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We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…

We propose and analyze a general goal-oriented adaptive strategy for approximating quantities of interest (QoIs) associated with solutions to linear elliptic partial differential equations with random inputs. The QoIs are represented by…

A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…

We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…

Scaling foundation model training with Distributed Data Parallel (DDP) methods is bandwidth-limited. Existing infrequent communication methods like Local SGD were designed to synchronize only model parameters and cannot be trivially applied…

We introduce a new interacting particle system on $\mathbb{Z}$, \emph{slowed $t$-TASEP}. It may be viewed as a $q$-TASEP with additional position-dependent slowing of jump rates depending on a parameter $t$, which leads to discrete and…

The integration of Geographic Information Systems (GIS) and On-Line Analytical Processing (OLAP), denoted SOLAP, is aimed at exploring and analyzing spatial data. In real-world SOLAP applications, spatial and non-spatial data are subject to…

This paper proposes a new method for constructing multidimensional signal constellations (SC), referred to as SCOPT, for high-speed communication systems with enhanced energy efficiency (EE). In contrast to conventional approaches, the…

Using insight from numerical approximation of ODEs and the problem formulation and solution methodology of TD learning through a Galerkin relaxation, I propose a new class of TD learning algorithms. After applying the improved numerical…

Designing effective score functions in Conformal Prediction (CP) for time-series data remains challenging due to conservativeness and/or computational inefficiency. We propose Optimal Selection Conformal Prediction (OSCP), which…

As control systems grow in complexity, abstraction-based methods have become essential for designing controllers with formal guarantees. However, a key limitation of these methods is their reliance on discrete-time models, typically…

We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…

Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…

We introduce a stochastic framework into the open--source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic…

We present a methodology for the global sampled-data stabilization of systems with a compact absorbing set and input/measurement delays. The methodology is based on the Inter-Sample-Predictor, Observer, Predictor, Delay-Free Controller…

The performance of time-independent, orbital optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory…

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…

A distributed spatio-temporal information based cooperative positioning (STICP) algorithm is proposed for wireless networks that require three-dimensional (3D) coordinates and operate in the global navigation satellite system (GNSS) denied…

This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…