The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

Genetic algorithms, a class of nondeterministic algorithms in which the role of chance makes the precise nature of a solution impossible to guarantee, seem to be well suited to combinatorial-optimization problems in information retrieval. Provides an introduction to techniques and characteristics of genetic algorithms and illustrates their…

Discussion of text compression focuses on a method to reduce the amount of storage needed to represent a Markov model with an extended alphabet, by applying a clustering scheme that brings together similar states. Highlights include probability vectors; algorithms; implementation details; and experimental data with natural languages. (Author/LRW)

Describes a bottom-up procedure for discovering multivalued dependencies in observed data without knowing a priori the relationships among the attributes. The proposed algorithm is an application of technique designed for learning conditional independencies in probabilistic reasoning; a prototype system for automated database schema design has…

Considers problem of optimal scheduling of Boolean expression (each Boolean variable represents binary outcome of program module) on single-processor system. Optimization discussed consists of finding operand arrangement that minimizes average execution costs representing consumption of resources (elapsed time, main memory, number of…

Explains a proposed block of instruction that would give students in industrial engineering, operations research, systems engineering, and applied mathematics the basic understanding required to begin more advanced courses in simulation theory or applications. (DDR)