Related papers: Maximizing Algebraic Connectivity in Interconnecte…
Multi-relational graph is a ubiquitous and important data structure, allowing flexible representation of multiple types of interactions and relations between entities. Similar to other graph-structured data, link prediction is one of the…
We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the…
Some networked systems can be better modelled by multilayer structure where the individual nodes develop relationships in multiple layers. Multilayer networks with similar nodes across layers are also known as multiplex networks. This…
In this paper, we consider the network utility maximization problem with various user priorities via jointly optimizing user association, load distribution and power control in a load-coupled heterogeneous network. In order to tackle the…
This paper addresses the distributed optimization of the finite condition number of the Laplacian matrix in multi-agent systems. The finite condition number, defined as the ratio of the largest to the second smallest eigenvalue of the…
Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_i, i=1,\ldots,n$, with each graph consisting…
The algebraic connectivity of a graph $G$ in a finite dimensional real normed linear space $X$ is a geometric counterpart to the Fiedler number of the graph and can be regarded as a measure of the rigidity of the graph in $X$. We analyse…
The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…
Motivated by broad applications in various fields of engineering, we study a network resource allocation problem where the goal is to optimally allocate a fixed quantity of resources over a network of nodes. We consider large scale networks…
We investigate the bounds on algebraic connectivity of graphs subject to constraints on the number of edges, vertices, and topology. We show that the algebraic connectivity for any tree on $n$ vertices and with maximum degree $d$ is bounded…
To design control strategies that predictably manipulate a system's behavior, it is first necessary to understand how the system's structure relates to its response. Many complex systems can be represented as multilayer networks whose…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the…
This paper is concerned with the distributed linear quadratic optimal control problem. In particular, we consider a suboptimal version of the distributed optimal control problem for undirected multi-agent networks. Given a multi-agent…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies…
Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good…