This article focuses on the machine learning aspects of the problem, and the use of pattern recognition techniques leading to interesting, new findings about twin primes. Twin primes are prime numbers p such that p + 2 is also prime. For instance, 3 and 5, or 29 and 31. A famous, unsolved and old mathematical conjecture states that there are infinitely many such primes, but a proof still remains elusive to this day. Twin primes are far rarer than primes: there are infinitely more primes than there are twin primes, in the same way that that there are infinitely more integers than there are prime integers.
Saturday, September 4, 2021
Thursday, May 13, 2021
Despite my long statistical and machine learning career both in academia and in the industry, I never heard of complex random variables until recently, when I stumbled upon them by chance while working on some number theory problem. However, I learned that they are used in several applications, including signal processing, quadrature amplitude modulation, information theory and actuarial sciences.
In this article, I provide a short overview of the topic, with application to understanding why the Riemann hypothesis (arguably the most famous unsolved mathematical conjecture of all times) might be true, using probabilistic arguments. Stat-of-the-art, recent developments about this conjecture are discussed in a way that most machine learning professionals can understand. The style of my presentation is very compact, with numerous references provided as needed. It is my hope that this will broaden the horizon of the reader, offering new modeling tools to her arsenal, and an off-the-beaten-path reading. The level of mathematics is rather simple and you need to know very little (if anything) about complex numbers. After all, these random variables can be understood as bivariate vectors (X, Y) with X representing the real part and Y the imaginary part. They are typically denoted as Z = X + iY, where the complex number i (whose square is equal to -1) is the imaginary unit. There are some subtle differences with bivariate real variables. The complex Gaussian variable is of course the most popular case.
Read full article here.
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This article focuses on the machine learning aspects of the problem, and the use of pattern recognition techniques leading to interesting,...
Despite my long statistical and machine learning career both in academia and in the industry, I never heard of complex random variables unti...
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