Research
Research
Research
Research
12,714+ open-access research outputs.
Optimized charging of electric vehicles (EVs) at public locations consists of two decisions: how much energy to deliver at what times, which is continuous, and where to plug in, which is binary. This …
This paper presents a real-time computational framework for multi-node distributed optimization by extending the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Our appro…
Random matrices provide a well-established statistical model for a range of arithmetic phenomena. In this paper, we investigate the extent to which one- and two-dimensional convolutional neural networ…
We formalize the Wu-Ritt characteristic set method for the triangular decomposition of polynomial systems in the Lean 4 theorem prover. Our development includes the core algebraic notions of the metho…
Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited,…
Motivated by the Cauchy--Szeg\H{o} projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we develop a martin…
In this investigation, we conduct a systematic computational search for potential singularities in 3D Navier-Stokes flows on a periodic domain $\Omega$ based on the Ladyzhenskaya-Prodi-Serrin conditio…
We study finite horizon reachable set estimation for unknown discrete-time dynamical systems using only sampled state trajectories. Rather than treating scenario optimization as a black-box tool, we s…
This paper studies an integrated learning and optimization problem in which a prediction model estimates the right-hand-side parameters of a linear program (LP) using a contextual vector. Considering …
Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations re…
Incentive design problems consider a system planner who steers self-interested agents toward a socially optimal Nash equilibrium by issuing incentives in the presence of information asymmetry, that is…
This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-con…
In this contribution we present recent developments in the formulation and solution of Initial Boundary Value Problems (IBVPs). Building upon a modern variational action formulation of classical dynam…
For a connected simple graph $G$ on $n$ vertices with chromatic number $\chi$, the distance Laplacian matrix is $\DL( G)=\mathrm{diag}(\mathrm{Tr}_{ G}(v_1),\dots,\mathrm{Tr}_{ G}(v_n)) - D( G)$, wher…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a sign…
We present a 5D-lifted analytic-profile program for finite-time singularity formation in the 3D incompressible Navier--Stokes equations on the periodic torus $\T^3$. The core of the construction is a …
The Bethe Ansatz provides exact solutions for certain interacting quantum many-body systems, yet its success is confined to narrow regimes and breaks down abruptly outside them. Despite extensive deve…
We present an integrated version of the global program proving that every prescribed prime \(q_0\ge 5\) occurs in some \(3\times 3\) magic square whose nine entries are distinct positive primes. The m…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respec…
The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a mo…
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