Related papers: Alan Baker
Let $\mathscr{L}$ denote the $\mathbf{Q}$-vector space of logarithms of algebraic numbers. In this expository work, we provide an introduction to the study of ranks of matrices with coefficients in $\mathscr{L}$. We begin by considering a…
In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.
We give a systematic method of providing numerical evidence for higher order Stark-type conjectures such as (in chronological order) Stark's conjecture over $\mathbb{Q}$, Rubin's conjecture, Popescu's conjecture, and a conjecture due to…
The complex dynamics of baker's map and its variants in an infinite-precision mathematical domain have been extensively analyzed in the past five decades. However, their real structure implemented in a finite-precision computer remains…
We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
Alzheimer's Disease Analysis Model (ADAM) is a multi-agent reasoning large language model (LLM) framework designed to integrate and analyze multimodal data, including microbiome profiles, clinical datasets, and external knowledge bases, to…
This paper summarizes and discusses the methodological research in human genetic linkage analysis, leading up to and following from the paper of C. A. B. Smith presented as a Royal Statistical Society discussion paper in 1953. This paper…
This article describes a procedure to generate a snapshot of the structure of a specific scientific community and their outputs based on the information available in Google Scholar Citations (GSC). We call this method MADAP (Multifaceted…
The theoretical physicist and mathematician Aristophanes Dimakis passed away on July 8, 2021, at the age of 68, in Athens, Greece. We briefly review his life, career and scientific achievements.
In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation…
Quite a long time ago several authors (see,e.g., \cite{Der}, \cite{Pe} ) mentioned that among pioneers of the quark idea we should take into consideration one more (in addition to M. Gell-Mann and G. Zweig) author, Andr\'{e} Petermann (1922…
Alzheimer's Disease (AD) and related dementia are a growing global health challenge due to the aging population. In this paper, we present ADMarker, the first end-to-end system that integrates multi-modal sensors and new federated learning…
Beginning in the 1970s, Alexander Philip Dawid has been a leading contributor to the foundations of statistics and especially to the development and application of Bayesian statistics. He is also known for his work on causality, especially…
We show a large class of analytic submanifolds of C^n to be strongly extremal. This generalizes V. Sprindzhuk's solution of the complex case of Mahler's Problem, and settles complex analogues of conjectures made in the 1970s by Baker and…
This article is a brief Retrospective on the life and work of Robert W. Zwanzig, who formulated nonequilibrium statistical mechanics and who passed away in May of this year.
In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists for over 50 years. A version of this note also serves as an…
A well established agenda on the research output, impact, and structure of global scientific elites such as Nobel Prize laureates has generated interest in the scientific elites from developing countries. This study deploys science mapping…
The symbol length of ${_pBr}(k(\!(\alpha_1)\!)\dots(\!(\alpha_n)\!))$ for an algebraically closed field $k$ of $\operatorname{char}(k) \neq p$ is known to be $\lfloor \frac{n}{2} \rfloor$. We prove that the symbol length for the case of…
The Nobel Memorial Prize in Economics has been awarded annually since 1969. Who wins the prize is a topic of much interest and tracks the whole course of the academic discipline over the last 57 years. Explaining who wins the prize in any…