Gil Alon
YOU?
Author Swipe
View article: Spectral gap for the signed interchange process with arbitrary sets
Spectral gap for the signed interchange process with arbitrary sets Open
In 2020, F. Cesi introduced a random walk on the hyperoctahedral group $B_n$ and analysed its spectral gap when the allowed generators are transpositions and diagonal elements corresponding to singletons. In this paper we extend the allowe…
View article: On the geometry of zero sets of central quaternionic polynomials II
On the geometry of zero sets of central quaternionic polynomials II Open
Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and p…
View article: CSM Software: Continuous Symmetry and Chirality Measures for Quantitative Structural Analysis
CSM Software: Continuous Symmetry and Chirality Measures for Quantitative Structural Analysis Open
We present a comprehensive and updated Python-based open software to calculate continuous symmetry measures (CSMs) and their related continuous chirality measure (CCM) of molecules across chemistry. These descriptors are used to quantify d…
View article: On the geometry of zero sets of central quaternionic polynomials
On the geometry of zero sets of central quaternionic polynomials Open
Let R be the ring of polynomials in n central variables over the real quaternion algebra H, and let I be a left ideal in R. We prove that if a polynomial p in R vanishes at all the common zeros of I in H^n with commuting coordinates, then …
View article: On the stopping time of the Collatz map in $\mathbb{F}_2[x]$
On the stopping time of the Collatz map in $\mathbb{F}_2[x]$ Open
We study the stopping time of the Collatz map for a polynomial $f \in \mathbb{F}_2[x]$, and bound it by $O({\rm deg} (f)^{1.5})$, improving upon the quadratic bound proven by Hicks, Mullen, Yucas and Zavislak. We also prove the existence a…
View article: Continuous symmetry and chirality measures: approximate algorithms for large molecular structures
Continuous symmetry and chirality measures: approximate algorithms for large molecular structures Open
Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional …
View article: On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs
On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs Open
In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlyin…
View article: Galois groups over rational function fields over skew fields
Galois groups over rational function fields over skew fields Open
Let be a skew field of finite dimension over its center . We solve the Inverse Galois Problem over the field of fractions of the ring of polynomial functions over in the variable , if contains an ample field.
View article: Diagnosis Prevalence vs. Efficacy in Machine-learning Based Diagnostic Decision Support
Diagnosis Prevalence vs. Efficacy in Machine-learning Based Diagnostic Decision Support Open
Many recent studies use machine learning to predict a small number of ICD-9-CM codes. In practice, on the other hand, physicians have to consider a broader range of diagnoses. This study aims to put these previously incongruent evaluation …
View article: Galois groups over rational function fields over skew fields
Galois groups over rational function fields over skew fields Open
Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.
View article: A Quaternionic Nullstellensatz
A Quaternionic Nullstellensatz Open
We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternion…
View article: Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis
Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis Open
Symmetry of proteins, an important source of their elegant structure and unique functions, is not as perfect as it may seem. In the framework of continuous symmetry, in which symmetry is no longer a binary yes/no property, such imperfectio…
View article: The mean-field quantum Heisenberg ferromagnet via representation theory
The mean-field quantum Heisenberg ferromagnet via representation theory Open
We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function $α_k 2^{α_1+\dotsb+α_n}$ where $α_k$ is the number of cycles of le…
View article: Automorphisms of Products of Drinfeld Half Planes
Automorphisms of Products of Drinfeld Half Planes Open
The Drinfeld upper half-planes play the role of symmetric spaces in the $p$-adic analytic world. We find the automorphism group of a product of such spaces, where each may be defined over a different field. We deduce a rigidity theorem for…