Mathematical modelling Books

Book SynopsisThe book is an introduction, for both graduate students and newcomers to the field of the modern theory of mesoscopic complex systems, time series, hypergraphs and graphs, scaled random walks, and modern information theory. As these are applied for the exploration and characterization of complex systems. Our self-consistent review provides the necessary basis for consistency. We discuss a number of applications such diverse as urban structures and musical compositions.

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Book SynopsisThis volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like models for wireless networks, models of Nash networks, dynamic models of advertising, application of reliability models in economics, support vector machines, optimization, complementarity modeling and games.Table of ContentsModeling a Jamming Game for Wireless Networks (A Garnaev); Existence of Nash Networks in the One-Way Flow Model of Network Formation (J Derks et al.); Strategic Advertisement with Externalities: A New Dynamic Approach (R Joosten); A New Axiomatization of the Shapley Value for TU-Games in Terms of Semi-Null Players Applied to 1-Concave Games (T S H Driessen); Coextrema Additive Operators (T Ui et al.); Models without Main Players (T S Arthanari); Weak Convergence of an Iterative Scheme with a Weaker Coefficient Condition (Y Kimura); Complementarity Modeling and Game Theory: A Survey (S K Neogy & A K Das); and other papers.

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Book SynopsisThis monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others.Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.Table of ContentsThis monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

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Book SynopsisThis volume contains the selected contributed papers of the BIOMAT 2010 International Symposium which has been organized as a joint conference with the 2010 Annual Meeting of the Society for Mathematical Biology (www.smb.org) by invitation of the Director Board of this Society. The works presented at Tutorial and Plenary Sessions by expert keynote speakers have been also included.This book contains state-of-the-art articles on special research topics on mathematical biology, biological physics and mathematical modelling of biosystems; comprehensive reviews on interdisciplinary areas written by prominent leaders of scientific research groups. The treatment is both pedagogical and sufficiently advanced to enhance future scientific research.Table of ContentsUsing DNA Knots to Assay Viral Genome Packing (De W Sumners); Mathematical Programming Approach to the Modelling of Biological Macromolecular Structures (R P Mondaini & S P Vilela); Control of West Nile Virus by Insecticide in the Presence of an Avian Reservoir (E Baurin et al.); Mating Strategies and the Allee Effect: A Comparison of Mathematical Models (D I Wallace et al.); The Spatiotemporal Dynamics of African Cassava Mosaic Disease (Z Lawrence & D I Wallace); The Humoral Immune Response: Complexity and Theoretical Challenges (G Shahaf et al.); DNA Library Screening and Transversal Designs (J Guo et al.); Qualitative Analysis of Chemical Bioreactors Behavior (A M Diaz et al.); A Pedigree Analysis including Persons with Several Degrees of Separation and Qualitative Data (C E M Pearce et al.); Effects of Motility and Contact Inhibition on Tumour Viability: A Discrete Simulation Using the Cellular Potts Model (J Li & J Lowengrub); and other papers.

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Book SynopsisThe subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.Table of ContentsSurvey of Numerical Methods to Solve Ordinary and Partial Fractional Differential Equations; Specific and Efficient Methods to Solve Ordinary and Partial Fractional Differential Equations; Fractional Variational Principles; Continuous-Time Random Walks (CTRWs); Applications to Finance and Economics; Generalized Stirling Numbers of First and Second Kind in the Framework of Fractional Calculus.

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Book SynopsisThis review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most recent LPV identification methods for both discrete-time and continuous-time models, using different approaches such as optimization methods for input/output LPV models Identification, set membership methods, optimization methods and subspace methods for state-space LPV models identification and orthonormal basis functions methods. Since there is a strong connection between LPV systems, hybrid switching systems and piecewise affine models, identification of hybrid switching systems and piecewise affine systems will be considered as well.Table of ContentsAn Unified Framework for LPV, Switching and Affine Models Identification (B Bamieh et al.); Set-Membership Identification of LPV Models with Uncertain Time-Varying Parameters (V Cerone et al.); Set Membership Identification of State Space LPV Systems (C Novara); Identification of Discrete-Time and Continuous-Time Input/Output LPV Models (V Laurain et al.); Reducing the Dimensions of Data Matrices Involved in LPV Subspace Identification Methods (V Verdult & M Verhaegen); An Open Loop and Closed Loop LPV Subspace Identification Algorithm (J-W van Wingerden & M Verhaegen); Subspace Identification of Continuous-Time State-Space LPV Models (M Bergamasco & M Lovera); Identification of Continuous-Time LPV Systems Using the Subspace Successive Approximations Algorithm (P L dos Santos et al.); LPV Identification using Series-Expansion Models (R Toth et al.); Expectation Maximization and Gradient Methods for LPV State-Space Models Identification (A Wills et al.); Piecewise Affine Identification of Interconnected Systems with LFR Structure (S Paoletti & A Garulli); Identification and Model (In)validation of Switched Affine Systems (C Feng et al.).

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Book SynopsisWave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.The book comprising seven reviews aims at discussing new challenges in WT and perspectives of its development. A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea. The reviews cover a variety of applications of WT, including water waves, optical fibers, WT experiments on a metal plate and observations of astrophysical WT.Table of ContentsWave Turbulence, A Story Far From Over (A C Newell & B Rumpf); Fluctuations of the Energy Flux in Wave Turbulence (S Aumaitre, E Falcon & S Fauve); Wave Turbulence in Astrophysics (S Galtier); Optical Wave Turbulence (S K Turitsyn, S A Babin, E G Turitsyna, G E Falkovich, E V Podivilov & D V Churkin); Wave Turbulence in a Thin Elastic Plates (G During and N Mordant); Gravity Wave Turbulence in a Large Flume (R Bedard, S Lukaschuk & S Nazarenko); Towards a New Picture of Wave Turbulence (V Shrira & S Annenkov).

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Book SynopsisThe aim of the book is to present side-by-side representative and cutting-edge samples of work in mathematical psychology and the analytic philosophy with prominent use of mathematical formalisms.Table of ContentsThe Impossibility of a Satisfactory Population Ethics (Gustaf Arrhenius); Explaining Interference Effects Using Quantum Probability Theory (Jerome R Busemeyer and Jennifer S Trueblood); Defining Goodness and Badness in Terms of Betterness without Negation (Erik Carlson); Optimality in Multisensory Integration Dynamics: Normative and Descriptive Aspects (Hans Colonius and Adele Diederich); On the Reverse Problem of Fechnerian Scaling (Ehtibar Dzhafarov); Bayesian Adaptive Estimation: A Theoretical Review (Janne V Kujala); Probabilistic Lattices: Theory with an Application to Decision Theory (Louis Narens); Presumption of Equality as a Requirement of Fairness (Wlodek Rabinowicz); Ternary Paired Comparisons Induced by Semi- or Interval Order Preferences (Michel Regenwetter and Clintin P Davis-Stober); Knowledge Spaces Regarded as Set Representations of Skill Structures (Reinhard Suck); Experimental Discrimination of the World's Simplest and Most Antipodal Models: The Parallel-Serial Issue (James T Townsend, Haiyuan Yang, and Devin M Burns); Model Selection with Informative Normalized Maximum Likelihood: Data Prior and Model Prior (Jun Zhang).

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Book SynopsisForeword by Stephen L Adler (Institute for Advanced Study, USA)Illustrations by Peggy Adler The term Phyllotaxis refers to the patterns on plants formed by the arrangement of repeated biological units. In nearly all cases, the Fibonacci Numbers and the Golden Ratio occur in these arrangements. This topic has long fascinated scientists. Over a period of more than two decades, Irving Adler wrote a number of papers that construct a rigorously derived mathematical model for Phyllotaxis, which are major and enduring contributions to the field. These papers are collected in this reprint volume to enable their access to a wider readership.Table of ContentsIntroduction; A Model of Contact Pressure in Phyllotaxis; A Model of Space Filling in Phyllotaxis; The Consequences of Contact Pressure in Phyllotaxis; An Application of the Contact Model of Phyllotaxis to the Close Packing of Spheres around a Cylinder in Biological Fine Structure; The Role of Continued Fractions in Phyllotaxis; The Role of Mathematics in Phyllotaxis; Generating Phyllotaxis Patterns on a Cylindrical Point Lattice; A Yardstick for Measuring the Adequacy of a Model of Phyllotaxis.

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Book SynopsisCrystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. They got their name, because in three dimensions they occur as the symmetry groups of a crystal (which we imagine to extend to infinity in all directions). The book is divided into two parts. In the first part, the basic theory of crystallographic groups is developed from the very beginning, while in the second part, more advanced and more recent topics are discussed. So the first part of the book should be usable as a textbook, while the second part is more interesting to researchers in the field. There are short introductions to the theme before every chapter. At the end of this book is a list of conjectures and open problems. Moreover there are three appendices. The last one gives an example of the torsion free crystallographic group with a trivial center and a trivial outer automorphism group.This volume omits topics about generalization of crystallographic groups to nilpotent or solvable world and classical crystallography. We want to emphasize that most theorems and facts presented in the second part are from the last two decades. This is after the book of L Charlap “Bieberbach groups and flat manifolds” was published.

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Book SynopsisThis book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.Table of ContentsInterpolating Splines of Degree n; Interpolating Cubic Splines; Interpolating Cubic Splines with Several Extreme Characteristics; Smoothing Cubic Splines; Estimation of Smoothing Parameters; Interpolating Quadratic Splines; Smoothing Quadratic Splines; Splines and Average Functions; Compartment Models; Calculability and Identifiability; Compartment Models and Associated Residence Time Distributions; Calculation Methods Related to Compartment Models; Varied Minimum Chi-square Parameter Estimation; Pharmacokinetics for Multiple Applications; Mathematica(R) Programs for Selected Problems.

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Book SynopsisThis book documents the journey undertaken by educators from the Mathematics and Mathematics Education (MME) Academic Group in the National Institute of Education (NIE) and Singapore schools during a Mathematical Modelling Outreach (MMO) event in June 2010 under the guidance of renowned experts in the field of mathematical modelling. The main goal of MMO was to reach out to Singapore primary and secondary schools and introduce the potentials of mathematical modelling as a platform for eliciting mathematical thinking, communication, and reasoning among students. This book contributes to the expanding literature on mathematical modelling by offering voices from the Singaporean context. It suggests how theoretical perspectives on mathematical modelling can be transformed into actual practice in schools, all within the existing infrastructure of the current Singapore mathematics curriculum. More importantly, the book provides documentary evidence on how plans put in place through MMO in 2010 have since been realised.The publication of this book is hence timely at this juncture. Not only does the book record how MMO was among the first pebbles launched into the pond, it also serves as a bridge over which educators can stand upon to view how the ripple effect had developed from the initial MMO pebble and the directions it may continue to extend. Perhaps in the process, other ripples in the teaching, learning, and research of mathematical modelling can be created.Table of ContentsIntroduction; Setting the Stage for Mathematical Modelling in Schools: Promotion of Mathematical Modelling Competencies in the Context of Modelling Projects; Problem Finding and Problem Posing for Mathematical Modelling; Mathematical Modelling in Singapore Schools: A Framework for Instruction; Mathematical Modelling in Australia; Mathematical Modelling in Japan; Fostering Mathematical Modelling in Schools: Learning through Modelling in the Primary Years; Fostering Mathematical Modelling in the Secondary Schools; Fostering Mathematical Competencies: Initial Perspectives from Singapore; Mathematical Modelling - An Example from an Inter-School Modelling Challenge; Mathematical Learning through Modelling Tasks: Learning through 'Designing a Cafe'; Learning through 'Plane Punctuality'; Learning through 'Mobile Phone Plan'; Learning through 'The Best Paper Plane'; Learning through 'Designing a Tent'; Learning through 'Dream Home'; Learning through 'The Unsinkable Titanic'; Implications and Future Directions: Bringing the Ideas Forward.

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Book SynopsisThe book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells.Table of ContentsTeaching Guide; Cancer and Somatic Evolution; Mathematical Modeling of Tumorigenesis; Basic Growth Dynamics and Deterministic Models: Single Species Growth; Two Species Competition Dynamics; Competition Between Genetically Stable and Unstable Cells; Chromosomal Instability and Tumor Growth; Angiogenesis Inhibitors, Promoters, and Spatial Growth; Evolutionary Dynamics and Stochastic Models: Evolutionary Dynamics of Tumor Initiation Through Oncogenes: The Gain-of-Function Model; Evolutionary Dynamics of Tumor Initiation Through Tumor-Suppressor Genes: The Loss-of-Function Model and Stochastic Tunneling; Microsatellite and Chromosomal Instability in Sporadic and Familial Cancers; Evolutionary Dynamics in Hierarchical Populations; Spatial Evolutionary Dynamics of Tumor Initiation; Complex Tumor Dynamics in Space; Stochastic Modeling of Cellular Growth, Treatment, and Resistance Generation; Evolutionary Dynamics of Drug Resistance in Chronic Myeloid Leukemia; Advanced Topics: Evolutionary Dynamics of Stem-Cell Driven Tumor Growth; Tumor Growth Kinetics and Disease Progression; Epigenetic Changes and The Rate of DNA Methylation; Telomeres and Cancer Protection; Gene Therapy and Oncolytic Virus Therapy; Immune Responses, Tumors Growth, and Therapies; Towards Higher Complexities: Social Interactions.

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Book SynopsisAnalysis, modeling, and simulation for better understanding of diverse complex natural and social phenomena often require powerful tools and analytical methods. Tractable approaches, however, can be developed with mathematics beyond the common toolbox. This book presents the white noise stochastic calculus, originated by T Hida, as a novel and powerful tool in investigating physical and social systems. The calculus, when combined with Feynman's summation-over-all-histories, has opened new avenues for resolving cross-disciplinary problems. Applications to real-world complex phenomena are further enhanced by parametrizing non-Markovian evolution of a system with various types of memory functions. This book presents general methods and applications to problems encountered in complex systems, scaling in industry, neuroscience, polymer physics, biophysics, time series analysis, relativistic and nonrelativistic quantum systems.Table of ContentsWhite Noise Analysis: Basic Notion and Terminology; Fluctuations with and without Memory; Fractional Brownian Motion; Complex Systems; Scaling in Industry; Modeling Single Neuron Activities and Interneuronal Connections; Biopolymer Conformation; Hurst Exponent in Time Series Analysis; Quantum Mechanics with Topological Constraints and Boundaries; Relativistic Quantum Mechanics.

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Book SynopsisThis is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation.The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Table of ContentsBasics of Probability Theory; Markov Chains; Markov Decision Processes; The Exponential Distribution and Poisson Process; Jump Markov Processes; Elements of Queueing Theory; Elements of Renewal Theory; Elements of Time Series; Elements of Stochastic Calculus; Elements of Mathematical Finance; Elements of Simulation.

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Book SynopsisThis is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation.The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Table of ContentsBasics of Probability Theory; Markov Chains; Markov Decision Processes; The Exponential Distribution and Poisson Process; Jump Markov Processes; Elements of Queueing Theory; Elements of Renewal Theory; Elements of Time Series; Elements of Stochastic Calculus; Elements of Mathematical Finance; Elements of Simulation.

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Book SynopsisMulti-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH).This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences.Table of ContentsIntroduction; Particle Methods with Background Mesh; Molecular Dynamics; Dissipative Particle Dynamics; Smoothed Particle Hydrodynamics; Special Topics of Particle Methods; Multiple Scale Simulation Using Particle Methods; Computer Implementation Issues of Particle Methods.

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Book SynopsisThis is a book of a series on interdisciplinary topics on the Biological and Mathematical Sciences. The chapters correspond to selected papers on special research themes, which have been presented at BIOMAT 2013 International Symposium on Mathematical and Computational Biology which was held in the Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada, on November 04 - 08, 2013. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. There are comprehensive reviews written by prominent scientific leaders of famous research groups.

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Book SynopsisThe book aims to highlight the fundamental concepts of queueing systems. It starts with the mathematical modeling of the arrival process (input) of customers to the system. It is shown that the arrival process can be described mathematically either by the number of arrival customers in a fixed time interval, or by the interarrival time between two consecutive arrivals. In the analysis of queueing systems, the book emphasizes the importance of exponential service time of customers. With this assumption of exponential service time, the analysis can be simplified by using the birth and death process as a model. Many queueing systems can then be analyzed by choosing the proper arrival rate and service rate. This facilitates the analysis of many queueing systems.Drawing on the author's 30 years of experience in teaching and research, the book uses a simple yet effective model of thinking to illustrate the fundamental principles and rationale behind complex mathematical concepts. Explanations of key concepts are provided, while avoiding unnecessary details or extensive mathematical formulas. As a result, the text is easy to read and understand for students wishing to master the core principles of queueing theory.Table of ContentsModeling of Queueing Systems; Queueing Systems with Losses; Queueing Systems Allowing Waiting; The Engset Loss and Delay Systems; Queueing Systems with a Single Server;

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Book SynopsisThe monograph applies sophisticated topological symmetry tools to biological applications of information theory, along with a Black-Scholes model invocation of the Data Rate Theorem which links information and control theories. The focus is on statistical mechanics and other models that explore pathological phase transitions — driven by changes in available rates of mitochondrial free energy — in physiological functions, a cutting-edge topic in the study of chronic disease. One of the key focuses is Alzheimer's disease — a relatively simple canonical example.Table of ContentsMathematical Preliminaries; A Symmetry-Breaking Model; A Data Rate Theorem Model; A Mutual Information Model; A Fragment Size Model; Extending the Perspective; Embodiment and Environment; Chronic Inflammation; What is to be Done?; Mathematical Appendix;

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Book SynopsisThis is a book of a series on interdisciplinary topics on the Mathematical and Biological Sciences. The chapters correspond to selected papers on special research themes, which have been presented at BIOMAT 2014 International Symposium on Mathematical and Computational Biology which was held in the Stefan Banach International Mathematical Centre at Bedlewo near Poznan, Poland on November 03 - 07, 2014. The treatment is both pedagogical yet advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. As in the other volumes of this series, there are new important results on the interdisciplinary fields of mathematical and biological sciences and comprehensive reviews written by prominent scientific leaders of famous research groups.Table of ContentsPopulation Dynamics: Modelling Sustainable Development for Decision Making (D Angulo, G Olivar and F Angulo); Wild Herbivores in Forests: Four Case Studies (Giorgio Sabetta and Ezio Venturino); Effect of Viral Disease in a Diffusive Plankton System (Nanda Das and Samares Pal); Pattern Recognition of Biological Phenomena: Exploration of Different Wave Patterns in a Model of the Bovine Estrous Cycle by Fourier Analysis (C Stotzel, R Ehrig, H M T Boer, J Plontzke and S Roblitz); A Spectral Similarity Measure between Time Series Applied to Identify Protein-Protein Interactions (G E Salcedo, A M Montoya and A F Arenas); Mathematical Modelling of Infectious Diseases: An Agent-based Modelling Framework to Study the Burden of Pertussis and the Impact of Preventive Measures (J-E Poirrier, C Philemotte and D Curran); Zoonotic Visceral Leishmaniasis: A Novel Model involving Dynamic Interactions of Humans, Dogs and Sandflies (H J Shimozako, Jianhong Wu and E Massad); Mathematical Models for Vaccination, Waning Immunity and Immune System Boosting: A General Framework (M V Barbarossa and G Rost); What is the Optimal Level of Information Dissemination during an Epidemic? (Marek Laskowski, Preeti Dubey, Murray E Alexander, Shannon Collinson, Jane M Heffernan and Seyed M Moghadas); Rich Dynamics of Hepatitis C Viral Infection with Logistic Proliferation (Sandip Banerjee); Computational Biology: In Silico Manipulation of Single DNA Molecules (P Cortini, M Barbi and P Carrivain); Very High Synchrony in Evolution of Organelles and Host Genomes (A I Chernyshova, Yu A Putintzeva and M G Sadovsky); A Method for Clustering Hemagglutinin Influenza Protein Sequences (X Li, H Jankowski, X Wang and Jane M Heffernan); Comparison of the Robustness of Entropy Measures for Protein Domain Families (R P Mondaini, Cecilia Mondaini and Edgar A G G do Amaral); Dynamic and Geometric Modelling of Biomolecular Structures: Dynamics of Z-Ring Formation in Liposomes (R A Barrio, C Varea, T Alarcon, C B Picallo and A Hernandez-Machado); Optimal Control of Protein Langevin Dynamics (R P Mondaini and S C de Albuquerque Neto); Time Asymmetry of Cross-correlation Functions as a Signature of Non-equilibrium Steady States (A Lemarchand and C Bianca); Modelling Physiological Disorders: Entropy of Protein Networks in Malignant Cells of Breast Cancer and Therapeutic Treatment (Jack A Tuszynski, N Carels and T M Tilli); Molecular Dynamics and Computational Drug Discovery: Molecular Dynamics and related Computational Methods with Applications to Drug Discovery (Jack A Tuszynski, T Luchko, P Vinter, Cassandra Churchill, K Sahu, F Gentile, Sara I Omar, N Nayebi, G Hu, K Wang and J Ruan); Multi-scale Models in Biological Sciences: On a Multi-scale Analysis of a Micro-model of Heat Transfer in Biological Tissues (Abdelhamid Ainouz); Multi-scale Modelling in Cell Dynamics (M Banerjee, M Benmir and V Volpert); Mathematical Morphology of Biological Structures: Topology of Cell Membranes (E I Kats and M I Monastyrsky); Geometry of Morphogenesis (N Morozova and R Penner); Comparing Shape Trajectories of Biological Soft Tissues in the Size-and-shape Space (V Varano, S Gabriele, L Teresi, I Dryden, P E Puddu, C Torromeo and P Piras);

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Book SynopsisThe goal of the book is to technologically enhance the preparation of mathematics schoolteachers using an electronic spreadsheet integrated with Maple and Wolfram Alpha — digital tools capable of sophisticated symbolic computations. The content of the book is a combination of mathematical ideas and concepts associated with pre-college problem solving curriculum and their extensions into more advanced mathematical topics.The book provides prospective and practicing teachers with a foundation for developing a deep understanding of many concepts fundamental to the teaching of school mathematics. It also provides the teachers with a technical expertise in designing spreadsheet-based computational environments.Consistent with the current worldwide guidelines for technology-enhanced teacher preparation, the book emphasizes the integration of context, mathematics, and technology as a method for teaching mathematics. Throughout the book, a number of mathematics education documents developed around the world (Australia, Canada, England, Japan, Singapore, United States) are reviewed as appropriate.Table of ContentsBasic Spreadsheet Functions and Techniques; Explorations with Addition and Multiplication Tables; Spreadsheet as a 3-D Modeling Tool; Prime Numbers; Mathematical Concepts as Tools in Spreadsheet Modeling; Pythagorean Triples; Recreational Mathematics; Historical Connection and Geometric Modeling; Computational Problem Solving in Context; Advanced Explorations with Fibonacci Numbers; Ideas for Individual Projects Using Integrated Spreadsheets;

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Book SynopsisThe goal of the book is to technologically enhance the preparation of mathematics schoolteachers using an electronic spreadsheet integrated with Maple and Wolfram Alpha — digital tools capable of sophisticated symbolic computations. The content of the book is a combination of mathematical ideas and concepts associated with pre-college problem solving curriculum and their extensions into more advanced mathematical topics.The book provides prospective and practicing teachers with a foundation for developing a deep understanding of many concepts fundamental to the teaching of school mathematics. It also provides the teachers with a technical expertise in designing spreadsheet-based computational environments.Consistent with the current worldwide guidelines for technology-enhanced teacher preparation, the book emphasizes the integration of context, mathematics, and technology as a method for teaching mathematics. Throughout the book, a number of mathematics education documents developed around the world (Australia, Canada, England, Japan, Singapore, United States) are reviewed as appropriate.Table of ContentsBasic Spreadsheet Functions and Techniques; Explorations with Addition and Multiplication Tables; Spreadsheet as a 3-D Modeling Tool; Prime Numbers; Mathematical Concepts as Tools in Spreadsheet Modeling; Pythagorean Triples; Recreational Mathematics; Historical Connection and Geometric Modeling; Computational Problem Solving in Context; Advanced Explorations with Fibonacci Numbers; Ideas for Individual Projects Using Integrated Spreadsheets;

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Book SynopsisThis book shows, for the very first time, how love stories — a vital issue in our lives — can be tentatively described with classical mathematics. Focus is on the derivation and analysis of reliable models that allow one to formally describe the expected evolution of love affairs from the initial state of indifference to the final romantic regime. The models are in full agreement with the basic philosophical principles of love psychology. Eight chapters are theoretically oriented and discuss the romantic relationships between important classes of individuals identified by particular psychological traits. The remaining chapters are devoted to case studies described in classical poems or in worldwide famous films.Table of ContentsCan We Model Love Stories?; Linear Models and Their Properties; Couples of Secure and Unbiased Individuals; Temporary Bluffing: The Case of Roxane and Cyrano; The Discovery of Hidden Components of the Appeal; Catastrophes in Love Stories: The Case of Beauty and the Beast and of Elizabeth and Darcy; Couples of Insecure and Unbiased Individuals: The Case of Scarlett and Rhett; Romantic Cycles: The Case of Kathe and Jules; The Case of Kathe and Jim; Environmental Stress and Romantic Chaos; Extra Emotional Compartments: The Case of Laura and Francesco; Triangular Love Stories and Unpredictability: The Case of Kathe, Jules, and Jim;

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Book SynopsisDas Lehrbuch vermittelt dem Leser grundlegende Kenntnisse über das, was zwischen Sende- und Empfangsantenne geschieht, da sie für eine plangemäße Funktion entscheidend sind. Die Wellenausbreitung bestimmt maßgebend die Übertragungsverfahren in der Funkkommunikation und beeinflusst in vielen HF-Anwendungen die Systemauslegung. Ziel des Buches ist, dem Leser diese Kenntnisse zu vermitteln sowie ihn in die Lage zu versetzen, Probleme und Möglichkeiten in Zusammenhang mit der Wellenausbreitung zu verstehen und beurteilen zu können.Table of ContentsReflexion, Transmission, Beugung und Streuung.- Troposphäre und Ionosphäre.- Mehrwegeausbreitung, Kanalmodellierung.- Messverfahren von Funkkanälen.- Peiltechnik incl. MUSIC und ESPRIT.- Mehrantennensysteme im Mobilfunk (MIMO).- Räumliche Entzerrung (Zero-Forcing, Matched-Filter, MMSE).

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Book SynopsisFractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.Table of ContentsEssentials of Fractional Calculus; Essentials of Linear Viscoelasticity; Fractional Viscoelastic models; Waves in Linear Viscoelastic Media: Dispersion and Dissipation; Waves in Linear Viscoelastic Media: Asymptotic Representations; Diffusion and Wave-Propagation via Fractional Calculus; Appendices: The Eulerian Functions; The Bessel Functions; The Error Functions; The Exponential Integral Functions; The Mittag - Leffler Functions; The Wright Functions.

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Book SynopsisSocial life of bacteria is in the focus of recent research. Bacteria are simple enough to be accessible by science, but still complex enough to show cooperation, division of labor, bet-hedging, cross-talk and synchronized activities, and a rich variety of social traits. A central question of evolutionary theory is the explanation why this social life did develop, and why these systems are evolutionary stable. This book introduces the reader into the theory of evolution, covering classical models and as well as recent developments. The theory developed is used to represent the up-to-date understanding of social bacteria.This book will be useful for students and lecturers interested in mathematical evolutionary theory, as well as for researchers as a reference.

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Book SynopsisA population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.

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Book SynopsisThis volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov-Maxwell, Fredholm, Lyapunov-Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.

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Book SynopsisQuestions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

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Book SynopsisThis volume provides a setting for a dialogue about ethics, when using mathematical models, and shows the need to continue and define a vocabulary for exploring ethical concerns. The text should act as a clear and strong code of ethics for those having to make ethical decisions.Trade ReviewThis collection of essays makes very interesting reading, reminding us of the ubiquity of modeling in our lives today and of the ethical considerations required of modelers and statisticians. Journal of the American Statistical Association T.G. Groleau, Bethel College, Indiana In summary, Ethics in Modeling does a good job of unveiling the ethical aspects of modeling and covers ethics from many angles. While most chapters would be beyond the grasp of the average undergraduate, they could make good background for a graduate seminar. The book is thought provoking and, at times, deeply philosophical. Anyone doing active modeling research would benefit by taking some time to dwell on these issues.Table of ContentsAcknowledgements. Introduction. How Do the Construction and/or Interpretation of Models Affect Our Decisions? Uses of modeling in science and society (J. Allison et al.). An epistemological view of decision aid technology with emphasis on expert systems (H.D. Carrier, W.A. Wallace). Models in the public sector: success, failure, and ethical behavior (J.M. Mulvey). How Do Values Become Incorporated in Models? Rhetoric and rigor in macroeconomic models: populist and orthodox swings in Latin America (P.D. McNelis). Ethical and modeling considerations in correcting the results of the 1990 decennial census (S.E. Fienberg). The role of models in managerial decision making, never say the model says (V.P. Barabba). What Are the Ethical Responsibilities of Model Builders? From model building to risk management: evolving standards of professional responsibility (N.P. Ross, S. Harris). On model building (J.D.C. Little). Morality and models (R.O. Mason). One-sided practice, can we do better? (J. Rosenhead). Where Do We Go from Here? Ethical concerns and ethical answers (S.I. Gass). Responsible policy modeling (W.E. Walker). Society's role in the ethics of modeling (E.H. Leet, W.A. Wallace). Appendix A: Authors. Appendix B: Ethics in Modeling Workshop agenda. Appendix C: Ethics in Modeling Workshop Participants. Author Index. Subject Index.

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Book SynopsisThe book covers structural, torsion, vibration, heat transfer, and fluid flow problems. It explains equations of equilibrium, stress-strain relations, interpolation functions, element design, symmetry, and FEM applications. Each chapter includes a question bank for self-study.

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Book SynopsisThis book surveys theoretical models in three broad areas of biology (the origin of life, the immune system, and memory in the brain), introducing mathematical and (mainly) computational models that have been used to construct simulations. Most current books on theoretical biology fall into one of two categories: (a) books that specialize in one area of biology and treat theoretical models in considerable depth; and (b) books that concentrate on purely mathematical models, with computers used only to find numerical solutions to differential equations, for example. Although some mathmatical models are considered in this book, the main emphasis is on stochastic computer modles of biological systems. Such techniques have a much greater potential for producting detailed, realistic models of individual systems, and are likely to be the preferred modelling methods of the future. By considering three different areas in biology, the book shows how several of these modelling techniques have beeTrade ReviewAnyone who is interested in the theoretical models of complicated living systems should have this in his or her library. * Bulletin of Mathematical Biology *Table of ContentsI: THE ORIGIN OF LIFE ; II: THE IMMUNE SYSTEM ; III: THE BRAIN

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Book SynopsisMembrane systems are a new class of distributed and parallel model of computation inspired by the subdivision of living cells into compartments delimited by membranes. Their hierarchical internal structure, their locality of interactions, their inherent parallelism and also their capacity to create new compartments, represent the distinguishing hallmarks of membrane systems.Membrane computing, the study of membrane systems, is a fascinating and fast growing area of research. The main streams of current investigations in Membrane Computing concern theoretical computer science and the modelling of complex systems. In this monograph Pierluigi Frisco considers the former trend: he presents an in-depth study of the formal language and computational complexity aspects of the most widely investigated models of membrane systems.This study gives a comprehensive understanding of the computational power of the models considered, shows different proof techniques used for such study, and introducesTable of ContentsPREFACE; ACKNOWLEDGEMENTS; BIBLIOGRAPHY; INDEX

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Book SynopsisThis book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.Table of ContentsIntroduction.- The boundary integral equation.- Basis functions, B-splines.- Description of the geometry.- Getting geometry information from CAD programs.- Numerical treatment of integral equations.- Numerical integration.- Steady state potential problems.- Static linear solid mechanics.- Body force effects.- Treatment of inhomogeneities/inclusions.- Material non-linear behaviour.- Applications in geomechanics.- Viscous flow problems.- Time dependent problems.- Summary and outlook.- Appendix A: Fundamental solutions.

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Book SynopsisThis open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.Table of ContentsDerivation of a cell-based mathematical model of excitable cells.- A cell-based model for ionic electrodiffusion in excitable tissue.- Modeling cardiac mechanics on a subcellular scale.- Operator splitting and finite difference schemes for solving the EMI model.- Solving the EMI equations using finite element methods.- Iterative solvers for EMI models.- Improving neural simulations with the EMI model.- Index.

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Book SynopsisThis monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework.Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes.It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.Table of ContentsIntroduction.- Review.- The mode decomposition problem.- Kernel mode decomposition networks (KMDNets).- Additional programming modules and squeezing.- Non-trigonometric waveform and iterated KMD.- Unknown base waveforms.- Crossing frequencies, vanishing modes, and noise.- Appendix.

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Book SynopsisRobotics technology has recently advanced to the point of being widely accessible for relatively low-budget research, as well as for graduate, undergraduate, and even secondary and primary school education. This lecture provides an example of how to productively use a cutting-edge advanced robotics platform for education and research by providing a detailed case study with the Sony AIBO robot, a vision-based legged robot. The case study used for this lecture is the UT Austin Villa RoboCup Four-Legged Team. This lecture describes both the development process and the technical details of its end result. The main contributions of this lecture are (i) a roadmap for new classes and research groups interested in intelligent autonomous robotics who are starting from scratch with a new robot, and (ii) documentation of the algorithms behind our own approach on the AIBOs with the goal of making them accessible for use on other vision-based and/or legged robot platforms.Table of ContentsIntroduction.- The Class.- Initial Behaviors.- Vision.- Movement.- Fall Detection.- Kicking.- Localization.- Communication.- General Architecture.- Global Map.- Behaviors.- Coordination.- Simulator.- UT Assist.- Conclusion.

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Book SynopsisData integration is a critical problem in our increasingly interconnected but inevitably heterogeneous world. There are numerous data sources available in organizational databases and on public information systems like the World Wide Web. Not surprisingly, the sources often use different vocabularies and different data structures, being created, as they are, by different people, at different times, for different purposes. The goal of data integration is to provide programmatic and human users with integrated access to multiple, heterogeneous data sources, giving each user the illusion of a single, homogeneous database designed for his or her specific need. The good news is that, in many cases, the data integration process can be automated. This book is an introduction to the problem of data integration and a rigorous account of one of the leading approaches to solving this problem, viz., the relational logic approach. Relational logic provides a theoretical framework for discussing data integration. Moreover, in many important cases, it provides algorithms for solving the problem in a computationally practical way. In many respects, relational logic does for data integration what relational algebra did for database theory several decades ago. A companion web site provides interactive demonstrations of the algorithms. Table of Contents: Preface / Interactive Edition / Introduction / Basic Concepts / Query Folding / Query Planning / Master Schema Management / Appendix / References / Index / Author Biography Don't have access? Recommend our Synthesis Digital Library to your library or purchase a personal subscription. Email info@morganclaypool.com for details.Table of ContentsPreface.- Interactive Edition.- Introduction.- Basic Concepts.- Query Folding.- Query Planning.- Master Schema Management.- Appendix.- References.- Index.- Author Biography.

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Book SynopsisRepresentations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. Biometric compression methods, the compact disc, the computerized axial tomography (CAT) scanner in medicine, JPEG compression, and spectral analysis of time-series data are among the many applications of classical Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Generalizing harmonic analysis to discrete spaces poses many challenges: a discrete representation of the space must be adaptively acquired; basis functions are not pre-defined, but rather must be constructed. Algorithms for efficiently computing and representing bases require dealing with the curse of dimensionality. However, the benefits can outweigh the costs, since the extracted basis functions outperform parametric bases as they often reflect the irregular shape of a particular state space. Case studies from computer graphics, information retrieval, machine learning, and state space planning are used to illustrate the benefits of the proposed framework, and the challenges that remain to be addressed. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers to explore this exciting area of research. Table of Contents: Overview / Vector Spaces / Fourier Bases on Graphs / Multiscale Bases on Graphs / Scaling to Large Spaces / Case Study: State-Space Planning / Case Study: Computer Graphics / Case Study: Natural Language / Future DirectionsTable of ContentsOverview.- Vector Spaces.- Fourier Bases on Graphs.- Multiscale Bases on Graphs.- Scaling to Large Spaces.- Case Study: State-Space Planning.- Case Study: Computer Graphics.- Case Study: Natural Language.- Future Directions.

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Book SynopsisMost subfields of computer science have an interface layer via which applications communicate with the infrastructure, and this is key to their success (e.g., the Internet in networking, the relational model in databases, etc.). So far this interface layer has been missing in AI. First-order logic and probabilistic graphical models each have some of the necessary features, but a viable interface layer requires combining both. Markov logic is a powerful new language that accomplishes this by attaching weights to first-order formulas and treating them as templates for features of Markov random fields. Most statistical models in wide use are special cases of Markov logic, and first-order logic is its infinite-weight limit. Inference algorithms for Markov logic combine ideas from satisfiability, Markov chain Monte Carlo, belief propagation, and resolution. Learning algorithms make use of conditional likelihood, convex optimization, and inductive logic programming. Markov logic has been successfully applied to problems in information extraction and integration, natural language processing, robot mapping, social networks, computational biology, and others, and is the basis of the open-source Alchemy system. Table of Contents: Introduction / Markov Logic / Inference / Learning / Extensions / Applications / ConclusionTable of ContentsIntroduction.- Markov Logic.- Inference.- Learning.- Extensions.- Applications.- Conclusion.

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