相关论文: Random Trees in Electrical Networks
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…
Transformers and transmission lines are critical components of a grid network. This paper analyzes the statistical properties of the electrical parameters of transmission branches and especially examines their interdependence on the voltage…
Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…
We study the minimum spanning tree distribution on the space of spanning trees of the $n$-by-$n$ grid for large $n$. We establish bounds on the decay rates of the probability of the most and the least probable spanning trees as…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…
Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
A fully nonparametric approach for making probabilistic predictions in multi-response regression problems is introduced. Random forests are used as marginal models for each response variable and, as novel contribution of the present work,…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
This thesis examines linearly edge-reinforced random walks on infinite trees. In particular, recurrence and transience of such random walks on general (fixed) trees as well as on Galton-Watson trees (i.e. random trees) is characterized, and…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of…