Preface to the English Edition. Preface to the German Edition. Real Interval Arithmetic. Further Concepts and Properties. Interval Evaluation and Range of Real Functions. Machine Interval Arithmetic. Complex Interval Arithmetic. Metric, Absolute, Value, and Width in. Inclusion of Zeros of a Function of One Real Variable. Methods for the Simultaneous Inclusion of Real Zeros of Polynomials. Methods for the Simultaneous Inclusion of Complex Zeros of Polynomials. Interval Matrix Operations. Fixed Point Iteration for Nonlinear Systems of Equations. Systems of Linear Equations Amenable to Interation. Optimality of the Symmetric Single Step Method with Taking Intersection after Every Component. On the Feasibility of the Gaussian Algorithm for Systems of Equations with Intervals as Coefficients. Hansen's Method. The Procedure of Kupermann and Hansen. Ireation Methods for the Inclusion of the Inverse Matrix and for Triangular Decompositions. Newton-like Methods for Nonlinear Systems of Equations. Newton-like Methods without Matrix Inversions. Newton-like Methods for Particular Systems of Nonlinear Equations. Newton-like Total step and Single Step Methods. Appendix A. The Order of Convergence of Iteration Methods in vn(Ic) and Mmn(iC) ). Appendix B. Realizations of Machine Interval Arithmetics in ALGOL 60. Appendix C. ALGOL Procedures. Bibliography. Index of Notation. Subject Index.

Introduction to Interval Computation

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)

/pdf/handbook-of-constraint-programming-53srutguo2.pdf

Handbook of Constraint Programming

https://digital.library.unt.edu/ark:/67531/metadc891681/m2/1/high_res_d/886897.pdf

Survey of sampling-based methods for uncertainty and sensitivity analysis

Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic. Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs. Guides readers to develop sound solutions, avoid known mistakes, and repeat successful design decisions. Presents comprehensive coveragefrom fundamental theories to current research trends. Written in a clear and engaging style by two masters of the field. Concludes each chapter with in-depth discussions of the key literature. Includes a full set of over 250 exercises, an on-line appendix with solutions to one-third of the exercises and 600 lecture slides

Digital arithmetic

Ordinary differential equations (ODEs) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last two decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determining unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past couple of decades, including structural identifiability analysis, practical identifiability analysis, and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV and influenza viruses are given to illustrate how to apply these identifiability analysis methods in practice.

/pdf/on-identifiability-of-nonlinear-ode-models-and-applications-i3qalbu5i0.pdf

On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics

Applied Interval Analysis

I. Introduction.- 1. Introduction.- 1.1 What Are the Key Concepts?.- 1.2 How Did the Story Start?.- 1.3 What About Complexity?.- 1.4 How is the Book Organized?.- II. Tools.- 2. Interval Analysis.- 2.1 Introduction.- 2.2 Operations on Sets.- 2.2.1 Purely set-theoretic operations.- 2.2.2 Extended operations.- 2.2.3 Properties of set operators.- 2.2.4 Wrappers.- 2.3 Interval Analysis.- 2.3.1 Intervals.- 2.3.2 Interval computation.- 2.3.3 Closed intervals.- 2.3.4 Interval vectors.- 2.3.5 Interval matrices.- 2.4 Inclusion Functions.- 2.4.1 Definitions.- 2.4.2 Natural inclusion functions.- 2.4.3 Centred inclusion functions.- 2.4.4 Mixed centred inclusion functions.- 2.4.5 Taylor inclusion functions.- 2.4.6 Comparison.- 2.5 Inclusion Tests.- 2.5.1 Interval Booleans.- 2.5.2 Tests.- 2.5.3 Inclusion tests for sets.- 2.6 Conclusions.- 3. Subpavings.- 3.1 Introduction.- 3.2 Set Topology.- 3.2.1 Distances between compact sets.- 3.2.2 Enclosure of compact sets between subpavings.- 3.3 Regular Subpavings.- 3.3.1 Pavings and subpavings.- 3.3.2 Representing a regular subpaving as a binary tree.- 3.3.3 Basic operations on regular subpavings.- 3.4 Implementation of Set Computation.- 3.4.1 Set inversion.- 3.4.2 Image evaluation.- 3.5 Conclusions.- 4. Contractors.- 4.1 Introduction.- 4.2 Basic Contractors.- 4.2.1 Finite subsolvers.- 4.2.2 Intervalization of finite subsolvers.- 4.2.3 Fixed-point methods.- 4.2.4 Forward-backward propagation.- 4.2.5 Linear programming approach.- 4.3 External Approximation.- 4.3.1 Principle.- 4.3.2 Preconditioning.- 4.3.3 Newton contractor.- 4.3.4 Parallel linearization.- 4.3.5 Using formal transformations.- 4.4 Collaboration Between Contractors.- 4.4.1 Principle.- 4.4.2 Contractors and inclusion functions.- 4.5 Contractors for Sets.- 4.5.1 Definitions.- 4.5.2 Sets defined by equality and inequality constraints.- 4.5.3 Improving contractors using local search.- 4.6 Conclusions.- 5. Solvers.- 5.1 Introduction.- 5.2 Solving Square Systems of Non-linear Equations.- 5.3 Characterizing Sets Defined by Inequalities.- 5.4 Interval Hull of a Set Defined by Inequalities.- 5.4.1 First approach.- 5.4.2 Second approach.- 5.5 Global Optimization.- 5.5.1 The Moore-Skelboe algorithm.- 5.5.2 Hansen's algorithm.- 5.5.3 Using interval constraint propagation.- 5.6 Minimax Optimization.- 5.6.1 Unconstrained case.- 5.6.2 Constrained case.- 5.6.3 Dealing with quantifiers.- 5.7 Cost Contours.- 5.8 Conclusions.- III. Applications.- 6. Estimation.- 6.1 Introduction.- 6.2 Parameter Estimation Via Optimization.- 6.2.1 Least-square parameter estimation in compartmental modelling.- 6.2.2 Minimax parameter estimation.- 6.3 Parameter Bounding.- 6.3.1 Introduction.- 6.3.2 The values of the independent variables are known.- 6.3.3 Robustification against outliers.- 6.3.4 The values of the independent variables are uncertain.- 6.3.5 Computation of the interval hull of the posterior feasible set.- 6.4 State Bounding.- 6.4.1 Introduction.- 6.4.2 Bounding the initial state.- 6.4.3 Bounding all variables.- 6.4.4 Bounding by constraint propagation.- 6.5 Conclusions.- 7. Robust Control.- 7.1 Introduction.- 7.2 Stability of Deterministic Linear Systems.- 7.2.1 Characteristic polynomial.- 7.2.2 Routh criterion.- 7.2.3 Stability degree.- 7.3 Basic Tests for Robust Stability.- 7.3.1 Interval polynomials.- 7.3.2 Polytope polynomials.- 7.3.3 Image-set polynomials.- 7.3.4 Conclusion.- 7.4 Robust Stability Analysis.- 7.4.1 Stability domains.- 7.4.2 Stability degree.- 7.4.3 Value-set approach.- 7.4.4 Robust stability margins.- 7.4.5 Stability radius.- 7.5 Controller Design.- 7.6 Conclusions.- 8. Robotics.- 8.1 Introduction.- 8.2 Forward Kinematics Problem for Stewart-Gough Platforms.- 8.2.1 Stewart-Gough platforms.- 8.2.2 From the frame of the mobile plate to that of the base.- 8.2.3 Equations to be solved.- 8.2.4 Solution.- 8.3 Path Planning.- 8.3.1 Graph discretization of configuration space.- 8.3.2 Algorithms for finding a feasible path.- 8.3.3 Test case.- 8.4 Localization and Tracking of a Mobile Robot.- 8.4.1 Formulation of the static localization problem.- 8.4.2 Model of the measurement process.- 8.4.3 Set inversion.- 8.4.4 Dealing with outliers.- 8.4.5 Static localization example.- 8.4.6 Tracking.- 8.4.7 Example.- 8.5 Conclusions.- IV. Implementation.- 9. Automatic Differentiation.- 9.1 Introduction.- 9.2 Forward and Backward Differentiations.- 9.2.1 Forward differentiation.- 9.2.2 Backward differentiation.- 9.3 Differentiation of Algorithms.- 9.3.1 First assumption.- 9.3.2 Second assumption.- 9.3.3 Third assumption.- 9.4 Examples.- 9.4.1 Example 1.- 9.4.2 Example 2.- 9.5 Conclusions.- 10. Guaranteed Computation with Floating-point Numbers.- 10.1 Introduction.- 10.2 Floating-point Numbers and IEEE 754.- 10.2.1 Representation.- 10.2.2 Rounding.- 10.2.3 Special quantities.- 10.3 Intervals and IEEE 754.- 10.3.1 Machine intervals.- 10.3.2 Closed interval arithmetic.- 10.3.3 Handling elementary functions.- 10.3.4 Improvements.- 10.4 Interval Resources.- 10.5 Conclusions.- 11. Do It Yourself.- 11.1 Introduction.- 11.2 Notions of C++.- 11.2.1 Program structure.- 11.2.2 Standard types.- 11.2.3 Pointers.- 11.2.4 Passing parameters to a function.- 11.3 INTERVAL Class.- 11.3.1 Constructors and destructor.- 11.3.2 Other member functions.- 11.3.3 Mathematical functions.- 11.4 Intervals with PROFIL/BIAS.- 11.4.1 BIAS.- 11.4.2 PROFIL.- 11.4.3 Getting started.- 11.5 Exercises on Intervals.- 11.6 Interval Vectors.- 11.6.1 INTERVAL_VECTOR class.- 11.6.2 Constructors, assignment and function call operators.- 11.6.3 Friend functions.- 11.6.4 Utilities.- 11.7 Vectors with PROFIL/BIAS.- 11.8 Exercises on Interval Vectors.- 11.9 Interval Matrices.- 11.10 Matrices with PROFIL/BIAS.- 11.11 Exercises on Interval Matrices.- 11.12 Regular Subpavings with PROFIL/BIAS.- 11.12.1 NODE class.- 11.12.2 Set inversion with subpavings.- 11.12.3 Image evaluation with subpavings.- 11.12.4 System simulation and state estimation with subpavings.- 11.13 Error Handling.- 11.13.1 Using exit.- 11.13.2 Exception handling.- 11.13.3 Mathematical errors.- References.

https://hal.archives-ouvertes.fr/hal-00845131/document

Olivier Didrit

Papers

Applied Interval Analysis

Applied interval analysis : with examples in parameter and state estimation, robust control and robotics

Guaranteed Analysis and Optimisation of Parametric Systems with Application to their Stability Degree