Research
Research
Research
Research
2,768+ 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…
The reciprocality means a duality in Kirchberg algebras between K-theory groups and strong extension groups. In the paper, we will find a certain class of unital simple Exel--Laca algebras for which t…
Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of c…
This paper presents various transcendence results in the ring of integers modulo infinitely large primes $\mathcal{A}$. In the ring $\mathcal{A}$, one can consider two notions of transcendence. One is…
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…
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 $d\mid \rho_U(p)$, …
This study presents a mathematical optimization framework and preliminary analysis for long-term investment planning in Puerto Rico's electric power system. We develop a high-resolution capacity expan…
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…
Here we report the spectroscopic and geometric confirmation of an extremely bright ($i=14.77$) and compact (Einstein radius of $\sim0.45''$) quadruply-lensed quasar at $z=2.22$, J1330$-$0905, which we…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dyna…
Large Foundation Model (LFM) inference is both memory- and compute-intensive, traditionally relying on GPUs. However, the limited availability and high cost have motivated the adoption of high-perform…
In this work we develop exact formulas to the number of solutions of $ax+by+cz=n$ in some special cases. In 2020, Binner gave a formula for the number of non negative integer solutions, $N(a,b,c;n)$ i…
The use of free energy perturbation (FEP) methods to study protein-ligand complexes is one of the most important tools in structure-based drug design. Because FEP methods typically rely on force field…
The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, define…
AI agents are increasingly deployed in real-world applications, including systems such as Manus, OpenClaw, and coding agents. Existing research has primarily focused on server-side efficiency, proposi…
In Bayesian inference for the Cox proportional hazards model, modeling the baseline hazard function is challenging. Recently, direct Bayesian inference using the partial likelihood is considered in th…
Life Cycle Assessment (LCA) is increasingly used to quantify and regulate the environmental impacts of Information and Communication Technology (ICT) systems. Since direct biosphere measurements are c…
Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments. These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty qua…
Problems in quantum chemical simulations, especially achieving accurate excited-state potential energy surfaces, are among the primary applications to achieve quantum utility. On near-term quantum har…
While no conclusive detections of exomoons have been reported to date, planet formation theories predict that satellites should be a common outcome of the collisional dynamics in early extrasolar syst…
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