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State-space models (SSMs), particularly the Mamba architecture, have emerged as powerful alternatives to Transformers for sequence modeling, offering linear-time complexity and competitive performance across diverse tasks. However, their…

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…

We present 3D-MPA, a method for instance segmentation on 3D point clouds. Given an input point cloud, we propose an object-centric approach where each point votes for its object center. We sample object proposals from the predicted object…

Radiography imaging protocols target on specific anatomical regions, resulting in highly consistent images with recurrent structural patterns across patients. Recent advances in medical anomaly detection have demonstrated the effectiveness…

Physical field reconstruction (PFR) aims to predict the state distribution of physical quantities (e.g., velocity, pressure, and temperature) based on limited sensor measurements. It plays a critical role in domains such as fluid dynamics…

Non-smooth and non-convex global optimization poses significant challenges across various applications, where standard gradient-based methods often struggle. We propose the Ball-Proximal Point Method, Broximal Point Method, or Ball Point…

In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…

This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…

Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…

Nuclei panoptic segmentation supports cancer diagnostics by integrating both semantic and instance segmentation of different cell types to analyze overall tissue structure and individual nuclei in histopathology images. Major challenges…

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…

We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning-insensitive method in the sense that it requires very little effort to…

Next Point-of-Interest (POI) recommendation is a critical task in location-based services, yet it faces the fundamental challenge of coupled spatiotemporal asymmetry inherent in urban mobility. Specifically, transition intents between…

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed the widely concerned issue of the previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is…

Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…

Classical Bundle Adjustment (BA) is fundamentally limited by its reliance on precise metric initialization and prior camera intrinsics. While modern dense matchers offer high-fidelity correspondences, traditional Structure-from-Motion (SfM)…

The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…

The isogeometric formulation of Boundary Element Method (BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems…

A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…

A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…