Related papers: The high-d landscapes paradigm: spin-glasses, and …
In the landscape, if there is to be any prospect of scientific prediction, it is crucial that there be states which are distinguished in some way. The obvious candidates are states which exhibit symmetries. Here we focus on states which…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
Finding the mean of the total number of stationary points for N-dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localisation at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
This paper introduces a new definition of multiscale neighborhoods in 3D point clouds. This definition, based on spherical neighborhoods and proportional subsampling, allows the computation of features with a consistent geometrical meaning,…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Deep neural networks exhibit a fascinating spectrum of phenomena ranging from predictable scaling laws to the unpredictable emergence of new capabilities as a function of training time, dataset size and network size. Analysis of these…
We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological…
A brief introductory overview in general terms is given of concepts, issues and applications of the paradigm of rugged landscapes in the contexts of physics and biology.
Automated scene analysis has been a topic of great interest in computer vision and cognitive science. Recently, with the growth of crowd phenomena in the real world, crowded scene analysis has attracted much attention. However, the visual…
A simple geometrical characterization of configuration space neighborhoods of local energy minima in spin glass landscapes is found by exhaustive search. Combined with previous Monte Carlo investigations of thermal domain growth, it allows…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…