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Introduction to Mathematical Structures and Proofs
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.
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Grokking Artificial Intelligence Algorithms
AI is primed to revolutionize the way we build applications, offering exciting new ways to solve problems, uncover insights, innovate new products, and provide better user experiences. Successful AI is based on a set of core algorithms that form a base of knowledge shared by all data scientists. Grokking Artificial Intelligence Algorithms is a fully-illustrated and interactive tutorial guide to the different approaches and algorithms that underpin AI. Written in simple language and with lots of visual references and hands-on examples, readers learn the concepts, terminology, and theory they need to effectively incorporate AI algorithms into their applications. Grokking Artificial Intelligence Algorithms uses simple language, jargon-busting explanations, and hand-drawn diagrams to open up complex algorithms. Don’t worry if you aren’t a calculus wunderkind; you’ll need only the algebra you picked up in math class. • Use cases for different AI algorithms • How to encode problems and solutions using data structures • Intelligent search for game playing • Ant colony algorithms for path finding • Evolutionary algorithms for optimization problems For software developers with high school-level algebra and calculus skills.
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Algorithms and Discrete Applied Mathematics
This book constitutes the proceedings of the 5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019, held in Kharagpur, India, in February 2019.The 22 papers presented together with 3 invited papers in this volume were carefully reviewed and selected from 86 submissions.The conference had papers in the areas of algorithms, graph theory, combinatorics, computational geometry, discrete geometry, and computational complexity.
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Optimization-based Molecular Dynamics Studies of SARS-CoV-2 Molecular Structures
COVID-19 has brought us extensive research databases in the fields of biophysics, biology, and bioinformatics. To extract valuable structural bioinformatic information of SARS-CoV-2 structural and nonstructural proteins, it is necessary to work with large-scale datasets of molecular dynamics (MD) trajectories that need to be optimized.This monograph serves as a comprehensive guide to optimization-based MD studies of the molecular structures of SARS-CoV-2 proteins and RNA. The book begins by performing local optimization, taking into account the three-body movement and optimizing the noncovalent bonds of each molecular structure. The optimized structures reach a transition state that offers the best stability and lowest energy. The optimization process utilizes a hybrid strategy that combines mathematical optimization with various local search algorithms. This approach significantly reduces data volume while eliminating irrelevant bioinformatics data.To gain a thorough understanding of molecular stability and the mechanism of action, it is essential to consider not only static NMR, X-ray, or cryo-EM structures but also dynamic information obtained through MD or Quantum Mechanics/Molecular Mechanics (QM/MM) simulations. These simulations capture the internal motions and dynamic processes of molecules. Furthermore, for each protein, the structural bioinformatics obtained from the optimized structure is validated by analyzing large-scale MD trajectory databases, which are openly and freely available online. The analysis includes key structural bioinformatics aspects such as salt bridge electrostatic interactions, hydrogen bonds, van der Waals interactions, and hydrophobic interactions specific to each SARS-CoV-2 molecular structure. The book also delves into discussions on drugs, vaccines, and the origins of the virus. Additionally, pandemic mathematical models, including those incorporating time delays, are explored.This book is particularly valuable for professionals working in practical computing roles within computational biochemistry, computational biophysics, optimization and molecular dynamics, structural bioinformatics, biological mathematics, and related fields. It serves as an accessible introduction to these disciplines and is also an excellent teaching resource for students.
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Algorithms and Computational Techniques Applied to Industry
This book presents algorithms and computational applications integrated in software that are being applied in the industry. It shows how companies using these tools are more competitive and efficient in the use and resources management. The book is organized in three sections, depending on the supply chain stage: procurement, including contact with costumers and product design; Production process, including relationship with suppliers and among departments; and Distribution, including logistics and transportation.
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Graphs, Algorithms, and Optimization
The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.
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Programming the Dynamic Analysis of Structures
This book presents a series of integrated computer programs in Fortran-90 for the dynamic analysis of structures, using the finite element method. Two dimensional continuum structures such as walls are covered along with skeletal structures such as rigid jointed frames and plane grids. Response to general dynamic loading of single degree freedom systems is calculated, and the author also examines multi degree of freedom systems (including earthquake analysis). Each chapter covers a different aspect of analytic theory and the corresponding program segments. It will be an essential tool for practising structural and civil engineers, whilst also being of interest to academics and postgraduate students.
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Distributed Graph Algorithms for Computer Networks
This book presents a comprehensive review of key distributed graph algorithms for computer network applications, with a particular emphasis on practical implementation. Topics and features: introduces a range of fundamental graph algorithms, covering spanning trees, graph traversal algorithms, routing algorithms, and self-stabilization; reviews graph-theoretical distributed approximation algorithms with applications in ad hoc wireless networks; describes in detail the implementation of each algorithm, with extensive use of supporting examples, and discusses their concrete network applications; examines key graph-theoretical algorithm concepts, such as dominating sets, and parameters for mobility and energy levels of nodes in wireless ad hoc networks, and provides a contemporary survey of each topic; presents a simple simulator, developed to run distributed algorithms; provides practical exercises at the end of each chapter.
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Algorithms and Discrete Applied Mathematics
This book constitutes the proceedings of the 9th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2023, which was held in Gandhinagar, India, during February 9-11, 2023.The 32 papers presented in this volume were carefully reviewed and selected from 67 submissions. The papers were organized in topical sections named: algorithms and optimization; computational geometry; game theory; graph coloring; graph connectivity; graph domination; graph matching; graph partition and graph covering.
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Data Mining and Knowledge Discovery with Evolutionary Algorithms
This book integrates two areas of computer science, namely data mining and evolutionary algorithms. Both these areas have become increasingly popular in the last few years, and their integration is currently an active research area. In general, data mining consists of extracting knowledge from data. The motivation for applying evolutionary algorithms to data mining is that evolutionary algorithms are robust search methods which perform a global search in the space of candidate solutions. This book emphasizes the importance of discovering comprehensible, interesting knowledge, which is potentially useful for intelligent decision making. The text explains both basic concepts and advanced topics
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Dynamical Systems, Graphs, and Algorithms
This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.
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Wireless Algorithms, Systems, and Applications
This book constitutes the proceedings of the 14th International Conference on Wireless Algorithms, Systems, and Applications, WASA 2019, held in Honolulu, HI, USA, in June 2019. The 43 full and 11 short papers presented were carefully reviewed and selected from 143 submissions. The papers deal with new ideas and recent advances in computer systems, wireless networks, distributed applications, and advanced algorithms that are pushing forward the new technologies for better information sharing, computer communication, and universal connected devices in various environments, especially in wireless networks.
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003.The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.
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Approximation and Online Algorithms
This book constitutes the thoroughly refereed workshop post-proceedings of the 16th International Workshop on Approximation and Online Algorithms, WAOA 2018, held in Helsinki, Finland, in August 2018 as part of ALGO 2018. The 19 revised full papers presented together with one invited paper in this book were carefully reviewed and selected from 44 submissions. Topics of interest for WAOA 2016 were: graph algorithms; inapproximability results; network design; packing and covering; paradigms for the design and analysis of approximation and online algorithms; parameterized complexity; scheduling problems; algorithmic game theory; algorithmic trading; coloring and partitioning; competitive analysis; computational advertising; computational finance; cuts and connectivity; geometric problems; mechanism design; resource augmentation; and real-world applications.
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Algorithms for Quadratic Matrix and Vector Equations
This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.
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WALCOM: Algorithms and Computation
This book constitutes the refereed proceedings of the 7th International Workshop on Algorithms and Computation, WALCOM 2013, held in Kharagpur, India, in February 2013. The 29 full papers presented were carefully reviewed and selected from 86 submissions. The papers are organized in topical sections on computational geometry, approximation and randomized algorithms, parallel and distributed computing, graph algorithms, complexity and bounds, and graph drawing.
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Approximation and Online Algorithms
This book constitutes the thoroughly refereed workshop post-proceedings of the 19th International Workshop on Approximation and Online Algorithms, WAOA 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 16 revised full papers presented in this book were carefully reviewed and selected from 31 submissions. The papers focus on the design and analysis of algorithms for online and computationally hard problems.
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Parallel Architectures and Bioinspired Algorithms
This monograph presents examples of best practices when combining bioinspired algorithms with parallel architectures. The book includes recent work by leading researchers in the field and offers a map with the main paths already explored and new ways towards the future.Parallel Architectures and Bioinspired Algorithms will be of value to both specialists in Bioinspired Algorithms, Parallel and Distributed Computing, as well as computer science students trying to understand the present and the future of Parallel Architectures and Bioinspired Algorithms.
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Algorithms and Architectures for Parallel Processing
The three volume set LNCS 13155, 13156, and 13157 constitutes the refereed proceedings of the 21st International Conference on Algorithms and Architectures for Parallel Processing, ICA3PP 2021, which was held online during December 3-5, 2021. The total of 145 full papers included in these proceedings were carefully reviewed and selected from 403 submissions. They cover the many dimensions of parallel algorithms and architectures including fundamental theoretical approaches, practical experimental projects, and commercial components and systems. The papers were organized in topical sections as follows:Part I, LNCS 13155: Deep learning models and applications; software systems and efficient algorithms; edge computing and edge intelligence; service dependability and security algorithms; data science; Part II, LNCS 13156: Software systems and efficient algorithms; parallel and distributed algorithms and applications; data science; edge computing and edge intelligence; blockchain systems; deept learning models and applications; IoT; Part III, LNCS 13157: Blockchain systems; data science; distributed and network-based computing; edge computing and edge intelligence; service dependability and security algorithms; software systems and efficient algorithms.
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Algorithms and Computations
th This volume contains the proceedings of the 10 ISAAC conference (Tenth - nual International Symposium on Algorithms And Computation) held in Ch- nai, India. This year's conference attracted 71 submissions from as many as 17 di erent countries. Each submission was reviewed by at least three independent referees. After a week-long e-mail discussion, the program committee agreed to include 40 papers in the conference program. The high acceptance rate is clearly an indication of the quality of the papers received. We thank the program c- mittee members and the reviewers for their sincere e orts. We were fortunate to have three invited speakers this year, providing for a very attractive program: Kurt Mehlhorn (MPI, Saarbruck .. en, Germany), Eva T- dos (Cornell University, U.S.A.), and Kokichi Sugihara (Univ. of Tokyo, Japan). Moreover, the conference was preceded by a tutorial on a cutting-edge area, Web Algorithmics by Monika Henzinger (Compaq Systems Research Center, Palo Alto, U.S.A.) as a joint event with FST&TCS 99 (Foundations of Software Te- nology and Theoretical Computer Science, December 13-15, 1999, Chennai).Asa post conference event, a two-day workshop on Approximate Algorithms by R.Ravi (CMU, U.S.A.) and Naveen Garg (IIT, Delhi) was organized. We thank all the in- ted speakers and special event speakers for agreeing to participate in ISAAC'99.
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Conceptual Structures: Current Practices
This book is the proceedings of the Second International Conference on Conceptual Structures, ICCS '94, held at College Park, Maryland, USA in August 1994.This proceedings presents, on an international scale, up-to- the-minute research results on theoretical and applicational aspects of conceptual graphs, particularly on the use of contexts in knowledge representation. The concept of contexts is highly important for all kinds of knowledge-intensive systems. The book is organized into sections on natural language understanding, rational problem solving, conceptual graph theory, contexts and canons, and data modeling.
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Algorithms For Big Data
This unique volume is an introduction for computer scientists, including a formal study of theoretical algorithms for Big Data applications, which allows them to work on such algorithms in the future. It also serves as a useful reference guide for the general computer science population, providing a comprehensive overview of the fascinating world of such algorithms.To achieve these goals, the algorithmic results presented have been carefully chosen so that they demonstrate the important techniques and tools used in Big Data algorithms, and yet do not require tedious calculations or a very deep mathematical background.
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Analysis and Computation of Microstructure in Finite Plasticity
This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.
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Beyond Databases, Architectures, and Structures
This book constitutes the refereed proceedings of the 10th IEEE International Conference Beyond Databases, Architectures, and Structures, BDAS 2014, held in Ustron, Poland, in May 2014. This book consists of 56 carefully revised selected papers that are assigned to 11 thematic groups: query languages, transactions and query optimization; data warehousing and big data; ontologies and semantic web; computational intelligence and data mining; collective intelligence, scheduling, and parallel processing; bioinformatics and biological data analysis; image analysis and multimedia mining; security of database systems; spatial data analysis; applications of database systems; Web and XML in database systems.
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Graph Theory with Algorithms and its Applications
The book has many important features which make it suitable for both undergraduate and postgraduate students in various branches of engineering and general and applied sciences. The important topics interrelating Mathematics & Computer Science are also covered briefly. The book is useful to readers with a wide range of backgrounds including Mathematics, Computer Science/Computer Applications and Operational Research. While dealing with theorems and algorithms, emphasis is laid on constructions which consist of formal proofs, examples with applications. Uptill, there is scarcity of books in the open literature which cover all the things including most importantly various algorithms and applications with examples.
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Statistical Analysis of Graph Structures in Random Variable Networks
This book studies complex systems with elements represented by random variables. Its main goal is to study and compare uncertainty of algorithms of network structure identification with applications to market network analysis. For this, a mathematical model of random variable network is introduced, uncertainty of identification procedure is defined through a risk function, random variables networks with different measures of similarity (dependence) are discussed, and general statistical properties of identification algorithms are studied. The volume also introduces a new class of identification algorithms based on a new measure of similarity and prove its robustness in a large class of distributions, and presents applications to social networks, power transmission grids, telecommunication networks, stock market networks, and brain networks through a theoretical analysis that identifies network structures. Both researchers and graduate students in computer science, mathematics, and optimization will find the applications and techniques presented useful.
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Randomized Algorithms: Approximation, Generation, and Counting
Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.
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Heuristic Approach to Possibilistic Clustering: Algorithms and Applications
The present book outlines a new approach to possibilistic clustering in which the sought clustering structure of the set of objects is based directly on the formal definition of fuzzy cluster and the possibilistic memberships are determined directly from the values of the pairwise similarity of objects. The proposed approach can be used for solving different classification problems. Here, some techniques that might be useful at this purpose are outlined, including a methodology for constructing a set of labeled objects for a semi-supervised clustering algorithm, a methodology for reducing analyzed attribute space dimensionality and a methods for asymmetric data processing. Moreover, a technique for constructing a subset of the most appropriate alternatives for a set of weak fuzzy preference relations, which are defined on a universe of alternatives, is described in detail, and a method for rapidly prototyping the Mamdani’s fuzzy inference systems is introduced. This book addresses engineers, scientists, professors, students and post-graduate students, who are interested in and work with fuzzy clustering and its applications
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Network Algorithms, Data Mining, and Applications
This proceedings presents the result of the 8th International Conference in Network Analysis, held at the Higher School of Economics, Moscow, in May 2018. The conference brought together scientists, engineers, and researchers from academia, industry, and government. Contributions in this book focus on the development of network algorithms for data mining and its applications. Researchers and students in mathematics, economics, statistics, computer science, and engineering find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks. Machine learning techniques in network settings including community detection, clustering, and biclustering algorithms are presented with applications to social network analysis.
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Knowledge Acquisition: Approaches, Algorithms and Applications
This book constitutes the thoroughly refereed post-workshop proceedings of the 2008 Pacific Rim Knowledge Acquisition Workshop, PKAW 2008, held in Hanoi, Vietnam, in December 2008 as part of 10th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2008. The 20 revised papers presented were carefully reviewed and selected from 57 submissions and went through two rounds of reviewing and improvement. The papers are organized in topical sections on machine learning and data mining, incremental knowledge acquisition, web-based techniques and applications, as well as domain specific knowledge acquisition methods and applications.
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Mathematical Foundations of Nature-Inspired Algorithms
This book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search. Algorithms are analyzed from a wide spectrum of theories and frameworks to offer insight to the main characteristics of algorithms and understand how and why they work for solving optimization problems. In-depth mathematical analyses are carried out for different perspectives, including complexity theory, fixed point theory, dynamical systems, self-organization, Bayesian framework, Markov chain framework, filter theory, statistical learning, and statistical measures. Students and researchers in optimization, operations research, artificial intelligence, data mining, machine learning, computer science, and management sciences will see the pros and cons of a variety of algorithms through detailed examples and a comparison of algorithms.
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Algorithms and Architectures for Cryptography and Source Coding in Non-Volatile Flash Memories
In this work, algorithms and architectures for cryptography and source coding are developed, which are suitable for many resource-constrained embedded systems such as non-volatile flash memories. A new concept for elliptic curve cryptography is presented, which uses an arithmetic over Gaussian integers. Gaussian integers are a subset of the complex numbers with integers as real and imaginary parts. Ordinary modular arithmetic over Gaussian integers is computational expensive. To reduce the complexity, a new arithmetic based on the Montgomery reduction is presented. For the elliptic curve point multiplication, this arithmetic over Gaussian integers improves the computational efficiency, the resistance against side channel attacks, and reduces the memory requirements. Furthermore, an efficient variant of the Lempel-Ziv-Welch (LZW) algorithm for universal lossless data compression is investigated. Instead of one LZW dictionary, this algorithm applies several dictionaries to speed up the encoding process. Two dictionary partitioning techniques are introduced that improve the compression rate and reduce the memory size of this parallel dictionary LZW algorithm.
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Structures in Concurrency Theory
This book is the proceedings of the Structures in Concurrency Theory workshop (STRICT) that was held from 11 th to l3th May 1995 in Berlin, Germany. It includes three invited contributions - by J. de Bakker, E. Best et aI, and E. R. Olderog and M. Schenke - and all papers which were submitted and accepted for presentation. Concurrency Theory deals with formal aspects of concurrent systems. It uses partly competing and partly complementary formalisms and structures. The aim of this workshop was to present and compare different formalisms and results in Concurrency Theory. STRICT was organized by the Humboldt-University Berlin and the ESPRIT Basic Research Working Group CALIBAN. Original papers had been sought from all scientists in the field of Concurrency Theory. The Programme Committee selected twenty contributions with various different topics, including Petri Nets, Process Algebras, Distributed Algorithms, Formal Semantics, and others. I am grateful to the Programme Committee and to the other referees for the careful evaluation of the submitted papers.
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Spatially Structured Evolutionary Algorithms
Evolutionary algorithms (EAs) is now a mature problem-solving family of heuristics that has found its way into many important real-life problems and into leading-edge scientific research. Spatially structured EAs have different properties than standard, mixing EAs. By virtue of the structured disposition of the population members they bring about new dynamical features that can be harnessed to solve difficult problems faster and more efficiently. This book describes the state of the art in spatially structured EAs by using graph concepts as a unifying theme. The models, their analysis, and their empirical behavior are presented in detail. Moreover, there is new material on non-standard networked population structures such as small-world networks.The book should be of interest to advanced undergraduate and graduate students working in evolutionary computation, machine learning, and optimization. It should also be useful to researchers and professionals working in fields where the topological structures of populations and their evolution plays a role.
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Jewels Of Stringology: Text Algorithms
The term “stringology” is a popular nickname for text algorithms, or algorithms on strings. This book deals with the most basic algorithms in the area. Most of them can be viewed as “algorithmic jewels” and deserve reader-friendly presentation. One of the main aims of the book is to present several of the most celebrated algorithms in a simple way by omitting obscuring details and separating algorithmic structure from combinatorial theoretical background. The book reflects the relationships between applications of text-algorithmic techniques and the classification of algorithms according to the measures of complexity considered. The text can be viewed as a parade of algorithms in which the main purpose is to discuss the foundations of the algorithms and their interconnections. One can partition the algorithmic problems discussed into practical and theoretical problems. Certainly, string matching and data compression are in the former class, while most problems related to symmetries and repetitions in texts are in the latter. However, all the problems are interesting from an algorithmic point of view and enable the reader to appreciate the importance of combinatorics on words as a tool in the design of efficient text algorithms.In most textbooks on algorithms and data structures, the presentation of efficient algorithms on words is quite short as compared to issues in graph theory, sorting, searching, and some other areas. At the same time, there are many presentations of interesting algorithms on words accessible only in journals and in a form directed mainly at specialists. This book fills the gap in the book literature on algorithms on words, and brings together the many results presently dispersed in the masses of journal articles. The presentation is reader-friendly; many examples and about two hundred figures illustrate nicely the behaviour of otherwise very complex algorithms.
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Optimization Algorithms on Matrix Manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms.The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
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Research and Trends in Data Mining Technologies and Applications
Activities in data warehousing and mining are constantly emerging. Data mining methods, algorithms, online analytical processes, data mart and practical issues consistently evolve, providing a challenge for professionals in the field. ""Research and Trends in Data Mining Technologies and Applications"" focuses on the integration between the fields of data warehousing and data mining, with emphasis on the applicability to real-world problems. This book provides an international perspective, highlighting solutions to some of researchers' toughest challenges. Developments in the knowledge discovery process, data models, structures, and design serve as answers and solutions to these emerging challenges.
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Intersection and Decomposition Algorithms for Planar Arrangements
Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport–Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed. Researchers in computational and combinatorial geometry should find much to interest them in this book.
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Modern Data Mining Algorithms in C++ and CUDA C
Discover a variety of data-mining algorithms that are useful for selecting small sets of important features from among unwieldy masses of candidates, or extracting useful features from measured variables. As a serious data miner you will often be faced with thousands of candidate features for your prediction or classification application, with most of the features being of little or no value. You’ll know that many of these features may be useful only in combination with certain other features while being practically worthless alone or in combination with most others. Some features may have enormous predictive power, but only within a small, specialized area of the feature space. The problems that plague modern data miners are endless. This book helps you solve this problem by presenting modern feature selection techniques and the code to implement them. Some of these techniques are:Forward selection component analysisLocal feature selectionLinking features and a target with a hidden Markov modelImprovements on traditional stepwise selectionNominal-to-ordinal conversion All algorithms are intuitively justified and supported by the relevant equations and explanatory material. The author also presents and explains complete, highly commented source code. The example code is in C++ and CUDA C but Python or other code can be substituted; the algorithm is important, not the code that's used to write it. What You Will LearnCombine principal component analysis with forward and backward stepwise selection to identify a compact subset of a large collection of variables that captures the maximum possible variation within the entire set.Identify features that may have predictive power over only a small subset of the feature domain. Such features can be profitably used by modern predictive models but may be missed by other feature selection methods.Find an underlying hidden Markov model that controls the distributions of feature variables and the target simultaneously. The memory inherent in this method is especially valuable in high-noise applications such as prediction of financial markets.Improve traditional stepwise selection in three ways: examine a collection of 'best-so-far' feature sets; test candidate features for inclusion with cross validation to automatically and effectively limit model complexity; and at each step estimate the probability that our results so far could be just the product of random good luck. We also estimate the probability that the improvement obtained by adding a new variable could have been just good luck. Take a potentially valuable nominal variable (a category or class membership) that is unsuitable for input to a prediction model, and assign to each category a sensible numeric value that can be used as a model input. Who This Book Is For Intermediate to advanced data science programmers and analysts.
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
This is the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006. The book presents 44 carefully reviewed and revised full papers. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, embeddings and metric space methods, and more.
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