Download or read book Partitions written by Frank Hwang and published by World Scientific. This book was released on 2013 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The clustering problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory OCo or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Download or read book Partitions Optimality And Clustering Vol Ii Multi parameter written by Frank Kwang-ming Hwang and published by World Scientific. This book was released on 2013-04-24 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The “clustering” problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory — or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Download or read book Partitions Multi parameter written by Frank Hwang and published by World Scientific Publishing Company Incorporated. This book was released on 2013 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Bounded-shape sum-partition problems: polyhedral approach. 1.1. Linear objective: solution by LP. 1.2. Enumerating vertices of the partition polytopes and corresponding partitions using edge-directions. 1.3. Representation, characterization and enumeration of vertices of partition polytopes: distinct partitioned vectors. 1.4. Representation, characterization and enumeration of vertices of partition polytopes: general case. 2. Constrained-shape and single-size sum-partition problems: polynomial approach. 2.1. Constrained-shape partition polytopes and (almost-) separable partitions. 2.2. Enumerating separable and limit-separable partitions of constrained-shape. 2.3. Single-size partition polytopes and cone-separable partitions. 2.4. Enumerating (limit-) cone-separable partitions -- 3. Partitions over multi-parameter spaces: combinatorial structure. 3.1. Properties of partitions. 3.2. Counting and enumerating partition classes of single-size. 3.3. Consistency and sortability of particular partition-properties -- 4. Clustering problems over multi-parameter spaces. 4.1. Geometric properties of optimal partitions. 4.2. Geometric properties of optimal partitions for d = 2 -- 5. Sum-multipartition problems over single-parameter spaces. 5.1. Multipartitions. 5.2. Single-multishape multipartition polytopes. 5.3. Constrained-multishape multipartition polytopes. 5.4. Combinatorial properties of multipartitions. 5.5. Constrained-multishape multipartition problems with asymmetric Schur convex objective: optimization over multipartition polytopes. 5.6. Sum multipartition problems: explicit solutions -- 6. Applications. 6.1. Assembly of systems. 6.2. Group testing. 6.3. Circuit card library. 6.4. Clustering. 6.5. Abstraction of finite state machines. 6.6. Multischeduling. 6.7. Cache assignment. 6.8. The blood analyzer problem. 6.9. Joint replenishment of inventory. 6.10. Statistical hypothesis testing. 6.11. Nearest neighbor assignment. 6.12. Graph partitions. 6.13. The traveling salesman problem. 6.14. Vehicle routing. 6.15. Division of property. 6.16. The consolidation of farmland

Download or read book Partitions Optimality And Clustering Volume I Single parameter written by Frank Kwang-ming Hwang and published by World Scientific. This book was released on 2011-12-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The “clustering” problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory — or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Download or read book Partitions written by Frank Hwang and published by World Scientific. This book was released on 2012 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The OC clusteringOCO problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory OCo or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory."

Download or read book Multiplicity in the Partitioning of Signed Graphs written by Nejat Arinik and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive edges are located inside the modules and negatives ones are in-between them. In practice, real-world networks are rarely perfectly balanced. When it is not the case, one wants to measure the magnitude of the imbalance and to identify the set of edges related to the network imbalance. The Correlation Clustering (CC) problem is precisely defined as finding the partition with minimal imbalance. Signed graph partitioning is an important task, which has many applications, as finding a balanced partition helps understanding the system modeled by the graph. However, the standard approach used in the literature is to find a single partition and focus the rest of the analysis on it, as if it was sufficient to fully characterize the studied system. Yet, it may not reflect the meso-structure of the network, and one may need to seek for other partitions to build a better picture. Although this need to look for multiplicity is extremely important from the end user's perspective, only a very few works took it into consideration in their analysis, up to now. In this thesis, we want to relax this traditional single-partition assumption to allow searching for multiple partitions in two separate situations. The first one arises in the context of signed multiplex networks. All traditional approaches proposed to partition multiplex networks in general are based on the single-partition assumption. To overcome this limitation, we propose a new partitioning method that integrates a meta-clustering process before merging the partitions of individual layers, which allows identifying structurally similar layers. The second situation is specific to the CC problem. When solving an instance of such problem, several or even many optimal partitions may coexist. If multiple optimal partitions coexist, one can then wonder how different/diverse they are. Put differently, we want to know what we loose when considering only one partition, while there might be multiple ones. In order to answer these questions, one should ideally enumerate completely the space of optimal partitions, and perform its analysis. To this end, we propose a new efficient solution space enumeration method and a cluster analysis-based framework in order to first enumerate the space of optimal partitions and then empirically study such space. Lastly, each of these previous situations requires to compute the similarity between partitions. In the context of graph partitioning, this task can be done through a so-called external evaluation measure. However, there exist many such measures, each having different characteristics. This makes it challenging to select the most appropriate for a given situation for the end user. To this end, we propose a new empirical evaluation framework in order to produce results that end users can easily interpret. For a collection of candidate measures, it first consists in describing their behavior by computing them for a generated dataset of parametric partitions, obtained by applying a set of predefined parametric partition transformations. Second, our framework characterizes the measures in terms of how they are affected by these parameters and transformations.

Download or read book Optimum Partition Parameter of Divide And Conquer Algorithm written by Mohammad Zaidul Karim and published by LAP Lambert Academic Publishing. This book was released on 2012-03 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divide and Conquer is a well known algorithmic procedure for solving closest pair problems.In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. It is theoretically and practically observed that sometimes partitioning the problem space into more than two parts can give better performances. In this work we proposed that dividing the problem space into (n) number of parts can give better result.We organized the book as follows, in Chapter 2, we discussed Divide-and-Conquer algorithm and Closest-Pair problem. In Chapter 3, we reviewed previous works about Divide-and- Conquer algorithm to solve Closest-Pair problem. In Chapter 4, we present detailed version of the Basic-2 algorithm and give the correspondent proof of correctness as presented by Jose C. Pereira & Fernando G. Lobo (2010). In Chapter 5, some previous proofs are given where is proven that 2-ary system is not the best choice for all the algorithms. The results in this chapter are based on [Kayk98]. In Chapter 6, a new procedure of divide and conquer rule is presented to solve the closest pair of points problem. In Chapter 7, we discussed future work and conclude our work.

Download or read book Partitions written by Frank Hwang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partitions Single parameter written by Frank Hwang and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partitions Hypergeometric Systems and Dirichlet Processes in Statistics written by Shuhei Mano and published by Springer. This book was released on 2018-07-12 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.

Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Download or read book Applications of Evolutionary Computing written by Mario Giacobini and published by Springer Science & Business Media. This book was released on 2007-04-02 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed joint proceedings of seven workshops on evolutionary computing, EvoWorkshops 2007, held in Valencia, Spain in April 2007. It examines evolutionary computation in communications, networks, and connected systems; finance and economics; image analysis and signal processing; and transportation and logistics. Coverage also details evolutionary algorithms in stochastic and dynamic environments.

Download or read book Asymptotic Expansion of a Partition Function Related to the Sinh model written by Gaëtan Borot and published by Springer. This book was released on 2016-12-08 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.

Download or read book Precipitation Partitioning by Vegetation written by John T. Van Stan, II and published by Springer Nature. This book was released on 2020-01-01 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents research on precipitation partitioning processes in vegetated ecosystems, putting them into a global context. It describes the processes by which meteoric water comes into contact with the vegetation's canopy, typically the first surface contact of precipitation on land. It also discusses how precipitation partitioning by vegetation impacts the amount, patterning, and chemistry of water reaching the surface, as well as the amount and timing of evaporative return to the atmosphere. Although this process has been extensively studied, this is the first review of the global literature on the partitioning of precipitation by forests, shrubs, crops, grasslands and other less-studies plant types. The authors offer global contextualization combined with a detailed discussion of the impacts for the climate and terrestrial ecohydrological systems. As such, this comprehensive overview is a valuable reference tool for a wide range of specialists and students in the fields of geoscience and the environment.

Download or read book Multi Parametric Programming written by Efstratios N. Pistikopoulos and published by Wiley-VCH. This book was released on 2007-04-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first book to cover all aspects of multi-parametric programming and its applications in process systems engineering includes theoretical developments and algorithms in multi-parametric programming with applications from the manufacturing sector and energy and environment analysis. The volume thus reflects the importance of fundamental research in multi-parametric programming applications, developing mechanisms for the transfer of the new technology to industrial problems. Since the topic applies to a wide range of process systems, as well as due to the interdisciplinary expertise required to solve the challenge, this reference will find a broad readership. Inspired by the leading authority in the field, the Centre for Process Systems Engineering at Imperial College London.

Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Download or read book Aspects of Exchangeable Partitions and Trees written by Christopher Kenneth Haulk and published by . This book was released on 2011 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exchangeability -- the probabilistic symmetry meaning ì̀nvariance under the action of the symmetric group, '' or less formally, ì̀rrelevance of labels or indices'' -- has been the subject of continuing interest to probabilists and statisticians since de Finetti's celebrated characterization of infinite exchangeable sequences of Bernoulli random variables as mixtures of IID sequences. The topic of this dissertation is exchangeability as it pertains to random partitions and trees. The main result is a de Finetti-type theorem characterizing a class of exchangeable trees called hierarchies which arise in connection with fragmentation processes and hierarchical clustering problems. The other results are somewhat related in that they involve consideration of moments of statistics of exchangeable partitions or trees. One of these concerns random trees with leaves labeled by consecutive natural numbers which are exchangeable in the sense that deterministic permutation of the leaf labels does not change the distribution of the tree. In such trees, the set of interleaf distances is exchangeable, and so, for example, the distance between leaf 1 and leaf 2 is equal in distribution to the distance between leaf 2 and leaf 3. Distributional constraints of this type arising from exchangeability can be used to characterize finite dimensional marginals of well-understood trees such as the Brownian CRT. As an application we show that the Brownian CRT is the scaling limit of uniform random hierarchies. Another result is the characterization of the two-parameter family of Ewens-Pitman partitions by a kind of deletion property: speaking loosely, the Ewens-Pitman family is the class of exchangeable partitions in which the block containing 1 carries no information about the rest of the partition.