相关论文: Analytic continuation over complex landscapes

We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We…

We develop a landscape-flux framework to investigate observed frequency distributions of vegetation and the stability of these ecological systems under fluctuations. The frequency distributions can characterize the population-potential…

Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…

Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…

We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…

We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical…

Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network…

In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction…

Due to climate change, overgrazing, and deforestation, arid ecosystems are vulnerable to desertification and land degradation. As aridity increases, vegetation cover loses spatial homogeneity and self-organizes into heterogeneous vegetation…

By a classical theorem transversal homoclinic points of maps lead to shift dynamics on a maximal invariant set, also referred to as a homoclinic tangle. In this paper we study the fate of homoclinic tangles in parameterized systems from the…

Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…

We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also…

Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…

While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…

Geometrical properties of landscapes result from the geological processes that have acted through time. The quantitative analysis of natural relief represents an objective form of aiding in the visual interpretation of landscapes, as…

In this article, we review some of our approaches to granular dynamics, now well known to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they…

We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…