arXiv subjects

Jeremy L. England

Publications and source records attributed to Jeremy L. England.

14 recordsLinked to original sources

arXiv2021

Learning about learning by many-body systems

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems' learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

cond-mat.stat-mech↗

arXiv2021

GNisi: A graph network for reconstructing Ising models from multivariate binarized data

Ising models are a simple generative approach to describing interacting binary variables. They have proven useful in a number of biological settings because they enable one to represent observed many-body correlations as the separable consequence of many direct, pairwise statistical interactions. The inference of Ising models from data can be computationally very challenging and often one must be satisfied with numerical approximations or limited precision. In this paper we present a novel method for the determination of Ising parameters from data, called GNisi, which uses a Graph Neural network trained on known Ising models in order to construct the parameters for unseen data. We show that GNisi is more accurate than the existing state of the art software, and we illustrate our method by applying GNisi to gene expression data.

cs.LG↗

arXiv2021

Low rattling: A predictive principle for self-organization in active collectives

Self-organization is frequently observed in active collectives, from ant rafts to molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random, while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally in shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing towards future approaches for design and control of active particle mixtures and metamaterials.

cond-mat.stat-mech↗

arXiv2020

Quantifying many-body learning far from equilibrium with representation learning

Far-from-equilibrium many-body systems, from soap bubbles to suspensions to polymers, learn the drives that push them. This learning has been observed via thermodynamic properties, such as work absorption and strain. We move beyond these macroscopic properties that were first defined for equilibrium contexts: We quantify statistical mechanical learning with machine learning. Our toolkit relies on a structural parallel that we identify between far-from-equilibrium statistical mechanics and representation learning, which is undergone by neural networks that contain bottlenecks, including variational autoencoders. We train a variational autoencoder, via unsupervised learning, on configurations assumed by a many-body system during strong driving. We analyze the neural network's bottleneck to measure the many-body system's classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures, more reliably and more precisely identifying and quantifying learning by matter.

cond-mat.stat-mech↗

arXiv2019

Self-organized novelty detection in driven spin glasses

We consider a glassy system of interacting spins driven by continual switching amongst a finite set of nonuniform external fields. We find that the system evolves over time towards configurations that minimize the work absorbed from this external drive. The configurations which achieve this are specific to the details of the external fields used to drive the system, and therefore act effectively as a self-organized novelty-detector that embodies accurate predictions about the typical future of its external environment.

nlin.AO↗

arXiv2019

Drive-specific adaptation in disordered mechanical networks of bistable springs

Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external driving, which can alter the relative stability of different attractors. Under such circumstances, one may ask whether any clear relationship holds between the specific pattern of external driving and the particular attractor states selected by a driven multistable system. To gain insight into this question, we numerically study driven disordered mechanical networks of bistable springs which possess a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We find that the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low work absorption from it. Furthermore, we find that these drive-specific attractor states are even more stable than expected for a given level of work absorption. Our results suggest that the driven exploration of the vast configuration space of these systems is biased towards states with exceptional relationship to the driving environment, and could therefore be used to `discover' states with desired response properties in systems with a vast landscape of diverse configurations.

nlin.AO↗

arXiv2018

Design of conditions for emergence of self-replicators

A self-replicator is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nano-scale self-replicators has attracted keen interest in recent years, both because exponential amplification is an attractive method for generating high yields of specific products, and also because self-reproducing entities have the potential to be optimized or adapted through rounds of iterative selection. Substantial steps forward have been achieved both in the engineering of particular self-replicating molecules, and also in characterizing the physical basis for possible mechanisms of self-replication. At present, however, there is need for a theoretical treatment of what physical conditions are most conducive to the emergence of novel self-replicating structures from a reservoir of building blocks on a desired time-scale. Here we report progress in addressing this need. By analyzing the dynamics of a generic class of heterogeneous particle mixtures whose reaction rates emerge from basic physical interactions, we demonstrate that the spontaneous discovery of self-replication is controlled by relatively generic features of the chemical space, namely: the dispersion in the distribution of reaction timescales and bound-state energies. Based on this analysis, we provide quantitative criteria that may aid experimentalists in designing a system capable of producing self-replicators, and in estimating the likely timescale for exponential growth to start.

cond-mat.soft↗

arXiv2017

Information-theoretic bound on the entropy production to maintain a classical nonequilibrium distribution using ancillary control

There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium.

cond-mat.stat-mech↗

arXiv2017

Minimum energetic cost to maintain a target nonequilibrium state

In the absence of external driving, a system exposed to thermal fluctuations will relax to equilibrium. However, the constant input of work makes it possible to counteract this relaxation, and maintain the system in a nonequilibrium steady state. In this Article, we use the stochastic thermodynamics of Markov jump processes to compute the minimum rate at which energy must be supplied and dissipated to maintain an arbitrary nonequilibrium distribution in a given energy landscape. This lower bound depends on two factors: the undriven probability current in the equilibrium state, and the distance from thermal equilibrium of the target distribution. By showing the consequences of this result in a few simple examples, we suggest general implications for the required energetic costs of macromolecular repair and cytosolic protein localization.

cond-mat.stat-mech↗

arXiv2012

Statistical Physics of Self-Replication

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.

physics.bio-ph↗

arXiv2008

Potential for modulation of the hydrophobic effect inside chaperonins

Despite the spontaneity of some in vitro protein folding reactions, native folding in vivo often requires the participation of barrel-shaped multimeric complexes known as chaperonins. Although it has long been known that chaperonin substrates fold upon sequestration inside the chaperonin barrel, the precise mechanism by which confinement within this space facilitates folding remains unknown. In this study, we examine the possibility that the chaperonin mediates a favorable reorganization of the solvent for the folding reaction. We begin by discussing the effect of electrostatic charge on solvent-mediated hydrophobic forces in an aqueous environment. Based on these initial physical arguments, we construct a simple, phenomenological theory for the thermodynamics of density and hydrogen bond order fluctuations in liquid water. Within the framework of this model, we investigate the effect of confinement within a chaperonin-like cavity on the configurational free energy of water by calculating solvent free energies for cavities corresponding to the different conformational states in the ATP- driven catalytic cycle of the prokaryotic chaperonin GroEL. Our findings suggest that one function of chaperonins may be to trap unfolded proteins and subsequently expose them to a micro-environment in which the hydrophobic effect, a crucial thermodynamic driving force for folding, is enhanced.

q-bio.BM↗

arXiv2005

Morphogen Gradient from a Noisy Source

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.

q-bio.TO↗

arXiv2004

An Exact Model of Fluctuations in Gene Expression

Fluctuations in the measured mRNA levels of unperturbed cells under fixed conditions have often been viewed as an impediment to the extraction of information from expression profiles. Here, we argue that such expression fluctuations should themselves be studied as a source of valuable information about the underlying dynamics of genetic networks. By analyzing microarray data taken from Saccharomyces cerevisiae, we demonstrate that correlations in expression fluctuations have a highly statistically significant dependence on gene function, and furthermore exhibit a remarkable scale-free network structure. We therefore present what we view to be the simplest phenomenological model of a genetic network which can account for the presence of biological information in transcript level fluctuations. We proceed to exactly solve this model using a path integral technique and derive several quantitative predictions. Finally, we propose several experiments by which these predictions might be rigorously tested.

q-bio.MN↗

arXiv2003

Structural Determinant of Protein Designability

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.

cond-mat.soft↗