Research
Research
Research
Research
710+ open-access research outputs.
The exact-sequence structure behind the Arnold--Douglas--Gupta family of higher-order mixed finite elements for plane elasticity on barycentric refinements is made explicit. On each macro triangle, th…
Given a graph $G$, a subset $S \subseteq V(G)$ is \textit{cycle convex}, if for any vertex $v \in V(G) \setminus S$, the induced subgraph, $G[S \cup \{v\}]$ cannot form a cycle containing the vertex $…
The most important architectural problem in AI is not the size of the model but the absence of a layer that carries forward what the model has come to understand. Sessions end. Context windows fill. M…
ATANT v1.0 (arXiv:2604.06710) defined continuity as a system property with 7 required properties and introduced a 10-checkpoint, LLM-free evaluation methodology validated on a 250-story corpus. Since …
We present ATANT (Automated Test for Acceptance of Narrative Truth), an open evaluation framework for measuring continuity in AI systems: the ability to persist, update, disambiguate, and reconstruct …
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algor…
In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By simply choosing weights and specifying $1<p<\infty$, we are able to recover the identity by …
This paper extends the Kikuchi method to give algorithms for decisional $k$-sparse Learning With Errors (LWE) and $k$-sparse Learning Parity with Noise (LPN) problems for higher moduli $q$. We create …
This paper re-evaluates Jozsef Sutak (1865-1954), a Hungarian scholar-priest and professor, as a grey eminence rather than a genius, offering a counter-narrative to the history of Hungarian university…
Microswimmers in turbulent flows often navigate complex, heterogeneous, and obstacle-rich environments, where they exhibit intricate behaviors such as trapping at and escape from obstacles. We general…
We simplify the proof of the optimality of the Shortest Lower-Bound First (SLF) algorithm, introduced by Gupta, Kaplan, Lindermayr, Schl\"oter, and Yingchareonthawornchai [FOCS'25], for minimizing the…
We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order $\alpha\in[\frac…
This paper is concerned with Tur\'{a}n problems for (alternating) multilinear maps, with the aim of determining the maximum dimension $k$, called the isotropy index, for which every such map has an is…
Strong matrix properties, roughly speaking, refer to generic conditions on a matrix such that its spectral perturbation and pattern perturbation interact nicely to cover a neighborhood in the ambient …
Reliable global streamflow forecasting is essential for flood preparedness and water resource management, yet data-driven models often suffer from a performance gap when transitioning from historical …
We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermi…
A central task in quantum information science is state certification: testing whether an unknown state is $\epsilon_1$-close to a fixed target state, or $\epsilon_2$-far. Recent work has shown that su…
Conceptual hydrologic models remain the cornerstone of rainfall-runoff modeling, yet their calibration is often slow and numerically fragile. Most gradient-based parameter estimation methods rely on f…
We introduce Version 3 (V3) of the gridded near real-time Multi-Source Weighted-Ensemble Precipitation (MSWEP) product -- the first fully global, historical machine learning powered precipitation (P) …
Vizing and Gupta showed that the chromatic index $\chi'(G)$ of a graph $G$ is bounded above by $\Delta(G) + \mu(G)$, where $\Delta(G)$ and $\mu(G)$ denote the maximum degree and the maximum multiplici…
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