Adaptive Elastic Networks as models of supercooled liquids

The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.Comment: 12 pages, 14 figure

State Leakage and Coordination of Actions: Core of the Receiver's Knowledge

We revisit the problems of state masking and state amplification through the lens of empirical coordination by considering a state-dependent channel in which the encoder has causal and strictly causal state knowledge. We show that the problem of empirical coordination provides a natural framework in which to jointly study the problems of reliable communication, state masking, and state amplification. We characterize the regions of rate-equivocation-coordination trade-offs for several channel models with causal and strictly causal state knowledge. We introduce the notion of `core of the receiver's knowledge' to capture what the decoder can infer about all the signals involved in the model. We exploit this result to solve a channel state estimation zero-sum game in which the encoder prevents the decoder to estimate the channel state accurately.Comment: preliminary draf

A model for the erosion onset of a granular bed sheared by a viscous fluid

We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a novel model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing $\theta_c$, beyond which the particle current grows linearly $J\sim \theta-\theta_c$, in agreement with experiments. The stationary state is reached after a transient time $t_{\rm conv}$ which diverges near the transition as $t_{\rm conv}\sim |\theta-\theta_c|^{-z}$ with $z\approx 2.5$. The model also makes quantitative testable predictions for the drainage pattern: the distribution $P(\sigma)$ of local current is found to be extremely broad with $P(\sigma)\sim J/\sigma$, spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with $q$-models. We discuss the relationship between our erosion model and models for the depinning transition of vortex lattices in dirty superconductors, where our results may also apply.Comment: 5 pages, 6 figure

Learning the distribution of latent variables in paired comparison models with round-robin scheduling

Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents, where n is much larger than N. Individual are represented by independent and identically distributed random parameters characterizing their abilities.The paper studies the maximum likelihood estimator of the parameters distribution. The analysis relies on the construction of a graphical model encoding conditional dependencies of the observations which are the outcomes of the first n contests each individual is involved in. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. This paper sets the focus on graphical models obtained from round-robin scheduling of these contests.Following a classical construction in learning theory, the asymptotic likelihood is used to measure performance of the maximum likelihood estimator. Risk bounds for this estimator are finally obtained by sub-Gaussian deviation results for Markov chains applied to the graphical model

Architecture and Co-Evolution of Allosteric Materials

We introduce a numerical scheme to evolve functional materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures and the correlations among them can be computed. As an example, we consider an "allosteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites and that the amplitude of the elastic response varies non-monotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a new window to study the relationship between structure, function, and correlations emerging during evolution.Comment: 6 pages, 5 figures, SI: 2 pages, 4 figure

Principles for optimal cooperativity in allosteric materials

Allosteric proteins transmit a mechanical signal induced by binding a ligand. However, understanding the nature of the information transmitted and the architectures optimizing such transmission remains a challenge. Here we show using an {\it in-silico} evolution scheme and theoretical arguments that architectures optimized to be cooperative, which propagate efficiently energy, {qualitatively} differ from previously investigated materials optimized to propagate strain. Although we observe a large diversity of functioning cooperative architectures (including shear, hinge and twist designs), they all obey the same principle {of displaying a {\it mechanism}, i.e. an extended {soft} mode}. We show that its optimal frequency decreases with the spatial extension $L$ of the system as $L^{-d/2}$, where $d$ is the spatial dimension. For these optimal designs, cooperativity decays logarithmically with $L$ for $d=2$ and does not decay for $d=3$. Overall our approach leads to a natural explanation for several observations in allosteric proteins, and { indicates an experimental path to test if allosteric proteins lie close to optimality}.Comment: 11 pages, 9 figures in the main text, 9 pages 9 figures in the supplemental materia

Représentation logique et spatiale de la réglementation des activités humaines en zone côtière

International audienceThe measurement of anthropic uses impact on environnement is a major stake of sustainable coastal zones management. That implies to be able to describe and understand the progress and organisation of present human activities. In fact we need to develop tools allowing a dynamic description of the processes related to the coastal zone human activities. In this way, and this is particularly true in a marine area, it is indeed fundamental to be able to reach quickly the lawful constraints and analyse their space and time articulations. Applied to the case of fishing in the Iroise sea, a method to carry out a logical regulation structuring is proposed. Its integration within a Geographic Information System (GIS) can produce space representations in an automated way and according to varied requests.La mesure de l'impact des usages anthropiques sur l'environnement est un enjeu majeur du développement durable des zones côtières. Cela implique avant tout de pouvoir décrire et comprendre le déroulement et les modalités de l'organisation des activités humaines ; d'où la nécessité de développer des outils décrivant la dynamique des processus qui leur sont associés. Il est donc fondamentale, et cela est particulièrement vrai en milieu marin, de pouvoir accéder rapidement aux contraintes réglementaires et d'analyser leur articulation dans l'espace et dans le temps. Une méthode de structuration logique de la réglementation appliquée au cas de la pêche en mer d'Iroise est proposée dans un objectif opérationnel de gestion des usages. Son intégration au sein d'un Système d'Information Géographique (SIG) produit des représentations spatiales de manière automatisée et à partir de requêtes variées