arXiv subjects

Erik Aurell

Publications and source records attributed to Erik Aurell.

At least 73 records · Page 4Linked to original sources

arXiv2014

SEK: Sparsity exploiting $k$-mer-based estimation of bacterial community composition

Motivation: Estimation of bacterial community composition from a high-throughput sequenced sample is an important task in metagenomics applications. Since the sample sequence data typically harbors reads of variable lengths and different levels of biological and technical noise, accurate statistical analysis of such data is challenging. Currently popular estimation methods are typically very time consuming in a desktop computing environment. Results: Using sparsity enforcing methods from the general sparse signal processing field (such as compressed sensing), we derive a solution to the community composition estimation problem by a simultaneous assignment of all sample reads to a pre-processed reference database. A general statistical model based on kernel density estimation techniques is introduced for the assignment task and the model solution is obtained using convex optimization tools. Further, we design a greedy algorithm solution for a fast solution. Our approach offers a reasonably fast community composition estimation method which is shown to be more robust to input data variation than a recently introduced related method. Availability: A platform-independent Matlab implementation of the method is freely available at http://www.ee.kth.se/ctsoftware; source code that does not require access to Matlab is currently being tested and will be made available later through the above website.

q-bio.GN↗

arXiv2014

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a mean flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which results from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are carried out in the multi-time formalism and in the advection-dissipation limit where the Stokes number (St) of the flow tends to zero and the Peclet number (Pe) diverges but the combination St times Pe remains constant.

cond-mat.stat-mech↗

arXiv2014

Improving contact prediction along three dimensions

Correlation patterns in multiple sequence alignments of homologous proteins can be exploited to infer information on the three-dimensional structure of their members. The typical pipeline to address this task, which we in this paper refer to as the three dimensions of contact prediction, is to: (i) filter and align the raw sequence data representing the evolutionarily related proteins; (ii) choose a predictive model to describe a sequence alignment; (iii) infer the model parameters and interpret them in terms of structural properties, such as an accurate contact map. We show here that all three dimensions are important for overall prediction success. In particular, we show that it is possible to improve significantly along the second dimension by going beyond the pair-wise Potts models from statistical physics, which have hitherto been the focus of the field. These (simple) extensions are motivated by multiple sequence alignments often containing long stretches of gaps which, as a data feature, would be rather untypical for independent samples drawn from a Potts model. Using a large test set of proteins we show that the combined improvements along the three dimensions are as large as any reported to date.

q-bio.BM↗

arXiv2014

Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences

Direct-Coupling Analysis is a group of methods to harvest information about coevolving residues in a protein family by learning a generative model in an exponential family from data. In protein families of realistic size, this learning can only be done approximately, and there is a trade-off between inference precision and computational speed. We here show that an earlier introduced $l_2$-regularized pseudolikelihood maximization method called plmDCA can be modified as to be easily parallelizable, as well as inherently faster on a single processor, at negligible difference in accuracy. We test the new incarnation of the method on 148 protein families from the Protein Families database (PFAM), one of the largest tests of this class of algorithms to date.

q-bio.QM↗

arXiv2014

Perturbative large deviation analysis of non-equilibrium dynamics

Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not known in closed form. We consider the problem of constructing successive approximations to an (unknown) large deviation functional and show that the non-equilibrium probability distribution the takes a Gibbs-Boltzmann form with a set of auxiliary (non-physical) energy functions. The expectation values of these auxiliary energy functions and their conjugate quantities satisfy a closed system of equations which can imply a considerable reduction of dimensionality of the dynamics. We show that the accuracy of the approximations can be tested self-consistently without solving the full non- equilibrium equations. We test the general procedure on the simple model problem of a relaxing 1D Ising chain.

cond-mat.stat-mech↗

arXiv2013

A novel local search based on variable-focusing for random K-SAT

We introduce a new local search algorithm for satisfiability problems. Usual approaches focus uniformly on unsatisfied clauses. The new method works by picking uniformly random variables in unsatisfied clauses. A Variable-based Focused Metropolis Search (V-FMS) is then applied to random 3-SAT. We show that it is quite comparable in performance to the clause-based FMS. Consequences for algorithmic design are discussed.

cs.AI↗

arXiv2013

Lognormality and oscillations in the coverage of high-throughput transcriptomic data towards gene ends

High-throughput transcriptomics experiments have reached the stage where the count of the number of reads alignable to a given position can be treated as an almost-continuous signal. This allows to ask questions of biophysical/biotechnical nature, but which may still have biological implications. Here we show that when sequencing RNA fragments from one end, as it is the case on most platforms, an oscillation in the read count is observed at the other end. We further show that these oscillations can be well described by Kolmogorov's 1941 broken stick model. We investigate how the model can be used to improve predictions of gene ends (3' transcript ends) but conclude that with present data the improvement is only marginal. The results highlight subtle effects in high-throughput transcriptomics experiments which do not have a biological origin, but which may still be used to obtain biological information.

q-bio.GN↗

arXiv2013

Maximum likelihood reconstruction for Ising models with asynchronous updates

We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases, one in which we know both the spin history and the update times and one in which we only know the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.

physics.data-an↗

arXiv2013

Optimal stochastic transport in inhomogeneous thermal environments

We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it has been recently shown that a space dependent temperature breaks the time reversal symmetry of the fast velocity degrees of freedom resulting in an anomalous contribution to the entropy production of the overdamped dynamics. We show that optimization of entropy production is determined by an auxiliary deterministic problem describing motion on a curved manifold in a potential. The "anomalous contribution" to entropy plays the role of the potential and the inverse of the diffusion tensor is the metric. We also find that entropy production is not minimized by adiabatically slow, quasi-static protocols but there is a finite optimal duration for the transport process. As an example we discuss the case of a linearly space dependent diffusion coefficient.

cond-mat.stat-mech↗

arXiv2013

Witness of unsatisfiability for a random 3-satisfiability formula

The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $α$ exceeds a critical value $α_s \approx 4.267$. However, rigorously proving the unsatisfiability of a given large 3-SAT instance is extremely difficult. In this paper we apply the mean-field theory of statistical physics to the unsatisfiability problem, and show that a specific type of UNSAT witnesses (Feige-Kim-Ofek witnesses) can in principle be constructed when the clause density $α> 19$. We then construct Feige-Kim-Ofek witnesses for single 3-SAT instances through a simple random sampling algorithm and a focused local search algorithm. The random sampling algorithm works only when $α$ scales at least linearly with the variable number $N$, but the focused local search algorithm works for clause densty $α> c N^{b}$ with $b \approx 0.59$ and prefactor $c \approx 8$. The exponent $b$ can be further decreased by enlarging the single parameter $S$ of the focused local search algorithm.

cs.CC↗

arXiv2013

Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models

Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

q-bio.QM↗

arXiv2012

Anomalous thermodynamics at the micro-scale

Particle motion at the micro-scale is an incessant tug-of-war between thermal fluctuations and applied forces on one side, and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia - the overdamped approximation - gives an excellent effective description of the actual particle mechanics. In sharp contrast with this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment is considered, in presence of temperature gradients. In the limit of vanishingly small, yet finite inertia, we find that the entropy production is dominated by a contribution that is anomalous, i.e. has no counterpart in the overdamped approximation. This phenomenon, that we call entropic anomaly, is due to a symmetry-breaking that occurs when moving to the small, finite inertia limit. Strong production of anomalous entropy is traced back to intense sweeps down the temperature gradient.

cond-mat.stat-mech↗

arXiv2012

Inverse Ising inference using all the data

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of $l_1$-regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

cond-mat.dis-nn↗

arXiv2012

Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries

The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and identically distributed (IID) zero-mean Gaussian and minimize the l1-norm of x under the constraint y = Dx. In this paper, the performance of l1-reconstruction is analyzed, when the dictionary is bi-orthogonal D = [O1 O2], where O1,O2 are independent and drawn uniformly according to the Haar measure on the group of orthogonal M x M matrices. By an application of the replica method, we obtain the critical conditions under which perfect l1-recovery is possible with bi-orthogonal dictionaries.

cs.IT↗

arXiv2012

Quasi-potential landscape in complex multi-stable systems

Developmental dynamics of multicellular organism is a process that takes place in a multi-stable system in which each attractor state represents a cell type and attractor transitions correspond to cell differentiation paths. This new understanding has revived the idea of a quasi-potential landscape, first proposed by Waddington as a metaphor. To describe development one is interested in the "relative stabilities" of N attractors (N>2). Existing theories of state transition between local minima on some potential landscape deal with the exit in the transition between a pair attractor but do not offer the notion of a global potential function that relate more than two attractors to each other. Several ad hoc methods have been used in systems biology to compute a landscape in non-gradient systems, such as gene regulatory networks. Here we present an overview of the currently available methods, discuss their limitations and propose a new decomposition of vector fields that permit the computation of a quasi-potential function that is equivalent to the Freidlin-Wentzell potential but is not limited to two attractors. Several examples of decomposition are given and the significance of such a quasi-potential function is discussed.

q-bio.MN↗

arXiv2012

Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory.

cond-mat.dis-nn↗

arXiv2012

Refined Second Law of Thermodynamics for fast random processes

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport. General discussion is illustrated by numerical analysis of a model for micron-size particle manipulated by optical tweezers.

cond-mat.stat-mech↗

arXiv2011

Boundary layers in stochastic thermodynamics

We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give a new interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

cond-mat.stat-mech↗