98 research outputs found
Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel
We introduce a thermodynamic (large deviation) formalism for computing error
exponents in error-correcting codes. Within this framework, we apply the
heuristic cavity method from statistical mechanics to derive the average and
typical error exponents of low-density parity-check (LDPC) codes on the binary
erasure channel (BEC) under maximum-likelihood decoding.Comment: 5 pages, 4 figure
A Model for the Generation and Transmission of Variations in Evolution
The inheritance of characteristics induced by the environment has often been
opposed to the theory of evolution by natural selection. Yet, while evolution
by natural selection requires new heritable traits to be produced and
transmitted, it does not prescribe, per se, the mechanisms by which this is
operated. The mechanisms of inheritance are not, however, unconstrained, since
they are themselves subject to natural selection. We introduce a general,
analytically solvable mathematical model to compare the adaptive value of
different schemes of inheritance. Our model allows for variations to be
inherited, randomly produced, or environmentally induced, and, irrespectively,
to be either transmitted or not during reproduction. The adaptation of the
different schemes for processing variations is quantified for a range of
fluctuating environments, following an approach that links quantitative
genetics with stochastic control theory
Evolution of sparsity and modularity in a model of protein allostery
The sequence of a protein is not only constrained by its physical and
biochemical properties under current selection, but also by features of its
past evolutionary history. Understanding the extent and the form that these
evolutionary constraints may take is important to interpret the information in
protein sequences. To study this problem, we introduce a simple but physical
model of protein evolution where selection targets allostery, the functional
coupling of distal sites on protein surfaces. This model shows how the
geometrical organization of couplings between amino acids within a protein
structure can depend crucially on its evolutionary history. In particular, two
scenarios are found to generate a spatial concentration of functional
constraints: high mutation rates and fluctuating selective pressures. This
second scenario offers a plausible explanation for the high tolerance of
natural proteins to mutations and for the spatial organization of their least
tolerant amino acids, as revealed by sequence analyses and mutagenesis
experiments. It also implies a faculty to adapt to new selective pressures that
is consistent with observations. Besides, the model illustrates how several
independent functional modules may emerge within a same protein structure,
depending on the nature of past environmental fluctuations. Our model thus
relates the evolutionary history and evolutionary potential of proteins to the
geometry of their functional constraints, with implications for decoding and
engineering protein sequences
Biologie statistique / Statistical biology
Recherche Page web : https://www.college-de-france.fr/site/en-cirb/rivoire.htm. Notre équipe cherche à comprendre les principes sous-jacents aux capacités d’adaptation des systèmes biologiques. Notre approche est inspirée de la physique statistique et combine des analyses de séquences génomiques, des expériences quantitatives in vitro et des modèles mathématiques. Nos projets actuels sont organisés autour de trois systèmes modèles : les anticorps, les protéases et les génomes bactériens. Nos ..
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