arXiv subjects

Erik Aurell

Publications and source records attributed to Erik Aurell.

At least 55 records · Page 3Linked to original sources

arXiv2018

Exploring the diluted ferromagnetic p-spin model with a Cavity Master Equation

We introduce a new solution to Glauber multi-spin dynamics on random graphs. The solution is based on the recently introduced Cavity Master Equation (CME), a time-closure turning the in principle exact Dynamic Cavity Method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one Monte Carlo run on the same problem. We show that CME correctly models the ferromagnetic $p$-spin Glauber dynamics from high temperatures down to and below the spinoidal transition. We also show that CME allows a novel exploration of the low-temperature spin-glass phase of the model.

cond-mat.dis-nn↗

arXiv2018

A unified picture of strong coupling stochastic thermodynamics and time reversals

Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the log-ratio of forward and backward system path probabilities, is in one-to-one relation with the log-ratios of joint initial conditions of the system and the bath. A version of strong-coupling statistical thermodynamics where the system-bath interaction vanishes at the beginning and the end of a process is, as is also weak-coupling stochastic thermodynamics, related the bath initially in equilibrium by itself. The heat is then the change of bath energy over the process. It is discussed when this heat is a functional of system history alone. The version of strong-coupling statistical thermodynamics introduced by Seifert and Jarzynski is related to the bath initially in conditional equilibrium with respect to the system. This leads to heat as another functional of system history which needs to be determined by thermodynamic integration. The log-ratio of forward and backward system path probabilities in a stochastic process is finally related to log-ratios of initial conditions of a combined system and bath. It is shown that the entropy production formulas of stochastic processes under general class of time reversals are given by change of a bath energy in a larger underlying Hamiltonian system. The paper highlights the centrality of time reversal in stochastic thermodynamics, also in the case of strong coupling.

cond-mat.stat-mech↗

arXiv2017

Correlation-Compressed Direct Coupling Analysis

Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The corresponding inference problems are challenging since the normalization constant (partition function) of the Ising/Potts distributions cannot be computed efficiently on large instances. Different ways to address this issue have hence given size to a substantial methodological literature. In this paper we investigate how these methods could be used on much larger datasets than studied previously. We focus on a central aspect, that in practice these inference problems are almost always severely under-sampled, and the operational result is almost always a small set of leading (largest) predictions. We therefore explore an approach where the data is pre-filtered based on empirical correlations, which can be computed directly even for very large problems. Inference is only used on the much smaller instance in a subsequent step of the analysis. We show that in several relevant model classes such a combined approach gives results of almost the same quality as the computationally much more demanding inference on the whole dataset. We also show that results on whole-genome epistatic couplings that were obtained in a recent computation-intensive study can be retrieved by the new approach. The method of this paper hence opens up the possibility to learn parameters describing pair-wise dependencies in whole genomes in a computationally feasible and expedient manner.

physics.bio-ph↗

arXiv2017

Steady diffusion in a drift field: a comparison of large deviation techniques and multiple-scale analysis

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while the effective diffusion has two terms. One is of the equilibrium type and satisfies an Einstein relation with the effective mobility while the other is quadratic in the applied force. In this contribution we present two new methods to obtain these results, on the one hand using large deviation techniques, and on the other by a multiple-scale analysis, and compare the two. We consider both systems with discrete internal states and continuous internal states. We show that the auxiliary equations in the multiple-scale analysis can also be derived in second-order perturbation theory in a large deviation theory of a generating function (discrete internal states) or generating functional (continuous internal states). We discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state.

cond-mat.stat-mech↗

arXiv2017

On work and heat in time-dependent strong coupling

This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers-Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly the force has delta-function support at the initial and final time, an effect that has been observed previously. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly they only give a finite contribution to the work that enter in Jarzynski's equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell \& Eichhorn, 2015).

cond-mat.stat-mech↗

arXiv2017

Statistical properties of interaction parameter estimates in direct coupling analysis

We consider the statistical properties of interaction parameter estimates obtained by the direct coupling analysis (DCA) approach to learning interactions from large data sets. Assuming that the data are generated from a random background distribution, we determine the distribution of inferred interactions. Two inference methods are considered: the L2 regularized naive mean-field inference procedure (regularized least squares, RLS), and the pseudo-likelihood maximization (plmDCA). For RLS we also study a model where the data matrix elements are real numbers, identically and independently generated from a Gaussian distribution; in this setting we analytically find that the distribution of the inferred interactions is Gaussian. For data of Boolean type, more realistic in practice, the inferred interactions do not generally follow a Gaussian. However, extensive numerical simulations indicate that their distribution can be characterized by a single function determined by a few system parameters after normalization by the standard deviation. This property holds for both RLS and plmDCA and may be exploitable for inferring the distribution of extremely large interactions from simulations for smaller system sizes.

physics.data-an↗

arXiv2016

On one-step replica symmetry breaking in the Edwards-Anderson spin glass model

We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a Generalized Belief Propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter $y$, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to Bethe approximation case for tree-like graphs, where it has been shown that 1RSB Belief Propagation equations admit a Survey Propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of Generalized Survey Propagation equations for the single instance graph case.

cond-mat.dis-nn↗

arXiv2016

A Cavity Master Equation for the continuous time dynamics of discrete spins models

We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean field ferromagnet and the dynamics of the one dimensional Ising system. We then present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the Random Field Ising model, and the Viana-Bray spin-glass model.

cond-mat.dis-nn↗

arXiv2016

An observation of circular RNAs in bacterial RNA-seq data

Circular RNAs (circRNAs) are a class of RNA with an important role in micro RNA (miRNA) regulation recently discovered in Human and various other eukaryotes as well as in archaea. Here, we have analyzed RNA-seq data obtained from {\it Enterococcus faecalis} and {\it Escherichia coli} in a way similar to previous studies performed on eukaryotes. We report observations of circRNAs in RNA-seq data that are reproducible across multiple experiments performed with different protocols or growth conditions.

q-bio.GN↗

arXiv2016

Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry

We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multi-scale analysis. As an example we consider coupled diffusions in $3$-dimensional space and on the group manifold $SO(3)$ of proper rotations, generalizing results obtained by H. Brenner (1981). We show in detail how the analysis can be conveniently be carried out using local charts and invariance arguments. As a further example we consider coupled diffusions in $2$-dimensional complex space and on the group manifold $SU(2)$. We show that although the local operators may be the same as for $SO(3)$, due to the global nature of the solvability conditions the resulting diffusion will be different, and generally more isotropic.

cond-mat.stat-mech↗

arXiv2016

Diffusion of a Brownian ellipsoid in a force field

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

cond-mat.stat-mech↗

arXiv2016

Entropy production of a Brownian ellipsoid in the overdamped limit

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

cond-mat.stat-mech↗

arXiv2015

Causal analysis, Correlation-Response and Dynamic cavity

The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non- equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.

cond-mat.stat-mech↗

arXiv2015

The Bulk and The Tail of Minimal Absent Words in Genome Sequences

Minimal absent words (MAW) of a genomic sequence are subsequences that are absent themselves but the subwords of which are all present in the sequence. The characteristic distribution of genomic MAWs as a function of their length has been observed to be qualitatively similar for all living organisms, the bulk being rather short, and only relatively few being long. It has been an open issue whether the reason behind this phenomenon is statistical or reflects a biological mechanism, and what biological information is contained in absent words. In this work we demonstrate that the bulk can be described by a probabilistic model of sampling words from random sequences, while the tail of long MAWs is of biological origin. We introduce the novel concept of a core of a minimal absent word, which are sequences present in the genome and closest to a given MAW. We show that in bacteria and yeast the cores of the longest MAWs, which exist in two or more copies, are located in highly conserved regions the most prominent example being ribosomal RNAs (rRNAs). We also show that while the distribution of the cores of long MAWs is roughly uniform over these genomes on a coarse-grained level, on a more detailed level it is strongly enhanced in 3' untranslated regions (UTRs) and, to a lesser extent, also in 5' UTRs. This indicates that MAWs and associated MAW cores correspond to fine-tuned evolutionary relationships, and suggest that they can be more widely used as markers for genomic complexity.

q-bio.GN↗

arXiv2015

Dynamic message-passing approach for kinetic spin models with reversible dynamics

A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally tree-like topology is presented. The method builds on $(a)$ a graph expansion to eliminate loops from the normalizations of each step in the dynamics, and $(b)$ an assumption that a set of auxilary probability distributions on histories of pairs of spins mainly have dependencies that are local in time. The closure is then effectuated by projecting these probability distributions on $n$-step Markov processes. The method is shown in detail on the level of ordinary Markov processes ($n=1$), and outlined for higher-order approximations ($n>1$). Numerical validations of the technique are provided for the reconstruction of the transient and equilibrium dynamics of the kinetic Ising model on a random graph with arbitrary connectivity symmetry.

cond-mat.dis-nn↗

arXiv2015

Time reversals of irreversible quantum maps

We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability to observe a transition between two states under the forward and the time reversed dynamics, and leads, as in the classical case, to fluctuation relations as tautological identities. As in classical dynamics in contact with a heat bath, time reversal is not unique, and we discuss several possibilities. For any bistochastic map its dual map preserves the trace and describes a legitimate dynamics reversed in time, in that case the entropy production in the environment vanishes. For a generic stochastic map we construct a simple quantum operation which can be interpreted as a time reversal. For instance, the decaying channel, which sends the excited state into the ground state with a certain probability, can be reversed into the channel transforming the ground state into the excited state with the same probability.

quant-ph↗

arXiv2014

On the von Neumann entropy of a bath linearly coupled to a driven quantum system

The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman-Vernon theory. In the classical limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of $k_BT$, the second another functional with no analogue in stochastic thermodynamics, and the third is a boundary term.

cond-mat.stat-mech↗

arXiv2014

Whole genome mapping of 5' RNA ends in bacteria by tagged sequencing : A comprehensive view in Enterococcus faecalis

Enterococcus faecalis is the third cause of nosocomial infections. To obtain the first comprehensive view of transcriptional organizations in this bacterium, we used a modified RNA-seq approach enabling to discriminate primary from processed 5'RNA ends. We also validated our approach by confirming known features in Escherichia coli. We mapped 559 transcription start sites and 352 processing sites in E. faecalis. A blind motif search retrieved canonical features of SigA- and SigN-dependent promoters preceding TSSs mapped. We discovered 95 novel putative regulatory RNAs, small- and antisense RNAs, and 72 transcriptional antisense organisations. Presented data constitute a significant insight into bacterial RNA landscapes and a step towards the inference of regulatory processes at transcriptional and post-transcriptional levels in a comprehensive manner.

q-bio.GN↗