Related papers: Nondiscriminatory Propagation on Trees
We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split…
We study the spreading dynamics on graphs with a power law degree distribution p_k ~ k^-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
We introduce the discrete-time treatment number of a graph, in which each vertex is in exactly one of three states at any given time-step: compromised, vulnerable, or treated. Our treatment number is distinct from other graph searching…
Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…
For irreducible, time-homogeneous Markov networks, mutual linearity has recently been established for both occupation probabilities and network currents in the stationary regime as well as in the non-stationary regime in Laplace space. The…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Widespread interest in the diffusion of information through social networks has produced a large number of Social Dynamics models. A majority of them use theoretical hypothesis to explain their diffusion mechanisms while the few empirically…
In this paper, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is…
A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical…
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of the X_i and…
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix of the graph. In this survey article, we compute formulas…
Detecting malicious activity within an enterprise computer network can be framed as a temporal link prediction task: given a sequence of graphs representing communications between hosts over time, the goal is to predict which edges…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has some data packets to broadcast. It encodes these data packets into $n$ coded packets in…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…