相关论文: Navigation on a Poisson point process

Consider a 2D coordinate space with a set of red and a set of blue points. We define a scenic point as a point that is equidistant to a red point and a blue point. The set of contiguous scenic points form a scenic path. The perpendicular…

We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of…

We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long…

We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…

In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of…

A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of transversals of size k in a rooted tree T. We define a partial order on the set of all rooted trees with n…

This paper brings together the concepts of navigation transformation and harmonic functions to form navigation functions that are correct-by-construction in the sense that no tuning is required. The form of the navigation function is…

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…

The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…

Current theories suggest that adaptive decision-making necessitates the interaction between multiple decision-making systems. The computational definitions of different models of decision-making suggest interactions with task demands and…

We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…

We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

We prove consistency of four different approaches to formalizing the idea of minimum average edge-length in a path linking some infinite subset of points of a Poisson process. The approaches are (i) shortest path from origin through some…

A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is…

A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…

The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…

Following the pivotal work of Sevastyanov, who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes under different types of branching and immigration…

We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave…