arXiv preprints from January 1, 2026 through September 7, 2026 — 11:22:24 EST
Modeling multivariate extremes using a geometric perspective leverages the shape of the multivariate point cloud to make inference on joint tail probabilities. While the original statistical framework for geometric extremes was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer...
Prognostic factor evaluation and prediction model development are central to precision oncology, enabling patient risk stratification and individualized treatment selection. Unified predictions that synthesize information from existing models are valuable for comprehensive and consistent risk assessment. Many studies also seek to...
Curve fitting for physical, biological, and engineering data typically forces a choice between interpretable but rigid parametric forms and flexible but physically opaque smoothers. This paper introduces the Growth-Decay Curve (GDC), a physics-informed basis derived as the product of a lognormal growth cumulative distribution function...
We study nonzero-frequency phase-locked motions in asymmetrically coupled Kuramoto networks. Such motions are relative equilibria with fixed phase differences and a nonzero common angular velocity, and we call them dancing equilibria. Their existence requires all coupling sums to have the same nonzero value. We show that neither...
Safety-critical optimization applications, such as real-time power system operation, maintain feasibility at every intermediate step, not merely at convergence. Existing approaches either violate constraints mid-solve (interior-point methods) or enforce feasibility through per-instant quadratic programming subproblems with cubic...
The average performance of FirstFit online coloring on trees in the random order model is completely determined in recent works of Frei et al. and Bosek et al., showing $Θ(\log n /\log\log n)$ number of colors, improving the $Θ(\log n)$ colors in the adversarial model. We provide a few further results on slightly more general graph...
In this paper, we use completed root views to study measure sofic entropy of Poisson actions of locally compact sofic groups. We prove that, for every noncompact locally compact second countable sofic group and every locally compact sofic approximation, each positive-intensity Poisson action has completely positive measure sofic...
This document reports over 15 counterexamples found using GPT Pro over the course of 12 months, for problems in combinatorics, number theory, convexity, analysis, and other areas. The counterexamples concern both (reasonably) well-known problems as well as lesser known instances. The counterexamples are accompanied by the repo...
Let $p$ be an odd prime and let $K/\mathbb{Q}_p$ be a finite unramified extension. From a finite presentation by roots of unity of order prime to $p$, we construct a localized Iwasawa pseudomeasure on $\mathbb{Z}_p^\times$. Although the pseudomeasure depends on the chosen presentation, its image modulo bounded measures depends only on...
Let $J_r^{SU(n)}(K;q)$ denote the reduced $SU(n)$ quantum invariant of a zero-framed knot $K$, colored by the $r$th symmetric power of the defining representation and normalized to be $1$ for the unknot. For every fixed $n\ge2$ we prove the Chen--Liu--Zhu cyclotomic expansion conjecture: there are unique coefficients...
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a right Auslander-Reiten-Serre (ARS for short) duality $(τ, η)$ in the sense of Iyama, Nakaoka and Palu. We show $(τ, η)$ induces right ARS dualities on the relative theories of $(\mathcal{C},\mathbb{E},\mathfrak{s})$. Under relative structures, we show...
Let $A, T \in M_n(\mathbb{C})$ and let $Δ_A(T) = AT - TA$ denote the inner derivation induced by $A$. We determine when $T$ and $Δ_A(T)$ are nilpotent under the second-order relation $$ Δ_A^2(T) + α\, Δ_A(T) + β\, T = 0, \qquad α, β\in \mathbb{R}, $$ according to the location of the roots of $z^2 + αz + β$. If the roots have...
Fix an integer $p\geq 2$ and $0<s<1$. We construct an ergodic $\times p$-invariant measure $μ$ on $\mathbb T^2$ of dimension $s$, such that every line projection preserves dimension, including when the corresponding projected IFS has exact overlaps. In fact, our measure assigns mass $O(w^s)$ to every planar tube of width $w$. The...
The main focuses of the article are limit theorems of Wasserstein projection in the convex order which are useful for inference tasks. The main results rely on the establishment of dual attainment, stability and several useful observations. The first is a clean criterion to invoke the Wasserstein projection dualities on the classical...
We prove a purely classical, coding-theoretic characterization of Hausdorff and packing dimensions in \(\mathbb R^n\). A \emph{ball code} assigns names to closed balls of \(\mathbb R^n\): it is a partial map from a prefix-free set of finite binary strings to balls. For every nonempty \(E\subseteq\mathbb R^n\), the Hausdorff dimension...
A company with a fixed artificial intelligence (AI) budget must decide which large language model (LLM) handles each recurring workload. What it lacks is the quality table, how well each model performs on each workload. Given that table, the decision is a multiple-choice knapsack problem and is routine to solve, so estimating it is...
Let $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\mathrm{SL}_2 (\mathbb {Z}) $ with Hecke eigenvalues $λ_j (n)$ and Laplace eigenvalue $1/4+t_j^2$. In this paper, we consider the short-interval variant of the twisted spectral large sieve inequality of Luo for $ λ_j (n) n^{it_j} $ on the range $t_j \leqslant T$ and...
Let $K$ be a field containing $\mathbb{Q}$, let $Γ$ be the ring of all functions from the positive integers to $K$ under Dirichlet convolution, and let $Γ_n$ be its truncation to functions supported on $[1,n]$. In [Snellman, Homology Homotopy Appl. 2 (2000), 17-27; arXiv:math/9904143] it was shown that $Γ_n$ is a polynomial ring...
Salient object detection in optical remote sensing images (ORSI-SOD) requires dense predictions that preserve object completeness and structural continuity under complex backgrounds, scale variation, and irregular object shapes. Existing methods often localize salient regions, but their predictions may still suffer from structural...
Natural Language Processing methods have enabled novel solutions and advances in the field of privacy, particularly in the sub-domain of text-to-text privatization, where the goal is to transform a sensitive input text into a privatized output by ideally masking (in)directly identifiable or otherwise private information. The...
Recent advances in large reasoning models (LRMs) have shown strong performance on complex problems through long chain-of-thought (Long CoT) reasoning. However, distilling such trajectories into smaller student models remains challenging: direct Long CoT supervision often provides limited gains and can be less effective than concise...
Retrieval-Augmented Generation (RAG) improves the factuality of large language models (LLMs), yet existing RAG systems often struggle with complex, multi-step reasoning that requires adaptive retrieval and continuous revision of intermediate contexts. Recent reinforcement learning (RL)-based agentic RAG methods partially alleviate...
Long-horizon story-driven video generation requires a production agent to coordinate narrative decomposition, state tracking, shot design, prompt construction, rendering, and revision across interdependent scenes. Existing adaptive video systems primarily refine requests or reusable skills, leaving recurring production failures...
Multi-access speculative inference (Multi-SPIN) extends SPIN to multi-device edge networks to accelerate cooperative token generation. It allows on-device small language models (SLMs) to autoregressively draft multiple tokens for individual generation tasks, while an edge-server large language model (LLM) verifies them in parallel....
This paper introduces a hybrid fact-checking framework that integrates Knowledge Graph-based semantic memory with adversarial multi-agent reasoning for explainable misinformation detection. The proposed system follows a memory-first, web-fallback architecture, in which input claims are initially evaluated against a dual-index...