Related papers: Localization and Pattern Formation in BBGKY Hierar…
In many physical systems, dynamics is ruled by structures of atypical chaoticity. These structures may occupy a very small volume in phase space and can thus be very difficult to locate numerically. In this article, we review an algorithm,…
We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We…
Efforts toward a comprehensive description of behavior have indeed facilitated the development of representation-based approaches that utilize deep learning to capture behavioral information. As behavior complexity increases, the expressive…
We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled…
We use a composite gravitational galactic model consisting of a disk, a halo, a massive nucleus and a strong nuclear bar, in order to study the connections between global and local parameters in a realistic dynamical system. The local model…
In this paper we examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional…
The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Solutions to the BBGKY hierarchy of equations for molecular Brownian particle in ideal gas are considered, and exact relations are derived between probability distribution of path of the particle, its derivatives in respect to gas density…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
Localizing behaviors of neural networks to a subset of the network's components or a subset of interactions between components is a natural first step towards analyzing network mechanisms and possible failure modes. Existing work is often…
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
We consider deterministic self-propelled particles with anti-alignment interactions. An asymptotically exact kinetic theory for particle scattering at low densities is constructed by a non-local closure of the BBGKY-hierarchy, involving…
We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models we show that the correlation between a particle's mobility and the degree of local order in…
We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…