Related papers: Alan M. Turing: The Applications of Probability to…
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…
Ciphers are a powerful tool for encrypting communication. There are many different cipher types, which makes it computationally expensive to solve a cipher using brute force. In this paper, we frame the decryption task as a classification…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
In recent years linguistic typology, which classifies the world's languages according to their functional and structural properties, has been widely used to support multilingual NLP. While the growing importance of typological information…
Random number generators are widely used in practical algorithms. Examples include simulation, number theory (primality testing and integer factorization), fault tolerance, routing, cryptography, optimization by simulated annealing, and…
Considering computer systems, security is the major concern with usability. Security policies need to be developed to protect information from unauthorized access. Passwords and secrete codes used between users and information systems for…
Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…
We study the classical Election problem in anonymous net- works, where solutions can rely on the use of random bits, which may be either shared or unshared among nodes. We provide a complete char- acterization of the conditions under which…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial…
Maintaining anonymity in natural language communication remains a challenging task. Even when the number of candidate authors is large, standard authorship attribution techniques that analyze writing style predict the original author with…
This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…
In the era of generative artificial intelligence and the Internet of Things, while there is explosive growth in the volume of data and the associated need for processing, analysis, and storage, several new challenges are faced in…
The widespread use of preprint repositories such as arXiv has accelerated the communication of scientific results but also introduced overlooked security risks. Beyond PDFs, these platforms provide unrestricted access to original source…
Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a…
A while ago, I developed what I called an encryption method. The most favorable of reviews did not see a method but a collection of techniques. Be that as it may, the process used, is described in the paper, Windtalking Computers. This…