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The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…
Modeling spatial processes that exhibit both smooth and rough features poses a significant challenge. This is especially true in fields where complex physical variables are observed across spatial domains. Traditional spatial techniques,…
Generalized or extended finite element methods (GFEM/XFEM) are in general badly conditioned and have numerous additional degrees of freedom (DOF) compared with the FEM because of introduction of enriched functions. In this paper, we develop…
In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of…
Cluster randomized trials (CRTs) offer a practical alternative for addressing logistical challenges and ensuring feasibility in community health, education, and prevention studies, even though randomized controlled trials are considered the…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…
Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…
Machine-learning methods in biochemistry commonly represent molecules as graphs of pairwise intermolecular interactions for property and structure predictions. Most methods operate on a single graph, typically the minimal free energy (MFE)…
The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study…
Network embedding, which learns low-dimensional vector representation for nodes in the network, has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
Simulating a depositional (or stratigraphic) sequence conditionally on borehole data is a long-standing problem in hydrogeology and in petroleum geostatistics. This paper presents a new rule-based approach for simulating depositional…
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links.…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns.…
Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes…
We present the Continuous Empirical Cubature Method (CECM), a novel algorithm for empirically devising efficient integration rules. The CECM aims to improve existing cubature methods by producing rules that are close to the optimal,…