The balance of growth and risk in population dynamics

Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize returns, is tempered by the space/time properties of the environment. We investigate how the environment shape optimal growth and population distribution in such conditions. We uncover a trade-off between risks and returns by revisiting a common growth model over general graphs. Our results reveal a rich and nuanced picture: fruitful strategies commonly lead to risky positions, but this tension may nonetheless be alleviated by the geometry of the explored space. The applicability of our conclusions is subsequently illustrated over an empirical study of financial data.Comment: 11 pages, 5 figure

Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations

We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.Comment: 13 pages, 5 figure

Criticality in the approach to failure in amorphous solids

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $\Sigma_{\max}$ where failure occurs. This observation suggested that $\Sigma_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($\Sigma<\Sigma_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $\Sigma_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $\theta$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.Comment: 6 pages, 5 figure

Simultaneous identification of specifically interacting paralogs and inter-protein contacts by Direct-Coupling Analysis

Understanding protein-protein interactions is central to our understanding of almost all complex biological processes. Computational tools exploiting rapidly growing genomic databases to characterize protein-protein interactions are urgently needed. Such methods should connect multiple scales from evolutionary conserved interactions between families of homologous proteins, over the identification of specifically interacting proteins in the case of multiple paralogs inside a species, down to the prediction of residues being in physical contact across interaction interfaces. Statistical inference methods detecting residue-residue coevolution have recently triggered considerable progress in using sequence data for quaternary protein structure prediction; they require, however, large joint alignments of homologous protein pairs known to interact. The generation of such alignments is a complex computational task on its own; application of coevolutionary modeling has in turn been restricted to proteins without paralogs, or to bacterial systems with the corresponding coding genes being co-localized in operons. Here we show that the Direct-Coupling Analysis of residue coevolution can be extended to connect the different scales, and simultaneously to match interacting paralogs, to identify inter-protein residue-residue contacts and to discriminate interacting from noninteracting families in a multiprotein system. Our results extend the potential applications of coevolutionary analysis far beyond cases treatable so far.Comment: Main Text 19 pages Supp. Inf. 16 page

Expectation propagation on the diluted Bayesian classifier

Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse feature selection in the context of binary classification by leveraging a computational scheme known as expectation propagation (EP). The algorithm is used in order to train a continuous-weights perceptron learning a classification rule from a set of (possibly partly mislabeled) examples provided by a teacher perceptron with diluted continuous weights. We test the method in the Bayes optimal setting under a variety of conditions and compare it to other state-of-the-art algorithms based on message passing and on expectation maximization approximate inference schemes. Overall, our simulations show that EP is a robust and competitive algorithm in terms of variable selection properties, estimation accuracy and computational complexity, especially when the student perceptron is trained from correlated patterns that prevent other iterative methods from converging. Furthermore, our numerical tests demonstrate that the algorithm is capable of learning online the unknown values of prior parameters, such as the dilution level of the weights of the teacher perceptron and the fraction of mislabeled examples, quite accurately. This is achieved by means of a simple maximum likelihood strategy that consists in minimizing the free energy associated with the EP algorithm.Comment: 24 pages, 6 figure

Physique statistique des systèmes désordonnés

This Thesis presents several aspects of the stochastic growth, through its most paradig-matic model, the Kardar-Parisi-Zhang equation (KPZ). Albeit very simple, this equa-tion shows a rich behaviour and has been extensively studied for decades. The existenceof a new universality class is now well established, containing numerous growth modelslike the Eden model or the Polynuclear Growth Model. The KPZ equation is closelyrelated to optimisation problems (the Directed Polymer) or turbulence of uids (theBurgers equation), a feature that underlines its importance. Nonetheless, the bound-aries of this universality class are still vague. The focus of this Thesis is to probe thoselimits through various modifications of the models. It is divided in four chapters:i) First, we present theoretical tools, borrowed from integrable systems, that allowto characterize in great details the evolution of the interface. Those tools exhibitconsiderable exibility due to the large corpus of work on integrable systems, and weillustrate it by tackling the case of confined geometry (growth close to a hard wall).ii) We investigate the inuence of the disorder distribution, and more specificallythe importance of large events, with heavy-tailed distributions. Those extreme eventsstretch the interface and notably modify the main scaling exponents. The consequenceson optimization strategies in disorder landscapes are emphasized.iii) The presence of correlations in the disorder is of natural experimental interest.Although they do not impact the KPZ class, they greatly inuence the average speed ofgrowth. The latter quantity is often overlooked because it is non-universal and ratherill-defined. Nonetheless, we show that a generic optimal average speed exists in presenceof time correlations, due to a competition between exploration and exploitation.iv) Finally, we consider a set of experiments about chemical front growth in porousmedium. While this growth process is not related to KPZ in an immediate way, wepresent different tools that effciently reproduce the observations.Along that work, the consequences of each Chapter in various domains, like opti-misation strategies, turbulence, population dynamics or finance, are detailed.Cette thèse présente plusieurs aspects de la croissance stochastique des interfaces, par lebiais de son modèle le plus étudié, l'équation de Kardar-Parisi-Zhang (KPZ). Bien qued'expression très simple, cette équation recèle une grande richesse phénoménologiqueet est l'objet d'une recherche intensive depuis des dizaines d'années. Cela a conduit àl'émergence d'une nouvelle classe d'universalité, contenant des modèles de croissanceparmi les plus courants, tels que le Eden model ou encore le Polynuclear Growth Model.L'équation KPZ est également reliée à des problèmes d'optimisation en présence dedésordre (le Polymère Dirigé), ou encore à la turbulence des uides (l'équation de Burger), renforçant son intérêt. Cependant, les limites de cette classe d'universalitésont encore mal comprises. L'objet de cette thèse est, après avoir présenté les progrèsles plus récents dans le domaine, de tester les limites de cette classe d'universalité. Lathèse s'articule en quatre parties :i) Dans un premier temps, nous présentons des outils théoriques qui permettent decaractériser finement l'évolution de l'interface. Ces outils montrent une grande flexibilité, que nous illustrons en considérant le cas d'une géométrie confinée (une interfacecroissant le long d'une paroi).ii) Nous nous penchons ensuite sur l'influence du désordre, et plus particulièrementl'importance des évènements extrêmes dans la mécanique de croissance. Les largesfluctuations du désordre déforment l'interface et conduisent à une modification notabledes exposants de scaling. Nous portons une attention particulière aux conséquencesd'un tel désordre sur les stratégies d'optimisation en milieu désordonné.iii) La présence de corrélations dans le désordre est d'un intérêt expérimentalimmédiat. Bien qu'elles ne modifient pas la classe d'universalité, elles influent grandement sur la vitesse de croissance moyenne de l'interface. Cette partie est dédiée àl'étude de cette vitesse moyenne, souvent négligée car délicate à définir, et à l'existenced'un optimum de croissance intimement lié à la compétition entre exploration et exploitation.iv) Enfin, nous considérons un exemple expérimental de croissance stochastique (quin'appartient toutefois pas à la classe KPZ) et développons un formalisme phénoménologiquepour modéliser la propagation d'une interface chimique dans un milieu poreux désordonné.Tout au long du manuscrit, les conséquences des phénomènes observées dans desdomaines variés, tels que les stratégies d'optimisation, la dynamique des populations,la turbulence ou la finance, sont détaillées

Stochastic growth models : universality and fragility

Cette thèse présente plusieurs aspects de la croissance stochastique des interfaces, par lebiais de son modèle le plus étudié, l'équation de Kardar-Parisi-Zhang (KPZ). Bien qued'expression très simple, cette équation recèle une grande richesse phénoménologiqueet est l'objet d'une recherche intensive depuis des dizaines d'années. Cela a conduit àl'émergence d'une nouvelle classe d'universalité, contenant des modèles de croissanceparmi les plus courants, tels que le Eden model ou encore le Polynuclear Growth Model.L'équation KPZ est également reliée à des problèmes d'optimisation en présence dedésordre (le Polymère Dirigé), ou encore à la turbulence des uides (l'équation de Burger), renforçant son intérêt. Cependant, les limites de cette classe d'universalitésont encore mal comprises. L'objet de cette thèse est, après avoir présenté les progrèsles plus récents dans le domaine, de tester les limites de cette classe d'universalité. Lathèse s'articule en quatre parties :i) Dans un premier temps, nous présentons des outils théoriques qui permettent decaractériser finement l'évolution de l'interface. Ces outils montrent une grande flexibilité, que nous illustrons en considérant le cas d'une géométrie confinée (une interfacecroissant le long d'une paroi).ii) Nous nous penchons ensuite sur l'influence du désordre, et plus particulièrementl'importance des évènements extrêmes dans la mécanique de croissance. Les largesfluctuations du désordre déforment l'interface et conduisent à une modification notabledes exposants de scaling. Nous portons une attention particulière aux conséquencesd'un tel désordre sur les stratégies d'optimisation en milieu désordonné.iii) La présence de corrélations dans le désordre est d'un intérêt expérimentalimmédiat. Bien qu'elles ne modifient pas la classe d'universalité, elles influent grandement sur la vitesse de croissance moyenne de l'interface. Cette partie est dédiée àl'étude de cette vitesse moyenne, souvent négligée car délicate à définir, et à l'existenced'un optimum de croissance intimement lié à la compétition entre exploration et exploitation.iv) Enfin, nous considérons un exemple expérimental de croissance stochastique (quin'appartient toutefois pas à la classe KPZ) et développons un formalisme phénoménologiquepour modéliser la propagation d'une interface chimique dans un milieu poreux désordonné.Tout au long du manuscrit, les conséquences des phénomènes observées dans desdomaines variés, tels que les stratégies d'optimisation, la dynamique des populations,la turbulence ou la finance, sont détaillées.This Thesis presents several aspects of the stochastic growth, through its most paradig-matic model, the Kardar-Parisi-Zhang equation (KPZ). Albeit very simple, this equa-tion shows a rich behaviour and has been extensively studied for decades. The existenceof a new universality class is now well established, containing numerous growth modelslike the Eden model or the Polynuclear Growth Model. The KPZ equation is closelyrelated to optimisation problems (the Directed Polymer) or turbulence of uids (theBurgers equation), a feature that underlines its importance. Nonetheless, the bound-aries of this universality class are still vague. The focus of this Thesis is to probe thoselimits through various modifications of the models. It is divided in four chapters:i) First, we present theoretical tools, borrowed from integrable systems, that allowto characterize in great details the evolution of the interface. Those tools exhibitconsiderable exibility due to the large corpus of work on integrable systems, and weillustrate it by tackling the case of confined geometry (growth close to a hard wall).ii) We investigate the inuence of the disorder distribution, and more specificallythe importance of large events, with heavy-tailed distributions. Those extreme eventsstretch the interface and notably modify the main scaling exponents. The consequenceson optimization strategies in disorder landscapes are emphasized.iii) The presence of correlations in the disorder is of natural experimental interest.Although they do not impact the KPZ class, they greatly inuence the average speed ofgrowth. The latter quantity is often overlooked because it is non-universal and ratherill-defined. Nonetheless, we show that a generic optimal average speed exists in presenceof time correlations, due to a competition between exploration and exploitation.iv) Finally, we consider a set of experiments about chemical front growth in porousmedium. While this growth process is not related to KPZ in an immediate way, wepresent different tools that effciently reproduce the observations.Along that work, the consequences of each Chapter in various domains, like opti-misation strategies, turbulence, population dynamics or finance, are detailed