Bernouilli lattice processes may be one of the simplest examples of point processes, and can be used as an introduction to learn about more complex spatial processes that rely on advanced measure theory for their definition. In this article, we show the differences and analogies between Bernouilli lattice processes on the standard rectangular or hexagonal grid, and the Poisson process, including convergence of discrete lattice processes to continuous Poisson process, mainly in two…

Summary:  Explaining data science to a non-data scientist isn’t as easy as it sounds.  You may know a lot about math, tools, techniques, data, and computer architecture but the question is how do you explain this briefly without getting buried in the detail.  You might try this approach.

We’ve all been…

Product of two large primes are at the core of many encryption algorithms, as factoring the product is very hard for numbers with a few hundred digits. The two prime factors are associated with the encryption keys (public and private keys). Here we describe a new approach to factoring a big number that is the product of two primes of roughly the same size. It is designed especially to handle this problem and identify flaws in encryption algorithms.  …

We discuss a simple trick to significantly accelerate the convergence of an algorithm when the error term decreases in absolute value over successive iterations, with the error term oscillating (not necessarily periodically) between positive and negative values. 

We first illustrate the technique on a well known and simple case: the computation of log 2 using its well know, slow-converging series. We then discuss a very interesting and more complex case, before finally focusing on a…

The methodology described here has broad applications, leading to new statistical tests, new type of ANOVA (analysis of variance), improved design of experiments, interesting fractional factorial designs, a better understanding of irrational numbers leading to cryptography, gaming and Fintech applications, and high quality random numbers generators (and when you really need them). It also features exact arithmetic / high performance computing and distributed algorithms to compute millions of…