Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

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Iterative Methods for Sparse Linear Systems

Our experience of the world is multimodal - we see objects, hear sounds, feel texture, smell odors, and taste flavors Modality refers to the way in which something happens or is experienced and a research problem is characterized as multimodal when it includes multiple such modalities In order for Artificial Intelligence to make progress in understanding the world around us, it needs to be able to interpret such multimodal signals together Multimodal machine learning aims to build models that can process and relate information from multiple modalities It is a vibrant multi-disciplinary field of increasing importance and with extraordinary potential Instead of focusing on specific multimodal applications, this paper surveys the recent advances in multimodal machine learning itself and presents them in a common taxonomy We go beyond the typical early and late fusion categorization and identify broader challenges that are faced by multimodal machine learning, namely: representation, translation, alignment, fusion, and co-learning This new taxonomy will enable researchers to better understand the state of the field and identify directions for future research

Multimodal Machine Learning: A Survey and Taxonomy

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.

The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.

The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.

The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.

- Covers the whole field of constraint programming
- Survey-style chapters
- Five chapters on applications

Table of Contents

Foreword (Ugo Montanari) 
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) 
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) 
Chapter 3. Constraint Propagation (Christian Bessiere) 
Chapter 4. Backtracking Search Algorithms (Peter van Beek) 
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) 
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons) 
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) 
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith) 
Part II : Extensions, Languages, and Applications

Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) 
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) 
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) 
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) 
Chapter 17. Constraints over Structured Domains
(Carmen Gervet) 
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings) 
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) 
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

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Handbook of Constraint Programming

ly, this program guesses nondeterministically the correct permutation via permutation(Xs,Ys), and ordered checks that the permutation is actually ordered. Operationally, the behavior is as follows. A query involving sort is reduced to a query involving permutation and ordered. A failure-driven loop ensues. A permutation of the list is generated by permutation and tested by ordered. If the permuted list is not ordered, the execution backtracks to the permutation goal, which generates another permutation to be tested. Eventually an ordered permutation is generated and the computation terminates. Permutation sort is a highly inefficient sorting algorithm, requiring time super-exponential in the size of the list to be sorted. Pushing the tester into the generator, however, leads to a reasonable algorithm. The generator for permutation sort, permutation, selects an arbitrary element and recursively permutes the rest of the list. The tester, ordered, verifies that the first two elements of the permutation are in order, then recursively checks the rest. If we view the combined recursive permutation and ordered goals as a recursive sorting process, we have the basis for insertion sort, Program 3.21. To sort a list, sort the tail of the list and insert the head of the list into its correct place in the order. The arbitrary selection of an element has been replaced by choosing the first element. Another example of the advantage of intertwining generating and testing can be seen with programs solving the N queens problem. The N queens problem requires the placement of N pieces on an Nby-N rectangular board so that no two pieces are on the same line: horizontal, vertical, or diagonal. The original formulation called for 8 queens to be placed on a chessboard, and the criterion of not being on the same line corresponds to two queens not attacking each other under the rules of chess. Hence the problem's name. 253 Nondeterministic Programming

The art of Prolog

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This article overviews many of these approaches in a tutorial fashion.

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Algorithms for constraint-satisfaction problems: a survey

A DCG consists of a set of rules in a notation based on logic programming. Each rule is similar to a context-free rule, with variables to show connections between the constituents involved, and an arbitrary test or action can be appended to the rule (for example, to handle number-agreement). DCGs are an extension of the grammar-rule notation in PROLOG , and can be used to parse a string simply by interpreting them in a manner similar to the execution of a Prolog program.

Definite Clause Grammars

If one approximates the vocal tract as a series of fixed length tubes (which is equivalent to representing it as an all-pole digital filter) it becomes possible to predict successive samples of the speech wave as linear combinations of previous samples. The coefficients in the linear combination characterize the shape of the vocal tract. A sequence of sets of coefficients can be used to characterize the changing shape of the vocal tract over time. This representation is widely used because of the particularly efficient algorithms associated with it.

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Linear Predictive Coding

A context-free grammar is a collection of context-free phrase structure rules. Each such rule names a constituent type and specifies a possible expansion thereof. The standard notation is: 

$$ {\rm{lhs}}\,\, \to \,\,{\rm{rh}}{{\rm{s}}_{\rm{1}}}\,\,.\,\,.\,\,.\,\,{\rm{rh}}{{\rm{s}}_{\rm{n}}} $$

where lhs names the constituent, and rhs1 through rhsn the expansion. Such rules are context-free rules because the expansion is unconditional — the environment of the constituent to be expanded is irrelevant.

Context-Free Grammar

A solution technique for discrete optimisation problems which is widely used outside Al and is closely related to the A* algorithm . The task is to find the optimally valued tip of a walkable search tree. A subtree of the search tree need not be searched if a computation at its root yields a bound for its set of tip values which implies that none of them can be optimal.

Branch-and-Bound Algorithms

We outline the progress we have made in connection with the Alvey Grant "Proving Properties of Logic Programs" (SERC GRjDj44270 and Alvey IKBS 137). This grant runs for three years from 1st November 1985. The grant holders are Professor Alan Bundy and Dr Don Sannella and it employs or has employed Dr Fausto Giunchiglia, Frank van Harmelen, Jane Hesketh, Dr Alan Smaill and Dr Lincoln Wallen as Research Associates. Pete Madden and Andrew Stevens are attached Ph.D. students.

Lincoln Wallen

Papers

Definite Clause Grammars

Linear Predictive Coding

Context-Free Grammar

Branch-and-Bound Algorithms

Proving properties of logic programs: A Progress Report