Machine Learning Algorithms for Problem Solving in Computational Applications

With its intuitive yet rigorous approach to machine learning, this text provides students with the fundamental knowledge and practical tools needed to conduct research and build data-driven products. The authors prioritize geometric intuition and algorithmic thinking, and include detail on all the essential mathematical prerequisites, to offer a fresh and accessible way to learn. Practical applications are emphasized, with examples from disciplines including computer vision, natural language processing, economics, neuroscience, recommender systems, physics, and biology. Over 300 color illustrations are included and have been meticulously designed to enable an intuitive grasp of technical concepts, and over 100 in-depth coding exercises (in Python) provide a real understanding of crucial machine learning algorithms. A suite of online resources including sample code, data sets, interactive lecture slides, and a solutions manual are provided online, making this an ideal text both for grad

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides a theoretical account of the fundamentals underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics, the book covers a wide array of central topics unaddressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for advanced undergraduates or beginning graduates, the text makes the fundamentals and algorithms of machine learning accessible t

Schemas in Problem Solving explores a theory of schema development and studies the applicability of the theory as a unified basis for understanding learning, instruction and assessment. The theory's prescriptions for teaching are direct, and its application to assessment suggests new directions for tests. After examining the roots of the theory in earlier work by philosophers and psychologists, Marshall illustrates the main features of her theory with experimental evidence from students who are learning to recognize and solve arithmetic story problems. She describes individual performance with traditional empirical studies as well as computer simulation. The computer simulation reflects an approach in modelling cognition. Marshall's model links neural networks with symbolic systems to form a hybrid model that uses pattern matching of sets of features as well as logical step-by-step rules.

Schemas in Problem Solving explores a theory of schema development and studies the applicability of the theory as a unified basis for understanding learning, instruction and assessment. The theory's prescriptions for teaching are direct, and its application to assessment suggests new directions for tests. After examining the roots of the theory in earlier work by philosophers and psychologists, Marshall illustrates the main features of her theory with experimental evidence from students who are learning to recognize and solve arithmetic story problems. She describes individual performance with traditional empirical studies as well as computer simulation. The computer simulation reflects an approach in modelling cognition. Marshall's model links neural networks with symbolic systems to form a hybrid model that uses pattern matching of sets of features as well as logical step-by-step rules.

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

The fundamental algorithms in data mining and machine learning form the basis of data science, utilizing automated methods to analyze patterns and models for all kinds of data in applications ranging from scientific discovery to business analytics. This textbook for senior undergraduate and graduate courses provides a comprehensive, in-depth overview of data mining, machine learning and statistics, offering solid guidance for students, researchers, and practitioners. The book lays the foundations of data analysis, pattern mining, clustering, classification and regression, with a focus on the algorithms and the underlying algebraic, geometric, and probabilistic concepts. New to this second edition is an entire part devoted to regression methods, including neural networks and deep learning.

In the age of data-driven problem-solving, applying sophisticated computational tools for explaining substantive phenomena is a valuable skill. Yet, application of methods assumes an understanding of the data, structure, and patterns that influence the broader research program. This Element offers researchers and teachers an introduction to clustering, which is a prominent class of unsupervised machine learning for exploring and understanding latent, non-random structure in data. A suite of widely used clustering techniques is covered in this Element, in addition to R code and real data to facilitate interaction with the concepts. Upon setting the stage for clustering, the following algorithms are detailed: agglomerative hierarchical clustering, k-means clustering, Gaussian mixture models, and at a higher-level, fuzzy C-means clustering, DBSCAN, and partitioning around medoids (k-medoids) clustering.

This book will help readers understand fundamental and advanced statistical models and deep learning models for robust speaker recognition and domain adaptation. This useful toolkit enables readers to apply machine learning techniques to address practical issues, such as robustness under adverse acoustic environments and domain mismatch, when deploying speaker recognition systems. Presenting state-of-the-art machine learning techniques for speaker recognition and featuring a range of probabilistic models, learning algorithms, case studies, and new trends and directions for speaker recognition based on modern machine learning and deep learning, this is the perfect resource for graduates, researchers, practitioners and engineers in electrical engineering, computer science and applied mathematics.

Successful investment strategies are specific implementations of general theories. An investment strategy that lacks a theoretical justification is likely to be false. Hence, an asset manager should concentrate her efforts on developing a theory rather than on backtesting potential trading rules. The purpose of this Element is to introduce machine learning (ML) tools that can help asset managers discover economic and financial theories. ML is not a black box, and it does not necessarily overfit. ML tools complement rather than replace the classical statistical methods. Some of ML's strengths include (1) a focus on out-of-sample predictability over variance adjudication; (2) the use of computational methods to avoid relying on (potentially unrealistic) assumptions; (3) the ability to “learn” complex specifications, including nonlinear, hierarchical, and noncontinuous interaction effects in a high-dimensional space; and (4) the ability to disentangle the variable search from the specific

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric conve

An indispensable guide enabling business and management students to develop their professional competences in real organizational settings, this new and fully updated edition of Problem Solving in Organizations equips the reader with the necessary toolkit to apply the theory to practical business problems. By encouraging the reader to use the theory and showing them how to do so in a fuzzy, ambiguous and politically charged, real-life organizational context, this book offers a concise introduction to design-oriented and theory-informed problem solving in organizations. In addition, it gives support for designing the overall approach to a problem-solving project as well as support for each of the steps of the problem-solving cycle: problem definition, problem analysis, solution design, interventions, and evaluation. Problem Solving in Organizations is suitable for readers with a wide range of learning objectives, including undergraduates and graduates studying business and management, M

An indispensable guide enabling business and management students to develop their professional competences in real organizational settings, this new and fully updated edition of Problem Solving in Organizations equips the reader with the necessary toolkit to apply the theory to practical business problems. By encouraging the reader to use the theory and showing them how to do so in a fuzzy, ambiguous and politically charged, real-life organizational context, this book offers a concise introduction to design-oriented and theory-informed problem solving in organizations. In addition, it gives support for designing the overall approach to a problem-solving project as well as support for each of the steps of the problem-solving cycle: problem definition, problem analysis, solution design, interventions, and evaluation. Problem Solving in Organizations is suitable for readers with a wide range of learning objectives, including undergraduates and graduates studying business and management, M

Written by leading researchers, this complete introduction brings together all the theory and tools needed for building robust machine learning in adversarial environments. Discover how machine learning systems can adapt when an adversary actively poisons data to manipulate statistical inference, learn the latest practical techniques for investigating system security and performing robust data analysis, and gain insight into new approaches for designing effective countermeasures against the latest wave of cyber-attacks. Privacy-preserving mechanisms and the near-optimal evasion of classifiers are discussed in detail, and in-depth case studies on email spam and network security highlight successful attacks on traditional machine learning algorithms. Providing a thorough overview of the current state of the art in the field, and possible future directions, this groundbreaking work is essential reading for researchers, practitioners and students in computer security and machine learning,

As one of the most comprehensive machine learning texts around, this book does justice to the field's incredible richness, but without losing sight of the unifying principles. Peter Flach's clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss. Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. Particular attention is paid to the central role played by features. The use of established terminology is balanced with the introduction of new and useful concepts, and summaries of relevant background material are provided with pointers for revision if necessary. These features ensure Machine Learning will set a new standard as an introductory textbook.

As one of the most comprehensive machine learning texts around, this book does justice to the field's incredible richness, but without losing sight of the unifying principles. Peter Flach's clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss. Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. Particular attention is paid to the central role played by features. The use of established terminology is balanced with the introduction of new and useful concepts, and summaries of relevant background material are provided with pointers for revision if necessary. These features ensure Machine Learning will set a new standard as an introductory textbook.

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric conve

Phase transitions typically occur in combinatorial computational problems and have important consequences, especially with the current spread of statistical relational learning as well as sequence learning methodologies. In Phase Transitions in Machine Learning the authors begin by describing in detail this phenomenon, and the extensive experimental investigation that supports its presence. They then turn their attention to the possible implications and explore appropriate methods for tackling them. Weaving together fundamental aspects of computer science, statistical physics and machine learning, the book provides sufficient mathematics and physics background to make the subject intelligible to researchers in AI and other computer science communities. Open research issues are also discussed, suggesting promising directions for future research.

Computational learning theory is a subject which has been advancing rapidly in the last few years. The authors concentrate on the probably approximately correct model of learning, and gradually develop the ideas of efficiency considerations. Finally, applications of the theory to artificial neural networks are considered. Many exercises are included throughout, and the list of references is extensive. This volume is relatively self contained as the necessary background material from logic, probability and complexity theory is included. It will therefore form an introduction to the theory of computational learning, suitable for a broad spectrum of graduate students from theoretical computer science and mathematics.

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector field. In other words, they infer a latent quantity from data. This book shows that it is thus formally possible to think of computational routines as learning machines, and to use the notion of Bayesian inference to build more flexible, efficient, or customised algorithms for computation. The text caters for Masters' and PhD students, as well as postgraduate researchers in artificial intelligence, computer science, statistics, and applied mathematics. Extensive background material is provided along with a wealth of figures, worked examples, and exercises (with solutions) to develop intuition.

This lucid, accessible introduction to supervised machine learning presents core concepts in a focused and logical way that is easy for beginners to follow. The author assumes basic calculus, linear algebra, probability and statistics but no prior exposure to machine learning. Coverage includes widely used traditional methods such as SVMs, boosted trees, HMMs, and LDAs, plus popular deep learning methods such as convolution neural nets, attention, transformers, and GANs. Organized in a coherent presentation framework that emphasizes the big picture, the text introduces each method clearly and concisely “from scratch” based on the fundamentals. All methods and algorithms are described by a clean and consistent style, with a minimum of unnecessary detail. Numerous case studies and concrete examples demonstrate how the methods can be applied in a variety of contexts.

This lucid, accessible introduction to supervised machine learning presents core concepts in a focused and logical way that is easy for beginners to follow. The author assumes basic calculus, linear algebra, probability and statistics but no prior exposure to machine learning. Coverage includes widely used traditional methods such as SVMs, boosted trees, HMMs, and LDAs, plus popular deep learning methods such as convolution neural nets, attention, transformers, and GANs. Organized in a coherent presentation framework that emphasizes the big picture, the text introduces each method clearly and concisely “from scratch” based on the fundamentals. All methods and algorithms are described by a clean and consistent style, with a minimum of unnecessary detail. Numerous case studies and concrete examples demonstrate how the methods can be applied in a variety of contexts.

The field of machine learning has matured to the point where many sophisticated learning approaches can be applied to practical applications. Thus it is of critical importance that researchers have the proper tools to evaluate learning approaches and understand the underlying issues. This book examines various aspects of the evaluation process with an emphasis on classification algorithms. The authors describe several techniques for classifier performance assessment, error estimation and resampling, obtaining statistical significance as well as selecting appropriate domains for evaluation. They also present a unified evaluation framework and highlight how different components of evaluation are both significantly interrelated and interdependent. The techniques presented in the book are illustrated using R and WEKA, facilitating better practical insight as well as implementation. Aimed at researchers in the theory and applications of machine learning, this book offers a solid basis for c

Offering a fundamental basis in kernel-based learning theory, this book covers both statistical and algebraic principles. It provides over 30 major theorems for kernel-based supervised and unsupervised learning models. The first of the theorems establishes a condition, arguably necessary and sufficient, for the kernelization of learning models. In addition, several other theorems are devoted to proving mathematical equivalence between seemingly unrelated models. With over 25 closed-form and iterative algorithms, the book provides a step-by-step guide to algorithmic procedures and analysing which factors to consider in tackling a given problem, enabling readers to improve specifically designed learning algorithms, build models for new applications and develop efficient techniques suitable for green machine learning technologies. Numerous real-world examples and over 200 problems, several of which are Matlab-based simulation exercises, make this an essential resource for graduate student

Focusing on the application of membranes in an engineering context, this hands-on computational guide makes previously challenging problems routine. It formulates problems as systems of equations solved with MATLAB, encouraging active learning through worked examples and end-of-chapter problems. The detailed treatments of dead-end filtration include novel approaches to constant rate filtration and filtration with a centrifugal pump. The discussion of crossflow microfiltration includes the use of kinetic and force balance models. Comprehensive coverage of ultrafiltration and diafiltration processes employs both limiting flux and osmotic pressure models. The effect of fluid viscosity on the mass transfer coefficient is explored in detail, the effects of incomplete rejection on the design and analysis of ultrafiltration and diafiltration are analysed, and quantitative treatments of reverse osmosis and nanofiltration process analysis and design are explored. Includes a chapter dedicated to

Focusing on the application of membranes in an engineering context, this hands-on computational guide makes previously challenging problems routine. It formulates problems as systems of equations solved with MATLAB, encouraging active learning through worked examples and end-of-chapter problems. The detailed treatments of dead-end filtration include novel approaches to constant rate filtration and filtration with a centrifugal pump. The discussion of crossflow microfiltration includes the use of kinetic and force balance models. Comprehensive coverage of ultrafiltration and diafiltration processes employs both limiting flux and osmotic pressure models. The effect of fluid viscosity on the mass transfer coefficient is explored in detail, the effects of incomplete rejection on the design and analysis of ultrafiltration and diafiltration are analysed, and quantitative treatments of reverse osmosis and nanofiltration process analysis and design are explored. Includes a chapter dedicated to

Machine learning methods extract value from vast data sets quickly and with modest resources. They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors,

This book presents an integrated collection of representative approaches for scaling up machine learning and data mining methods on parallel and distributed computing platforms. Demand for parallelizing learning algorithms is highly task-specific: in some settings it is driven by the enormous dataset sizes, in others by model complexity or by real-time performance requirements. Making task-appropriate algorithm and platform choices for large-scale machine learning requires understanding the benefits, trade-offs and constraints of the available options. Solutions presented in the book cover a range of parallelization platforms from FPGAs and GPUs to multi-core systems and commodity clusters, concurrent programming frameworks including CUDA, MPI, MapReduce and DryadLINQ, and learning settings (supervised, unsupervised, semi-supervised and online learning). Extensive coverage of parallelization of boosted trees, SVMs, spectral clustering, belief propagation and other popular learning algo

This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications in discrete approximation and statistics. The general approach considered in this text, first published in 2001, has permitted the development of finite algorithms for the rank regression problem. The key ideas are those of developing a general format for specifying the polyhedral function and the application of this to derive multiplier conditions to characterize optimality. Also considered is the application of the general approach to the development of active se

Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport–Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed. Researchers in computational and combinatorial geometry should find much to interest them in this book.

Machine learning methods originated from artificial intelligence and are now used in various fields in environmental sciences today. This is the first single-authored textbook providing a unified treatment of machine learning methods and their applications in the environmental sciences. Due to their powerful nonlinear modelling capability, machine learning methods today are used in satellite data processing, general circulation models(GCM), weather and climate prediction, air quality forecasting, analysis and modelling of environmental data, oceanographic and hydrological forecasting, ecological modelling, and monitoring of snow, ice and forests. The book includes end-of-chapter review questions and an appendix listing websites for downloading computer code and data sources. A resources website contains datasets for exercises, and password-protected solutions are available. The book is suitable for first-year graduate students and advanced undergraduates. It is also valuable for resear

Machine learning methods originated from artificial intelligence and are now used in various fields in environmental sciences today. This is the first single-authored textbook providing a unified treatment of machine learning methods and their applications in the environmental sciences. Due to their powerful nonlinear modelling capability, machine learning methods today are used in satellite data processing, general circulation models(GCM), weather and climate prediction, air quality forecasting, analysis and modelling of environmental data, oceanographic and hydrological forecasting, ecological modelling, and monitoring of snow, ice and forests. The book includes end-of-chapter review questions and an appendix listing websites for downloading computer code and data sources. A resources website contains datasets for exercises, and password-protected solutions are available. The book is suitable for first-year graduate students and advanced undergraduates. It is also valuable for resear

First published in 1993, this thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members? What general methods are useful for listing combinatorial structures? How can these be applied to those families which are of interest to theoretical computer scientists and combinatorialists? Amongst those families considered are unlabelled graphs, first order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colourable graphs. Some related work is also included, which compares the listing problem with the difficulty of solving the existence problem, the construction problem, the random sampling problem, and the counting problem. In particular, the difficulty of evaluating Pólya's cycle polynomial is demonstrated.

Thanks to high-speed computers and advanced algorithms, the important field of modelling multiphase flows is an area of rapid growth. This one-stop account – now in paperback, with corrections from the first printing – is the ideal way to get to grips with this topic, which has significant applications in industry and nature. Each chapter is written by an acknowledged expert and includes extensive references to current research. All of the chapters are essentially independent and so the book can be used for a range of advanced courses and the self-study of specific topics. No other book covers so many topics related to multiphase flow, and it will therefore be warmly welcomed by researchers and graduate students of the subject across engineering, physics, and applied mathematics.

The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems and develops techniques for solving them. A number of engineering case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality-constrained optimization and inequality-constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. Supplementary material including solutions, lecture slides and appendices are available online at www.cambridge.org/9780521

Inferring the precise locations and splicing patterns of genes in DNA is a difficult but important task, with broad applications to biomedicine. The mathematical and statistical techniques that have been applied to this problem are surveyed and organized into a logical framework based on the theory of parsing. Both established approaches and methods at the forefront of current research are discussed. Numerous case studies of existing software systems are provided, in addition to detailed examples that work through the actual implementation of effective gene-predictors using hidden Markov models and other machine-learning techniques. Background material on probability theory, discrete mathematics, computer science, and molecular biology is provided, making the book accessible to students and researchers from across the life and computational sciences. This book is ideal for use in a first course in bioinformatics at graduate or advanced undergraduate level, and for anyone wanting to kee