Research
Research
Research
Research
12,329+ open-access research outputs.
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not uniquely determine the…
We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly …
We define a torus $U \subset T = (\mathbb{C}^\times)^K$ which acts on the $\Delta$-Springer varieties $Y_{n,\lambda,s}$ defined by Griffin-Levinson-Woo and give a Borel-style presentation for the equi…
Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme …
We introduce an entropy-compatible neural network method for scalar hyperbolic conservation laws based on a computable surrogate of the Kru\v{z}kov entropy residual. The proposed loss is designed to e…
We study stability theory in Hilbert spaces quantitatively. We prove that the inner product on the unit ball is $(k,\epsilon)$-stable for all $k\ge \exp(\pi/\epsilon)$, and it is not $(k,\epsilon)$-st…
Passive Gamma Emission Tomography (PGET) is an IAEA-approved technique for verifying spent nuclear fuel assemblies prior to geological disposal. Reconstructing the emission and attenuation maps from P…
We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem fo…
In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction …
We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-nor…
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary con…
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable…
We study the deterministic recursion $n_{j+1} = n_j - \tau(n_j)$, where $\tau(n)$ denotes the divisor function, and the associated orbit length $a(x)$. Heuristics based on the average order of $\tau(n…
We consider the two families of even polynomials $\Xi_n$ and $\Lambda_n$ studied in~\cite{TallaWaffo2026arxiv2602.16761}, together with the rescaled polynomials $\widetilde{\Xi}_n(x):=\Xi_n(\sqrt{x})$…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal deri…
The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentrati…
We study adaptive aggregation for heterogeneous local SGD in convex finite-sum optimization, allowing heterogeneous local horizons, minibatch sizes, gradient noise, and participation. We introduce HEW…
Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show t…
A classical result of Cioab\u{a} states that if $G$ is a connected graph with the unit Perron vector $\mathbf{x}$, then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \le \frac{1}{2}$, …
Fully decentralized Muon is difficult because its nonlinear matrix-sign operator does not commute with linear gossip averaging. This makes decentralized Muon a structural design problem: in designing …
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