Research
Research
Research
Research
2,736+ open-access research outputs.
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
In renewable power-to-ammonia (ReP2A) systems, the intermittency of wind and solar generation propagates through electrolytic hydrogen production and induces thermal instability in the ammonia synthes…
Let $\alpha\colon G\curvearrowright A$ be an action of a countable discrete group on a separable unital $C^*$-algebra. We study the simplex $\mathrm{T}(A)^G$ of $G$-invariant traces and ask when it is…
We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural discrete analogues o…
We consider the spectrum of the Almost Mathieu operator (AMO) and show that the moments of the restriction of the Lebesgue measure to the intersection spectrum $\text{Leb}|_{\Sigma_{\alpha,\lambda}}$ …
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and ad…
In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially…
We prove a relative volume comparison theorem of Petersen-Wei for both $L^P$-bound of Bakry-\'{E}mery Ricci curvature and gradient of potential function. As an application, we give a modified proof fo…
We study a finite time horizon Markov decision process (MDP) consisting of several groups of multi-action finite-state restless bandit processes, which are identical within each group. The bandit proc…
Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that th…
In this paper, we consider the weighted $p$-Laplacian equation $$ \Delta_{p,f}u+au^{\sigma}\ln u=0$$ defined on a complete smooth metric measure space under the conditon that the $m$-Bakry-\'{E}mery R…
We extend earlier international efforts to optimise hexahedral-based spectral element methods on GPUs and vectorised CPUs to mixed element meshes additionally involving prismatic, pyramidic, and tetra…
We study problems on covering $[0,1)$ by shrinking intervals centered at the points $\{q_n x\}$, where $(q_n)_{n\in \mathbb{N}}$ is a given real-valued sequence and $x \in [0,1)$ is random. For real-v…
Generalized bent (gbent) functions from an $n$-variable Boolean space to $\mathbb{Z}_{2^k}$ are central in cryptography and sequence design. Instead of the usual binary decomposition, we introduce a $…
Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a family of series conta…
The 2023 Lahaina wildfire killed 102 people on a peninsula served by a single two-lane highway, making exit lane capacity the binding constraint on evacuation time. We model the evacuation as a system…
Public universities in the US must now meet digital accessibility (DA) standards under 2024 updates to Title II of the ADA. For math instructors, course materials must be screen-reader parsable, which…
Adapting Bauer and Furuta's constructions of the refinement of the Seiberg-Witten invariants, we establish the analogous stable cohomotopy refinement of the $Pin^{-}(2)$ monopole invariants proposed b…
van Emde Boas (1981) conjectured that computing a shortest non-zero vector of a lattice in an Euclidean space is NP-hard. In this paper, we prove that this conjecture is true and hence de-randomize th…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the provi…
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