Research
Research
Research
Research
4,339+ open-access research outputs.
We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ exhibits long-range checkerboard order at sufficiently high temperature. The model ha…
In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…
We investigate spherical collapse in Eddington-inspired Born--Infeld (EiBI) gravity in the subhorizon, pressureless, and quasi-static regime, emphasizing the matter-gradient correction that appears in…
For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and …
Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL),…
Retrieving or generating two-dimensional molecular structures on the basis of vibrational spectra has been well demonstrated via deep learning models. However, deciphering three-dimensional molecular …
Kinetic models based on the Bhatnagar-Gross-Krook (BGK) framework provide an efficient alternative to the Boltzmann equation for rarefied gas flows; however, existing formulations for gas mixtures rem…
Sub-gram flapping-wing flying insect robots (FIRs) are challenging to model because of mechanical complexity in their wings, unsteady aerodynamic flow, and the difficulty of making precise measurement…
We present a uniform framework for constructing $3$-designs from $\mathrm{GL}_2(\mathbb F_q)$-invariant subspaces of $\mathbb F_q[X,Y]_k$, the space of homogeneous polynomials of degree $k$. Given suc…
Reinforcement Learning (RL) post-training has become the standard for aligning generative models with human preferences, yet most methods rely on a single scalar reward. When multiple criteria matter,…
Text-guided molecular design is a key capability for AI-driven drug discovery, yet it remains challenging to map sequential natural-language instructions with non-linear molecular structures under str…
Let $U$ be a Lucas sequence, $p$ be prime, and $\rho_U(p)$ be the rank of appearance of $p$ in $U$. We derive closed-form formulas for the Dirichlet density of primes $p$ for which $d\mid \rho_U(p)$, …
The study of paper mills and similar businesses operating in the market for academic and education fraud services is frustrated by the lack of market price data on their various offerings. Here, we as…
We investigate degree bounds for fields of rational invariants of representations of finite groups. We prove many cases of a bound for $\mathbb{Z}/p\mathbb{Z}$ conjectured by Blum-Smith, Garcia, Hidal…
We propose a spectrum-configuration framework for open and disaggregated optical systems that maximizes throughput while guaranteeing the quality of transmission (QoT) margins. The framework jointly o…
Prompt optimization methods either analyze individual failures in isolation or compare prompt variants across examples, operating on single execution traces with no access to the reasoning process dis…
We study the set $S(q)$ of residue classes $r$ modulo the Pisano period $\pi(q)$ for which $q \mid \varphi(F_m)$ for every $m \equiv r \pmod{\pi(q)}$. We prove that if $q$ is a Sophie Germain prime an…
Seaweed (biparabolic) subalgebras form a large and structurally rich class of subalgebras of simple Lie algebras. We determine their adjoint cohomology. If $\mathfrak{s}$ is an indecomposable seawee…
This research note identifies a previously overlooked distinction between multi-objective reinforcement learning (MORL), and more conventional single-objective reinforcement learning (RL). It has prev…
Koll\'{a}r showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K…
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