Related papers: Stochastic homogenisation of nonlinear minimum-cos…
We analyze the $\Gamma$-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove…
We present an $m^{4/3+o(1)}\log W$-time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where $W$ is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known…
The selection of nodes that can serve as cluster heads, local sinks and gateways is a critical challenge in distributed sensor and communication networks. This paper presents a novel framework for identifying a minimal set of nexus nodes to…
We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenisation theory provides a coarse-grained…
A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method…
Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential…
In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $\gamma_e >0$ governing whether the flow is increased or decreased as it crosses…
We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…
In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges…
We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behaviour of…
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…
We study stochastic homogenisation of free-discontinuity surface functionals defined on piecewise rigid functions which arise in the study of fracture in brittle materials. In particular, under standard assumptions on the density, we show…
We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and…
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…
In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The…
Using the theory of $L^p$-graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value…