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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 a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…
In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a prototype model, we consider the spread of an infectious disease…
This paper considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems…
We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…
This paper addresses congested transport, which can be described, at macroscopic scales, by a continuity equation with a pressure variable generated from the hard-congestion constraint (maximum value of the density). The main goal of the…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…
At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a…
A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of…
We address the problem to control a population of noncooperative heterogeneous agents, each with convex cost function depending on the average population state, and all sharing a convex constraint, towards an aggregative equilibrium. We…
The perturbative expansion of tensorial field theories in Feynman graphs can be interpreted as weighted generating series of some piecewise linear varieties. This simple fact establishes a link between two a priori distinct fields: the…
In graph-theoretical terms, an edge in a graph connects two vertices while a hyperedge of a hypergraph connects any more than one vertices. If the hypergraph's hyperedges further connect the same number of vertices, it is said to be…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Motivated by the increasing appeal of robots in information-gathering missions, we study multi-agent path planning problems in which the agents must remain interconnected. We model an area by a topological graph specifying the movement and…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
The correspondence between weighted undirected graphs and reversible Markov chains via vertex random walks is simple and well known. Leveraging this correspondence and ideas from the theory of dynamical systems, we study the structural…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…