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A new family of block-sparse proportionate affine projection algorithms (BS-PAPA) is proposed to improve the performance for block-sparse systems. This is motivated by the recent block-sparse proportionate normalized least mean square…

The prevalence of employing attention mechanisms has brought along concerns on the interpretability of attention distributions. Although it provides insights about how a model is operating, utilizing attention as the explanation of model…

Bio-inspired Spiking Neural Networks (SNNs) provide an energy-efficient way to extract 3D spatio-temporal features. However, existing 3D SNNs have struggled with long-range dependencies until the recent emergence of Mamba, which offers…

Constrained problems are frequently encountered in classical and quantum optimization. Particle conservation, in particular, is commonly imposed when studying energy spectra of chemical and solid state systems. Though particle…

In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector…

In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…

High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of…

The Proximal Point Method (PPM) (Rockafellar, 1976) is a fundamental tool for nonsmooth convex optimization. However, its convergence is not linear under general convexity in the absence of strong convexity or other structural assumptions.…

We propose a novel method for parameterizations of triangle meshes by finding an optimal quasiconformal map that minimizes an energy consisting of a relative entropy term and a quasiconformal term. By prescribing a prior probability measure…

Insurance products frequently cover significant claims arising from a variety of sources. To model losses from these products accurately, actuarial models must account for high-severity claims. A widely used strategy is to apply a mixture…

In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…

We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…

Multi-view depth estimation has achieved impressive performance over various benchmarks. However, almost all current multi-view systems rely on given ideal camera poses, which are unavailable in many real-world scenarios, such as autonomous…

In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term…

We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical…

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…

The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…

This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by using regularized delta functions derived from composite B-splines. The conventional IB method, while effective for fluid-structure…

In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the…

State space models have shown significant promise in Natural Language Processing (NLP) and, more recently, computer vision. This paper introduces a new methodology leveraging Mamba and Masked Autoencoder networks for point cloud data in…