Research
Research
Research
Research
2,023+ open-access research outputs.
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 …
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration ma…
In Part I, we proved that a rational model for the fiberwise THH transfer of a map $f$ of fibrations over a base space is given by the Hochschild homology transfer of a cdga model of $f$. In this pape…
Suppose that $M$ is a closed manifold of dimension greater than two and $r\geq 2$. We show that there exists a $C^r$-diffeomorphism $f:M\longrightarrow M$ with a wild affine blender-horseshoe $\Lambda…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map …
We study compactness and L\"owenheim-Skolem properties of fragments of the class-sized logic $\mathcal{L}_{\infty \infty}$ and of class-sized versions of second-order and sort logics. In these fragmen…
We employ a Markov semigroup approach combined with the $\Gamma$-calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequence, we derive t…
We establish sharp Sobolev trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere, extending the corresponding Euclidean results o…
We study clustering through the partitions it induces on a finite labeled set $[n]=\{1,\dots,n\}$, and analyze how these partitions change under perturbations of a point configuration $X=(x_1,\dots,x_…
In this paper, we are motivated by the conjectures proposed by C.~Bender \textit{et al.}, \cite{C} in 2024. We have settled the first two conjectures negatively by providing a counter example in \cite…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are…
The 1-2-3 conjecture has been solved positively in 2024 for finite graphs and by extension for infinite graphs which are locally finite. The solution is non-constructive, and finding explicit solution…
We propose a quantitative notion of permutation stability for finitely generated groups. Our notion is related to, but distinct from, the ``stability rate'' introduced by Becker and Mosheiff (which is…
Let $F_n$, $W_n$, and $\widehat{K}_n$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n-1$, respectively. In this paper, we give new bounds for the Ra…
We show for $\kappa \in (4,8)$ that the canonical conformally covariant measure on the conformal loop ensemble (CLE$_\kappa$) gasket, previously constructed indirectly by the first co-author and Schou…
Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P…
In this work we develop exact formulas to the number of solutions of $ax+by+cz=n$ in some special cases. In 2020, Binner gave a formula for the number of non negative integer solutions, $N(a,b,c;n)$ i…
Scenario-based optimization problems can be solved via Benders decomposition, which separates first-stage (master problem) decisions from second-stage (subproblem) recourse actions and iteratively ref…
We prove that every ordinal $\alpha<\omega_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive…
Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer m…
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