Research
Research
Research
Research
25,482+ open-access research outputs.
We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to …
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
Let $\mathcal{R}$ be an association scheme with nontrivial relations $A_1,\ldots,A_d$. We call $\mathcal{R}$ amorphic if every possible fusion of its nontrivial relations gives rise to a fusion scheme…
This paper studies whether solutions of a class of nonlinear feedback systems remain bounded over time. The systems we consider arise naturally in synthetic biology, where the antithetic feedback cont…
Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohib…
We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, me…
Here, we investigate the solutions to equation \[f(f(-x)+x)=f(-f(x))+f(x),\qquad x\in\mathbb{R}\] that are prescribed on the non-positive half-line. We will refer to this prescribed function as the ge…
The problem of characterizing graphs with a prescribed number of main eigenvalues is a long-standing problem in spectral graph theory. Although some constructions are known, only a few produce infinit…
This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which gen…
In this work, we investigate the well-posedness of a stochastic heat equation with an arbitrary (but polynomial) nonlinearity in any dimension $d\geq 1$ perturbed by a multiplicative white noise in th…
A convex polyhedron is Rupert if a hole can be cut into it (making its genus $1$) such that an identical copy of the polyhedron can pass through the hole. Resolving a conjecture of Jerrard-Wetzel-Yuan…
Alternating sign matrices (ASMs) arise as the Dedekind-MacNeille completion of the Bruhat order on the symmetric group. They enjoy fruitful combinatorial and geometric properties, with a particularly …
In this paper, we study the rigidity properties of compact Kahler manifolds. Given a smooth family of compact Kahler manifolds X over the unit disk, we show that all the fibers are mutually isomorphic…
Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmetry. From a mathemati…
This paper explores the restriction behavior of silting-induced $t$-structures and co-$t$-structures on triangulated categories endowed with metrics. For compactly generated triangulated categories ad…
Power grid infrastructure is an increasingly significant source of wildfire ignitions and poses severe risks to communities in fire-prone regions. Public Safety Power Shutoffs (PSPS) have emerged as a…
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes s…
Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains chall…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into …
Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a…
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