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Corson F.,Ecole Normale Superieure de Paris
Physical Review Letters | Year: 2010

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are trees. It is shown here that this result is contingent on the assumption of a stationary flow through the network. When time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops. The transitions between different network topologies as the parameters of the problem vary are examined. These results may have strong implications for the structure and formation of natural networks, as is illustrated by the example of leaf venation networks. © 2010 The American Physical Society.

Plougonven R.,Ecole Normale Superieure de Paris | Zhang F.,Pennsylvania State University
Reviews of Geophysics | Year: 2014

For several decades, jets and fronts have been known from observations to be significant sources of internal gravity waves in the atmosphere. Motivations to investigate these waves have included their impact on tropospheric convection, their contribution to local mixing and turbulence in the upper troposphere, their vertical propagation into the middle atmosphere, and the forcing of its global circulation. While many different studies have consistently highlighted jet exit regions as a favored locus for intense gravity waves, the mechanisms responsible for their emission had long remained elusive: one reason is the complexity of the environment in which the waves appear; another reason is that the waves constitute small deviations from the balanced dynamics of the flow generating them; i.e., they arise beyond our fundamental understanding of jets and fronts based on approximations that filter out gravity waves. Over the past two decades, the pressing need for improving parameterizations of nonorographic gravity waves in climate models that include a stratosphere has stimulated renewed investigations. The purpose of this review is to present current knowledge and understanding on gravity waves near jets and fronts from observations, theory, and modeling, and to discuss challenges for progress in coming years. © 2013. American Geophysical Union. All Rights Reserved.

Felix M.-A.,Ecole Normale Superieure de Paris
Current Opinion in Genetics and Development | Year: 2012

Developmental systems can produce a variety of patterns and morphologies when the molecular and cellular activities within them are varied. With the advent of quantitative modeling, the range of phenotypic output of a developmental system can be assessed by exploring model parameter space. Here I review recent examples where developmental evolution is studied using quantitative models, which increasingly rely on empirically determined molecular signaling pathways and their crosstalk. Quantitative pathway evolution may result in dramatic morphological changes. Alternatively, in many developmental systems, the phenotypic output is robust to a range of parameter variation, and cryptic developmental evolution may occur without morphological change. Formalization and measurements of the relationship between genetic variation and parameter variation in developmental models remain in their infancy. © 2012 Elsevier Ltd.

Cottet A.,Ecole Normale Superieure de Paris
Physical Review Letters | Year: 2011

This work discusses theoretically the interplay between the superconducting and ferromagnetic proximity effects, in a diffusive normal metal strip in contact with a superconductor and a nonuniformly magnetized ferromagnetic insulator. The quasiparticle density of states of the normal metal shows clear qualitative signatures of triplet correlations with spin one (TCS1). When one goes away from the superconducting contact, TCS1 focus at zero energy under the form of a peak surrounded by dips, which show a typical spatial scaling behavior. This effect can coexist with a focusing of singlet correlations and triplet correlations with spin zero at finite but subgap energies. The simultaneous observation of both effects would enable an unambiguous characterization of TCS1. © 2011 American Physical Society.

Bach F.,Ecole Normale Superieure de Paris
Foundations and Trends in Machine Learning | Year: 2013

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the Lovasz extension of submodular functions provides a useful set of regularization functions for supervised and unsupervised learning. In this monograph, we present the theory of submodular functions from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems. In particular, we show how submodular function minimization is equivalent to solving a wide variety of convex optimization problems. This allows the derivation of new efficient algorithms for approximate and exact submodular function minimization with theoretical guarantees and good practical performance. By listing many examples of submodular functions, we review various applications to machine learning, such as clustering, experimental design, sensor placement, graphical model structure learning or subset selection, as well as a family of structured sparsity-inducing norms that can be derived and used from submodular functions. © 2013 F. Bach.

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