Research
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Research
Research
5,749+ open-access research outputs.
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) da…
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulatio…
We construct and analyze a thermodynamic extension of the recently proposed information geometric regularization of Cao and Sch\"afer. The construction extends their shock-mitigating Hessian metric ge…
The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains…
Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived g…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide suffici…
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
Finite horizon Sinai billiard maps are examples of uniformly hyperbolic systems with singularities. These discontinuities make it more difficult to develop the classical theory of thermodynamic formal…
We introduce the slack of a recording tableau in the quantum Littlewood-Richardson (LR) map and show that it inherits the needed data from LR-Sundaram tableaux to define the inverse of the quantum LR …
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang. Then, we proved a quantitative shieldin…
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…
We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamic…
We develop a $\mathbf{P}^1$-unstable non-$\mathbf{A}^1$-invariant theory of motivic spaces and spectra, and construct the Gysin map therein for regular immersions. This in particular gives the Gysin m…
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 $\text{Leb}|_{\Sigma_{\alpha,\lambda}}$ …
For the family of Lozi maps $L_{a,b}$, we consider parameter pairs for which the f\mbox{}ixed point $X$ has no homoclinic points and the period-two orbit $\{P,P'\}$ is attracting. For such parameters,…
The identity map of an Einstein manifold is a critical point of both the classical energy functional and the conformal-bienergy functional. In this paper, we investigate the conformal-biharmonic stabi…
For a time dependent Schr\"odinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show…
We study the surjectivity of certain maps involving local cohomology modules, which we can realize as a dual version of part of the investigation developed by Bhatt, Blickle, Lyubeznik, Singh and Zhan…
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