相关论文: Directed animals in the gas
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…
An important challenge in theoretical ecology is to find good, coarse-grained representations of complex food webs. Here we use the approach of generalized modeling to show that it may be possible to formulate a coarse-graining algorithm…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, defined in terms of trophic levels, is related to properties such as cycle structure, stability and…
We give a self-contained introduction to the theory of directed graphs, leading up to the relationship between the Perron-Frobenius eigenvectors of a graph and its autocatalytic sets. Then we discuss a particular dynamical system on a fixed…
Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources…
A rooted arborescence of a directed graph is a spanning tree directed towards a particular vertex. A recent work of Chepuri et al. showed that the arborescences of a covering graph of a directed graph G are closely related to the…
We define a random graph obtained via connecting each point of $\mathbb{Z}^d$ independently to a fixed number $1 \leq k \leq 2d$ of its nearest neighbors via a directed edge. We call this graph the directed $k$-neighbor graph. Two natural…
A race is held between ten species of organic gas molecules on a graphene substrate driven by thermal gradients via molecular dynamics. Fast conduction of the molecules is observed with selectivity for aromatic compounds. This selectivity…
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reconstructed from the shapes of its semi-infinite geodesics. In…