Related papers: Dense multigraphon-valued stochastic processes and…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…
We consider stochastic gradient descents on the space of large symmetric matrices of suitable functions that are invariant under permuting the rows and columns using the same permutation. We establish deterministic limits of these random…
Generative models for graph data are an important research topic in machine learning. Graph data comprise two levels that are typically analyzed separately: node-level properties such as the existence of a link between a pair of nodes, and…
We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in…
Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent…
We introduce a novel framework for the stability analysis of discrete-time linear switching systems with switching sequences constrained by an automaton. The key element of the framework is the algebraic concept of multinorm, which…
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
Spatiotemporal graph represents a crucial data structure where the nodes and edges are embedded in a geometric space and can evolve dynamically over time. Nowadays, spatiotemporal graph data is becoming increasingly popular and important,…
Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are…
This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…
Artificial intelligence for graphs has achieved remarkable success in modeling complex systems, ranging from dynamic networks in biology to interacting particle systems in physics. However, the increasingly heterogeneous graph datasets call…
The editing of a combinatorial object is the alteration of some of its elements such that the resulting object satisfies a certain fixed property. The edit problem for graphs, when the edges are added or deleted, was first studied…
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation, the Boolean model with…
Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces…
Graph neural networks have become an important tool for modeling structured data. In many real-world systems, intricate hidden information may exist, e.g., heterogeneity in nodes/edges, static node/edge attributes, and spatiotemporal…
In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…
Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata. These may be described as context-specific graphical models, since they are represented as directed…