Download or read book Tractability written by Lucas Bordeaux and published by Cambridge University Press. This book was released on 2014-02-06 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the techniques developed to circumvent computational intractability, a key challenge in many areas of computer science.
Download or read book Tractability of Multivariate Problems Linear information written by Erich Novak and published by European Mathematical Society. This book was released on 2008 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate problems occur in many applications. These problems are defined on spaces of $d$-variate functions and $d$ can be huge--in the hundreds or even in the thousands. Some high-dimensional problems can be solved efficiently to within $\varepsilon$, i.e., the cost increases polynomially in $\varepsilon^{-1}$ and $d$. However, there are many multivariate problems for which even the minimal cost increases exponentially in $d$. This exponential dependence on $d$ is called intractability or the curse of dimensionality. This is the first volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. It is devoted to tractability in the case of algorithms using linear information and develops the theory for multivariate problems in various settings: worst case, average case, randomized and probabilistic. A problem is tractable if its minimal cost is not exponential in $\varepsilon^{-1}$ and $d$. There are various notions of tractability, depending on how we measure the lack of exponential dependence. For example, a problem is polynomially tractable if its minimal cost is polynomial in $\varepsilon^{-1}$ and $d$. The study of tractability was initiated about 15 years ago. This is the first and only research monograph on this subject. Many multivariate problems suffer from the curse of dimensionality when they are defined over classical (unweighted) spaces. In this case, all variables and groups of variables play the same role, which causes the minimal cost to be exponential in $d$. But many practically important problems are solved today for huge $d$ in a reasonable time. One of the most intriguing challenges of the theory is to understand why this is possible. Multivariate problems may become weakly tractable, polynomially tractable or even strongly polynomially tractable if they are defined over weighted spaces with properly decaying weights. One of the main purposes of this book is to study weighted spaces and obtain necessary and sufficient conditions on weights for various notions of tractability. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It may be also suitable for graduate courses and seminars. The text concludes with a list of thirty open problems that can be good candidates for future tractability research.
Download or read book Tractability of Multivariate Problems Standard information for functionals written by Erich Novak and published by European Mathematical Society. This book was released on 2008 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability.
Download or read book Tractability of Complex Control Systems written by Laurent Alexis Dewhirst Lessard and published by Stanford University. This book was released on 2011 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is divided into two main parts. In the first part, we consider the problem of efficiently computing wavefront estimates for use in adaptive optics hardware on ground-based telescopes. Our contribution is a warm-started single-iteration multigrid algorithm that performs as well as conventional vector-matrix-multiplication methods, but at a fraction of the computational cost. We used numerical simulations to compare our algorithm to a variety of other published methods, and validated our findings at the Palomar Observatory. In the second part, we consider feedback control subject to an information constraint. Using a novel algebraic framework, we are able to prove many structural results, including a new convexity result, in a natural and purely algebraic way. We also develop a new condition we call internal quadratic invariance, under which the controller synthesis can be cast as a convex optimization problem. This describes the most general class of tractable decentralized control problems known to date. Both parts of the thesis fit into the broader question of tractability of complex systems. In the first part we look at a practical example which is difficult because of the large number of sensors and actuators. In the second part, we look at decentralized control, which is difficult because of the non-classical information constraint.
Download or read book On the Algorithmic Tractability of Single Nucleotide Polymorphism SNP Analysis and Related Problems written by Sebastian Wernicke and published by diplom.de. This book was released on 2014-04-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhaltsangabe:Abstract: This work brings together two areas of science biology and informatics that have only recently been connected in the emerging (and vastly growing) research field of Bioinformatics. In order to achieve a common basis for Parts 2 and 3 of this work, Part 1 intends to introduce the computer scientist to the relevant biological background and terminology (Chapter 2), and to familiarize the biologist with the relevant topics from theoretical computer science (Chapter 3). Chapter 2 first introduces some terminology from the field of genetics, thereby defining SNPs. We then motivate the analysis of SNPs by two applications, i.e. the analysis of evolutionary development and the field of pharmacogenetics. Especially the field of pharmacogenetics is capable of having an enormous impact on medicine and the pharmaceutical industry in the near future by using SNP data to predict the efficacy of medication. Chapter 3 gives a brief introduction to the field of computational complexity. We will see and motivate how algorithms are analyzed in theoretical computer science. This will lead to the definition of complexity classes , introducing the class NP which includes computationally hard problems. Some of the hard problems in the class NP can be solved efficiently using the tool of fixed-parameter tractability, introduced at the end of this chapter. An important application of SNP data is in the analysis of the evolutionary history of species development (phylogenetic analysis part two chapters 4 and 5). As will be made plausible in Chapter 5 using SNP data is in many ways superior to previous approaches of phylogenetic analysis. In order to analyze the development of species using SNP data, an underlying model of evolution must be specified. A popular model is the so-called perfect phylogeny, but the construction of this phylogeny is a computationally hard problem when there are inconsistencies (such as read-errors or an imperfect .t to the model of perfect phylogeny) in the underlying data. Chapter 4 analyzes the problem of forbidden submatrix removal which is closely connected to constructing perfect phylogenies we will see in Chapter 5 that its computational complexity is directly related to that of constructing a perfect phylogeny from data which is partially erroneous. In this chapter, we analyze the algorithmic tractability of forbidden submatrix removal , characterizing cases where this problem is NP-complete (being [...]
Download or read book Fixed parameter Tractability and Completeness III written by Rod G. Downey and published by . This book was released on 1992 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fixed parameter Tractability and Completeness II written by Rod G. Downey and published by . This book was released on 1992 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simulation of Timeliness and Tractability Conditions for Corn Production Systems written by Mehmet Yener Tulu and published by . This book was released on 1973 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Algorithms and Information Based Complexity written by Fred J. Hickernell and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.
Download or read book Constraint Processing written by Rina Dechter and published by Elsevier. This book was released on 2003-05-22 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning. In Constraint Processing, Rina Dechter, synthesizes these contributions, along with her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. Throughout, she focuses on fundamental tools and principles, emphasizing the representation and analysis of algorithms. - Examines the basic practical aspects of each topic and then tackles more advanced issues, including current research challenges - Builds the reader's understanding with definitions, examples, theory, algorithms and complexity analysis - Synthesizes three decades of researchers work on constraint processing in AI, databases and programming languages, operations research, management science, and applied mathematics
Download or read book Principles and Practice of Constraint Programming written by Peter J. Stuckey and published by Springer. This book was released on 2008-09-22 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 14th International Conference on Principles and Practice of Constraint Programming (CP 2008) held in Sydney, Australia, September 14–18, 2008. The conference was held in conjunction with the International Conference on Automated Planning and Scheduling (ICAPS 2008) and the International Conference on Knowledge Representation and R- soning (KR 2008). Information about the conference can be found at the w- sitehttp://www. unimelb. edu. au/cp2008/. Held annually, the CP conference series is the premier international conference on constraint programming. The conference focuses on all aspects of computing with constraints. The CP conf- ence series is organized by the Association for Constraint Programming (ACP). Information about the conferences in the series can be found on the Web at http://www. cs. ualberta. ca/~ai/cp/. Information about ACP can be found athttp://www. a4cp. org/. CP 2008 included two calls for contributions: a call for research papers, - scribing novel contributions in the ?eld, and a call for application papers, - scribing applications of constraint technology. For the ?rst time authors could directly submit short papers for consideration by the committee. The research track received 84 long submissions and 21 short submissions and the application track received 15 long submissions. Each paper received at least three reviews, which the authors had the opportunity to see and to react to, before the papers and their reviews were discussed extensively by the members of the Program Committee.
Download or read book The Design Inference written by William A. Dembski and published by Cambridge University Press. This book was released on 1998-09-13 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a reliable method for detecting intelligent causes: the design inference.The design inference uncovers intelligent causes by isolating the key trademark of intelligent causes: specified events of small probability. Design inferences can be found in a range of scientific pursuits from forensic science to research into the origins of life to the search for extraterrestrial intelligence. This challenging and provocative book shows how incomplete undirected causes are for science and breathes new life into classical design arguments. It will be read with particular interest by philosophers of science and religion, other philosophers concerned with epistemology and logic, probability and complexity theorists, and statisticians.
Download or read book Computability and Complexity written by Hubie Chen and published by MIT Press. This book was released on 2023-08-29 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, comprehensive, and rigorous introduction to the theory of computation. What is computable? What leads to efficiency in computation? Computability and Complexity offers a clear, comprehensive, and rigorous introduction to the mathematical study of the capabilities and limitations of computation. Hubie Chen covers the core notions, techniques, methods, and questions of the theory of computation before turning to several advanced topics. Emphasizing intuitive learning and conceptual discussion, this textbook’s accessible approach offers a robust foundation for understanding both the reach and restrictions of algorithms and computers. Extensive exercises and diagrams enhance streamlined, student-friendly presentation of mathematically rigorous material Includes thorough treatment of automata theory, computability theory, and complexity theory—including the P versus NP question and the theory of NP-completeness Suitable for undergraduate and graduate students, researchers, and professionals
Download or read book KI 2001 Advances in Artificial Intelligence written by Franz Baader and published by Springer Science & Business Media. This book was released on 2001-09-05 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Joint German/Austrian Conference on Artificial Intelligence, KI 2001, held in Vienna, Austria in September 2001. The 29 revised full technical papers presented together with one invited paper and four posters of industrial papers were carefully reviewed and selected from 79 submissions. All current aspects in AI are addressed, ranging from theoretical and foundational issues to industrial applications.
Download or read book The Routledge Companion to Philosophy of Psychology written by Sarah Robins and published by Routledge. This book was released on 2019-10-08 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Routledge Companion to Philosophy of Psychology, Second Edition is an invaluable guide and major reference source to the key topics, problems, concepts, and debates in philosophy of psychology and is the first companion of its kind. A team of renowned international contributors provide forty-eight chapters, organized into six clear parts: Historical background to philosophy of psychology Psychological explanation Cognition and representation The biological basis of psychology Perceptual experience Personhood. The Companion covers key topics, such as the origins of experimental psychology; folk psychology; behaviorism and functionalism; philosophy, psychology and neuroscience; the language of thought, modularity, nativism, and representational theories of mind; consciousness and the senses; dreams, emotion, and temporality; personal identity; and the philosophy of psychopathology. For the second edition, six new chapters have been added to address the following important topics: belief and representation in nonhuman animals; prediction error minimization; contemporary neuroscience; plant neurobiology; epistemic judgment; and group cognition. Essential reading for all students of philosophy of mind, science, and psychology, The Routledge Companion to Philosophy of Psychology will also be of interest to anyone studying psychology and its related disciplines.
Download or read book Theory and Applications of Satisfiability Testing SAT 2017 written by Serge Gaspers and published by Springer. This book was released on 2017-08-14 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Theory and Applications of Satisfiability Testing, SAT 2017, held in Melbourne, Australia, in August/September 2017. The 22 revised full papers, 5 short papers, and 3 tool papers were carefully reviewed and selected from 64 submissions. The papers are organized in the following topical sections: algorithms, complexity, and lower bounds; clause learning and symmetry handling; maximum satisfiability and minimal correction sets; parallel SAT solving; quantified Boolean formulas; satisfiability modulo theories; and SAT encodings.
Download or read book Principles and Practice of Constraint Programming CP 2005 written by Peter van Beek and published by Springer Science & Business Media. This book was released on 2005-09-22 with total page 906 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Conference on Principles and Practice of Constraint Programming, CP 2005, held in Sitges, Spain, in October 2005. The 48 revised full papers and 22 revised short papers presented together with extended abstracts of 4 invited talks and 40 abstracts of contributions to the doctoral students program as well as 7 abstracts of contributions to a systems demonstration session were carefully reviewed and selected from 164 submissions. All current issues of computing with constraints are addressed, ranging from methodological and foundational aspects to solving real-world problems in various application fields.
