相关论文: Introduction to the RSA algorithm and modular arit…

This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the…

In this paper, we present a brief survey of Reinforcement Learning (RL), with particular emphasis on Stochastic Approximation (SA) as a unifying theme. The scope of the paper includes Markov Reward Processes, Markov Decision Processes,…

An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…

This letter is the first part of a three-part tutorial focusing on rate-splitting multiple access (RSMA) for 6G. As Part I of the tutorial, the letter presents the basics of RSMA and its applications in light of 6G. To begin with, we first…

We propose a novel approach for the development, analysis, and verification of reductions between NP-complete problems. This method uses the URSA system, a SAT-based constraint solver and incorporates features that distinguish it from…

These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…

These lecture notes provide an overview of Neural Network architectures from a mathematical point of view. Especially, Machine Learning with Neural Networks is seen as an optimization problem. Covered are an introduction to Neural Networks…

Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…

An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.

Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…

Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested…

This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given…

A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.

We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization…

This project involves an implementation of the Rivest Shamir Adleman (RSA) encryption algorithm in C. It consists of generation of two random prime numbers and a number co- prime to phi(n) also called euler toitent function. These three are…

We introduce a new probabilistic public-key cryptosystem which combines the main ingredients of the well-known RSA and Rabin cryptosystems. We investigate the security and performance of our new scheme in comparison to the other two.

Let R be a commutative ring with identity and M be an R-module. The main purpose of this paper is to introduce and study the notion of $\psi$-second submodules of an R-module M.

This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied…

Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.