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Triesch E: Diskrete Mathematik

Diskrete Mathematik

Theorie und Werkzeuge zur Lösung von Abzähl- und Existenzproblemen

Computer Science Foundations and Applied Logic

Multi-valued and fuzzy logics provide mathematical and computational tools for handling imperfect information and decision-making with rational collective reasoning and irrational individual judgements.&nbsp;The suggested implementation of multi-valued logics is based on the uninorm and absorbing norm with generating functions defined by probability distributions. Natural extensions of these logics result in non-commutative and non-distributive logics. In addition to Boolean truth values, these logics handle subjective truth and false values and model irrational decisions. Dynamics of decision-making are specified by the subjective Markov process and learning – by neural network with extended Tsetlin neurons. Application of the suggested methods is illustrated by modelling of irrational economic decisions and biased reasoning in the wisdom-of-the-crowd method, and by control of mobile robots and navigation of their groups.Topics and features:<ul><li>Bridges the gap between fuzzy and probability methods</li><li>Includes examples in the field of machine-learning and robots’ control</li><li>Defines formal models of subjective judgements and decision-making</li><li>Presents practical techniques for solving non-probabilistic decision-making problems</li><li>Initiates further research in non-commutative and non-distributive logics</li></ul>The book forms a basis for theoretical studies and practice of decision-making under uncertainty and will be useful for computer scientists and mathematicians interested in multi-valued and fuzzy logic, as well as for engineers working in the field of data mining and data analysis.Dr. Evgeny Kagan&nbsp;is with&nbsp;the&nbsp;Faculty of&nbsp;Engineering, Ariel University, Israel; Dr. Alexander Rybalov is with&nbsp;the&nbsp;LAMBDA Laboratory, Tel-Aviv University, Israel; and Prof. Ronald Yager is with&nbsp;the&nbsp;Machine Learning Institute, Yona College, New York, USA.

Multi-Valued Logic for Decision-Making Under Uncertainty

Springer Handbooks

Springer Handbook of Reliability

Mathematical Sciences Research Institute Publications

This edited volume surveys Richman bidding combinatorial games, classical subtraction games and absolute additive theory. The recurring list of open problems, updated and annotated, will interest all practitioners of CGT and related fields including algebra, computer science, combinatorics, number theory and classical game theory.

Games of No Chance 6

Synthesis Lectures on Mathematics & Statistics

This book discusses the theory and practice of random number generators that are useful for computer simulation and computer security applications. &nbsp;Random numbers are ubiquitous in computation. They are used in randomized algorithms to perform sampling or choose randomly initialized parameters or perform Markov Chain Monte Carlo (MCMC). They are also used in computer security applications for various purposes such as cryptographic nuances or in authenticators. &nbsp;In practice, the random numbers used by any of these applications are from a pseudo-random sequence. These pseudo-random sequences are generated by RNGs (random number generators). This book discusses the theory underlying such RNGs, which are used by all programmers. However, few try to understand the theory behind them.&nbsp; This topic is an active area of research, particularly when the generators are used for cryptographic applications. The authors introduce readers to RNGs, how they are judged for quality, the mathematical and statistical theory behind them, as well as provide details on how these can be implemented in any programming language. The book discusses non-linear transformations that use classical linear generators for cryptographic applications and how to optimize to make such generators more efficient. In addition, the book provides up-to-date research on RNGs including a modern class of efficient RNGs and shows how to search for new RNGs with good quality and how to parallelize these RNGs.

In summary, this book:

<ul>
	<li>Discusses the theoretical basis and intuition of various random number generators without overly detailed proofs</li>
	<li>Enables readers to design, develop, modify, or experiment with new random number generators</li>
	<li>Provides comprehensive coverage of random number generation for both simulation and cryptographic applications</li>
</ul>

Design, Search, Theory, and Application

Random Number Generators for Computer Simulation and Cyber Security

De Gruyter Series in Probability and Stochastics

Stochastic Hierarchical Complex Dynamic Network-centric Models

Epidemiological Processes in the Biological and Social Sciences

Cambridge Studies in Advanced Mathematics

Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.

Equivariant Cohomology in Algebraic Geometry

Written from a Computational Topology point-of-view the intention of this book is to provide the reader with an easy and up-to-date access to a wide range of topics concerning topological, combinatorial, and geometric aspects of triangulated manifolds.As a compendium of many classical results, complemented with new material, the book is equipped with an extensive bibliography.&nbsp;An atlas of small triangulations is also included.The list of topics comprises: classification results, PL structures and Hauptvermutung, recognition techniques, computation of invariants, explicit constructions of examples, enumeration procedures, f-vectors of triangulations, vertex-minimal, vertex-transitive, and centrally symmetric examples, realizability issues, polytopality and tightness of triangulations.

Triangulated Manifolds

This book provides a comprehensive overview of practical cutting and packing problems, presenting practical algorithms for solving these problems from the perspective of combinatorial optimization. It also discusses the geometric properties and tools for cutting and packing problems.&nbsp;<div> </div><div>Problems of cutting and packing objects have been extensively studied for many years because of the numerous real-world applications-for instance, in the clothing, logistics, manufacturing, and material industries. They can be classified in three ways according to their dimensions: The one-dimensional problem is the most basic category of problems including knapsack problems, bin packing problems, and cutting stock problems. The two-dimensional geometric problems include rectangle packing problems, circle packing problems, and polygon packing problems. The three-dimensional problem is the most difficult category and has applications in container loading, cargo and warehouse management and so forth. Most of these variants are NP-hard, since they contain as a special case the knapsack problem or the bin packing problem, which are already known to be NP-hard. Therefore, heuristics and metaheuristics are essential for designing practical algorithms for these problems. In addition to practical algorithms for solving a wide variety of cutting and packing problems, the book also considers another feature of cutting and packing problems: the need to develop powerful geometric tools to handle the wide variety and complexity of shapes that need to be packed.</div><div> </div>

<div>This book provides a comprehensive overview of practical cutting and packing problems, presenting practical algorithms for solving these problems from the perspective of combinatorial optimization. It also discusses the geometric properties and tools for cutting and packing problems.&nbsp;</div><div> </div><div>Problems of cutting and packing objects have been extensively studied for many years because of the numerous real-world applications—for instance, in the clothing, logistics, manufacturing, and material industries. They can be classified in three ways according to their dimensions: The one-dimensional problem is the most basic category of problems including knapsack problems, bin packing problems, and cutting stock problems. The two-dimensional geometric problems include rectangle packing problems, circle packing problems, and polygon packing problems. The three-dimensional problem is the most difficult category and has applications in container loading, cargo and warehouse management and so forth. Most of these variants are NP-hard, since they contain as a special case the knapsack problem or the bin packing problem, which are already known to be NP-hard. Therefore, heuristics and metaheuristics are essential for designing practical algorithms for these problems. In addition to practical algorithms for solving a wide variety of cutting and packing problems, the book also considers another feature of cutting and packing problems: the need to develop powerful geometric tools to handle the wide variety and complexity of shapes that need to be packed.</div>&nbsp;&nbsp;

From the Perspective of Combinatorial Optimization

Cutting and Packing Problems

Professional Practice in Governance and Public Organizations

From Administrative Sources to Public Value

Data-Driven Learning in the EU

Annals of Mathematics Studies

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne’s theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions. This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Selected Chapters Of Number Theory: Special Numbers

Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical, and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be of interest to professionals, students, and a general audience.

The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.

Catalan Numbers

Agent-Based Models with MATLAB introduces Agent-Based Modeling (ABM), one of the most important methodologies for complex systems modeling. The book explores computational implementations and accompanying MATLAB software code as a means of inspiring readers to apply agent-based models to solve a diverse range of problems. It comes with a large amount of software code that accompanies the main text, and the modeling systems described in the book are implemented using MATLAB as the programming language. Despite the heavy mathematical components of Agent-Based Models and complex systems, it is possible to utilize these models without in-depth understanding of their mathematical fundamentals. This book enables computer scientists, mathematicians, researchers, and engineers to apply ABM in a wide range of research and engineering applications. It gradually advances from basic to more advanced methods while reinforcing complex systems through practical, hands-on applications of various computational models.

Agent-Based Models with MATLAB

Diskrete Mathematik

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