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Research
Research
9,888+ open-access research outputs.
We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a sing…
We study how long the SIRS process persists or how quickly it reaches extinction across various network topologies. Our results provide a three-part characterization of this process: In finite sparse …
Many stochastic systems are built by wiring typed components together, but the wiring is often neither purely sequential nor type-homogeneous. This paper develops categorical semantics for such system…
High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscos…
An \'{e}tale space over a topological space $Y$ is defined as a local homeomorphism from a topological space $X$ into $Y$. They often come up in topos theory because of the equivalence between sheaves…
Revealing the interaction topology underlying strategic behavior is fundamental to prediction, intervention, and policy design in networked systems. Yet the interaction matrix is often unobservable, a…
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connec…
Identifying robust designs for multi-energy systems is computationally challenging. As rigorous approaches are often computationally intractable, heuristics are employed to generate candidate designs.…
We study bijections between the positive cones of spaces of continuous functions vanishing at infinity that satisfy a norm additive condition. Such maps arise naturally in the study of nonlinear funct…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Max…
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations,…
A way to lower computational cost in large scale inverse problems and problems depending on poorly known model parameters is to replace the detailed model by an approximate one. Inverse problems are t…
Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In man…
We studied the Benamou--Brenier formulation of the Schr\"odinger problem, focusing on a gap between theoretical results and applications, that often involve measures with unbounded support. While the …
This expository paper explains, in the case of $\mathfrak{sl}_2$, the ideas introduced in the preprints (arXiv:2509.17007, 2604.22262), which develop a new framework for the study of multiplicities in…
Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate function…
Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we cons…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the tabl…
Column generation is a widely used decomposition technique for large-scale linear programs, but it often suffers from slow convergence due to poor initial dual estimates and dual oscillations. Stabili…
For $0\le k\le n$, write $\binom nk=uv$ where the primes dividing $u$ are at most $k$ and the primes dividing $v$ exceed $k$, and let $f(n)$ be the least $k$ with $u>n^2$; Erd\H{o}s problem 684 asks f…
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