相关论文: Error threshold in simple landscapes

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…

We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by…

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a…

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…

We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…

Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic…

A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (\mup and its depth extension), then some hyperparameters -- such as the learning rate --…

We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain…

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness…

Growing efforts to measure fitness landscapes in molecular and microbial systems are premised on a tight relationship between landscape topography and evolutionary trajectories. This relationship, however, is far from being straightforward:…

We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with "specialist" individuals that are adapted to the environment; this maximum moves…

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…

Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…

The quasispecies model of biological evolution for asexual organisms such as bacteria and viruses has attracted considerable attention of biological physicists. Many variants of the model have been proposed and subsequently solved using the…

Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding…

In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned…

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in…