Compressive sensing adaptation for polynomial chaos expansions

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.Comment: Submitted to Journal of Computational Physic

Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras

In this paper we show that the supergravity equations describing both cosmic billiards and a large class of black-holes are, generically, both Liouville integrable as a consequence of the same universal mechanism. This latter is provided by the Liouville integrable Poissonian structure existing on the dual Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive the explicit integration algorithm associated with all symmetric spaces U/H^{*} relevant to the description of time-like and space-like p-branes. The most important consequence of our approach is the explicit construction of a complete set of conserved involutive hamiltonians h_{\alpha} that are responsible for integrability and provide a new tool to classify flows and orbits. We believe that these will prove a very important new tool in the analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references adde

A Kac model for kinetic annihilation

In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We first establish the well-posedness of the particle system which exhibits no conserved quantities. We rigorously prove that, in some thermodynamic limit, a suitable hierarchy of kinetic equations is recovered for which tensorized solution to the homogenous Boltzmann with annihilation is a solution. For bounded collision kernels, this shows in particular that propagation of chaos holds true. Furthermore, we make conjectures about the limit behaviour of the particle system when hard-sphere interactions are taken into account.Comment: 40 page

Red Queen Coevolution on Fitness Landscapes

Species do not merely evolve, they also coevolve with other organisms. Coevolution is a major force driving interacting species to continuously evolve ex- ploring their fitness landscapes. Coevolution involves the coupling of species fit- ness landscapes, linking species genetic changes with their inter-specific ecological interactions. Here we first introduce the Red Queen hypothesis of evolution com- menting on some theoretical aspects and empirical evidences. As an introduction to the fitness landscape concept, we review key issues on evolution on simple and rugged fitness landscapes. Then we present key modeling examples of coevolution on different fitness landscapes at different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.). Springer Series in Emergence, Complexity, and Computation, 201

Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depends crucially on the qualia of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting or chaotic activity patterns. We study the influence of non-synaptic plasticity on the default dynamical state of recurrent neural networks. The non-synaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes, a regular synchronized, an overall chaotic and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interseeded by chaotic bursts which respond sensitively to input signals. We discuss these finding in the context of self-organized information processing and critical brain dynamics.Comment: 24 pages, 8 figure

STRUCTURING FOR GLOCALIZATION: THE MINIMAL NETWORK

Globalization and localization seem to be opposite concepts – a thesis and its antithesis. Nonetheless, managers seem to be able to handle the paradox posed by these two contradicting tensions by enacting, via action, a synthesis that allows for the co-presence of a high level of global integration and local adaptation (instead of a compromise between both), which has been labeled glocalization. We discuss how the concept of improvisation allows this synthesis by developing the two poles that ground it, namely ‘glocal’ strategy and ‘glocal’ organization. Global advantage requires a dialectical capability that organizations rarely achieve, and the importance of which orthodox management theory rarely recognizes. JEL codes: