Research
Research
Research
Research
1,340+ open-access research outputs.
We give a damped inexact Newton method for entropy-regularized least-squares on the nonnegative orthant that converges globally at a linear rate with $O(\log\epsilon^{-1})$ iteration complexity, local…
For a sequence $\gamma=(\gamma_n)_{n\ge 1}$, define \[ L_\gamma(z):=\sum_{n\ge 1}\gamma_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}\gamma_d\Bigr)z^n. \] We prove a short rigidity theorem: if…
``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…
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…
We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andr…
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…
In this paper, we study the Koshliakov zeta function $\eta_p(s)$, whose theory appears to be more involved than that of its counterpart $\zeta_p(s)$, owing to the fact that its defining series is not …
Andrews, Dixit, Schultz, and Yee conjecture the parity of a double Lambert series. In 2026, Amdeberhan, Andrews, and Ballantine offer some ideas that are pointing in the right direction for the proof.…
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend our study to the ge…
This work presents a bilevel coordination model that captures the hierarchical interaction between the transmission and distribution layers under a Distribution System Operator(DSO)-led configuration.…
We study a family of hyperbolic Lambert series of the form \[ S_m=\sum_{n=1}^\infty\left( \frac{n^{2m}}{\cosh(\pi n)-1} -\frac{(2^{2m+1}-(-1)^{m(m+1)/2}2^{m+1}+4) n^{2m}}{\cosh(2\pi n)-1} +\frac{2^{2m…
This survey-style note reviews constructive versions of the Peter--Weyl theorem in the Bishop--Coquand--Spitters line. Its main purpose is to clarify which parts of the classical Peter--Weyl package a…
We consider decentralized stochastic convex optimization on connected network, in which gradients of agents are unavailable and each agent can query only noisy function values of its own local objecti…
We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, ans…
In this paper, we study the asymptotic behaviour of the product tail probability $ \mathbb{P}(\xi_1\cdots\xi_N \geqslant n), $ where $\{\xi_1,\ldots,\xi_N\}$ is a finite collection of independent Po…
We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally c…
We introduce a novel method for estimating the self-similarity index of a general $H$-self-similar process with either stationary or non-stationary increments. The estimation algorithm is developed ba…
Intermittent demand fluctuations pose significant challenges in disaster logistics and medical supply systems. In this study, we formulate cumulative demand as a generalized L\'evy process composed of…
Developing effective control strategies for behind-the-meter energy storage to coordinate peak shaving and stacked services is essential for reducing electricity costs and extending battery lifetime i…
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