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…

Summary: The Gartner Magic Quadrant for Data Science and Machine Learning Platforms is just out the big news is how much more capable all the platforms have become.  Of course there are also some interesting winner and loser stories.

The Gartner Magic Quadrant for Data Science and Machine Learning Platforms is just out for 2020.  The really big news is how many excellent choices are now available.  In a remarkable move, the whole field…

In this notebook, we try to predict the positive (label 1) or negative (label 0) sentiment of the sentence. We use the UCI Sentiment Labelled Sentences Data Set.

Sentiment analysis is very useful in many areas. For example, it can be used for internet conversations moderation. Also, it is possible to predict ratings that users can assign to a certain product (food, household appliances, hotels,…