Related papers: Multiple multivariate subdivision schemes: matrix …
In this work, several multilevel decoupled algorithms are proposed for a mixed Navier-Stokes/Darcy model. These algorithms are based on either successively or parallelly solving two linear subdomain problems after solving a coupled…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
The multi-point Metropolis algorithm is an advanced MCMC technique based on drawing several correlated samples at each step and choosing one of them according to some normalized weights. We propose a variation of this technique where the…
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by…
Multilayer networks provide a more advanced and comprehensive framework for modeling real-world systems compared to traditional single-layer and multiplex networks. Unlike single-layer models, multilayer networks have multiple interacting…
This paper presents a new view of multi-user (MU) hybrid massive multiple-input and multiple-output (MIMO) systems from array signal processing perspective. We first show that the instantaneous channel vectors corresponding to different…
Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…
The i.i.d. assumption is a useful idealization that underpins many successful approaches to supervised machine learning. However, its violation can lead to models that learn to exploit spurious correlations in the training data, rendering…
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…
Transmission matrices, mapping the propagation of light from one end of the tissue to the other, form an important mathematical tool in the analysis of tissue scattering and the design of wavefront shaping systems. To understand the…
This work presents a multilevel variant of Stein variational gradient descent to more efficiently sample from target distributions. The key ingredient is a sequence of distributions with growing fidelity and costs that converges to the…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An…
Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on…
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral…
We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…
Representation learning of networks has witnessed significant progress in recent times. Such representations have been effectively used for classic network-based machine learning tasks like node classification, link prediction, and network…