Related papers: A stochastic matching model on hypergraphs
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…
Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Suppose that we are given an arbitrary graph $G=(V, E)$ and know that each edge in $E$ is going to be realized independently with some probability $p$. The goal in the stochastic matching problem is to pick a sparse subgraph $Q$ of $G$ such…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…