Research
Research
Research
Research
320+ open-access research outputs.
The quiet-Sun coronal electron-temperature ratio $R \equiv T_\mathrm{EUV}/T_B \approx 2.4$, stable across an eight-year solar cycle, is read here as a measurement of relative entropy between two diagn…
We report rogue-wave and lump patterns associated with Umemura polynomials, which arise in rational solutions of the third Painlev\'{e} equation. We first show that in many integrable equations such a…
In this paper we study the geometric structure induced by the canonical reciprocal cost function and its natural $n$-dimensional extension. In logarithmic coordinates, the potential depends only on th…
In this paper, a class of linear evolution equations with time delay is studied in which the presence of continuous spectrum on the imaginary axis obstructs the analysis of long-time dynamics. To addr…
A root lattice is a finite rank $\mathbb{Z}$-lattice generated by elements $x$ satisfying $x\cdot x=2$. It is well-known that the root lattices have an $ADE$ classification and they play a prominent r…
The interaction between phase oscillators is conservative if the phase volume is conserved throughout the dynamics. We derive a general condition, based on the notion of a pair-Hamiltonian, for the pa…
Despite the remarkable quality of LLM-based text-to-speech systems, their reliance on autoregressive Transformers leads to quadratic computational complexity, which severely limits practical applicati…
We compute Donaldson-Thomas(DT) invariants and their descendant invariants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety via several localization formulas. Assuming that the genus-one…
We consider the mean-field noisy Kuramoto-Daido model, which is a McKean-Vlasov equation on the circle with bimodal interaction $W(\theta)=\cos\theta+m\cos2\theta$ for $m\ge 0$ and interaction strengt…
We study the local convergence of diffusive mean-field systems, including Wasserstein gradient flows, min-max dynamics, and multi-species games. We establish exponential local convergence in $\chi^2$-…
In this paper discrete equations are derived from B\"{a}cklund transformations of the fifth Painlev\'{e} equation, including a new discrete equation which has ternary symmetry. There are two classes o…
We introduce a non-Markovian generalization of the classical M/M/1 queue by incorporating extended nonlocal time dynamics into Kolmogorov forward equations. We obtain the model by replacing the standa…
We conjecture a precise relation between the superconformal indices of two theories defined in different spacetime dimensions. The first is the three-dimensional ABJM theory describing the worldvolume…
Large Language Models (LLMs) have shown strong performance on code understanding tasks, yet they fundamentally lack the ability to perform precise, exhaustive mathematical reasoning about program beha…
We study prime Fano threefolds of genus 12 ($V_{22}$-varieties) with positive-dimensional automorphism groups in positive and mixed characteristic. We classify such varieties over any perfect field. I…
The rapid development of large language models has led to an increase in AI-generated text, with students increasingly using LLM-generated content as their own work, which violates academic integrity.…
In 1954, following a five-year research period in the U.S., Professor Hideki Yukawa returned to Japan and visited Kochi on March 21 to attend the unveiling ceremony for the first statue of him ever bu…
Time-delayed phase-oscillator networks model diverse biological and physical systems, yet standard first-order phase reductions cannot adequately capture their high-dimensional collective dynamics. In…
Modern computing architectures feature low-precision matrix multiplication units that achieve substantially higher throughput than their high-precision counterparts. Motivated by this architectural tr…
We study the free boundary $q$-Whittaker and Hall--Littlewood processes, two probability measures on sequences of partitions. We prove that a certain observable of the free boundary $q$-Whittaker proc…
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