相关论文: Blocking duality for $p$-modulus on networks and a…

The effective graph resistance, also known as the Kirchhoff index, is metric that is used to quantify the robustness of a network. We show that the optimisation problem of minimizing the effective graph resistance of a graph by adding a…

A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H…

The notion of $P$-algebra due to Margolis, building on work of Moore and Peterson, was motivated by the case of the Steenrod algebra at a prime and its modules. We develop aspects of this theory further, focusing especially on coherent…

The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network…

This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…

In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the…

Measuring robustness is a fundamental task for analyzing the structure of complex networks. Indeed, several approaches to capture the robustness properties of a network have been proposed. In this paper we focus on spectral graph theory…

The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…

We study nucleation dynamics of Ising model in a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in real-world networks. By introducing a variant of a recently developed forward flux…

Scientific studies increasingly collect multiple modalities of data to investigate a phenomenon from several perspectives. In integrative data analysis it is important to understand how information is heterogeneously spread across these…

This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and…

Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of…

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…

Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a…

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…

Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…

The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological…