Research
Research
Research
Research
8,573+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
The syntactic structure of a sentence can be represented as a tree where edges indicate syntactic dependencies between words. When that structure is a star, it has been demonstrated that the head shou…
Let $q_1, \ldots , q_t$ be distinct prime numbers. Let $a_1, \ldots , a_t$ be nonnegative integers. We establish effective lower bounds for $|z^d - q_1^{a_1} \ldots q_t^{a_t}|$ and for its greatest pr…
Local fine-tuning datasets routinely contain sensitive secrets such as API keys, personal identifiers, and financial records. Although ''local offline fine-tuning'' is often viewed as a privacy bounda…
We introduce the ARCH-m(X) model, a semiparametric extension of the ARCH-X framework in which the effect of a multivariate exogenous covariate vector X on the conditional variance is modeled through a…
In this paper we develop a consistent variable selection procedure for GARCH-X models that identifies the truly relevant exogenous covariates influencing volatility dynamics. The proposed method is ba…
Foundation segmentation models such as the Segment Anything Model (SAM) have demonstrated strong generalization across natural images; however, their robustness under clinically realistic medical imag…
We propose a density-valued vector autoregressive model with latent factors for multivariate time series of density functions. Motivated by weekly regional distributions of SARS-CoV-2 cycle threshold …
We study online regression with the square loss in a reproducing kernel Hilbert space under a dynamic regret criterion. The learner is compared with a time-varying comparator sequence, and the bounds …
Agentic systems increasingly act with user secrets for APIs, messaging platforms, and cloud services. Today's bearer-secret interfaces implement authorization by exposure: enabling action often means …
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. For $\alpha\in[0,1)$, we use $A_{\alpha}(G)$ and $\rho_{\alpha}(G)$ to denote the $A_{\alpha}$-matrix and the $A_{\alpha}$-spectral radiu…
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approac…
A classical result of Cioab\u{a} states that if $G$ is a connected graph with the unit Perron vector $\mathbf{x}$, then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \le \frac{1}{2}$, …
Let $P$ be a compact hyperbolic Coxeter truncation polytope of dimension $d\ge 3$, and let $\Gamma$ be the orbifold fundamental group of the associated Coxeter orbifold $\mathcal{O}_P$. Let $\mathscr{…
Let $-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on $\mathbb{H}$ where $V \in L^p(\mathbb{H}) \cap L^\infty(\mathbb{H})$ for some $p > 0$. If $(X_n)$ is a uniformly discrete sequence of comp…
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then use this representatio…
We implement an algorithm for solving the minimum weight perfect matching problem. Our code significantly outperforms the current state-of-the-art Blossom V algorithm on those families of instances wh…
We consider a superconducting altermagnet heterostructure and demonstrate that the interplay between altermagnetism and a selective filter of transverse momentum channels enables perfect nonreciprocal…
Motivated by the exact weight perfect matching problem and recent parameterized algorithms for finding an $\ell$-th smallest perfect matching, we study structural properties of edge-weight symmetries …
We provide a complete structural characterization of perfect quantum strategies for arbitrary quantum magic rectangle games. We derive necessary and sufficient conditions that jointly constrain the sh…
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