Related papers: Rhymes in primes
Replacement of papers q-bio/0605026 and q-bio/0607043 by a single manuscript (q-bio/0701029) follows suggestions from a magazine's referee
Compounding of natural language units is a very common phenomena. In this paper, we show, for the first time, that Twitter hashtags which, could be considered as correlates of such linguistic units, undergo compounding. We identify reasons…
The field of Machine Learning research is divided into subject areas, where each area tries to solve a specific problem, using specific methods. In recent years, borders have almost been erased, and many areas inherit methods from other…
We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
For earlier considered our sequence A166944 in [4] we prove three statements of its connection with twin primes. We also give a sufficient condition for the infinity of twin primes and pose several new conjectures; among them we propose a…
In this paper we consider a variety of mixed character sums. In particular we extend a bound of Heath-Brown and Pierce to the case of squarefree modulus, improve on a result of Chang for mixed sums in finite fields, we show in certain…
We report a method for estimating people's achievement based on their fame. Earlier we discovered (cond-mat/0310049) that fame of fighter pilot aces (measured as number of Google hits) grows exponentially with their achievement (number of…
We present a new and powerful algebraic framework for graph rewriting, based on drags, a class of graphs enjoying a novel composition operator. Graphs are embellished with roots and sprouts, which can be wired together to form edges. Drags…
In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.
We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
In this paper, we propose a joint architecture that captures language, rhyme and meter for sonnet modelling. We assess the quality of generated poems using crowd and expert judgements. The stress and rhyme models perform very well, as…
In this paper, we use a recent method given by Rudnev, Shakan, and Shkredov (2018) to improve results on sum-product type problems due to Pham and Mojarrad (2018).
There is an innate human tendency, one might call it the "league table mentality," to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would…
Contract bridge, a cooperative game characterized by imperfect information and multi-agent dynamics, poses significant challenges and serves as a critical benchmark in artificial intelligence (AI) research. Success in this domain requires…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
The ability to combine symbols to generate language is a defining characteristic of human intelligence, particularly in the context of artistic story-telling through lyrics. We develop a method for synthesizing a rap verse based on the…
The Algonauts 2025 Challenge just wrapped up a few weeks ago. It is a biennial challenge in computational neuroscience in which teams attempt to build models that predict human brain activity from carefully curated stimuli. Previous…