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In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…

Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large…

Beyond specific settings, many multi-agent learning algorithms fail to converge to an equilibrium solution, instead displaying complex, non-stationary behaviours such as recurrent or chaotic orbits. In fact, recent literature suggests that…

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping…

We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…

We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…

We introduce a novel framework to approximate the aggregate frequency dynamics of coherent generators. By leveraging recent results on dynamics concentration of tightly connected networks, and frequency weighted balanced truncation, a…

Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…

Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the…

Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions…

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Deep equilibrium models (DEQs) achieve infinitely deep network representations without stacking layers by exploring fixed points of layer transformations in neural networks. Such models constitute an innovative approach that achieves…

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…

Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this…

Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…

The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally,…

Batch effects pose a significant challenge in the analysis of single-cell omics data, introducing technical artifacts that confound biological signals. While various computational methods have achieved empirical success in correcting these…

In this paper, a class of neutral type competitive neural networks with mixed time-varying delays and leakage delays on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed…

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…