Related papers: On Finite Exchangeability and Conditional Independ…
We discuss properties which must be satisfied by a genetic network in order for it to allow differentiation. These conditions are expressed as follows in mathematical terms. Let $F$ be a differentiable mapping from a finite dimensional real…
In this paper, connections between independent sets and the variety of mutual-visibility sets are studied. It is proved that every outer mutual-visibility set of a graph is independent if and only if the graph is distance edge-critical.…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…
This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or…
In this paper, we consider the robustness of a basic model of a dynamical distribution network. In the first problem, i.e., optimal weight allocation, we minimize the H-inf- norm of the dynamical distribution network subject to allocation…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional…
We study the problem of allocating indivisible objects to a set of rational agents where each agent's final utility depends on the intrinsic valuation of the allocated item as well as the allocation within the agent's local neighbourhood.…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph. %An independent set with…