Research
Research
Research
Research
3,463+ open-access research outputs.
In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatn…
We construct and analyze a thermodynamic extension of the recently proposed information geometric regularization of Cao and Sch\"afer. The construction extends their shock-mitigating Hessian metric ge…
Topological entanglement entropy (TEE) is a key diagnostic of long-range entanglement in two-dimensional gapped phases of matter, but it can suffer from spurious contributions that overestimate the to…
This paper investigates the distribution of integral points on projective varieties via two distinct methods: the Ru-Vojta theorem and our higher-dimensional generalization of the Huang-Levin-Xiao ine…
The arrival of large language models (LLMs) capable of multi-step reasoning, tool use, and long-horizon planning has produced a qualitative shift in software engineering. Where earlier code-completion…
Let $K$ be a field with $2 \in K^\times$, and let $H_W$ denote the standard hyperbolic form on $W \oplus W^*$. We study the exterior spinor model $S = \bigwedge V(W)$ together with the spin-to-orthogo…
We present a framework for non-Abelian p-loop, fracton, and planon condensation in 3+1 dimensions by constructing extended cage-net fracton models using decoupled layers of the Hu-Geer-Wu (HGW) string…
We introduce dilogarithm identities through a beta integral-based technique that we apply to construct new 3 and 6-term functional identities of the type $\sum r^{-1}_i L(X_i) \in \pi^2 \mathbf{Q}$. W…
We study the flat CR twistor model $Q^{2,2}\subset \mathbb{CP}^3$ by explicit projective methods. Using the anti-holomorphic involution $j$ associated with the twistor fibration, we classify the proje…
In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions exec…
In a previous submission, we established a fundamental relation between tone networks and configurations. It was shown that the Eulerian tonnetz can be represented by a $\{12_3\}$ of Daublebsky von St…
We compute the Floer homology and Seiberg-Witten Floer homotopy type of Seifert rational homology $3$-spheres which fiber over $\mathbb{RP}^2$. We show that they are all $L$-spaces and their Floer hom…
Continuous Integration and Deployment (CI/CD) workflows are central to modern software delivery, yet the reliability of agentic AI bots operating within these workflows remain underexplored. Using pul…
We study ground states of the fermionic nonlinear Schr\"{o}dinger system $J_2(p)$ in $\R$, where $p>1$ denotes a polynomial exponent of the nonlinear term. It is known that the system $J_2(p)$ admits …
The choice of visualisation in empirical performance analysis is not a neutral presentation decision but an analytical one: different graphical forms reveal different features of the same dataset, and…
We determine the mod $p$ reductions of the semi-stable representations $V_{k, \mathcal{L}}$ of weight $k \in [p + 5, 2p]\cup[2p + 6, 3p + 1]$ and $v_p(\mathcal{L}) < 1-k/2$ for primes $p \geq 5$. In p…
We present a randomized augmenting paths-based algorithm to compute the maximum flow in a directed, uncapacitated graph in almost $m+nF$ time, matching the algorithm of Karger and Levine for undirecte…
Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic $K$-theory, and Levine--Morel's algebraic cobordism are all instances of…
We analyze an optimal stopping problem for random walk in random scenery on general graphs, and determine when it has a finite optimum. We use this to extend a theorem of Levine, Murugan, Peres, and U…
We establish a link between different relativistic variants of the Kepler problem. In particular, we show that solutions of the special relativistic model with fixed energy can be reparameterized as s…
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