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Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…
Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three…
A memory efficient approach to ensembling neural networks is to share most weights among the ensembled models by means of a single reference network. We refer to this strategy as Embedded Ensembling (EE); its particular examples are…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message passing approach to evaluate heterogeneous, node dependent probabilities of belonging to the giant or…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
The increasing complexity of cascading risks in urban systems necessitates robust, data-driven frameworks to model interdependencies across multiple domains. This study presents a foundational Bayesian network-based approach for analyzing…