  • Zohar Nussinov, Washington University in St. Louis
    Title: The detection of hidden spatial and spatio-temporal structures in complex physical systems by multi-scale clustering and some of their properties
    Abstract: TBA

  • David Pine, New York University
    Title: Colloidal lock and keys - towards self-replication
    Abstract: TBA

  • Raul Rechtman, University of Mexico
    Title: Motion of a cylinder attached to a spring subject to a flow
    Abstract: We present numerical solutions of the flow around a circular cylinder between parallel plates attached to a linear spring using the lattice Boltzmann equation. The problem was solved for a wide range of Reynolds numbers and different spring constants. We present results of the dynamics of the cylinder due to the spring and the drag force and its relation with the observed vortex shedding behind the cylinder.

  • Sriram Shastry, University of California, Santa Cruz
    Title: Quantum integrable models in finite dimensional Hilbert spaces
    Abstract: TBA

  • Robert Seiringer, McGill University
    Title: The Excitation Spectrum for Weakly Interacting Bosons
    Abstract: We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit.

  • Anneke Levelt-Sengers, NIST
    Title:Science and Technology for Development: An Initiative of the Network of Science Academies in the Americas

  • Jan Sengers, University of Maryland, College Park
    Title: Light scattering and shadowgraphy measurements of thermal nonequilibrium fluctuations in fluids
    Abstract: In the abstract of a paper, entitled Light scattering from fluids not in thermal equilibrium, published in Kinam 3A, 39 (1981), E.G.D. Cohen made the following prediction: "In a fluid not in thermal equilibrium, long-range correlations between fluctuations exist, due to mode-coupling effects, that are absent in fluids in equilibrium. Light scattering can reveal these correlations." This presentation will review the experimental evidence for the presence of these long-range fluctuations, including some very recent results demonstrating the effects of gravity and confinement on thermal nonequilibrium fluctuations.

  • Israel Michael Sigal, University of Toronto
    Title: Long distance behaviour of van der Waals forces
    Abstract: In this talk I will describe a recent work with my former student, Ioannis Anapolitanos, in which we derive long-range behaviour of van der Waals forces for an arbitrary system of neutral atoms. Discussions with Elliott Lieb played an important role in the scope of this work.

  • Avraham Soffer, Rutgers University
    Title: A model of quantum friction rigorous results
    Abstract: TBA

  • Shivaji Sondhi, Princeton University
    Title: The Statistical Mechanics of Quantum Satisfiability
    Abstract: The class QMA generalizes the idea of the class NP to quantum computers. A problem in the class QMA has a solution that is easily checked by a quantum computer and "complete" problems in this class are believed to be hard even for quantum computers. I will describe results on a random ensemble of a QMA complete problem that allow a first cut of a natural phase diagram for it as well as a striking "geometrization theorem" that suggests that almost all instances might even be a classical graph theoretic problem in disguise.

  • Eitan Tadmor, University of Maryland, College Park
    Title: Consensus and flocking in heterophily self-alignment dynamics
    Abstract: We discuss particle-based models for self-organized dynamics, with a focus on a prototype model driven by non-symmetric self-alignment. We explain the emergence of consensus and unconditional flocking when the interactions decay is sufficiently slow. When the self-alignment is compactly supported, then there are open questions regarding clustering and the emerging consensus in heterophily dynamics. These questions are linked to the connectivity of the underlying graph. The methodology carries over from particle to kinetic and hydrodynamic descriptions.

  • Giuseppe Toscani, Universita di Pavia
    Title: Fast diffusion asymptotics and Sobolev inequalities
    Abstract: Functional inequalities are often related to nonlinear evolution equations. Here we outline the relationship between Sobolev's inequality and fast diffusion equations. It is known that the di fference of the two terms in Sobolev's inequality (with optimal constant) measures a distance to the manifold of the optimal functions. We give an explicit estimate of the remainder term and establish an improved inequality, with explicit norms and fully detailed constants. Our approach is based on nonlinear evolution equations and improved entropy - entropy production estimates along the associated flow. Optimizing a relative entropy functional with respect to a scaling parameter, or handling properly second moment estimates, turns out to be the central technical issue. This is a new method in the theory of nonlinear evolution equations, which also applies to other interpolation inequalities of Gagliardo-Nirenberg-Sobolev type.

  • Jane Wang, Cornell University
    Title: How do Insects Fly and Turn
    Abstract: Insect's aerial acrobatics results from the concerted efforts of its brain, flight muscles, and flapping wings. To understand its flight, we started from the outer scale, analyzing the unsteady aerodynamics of flapping flight, and are gradually working toward the inner scale, deducing the control algorithms. We are particularly interested in seeking mechanistic explanations for their flight dynamics.
    In this talk, I will first describe the aerodynamics tricks that dragonfly employs to hover and fly efficiently. I will then describe how fruit flies recover from aerial stumbles, and how they make subtle wing movements to induce sharp turns in 40-80ms, or tens of wing beats. These work involves direction numerical simulations, reduced order models for unsteady fluid forces, and analyses of experimental data of insects in free flight.

  • Ned Wingreen, Princeton University
    Title: The role of enzyme clustering in metabolic regulation
    Abstract: Metabolism is the set of enzymatic reactions that cells use to generate energy and biomass. Interestingly, recent studies suggest that many metabolic enzymes assemble into higher-order structures, often in response to environmental conditions. Theoretically, we find that large-scale enzyme clusters, with no internal spatial ordering of enzymes, offer many of the same advantages as direct substrate channeling: accelerating intermediate processing, protecting intermediates from degradation/cross-reactions, and protecting the cell from toxic intermediates. I will discuss the requirements to realize these potential benefits of enzyme clustering, e.g. what are the necessary sizes, shapes, internal organizations, and external arrangements of functional enzyme clusters?

  • Horng-Tzer Yau, Harvard University
    Title: Random matrices and Dyson Brownian motion
    Abstract: TBA

  • Alexander Zamolodchikov, Rutgers University
    Title: On high energy scattering in Ising field theory
    Abstract: TBA

  • Robert Ziff, University of Michigan
    Title: Percolation on regular and hyperbolic lattices
    Abstract: Percolation figures in a wide variety of problems in statistical physics, including the problem of deterministic diffusion in a random environment studied by Eddie Cohen. We will discuss that work, along with several recent advances that have been made: determination of exact thresholds for large classes of lattices, finding retention in an invasion percolation problem, and studying correlations and crossing problems. Finally, recent work using the crossing idea to study percolation on hyperbolic lattices will be presented.

 

Short talks Schedule

SESSION A

A1: Vadim Tkachenko, Ben-Gurion University of the Negev, Israel
"Monodromy matrices of 1d periodic differential operators"
Abstract: We present a criterium for $4times4$-matrix to be the monodromy matrix of an ordinary periodic differential operator of order $4$

A2: Mohammad F.Maghrebi, MIT
Coauthors: Robert L. Jaffe, Mehran Kardar
"Rotating object: Non-equlibrium fluctuations in a stationary setup "
Abstract: A rotating object presents a simple case of stationary non-equilibrium. We consider the electromagnetic couplings of a dielectric rotating body to the surrounding vacuum. We find that even at zero temperature, where fluctuations are purely of quantum origin, the object radiates energy to the environment. This phenomenon can be interpreted as rotational friction of vacuum.

A3: Vladyslav Golyk, MIT
Coauthors: Matthias Kruger, Alexander McCauley, Mehran Kardar
"Radiative heat transfer between closely spaced objects"
Abstract: The near-field radiative heat transfer is most significant at small separations. We develop a gradient expansion which allows to compute the near-field radiative heat transfer between closely spaced, gently curved objects. Applying this method to the sphere-plate geometry, enables accurate calculation of the heat transfer up to separations $dleq R/100$, where $R$ is the sphere's radius.

A4: Scott Hottovy, University of Arizona Program in Applied Mathematics
Coauthors: Scott Hottovy*, Giovanni Volpe, and Jan Wehr "
"Thermophoresis of Brownian particles driven by colored noise
Abstract:A mesoscopic Brownian particle diffusing in a temperature gradient is driven by collisions with molecules of the surrounding fluid. The noise associated with these collisions is colored because of hydrodynamic memory. I will give a possible model for the particle's motion in the form of a system of stochastic differential equations. When the time correlation of the colored noise and the relaxation time of the particle are of the same order the effective approximating SDE, in the limit as these two time scales go to zero, involves a drift term that changes magnitude and sign, depending on the particle's mass, so that heavier particles move from colder places to hotter. I will discuss the interpretation and shortcomings of this model in relation to the physical process.

A5: Jeff Chen, University of Waterloo
"What can we learn from theoretical modeling of a membrane-interacting polymer?"
Abstract: Models of self-avoiding polymer chains and fluctuating two-dimensional surfaces have been widely used to provide fundamental understanding of the physical properties of a large variety of synthetic and biological systems. We discuss the structure of systems consisting of a polymer that interacts with a membrane surface, either by simple confinement or an attraction. We show that a number of characteristically different phases exist depending on the phenomenological parameters in the Helfrich model describing membrane properties as well as other basic parameters that describe polymer properties. Results were obtained from Monte Carlo simulations of the systems.  

A6: Dan Pirjol, IFIN, Bucharest
"Equivalence of interest rate models and lattice gases"
Abstract: We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure. These models include the Black, Derman, Toy and Black, Karasinski models in the terminal measure. It is shown that such interest rate models are equivalent with lattice gases with attractive two-body interactions, and are similar with a lattice gas model considered by Kac and Helfand. An explicit solution for the model is given as a sum over the lattice gas states, and is used to show that the model has a phase transition under changes in volatility.

A7: Etienne Bernard, MIT Coauthors: Etienne Bernard*, Werner Krauth
"The hard-disk melting transition"
Abstract: Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte Carlo algorithm [1] allows us to thermalize systems large enough to access the thermodynamic regime. I will show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order [2]. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.

  1. Bernard, E. P.; Krauth, W. & Wilson, D. B. Phys. Rev. E., 2009, 80, 056704
  2. Bernard, E. P. & Krauth, W. Phys. Rev. Lett., 2011, 107, 155704

A8: Matthias Kruger, MIT
Coauthors: J.M. Brader
"Sedimentation of colloidal particles under shear"
Abstract: Using a novel density functional theory, we study the effects of shear on dense colloidal suspensions. We find that a colloidal sediment is lifted (resuspended) under the application of shear, i.e., the height of the center of mass of the sediment increases. Under oscillatory shear, the center of mass motion resembles a driven damped oscillator and I will discuss the limits of small and large frequencies.

A9: Michael Kiessling, Rutgers University
"The Hartree limit for Born's statistical ensemble of the ground state of a bosonic atom"
Abstract: I report on a novel approach to the limit of infinitely many bosonic electrons bound to an infinitely massive nucleus in their atomic ground state. In this limit the ground state is governed by the Hartree theory. The strategy is to analyze Born's statistical ensemble with techniques developed originally for the classical configurational canonical ensemble, except that the Fischer information functional now plays the role of (the negative of) the Gibbs entropy. Besides establishing all the pertinent aspects of Hartree theory (factorization of the ground state wave function; the Hartree variational principle; existence and uniqueness of the minimizer), the method yields a law of large numbers for the particles. As a byproduct it is also shown that the minimal nuclear charge per electron required to bind N bosonic electrons grows monotonically with N.


SESSION B

B1: Sunchul Ji, Rutgers University
"The Cell Force, a 7-Dimensional Force Driving Goal-Directed Motions in the Living Cell"
Abstract: In analogy to the strong force invoked by physicists in the 1970's to account for the structural stability of atomic nuclei that harbor mutually repulsing protons, I was led to invoke the cell force to account for the stability of the goal-directed motions catalyzed by enzymes inside the living cell that are subject to randomizing effects of thermal motions [1, 2]. The cell force is postulated to be 7-dimensional [1, 2], since its complete characterization requires specifying its action not only in the geometric space (x, y, z) and time (t) but also in the information space, Iijk, where the i, j, and k axes encode the amount, meaning, and value, respectively, of information I. The first experimental evidence for the cell force concept was provided by the transcript level (TL) and transcription rate (TR) data measured with DNA microarrays from budding yeast undergoing the glucose-galactose shift [3]. These data can be displayed as clusters of points in a 6-dimensional TL or TR space, and the distances between all possible pairs of the points in either the TL or the TR space are calculated. When these distances are transformed into histograms by dividing them into a set of 30-50 distance classes (or bins) and counting the frequencies of occurrences in each distance class, the resulting distributions were found to fit the so-called "blackbody radiation-like equation" (BRE), y = (a/(Ax + B)5)/(eb/(Ax + B) - 1), where y is the frequency and x is the distance (or rate) class, and a, b, A and B are constants. Evidently BRE is of the same mathematical form as the blackbody radiation equation discovered by Planck in 1900. In addition, BRE was found also to fit the single-molecule enzymological data of cholesterol oxidase measured by Lu eta l. [4] and the protein stability data reported in [Dill et al., 2011]. All these processes (i.e., blackbody radiation, single-molecule enzymology, transcription, transcript level control, and protein stability) obeying BRE have one property in common - they implicate o r depend on thermal excitations of ground-state particles to higher energy levels. When the logarithms of the numerical values of a and b associated with different processes were plotted, two distinct trajectories were found - one passing through the processes occurring outside the cell and the other passing through the processes occurring inside the cell. It was therefore suggested in [2] that the first trajectory reflects the electromagnetic force and the second trajectory the cell force.
References:

  1. Ji, S. (1991). Biocybernetics: A Machine Theory of Biology, in Molecular Theories of Cell Life and Death, S. Ji (ed.), Rutgers University Press, New Brunswick, pp. 95-118.
  2. Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications. Springer, New York. Section 12.13.
  3. Garcia-Martinez, J., Aranda, A. and Perez-Ortin, J. E. (2004). Genomic Run-On Evaluates Transcription Rates for all Yeast Genes and Identifies Gene Regulatory Mechanisms, Mol Cell 15, 303-313.
  4. Lu, H. P., Xun, L. and Xie, X. S. (1998). Single-Molecule Enzymatic Dynamics, Science 282, 1877-1882
  5. Dill, K. A., Ghosh, K., and Schmit, J. D. (2011). Physical limits of cells and proteomes, Proc. Nat. Acad. Sci. USA 108 (44), 17876-17882.

B2: Shivani Patel, Rutgers University
Coauthors: Karl Carmona and Sungchul Ji
"Mechanism-Based Mutual Information Captures Metabolic Pathway-Specific Responses of Budding Yeast Toward Nutritional and Temperature Stresses"
Abstract: Using DNA microarrays, Garcia-Martinez et al. [1] and Castells-Roca et al. [2] measured transcript levels (TLs) and transcription rates (TRs) simultaneously from budding yeast at 6 time points after applying nutritional stress (i.e., glucose ? galactose) or temperature stress ( i.e., 25 ? 37° C). When the TR and TL values of an RNA molecule are plotted, a 'phase diagram' is obtained consisting of 5 vectors, each spanning one of the 5 time intervals defined by the 6 time points of measurement. The angles of these vectors reflect the mechanisms (of which there are 9) of interaction between the transcription and transcript degradation steps of an RNA molecule. If a metabolic pathway consists of n RNAs, there will be 5n so-called 'mechanism numbers' ranging from 1 to 9. By counting the frequency of each of these numbers that appear in the n phase diagrams belonging to a given pathway, it is possible to construct a histogram for that pathway consisting of 9 columns, each representing the probability of activating one of the 9 mechanisms in the pathway during the entire experimental period. Based on these histograms, Shannon entropy, H, and mutual information, MI, can be calculated : H(A) = -Sum (pi(A)log2 Pi(A)), where pi(A) is the probability of the ith mechanism being activated in Pathway A, and MI(A,B) = Sum (pi(A,B) log2[(pi(A, B)/pi(A) x pi(b)], where pi(A, B) is the joint probability of the ith mechanism being activated in both Pathways A and B, the index i running from 1 to 9. We studied the Shannon entropies of 10 pathways (including ATP synthesis, glycolysis, and oxidative phosphorylation) and the mutual information values between all possible pairs among the 10 pathways. Each pathway generates one H value and 9 MI values and the average of the latter has been interpreted as reflecting the average tendency of a pathway to couple with other pathways through one or more of the 9 possible mechanisms. The H and MI values were calculated before and after replacing the o riginal sets of RNA molecules belonging to the 10 pathways with the equally sized sets of randomly chosen RNAs in order to determine if the H and MI values are pathway-specific. A statistical analysis of the resulting H and MI values indicates (i) that Shannon entropies of the 10 pathways are similar with values around H = 2.5 and are unaffected by stresses nor by randomization of RNAs and (ii) that the MI values of all of the 10 the pathways increased upon randomization under the nutritional stress but not under temperature stress. These results indicate that the coupling patterns among metabolic pathways in yeast reorganize themselves in pathway-specific manner when stressed nutritionally but not by changing temperature. [1] Garcia-Martinez, J., Aranda, A., and Perez-Ortin, J. E. (2004). Genomic Run-On Evaluates Transcription Rates for All Yeast Genes and Identifies Gene Regulatory Mechanisms. Molecular Cell 15(2):303-313. [2] Castells-Roca L, García-Martínez J, Moreno J, Herrero E, Bellí G, et al. (2011). Heat Shock Response in Yeast Involves Changes in Both Transcription Rates and mRNA Stabilities. PLoS ONE 6(2): e17272. doi:10.1371/journal.pone.0017272

B3: Weronika Szafran, Rutgers University
Coauthor: Sungchul Ji
"Identifying Human Breast Cancer-Associated mRNA Molecules using DNA Microarrays"
Abstract: Using DNA microarrays, Perou et al. [Nature 406:747-52(2000)] measured the RNA levels of 8,102 genes in human breast cancer tissues obtained from 20 patients before and after treating with the anti-cancer drug, doxorubicin, for 16 weeks. From these data, we analyzed the RNA levels of 4,740 genes that showed at least one-fold (i.e., 100%) changes due to breast tumor (T) or to the treatment with the anti-cancer drug (D), doxorubicin. From each patient, two groups of data were obtained the ?T group and ?D group, depending on whether the RNA changes are due to tumor or due to drug treatment, respectively. Since ?T and ?D can be +, 0 or -, the RNA changes measured from a given patient can be divided into 9 classes defined thus: Type 1 (?T > 0, ?D = 0), Type 2 (?T > 0, ?D >0), Type 3 (?T = 0, ?D >0), Type 4 (?T 0), Type 5 (?T 0, ?D =0), Tye 6 (?T 0, ?D 0), Typ 7 (? = 0, ?D 0, ?D 0), andType 9 (?T = 0, ?D =0). The RNA molecules showing Type 4 or Type 8 changes are of special interest because the concentrations of these molecules are altered by tumor at least 100% relative to control which are reversed by doxorubicin treatment. Such RNA molecules are referred to as "responders". In contrast, the RNA molecules exhibiting Type 2 or Type 6 behaviors are of interest for toxicological reasons, because the concentrations of these RNA molecules are altered by both tumor and the drug in the same direction, thus most likely showing drug toxicity. Such RNA molecules are referred to as "non-responders". We found 76 RNA molecules (out of 4,740) that are responders and 19 that are non-responders in at least 10 of the 20 patients. We found no RNA molecules that behaved as either responders or non-responders in all of the 20 patients. Also it was relatively easy to find how a particular RNA molecule is beneficially affected by drug therapy in some patients wh ile adversely affected in other patients. In the future, the method described here may turn out to be very useful in personalized medicine, because it can provide information as to which patients specifically will benefit from doxorubicin treatment and which RNA molecules (and their associated structural and regulatory genes) can serve as potential targets for discovering new chemotherapeutic agents.

B4: John Barton, Rutgers University
Coauthors: Joel Lebowitz, Eugene Speer, Remi Monasson, Simona Cocco
"Progress on algorithms for solving the inverse Ising problem"
Abstract: I summarize progress in the development of the Cocco-Monasson adaptive cluster algorithm for solving the inverse Ising problem. Technical and algorithmic improvements have resulted in significant increases in speed. This algorithm has been successfully applied to correlation data from large (> 100 sites) networks of real neurons, inferring an Ising model which accurately reproduces the observed correlations.

B5: Venkateshan Kannan, Rutgers University
"Temperature profile and current characteristcs of one-dimensional harmonic alternating mass chains"
Abstract: We analyze the non-equilibrium steady states (NESS) of a one dimensional harmonic chain of $N$ atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile oscillates with period two in the bulk of the system. Depending on boundary conditions, either the heavier or the lighter particles in the bulk are hotter. We obtain exact expressions for the bulk temperature profile and steady state current in the limit $N rightarrow infty$. These depend on whether $N$ is odd or even. We explain this behavior of the system by showing that the contribution to the temperature at a particular site from each of the normal modes of oscillation depends on whether the site is even or odd.

B6: Eunghyun Lee, University of Helsinki
"The current distribution of the multihopping asymmetric diffusion model"
Abstract: We study the multihopping asymmetric diffusion model (MADM) with finite number of particles on Z. We find the transition probability and the current distribution of the model using the Bethe ansatz. The equivalence between the MADM and the two-sided PushASEP is confirmed from their transition probabilities.

B7: Ramis Movassagh, MIT
Coauthors: S. Bravyi, Libor Caha, D. Nagaj, P. W. Shor
"Criticality without frustration for quantum spin-1 chains"
Abstract: Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s? We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n.

B8: Maria Infusino, University of Reading
Coauthors: M. Infusino* and A. Volcic
"Uniform distribution on fractals"
Abstract: The interest for uniformly distributed (u.d.) sequences of points arises from various applications, mostly in the field of quasi-Monte Carlo integration methods. In this work, we introduce a general algorithm to explicitly construct new classes of u.d. sequences of points and of partitions on fractals generated by an IFS consisting of similarities which have the same ratio and which satisfy the open set condition (OSC).

B9: Tobias Kuna, University of Reading
Coauthors: V. Lucarini, T. Kuna*, J. Wouters and D. Faranda
"Sampling schemes of response in light of Ruelle's linear response theory"
Abstract: We study (numerical) sampling schemes to compute the linear response to a perturbation for dynamical systems. We demonstrate that one can use Ruelle's linear response theory to obtain a priori information of the behavior of different schemes.

PRESENTATIONS OF TALKS GIVEN AT THE 107th STATISTICAL MECHANICS CONFERENCE