Related papers: Alan M. Turing: The Applications of Probability to…

In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we…

The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

We discuss the legacy of Alan Turing and his impact on computability and analysis.

The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…

With the rapid development of quantum computers the currently secure cryptographic protocols may not stay that way. Quantum mechanics provides means to create an inherently secure communication channel that is protected by the laws of…

This paper describes privacy-preserving approaches for the statistical analysis. It describes motivations for privacy-preserving approaches for the statistical analysis of sensitive data, presents examples of use cases where such methods…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…

Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…

The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…

This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with…

The Unix command \texttt{find} is among the first commands taught to beginners, yet remains indispensable for experienced engineers. In this paper, we demonstrate that \texttt{find} possesses unexpected computational power, establishing…

Password users frequently employ passwords that are too simple, or they just reuse passwords for multiple websites. A common complaint is that utilizing secure passwords is too difficult. One possible solution to this problem is to use a…

In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…

Compression also known as entropy coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming for instance) renews an interest in fast compression that…