Related papers: Branches of localized patterned states
The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Over the last two decades, the Latent Position Model (LPM) has become a prominent tool to obtain model-based visualizations of networks. However, the geometric structure of the LPM is inherently symmetric, in the sense that outgoing and…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of…
We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose…
This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times…
Localized states universally appear when a periodic potential is perturbed by defects or terminated at its surface. In this Letter, we theoretically and experimentally demonstrate a mechanism that generates localized states through…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized…
Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate…