Research
Research
Research
Research
2,255+ open-access research outputs.
We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. We use this method to find the Frobenius numbers, genera, Betti elements, minimal…
Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine …
Superspecial curves are important objects in number theory and algebraic geometry, and the existence in genus $g \geq 4$ remains an open problem for all but finitely many characteristics $p > 0$. As a…
Let \(M\) be a closed connected oriented topological \(4\)-manifold. We prove that if \(F_1,\dots,F_r\subset M\) are pairwise disjoint connected locally flat topologically embedded nonorientable surfa…
For a one-parameter variation of biextension mixed Hodge structures, Brosnan and Pearlstein showed that the limit of the asymptotic height of the variation is given by a certain limit height of the ni…
This monograph studies $KK$-theory in its unbounded model. The central object is the $KK$-bordism group obtained by imposing the $KK$-bordism relation on unbounded $KK$-cycles. In the paradigm of nonc…
Type IIB string theory on AdS$_3 \times S^3\times T^4$ with RR flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4,4) supersymmetric 2d CFT parametrized by the integers…
Recent advances have shown the effectiveness of self-evolving LLM agents on tasks such as program repair and scientific discovery. In this paradigm, a planner LLM synthesizes an agent program that inv…
HAT-P-11 is a well-studied, active K dwarf hosting an eccentric, misaligned transiting sub-Neptune. As part of the HST Stellar Treasure Trove program (HST-AR-17551), we analyze absolutely calibrated o…
For a function $F$ represented as $F(x)=\sum_{n=0}^\infty{f_n (x) e^{2 \pi i \lambda_n x}},$ where each $f_n$ satisfies $\operatorname{spec}(f_n) \subset [0, 1]$ and $(\lambda_n)_{n\geq 0}\subset \mat…
Modern clinical practice increasingly depends on reasoning over heterogeneous, evolving, and incomplete patient data. Although recent advances in multimodal foundation models have improved performance…
While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 with large automorphis…
LLM-driven tools have significantly lowered barriers to writing SQL queries. However, user instructions are often underspecified, assuming the model understands implicit knowledge, such as dataset sch…
We introduce a new class of formal group laws whose modulus square construction yields Buchstaber's family of polynomials. This class is related to, but does not coincide with, the family of formal gr…
TOI-3884 b is a rare super-Neptune transiting a fully convective M dwarf that hosts a persistent giant polar spot. Because the planet occults this active region during every transit, the system offers…
In this paper, we construct a viable strange star model in the framework of the equation of state, $p_r=\frac{1}{3}(\rho-4B)$, proposed in the MIT bag model, where $B$ is termed as the bag constant. C…
Spiking Neural Networks (SNNs) have gained significant attention in edge computing due to their low power consumption and computational efficiency. However, existing implementations either use convent…
In today's in-person group discussions, smartphones are integrated as intelligent workstations; yet given their co-presence in such face-to-face interactions, whether and how they may enhance people's…
Recently, there has been increased interest in globally distributed training, which has the promise to both reduce training costs and democratize participation in building large-scale foundation model…
We establish a logarithmic Bott localization formula for global holomorphic sections of $T_X(-\log D)$ on a compact complex manifold $X$ with simple normal crossings divisor $D$. The zero scheme is al…
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