Research
Research
Research
Research
1,104+ open-access research outputs.
The accurate simulation of interface-dominated solid mechanics problems on complex microstructures remains challenging, particularly when interface-fitted quadrilateral or hexahedral meshes are diffic…
Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of c…
This paper presents various transcendence results in the ring of integers modulo infinitely large primes $\mathcal{A}$. In the ring $\mathcal{A}$, one can consider two notions of transcendence. One is…
Decentralized optimization provides a fundamental framework for large-scale learning and signal processing with distributed data. We study decentralized optimization with orthogonality constraints on …
We show that the global unique continuation principle holds for the parabolic fractional $p-$Laplace equation with very rough potentials $V(x,t) \in L^{p'}_tW^{-s,p'}_x$. Whereas the result is new eve…
We study the continuous-time structure of the difference-of-convex algorithm (DCA) for smooth DC decompositions with a strongly convex component. In dual coordinates, classical DCA is exactly the full…
Transitioning to a Circular Economy requires policies to drive sustainable practices. This study proposes a bilevel optimization framework to evaluate the combined use of carbon taxes and subsidies in…
We show that over the weak base theory $\mathrm{RCA}_0^*$, cohesive Ramsey's theorem for pairs $\mathrm{CRT}^2_2$ implies exponential closure of the definable cut $\mathrm{I}^0_1$, which is the inters…
We calibrate the reverse mathematical strength of a family of extensions of Ramsey's theorem to finite colorings of certain subsets of the natural numbers of unbounded finite dimension. Specifically, …
In arXiv:2508.14768, a variant of Goodstein's original process was recently introduced which, given a set $B\subseteq \mathbb{N}$ of bases, writes each $n\in\mathbb{N}$ in $B$-normal form, namely $n=b…
Linear inverse problems are highly common in practical real-world applications from industry to medical imaging. The forward operator is often built on some approximations of the studied system. Handl…
Order dimension theory measures the complexity of partially ordered sets by quantifying how far they are from being linearly ordered. In this paper we study classical bounding results for order dimens…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex rel…
Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a …
We formulate a $p$-adic optimisation problem on matrix factorisation, and investigate a heuristic method for it analogous to PCA.…
We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of a…
We systematically study categorical duality operators on spin (and anyon) chains with respect to an internal fusion category symmetry C. We parameterize duality operators on the quasi-local algebra in…
In this article, we introduce a minimization model via a non-convex transformed $\ell_p$ (TLp) penalty function with two parameters $a\in(0,\infty)$ and $p\in(0,1]$, where the case $p=1$ is known and …
Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparis…
Our first main contribution consists in establishing an explicit formula of the critical mass via the best constant of the Gagliardo-Nirenberg inequality for the mixed local-nonlocal Laplacian. We als…
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