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arXiv Preprints
A naive p-adic height on the Jacobians of curves of genus 2
Consider a genus 2 curve defined over $\mathbb{Q}$ given by an affine equation of the form $y^2 = f(x)$ for some polynomial $f$ of degree 5, and let $p$ be an odd prime. Extending work of Perrin-Riou for elliptic curves, we construct a naive $p$-adic...
math:math:NT
arXiv Preprints
A geometric perspective on plus-one generated arrangements of lines
We give a geometric characterisation of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line arrangements.
math:math:AG
arXiv Preprints
On Axial Symmetry in Convex Bodies
For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to the original body. A classical result states that the Kovner-Besicovitch...
math:math:MGcs:cs:CG
arXiv Preprints
Solution landscapes of ferronematics in microfluidic channels
We investigate solution landscapes for ferronematics i.e., a dilute suspension of magnetic nano-particles in a nematic liquid crystal host, in a reduced one-dimensional setting relevant for microfluidic problems. Solution landscapes show how critical...
physics:cond-mat:soft
arXiv Preprints
The Mahler measure of exact polynomials in three variables
We prove that under certain explicit conditions, the Mahler measure of a three-variable polynomial can be expressed in terms of elliptic curve $L$-values and Bloch-Wigner dilogarithmmic values, conditionally on Beilinson's conjecture. In some ca...
math:math:NT
arXiv Preprints
A Weiss-Williams theorem for spaces of embeddings and the homotopy type of spaces of long knots
We establish a pseudoisotopy result for embedding spaces in the line of that of Weiss and Williams for diffeomorphism groups. In other words, for $P\subset M$ a codimension at least three embedding, we describe the difference in a range of homotopica...
math:math:ATmath:math:GTmath:math:KT
arXiv Preprints
Divisible cube complexes and finite-order automorphisms of RAAGs
We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely the fundamental groups of a class of compact special cube complexes th...
math:math:GRmath:math:GT
arXiv Preprints
Bayesian variable selection in sample selection models using spike-and-slab priors
Sample selection models are a widely used approach for correcting bias caused by data that are missing not at random. Their formulation requires specifying the variables that influence the outcome and those that drive the selection process. This spec...
stat:stat:COstat:stat:ME
arXiv Preprints
Sparse Learning and Class Probability Estimation with Weighted Support Vector Machines
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of weighted Supp...
stat:stat:MEcs:cs:LGstat:stat:ML
arXiv Preprints
Is control of type I error rate needed in Bayesian clinical trial designs?
Practical employment of Bayesian trial designs is still rare. Even if accepted in principle, the regulators have commonly required that such designs be calibrated according to an upper bound for the frequentist type I error rate. This represents an i...
stat:stat:ME
arXiv Preprints
Chevalley formulae for the motivic Chern classes of Schubert cells and for the stable envelopes
We prove a Chevalley formula to multiply the motivic Chern classes of Schubert cells in a generalized flag manifold $G/P$ by the class of any line bundle $\mathcal{L}_λ$. Our formula is given in terms of the $λ$-chains of Lenart and Postnikov. Its ...
math:math:AGmath:math:COmath:math:RT
arXiv Preprints
Coherent Quantum Speed Limits
We establish a comprehensive theoretical framework for coherent quantum speed limits (QSLs), deriving fundamental bounds on the rate of quantum evolution that explicitly isolate the contribution of quantum coherence. By applying Hölder's inequa...
physics:quant-phphysics:cond-mat:quant-gas
arXiv Preprints
Harnack inequalities for equations of type prescribed scalar curvature
We give Harnack inequalities for solutions of equations of type prescribed scalar curvature in dimensions n $\ge$ 4.
math:math:AP
arXiv Preprints
Limits on the Primordial Black Holes Dark Matter with future MeV detectors
Primordial black holes (PBHs) are a compelling candidate for Dark Matter (DM). There remain significant parameter spaces to be explored despite current astrophysical observations have set strong limits. Utilizing advanced MeV observation instruments,...
physics:astro-ph:HE
arXiv Preprints
On the Frobenius fields of abelian varieties over number fields
Let $A$ be a non-CM simple abelian variety over a number field $K$. For a place $v$ of $K$ such that $A$ has good reduction at $v$, let $F(A,v)$ denote the Frobenius field generated by the corresponding Frobenius eigenvalues. Assuming $A$ has connect...
math:math:NT
arXiv Preprints
Lower bounds on fibered Yang-Mills functionals: generic nefness and semistability of direct images
The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of complex projec...
math:math:DGmath:math:AGmath:math:CV
arXiv Preprints
MLFEF: Machine Learning Fusion Model with Empirical Formula to Explore the Momentum in Competitive Sports
Tennis is so popular that coaches and players are curious about factors other than skill, such as momentum. This article will try to define and quantify momentum, providing a basis for real-time analysis of tennis matches. Based on the tennis Grand S...
cs:cs:LG
arXiv Preprints
The $\bar\partial$-problem on $Z(q)$-domains
Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists of the exis...
math:math:CV
arXiv Preprints
Cabello's nonlocality argument for multisetting high-dimensional systems and its experimental test
Recent advancements have expanded Hardy's nonlocality arguments into multisetting and multidimensional systems to enhance quantum correlations. In comparison with Hardy's nonlocal argument, Cabello's nonlocal argument (CNA) emerges as ...
physics:quant-ph
arXiv Preprints
Exact upper bounds for the minimum sizes of strong and weak separating path systems of cliques
We prove an upper bound of $n+9$ for the strong separation number of the complete graph $K_n$, and an upper bound of $n+1$ for its weak separation number. This improves on the previous best known bound of $(1+o(1))n$ for both cases.
math:math:CO