相关论文: Coarse chain recurrence, Morse graphs with finite …
Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches,…
Global coastlines and their dense populations have an uncertain future due to increased flooding, storms, and human modification. The distributary channel networks of deltas and marshes that plumb these coastlines present diverse…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Poincar\'e recurrence theorem implies the density of recurrent points for volume-preserving dynamical systems on compact domains. The density of closed orbits in the non-wandering set is one of the essential properties of Axiom A and chaos.…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows,…
We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…
We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the reals. In particular, we give a characterization of the real…
It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behavior. This behavior can be used to design analogs of more complex logic families and some…