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A Matrix Algebra Approach to Artificial Intelligence
The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines
Mathematical Formulas for Economists
This collection of formulas constitutes a compendium of mathematics for eco nomics and business. It contains the most important formulas, statements and algorithms in this significant subfield of modern mathematics and addresses primarily students of economics or business at universities, colleges and trade schools. But people dealing with practical or applied problems will also find this collection to be an efiicient and easy-to-use work of reference. First the book treats mathematical symbols and constants, sets and state ments, number systems and their arithmetic as well as fundamentals of com binatorics. The chapter on sequences and series is followed by mathematics of finance, the representation of functions of one and several independent vari ables, their differential and integral calculus and by differential and difference equations. In each case special emphasis is placed on applications and models in economics. The chapter on linear algebra deals with matrices, vectors, determinants and systems of linear equations. This is followed by the representation of struc tures and algorithms of linear programming. Finally, the reader finds formu las on descriptive statistics (data analysis, ratios, inventory and time series analysis), on probability theory (events, probabilities, random variables and distributions) and on inductive statistics (point and interval estimates, tests). Some important tables complete the work.
Bio-inspired credit risk analysis : Computational intelligence with support vector machines
Credit risk analysis is one of the most important topics in the field of financial risk management. Due to recent financial crises and regulatory concern of Basel II, credit risk analysis has been the major focus of financial and banking industry. Especially for some credit-granting institutions such as commercial banks and credit companies, the ability to discriminate good customers from bad ones is crucial. The need for reliable quantitative models that predict defaults accurately is imperative so that the interested parties can take either preventive or corrective action. Hence credit risk analysis becomes very important for sustainability and profit of enterprises. In such backgrounds, this book tries to integrate recent emerging support vector machines and other computational intelligence techniques that replicate the principles of bio-inspired information processing to create some innovative methodologies for credit risk analysis and to provide decision support information for interested parties.
Advanced Data Mining Techniques
This book covers the fundamental concepts of data mining, to demonstrate the potential of gathering large sets of data, and analyzing these data sets to gain useful business understanding. The book is organized in three parts. Part I introduces concepts. Part II describes and demonstrates basic data mining algorithms. It also contains chapters on a number of different techniques often used in data mining. Part III focusses on business applications of data mining. Methods are presented with simple examples, applications are reviewed, and relativ advantages are evaluated.
Adaptive Scalarization Methods in Multiobjective Optimization
This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that high-quality approximations of the efficient set are generated. These examinations are based on a general scalarization approach for arbitrary partial orderings defined by a closed pointed convex cone in the objective space. The application of the results to many other well-known scalarization methods is also presented. Background material of multiobjective optimization and scalarization approaches is concisely summarized at the beginning. The effectiveness of these new methods is demonstrated by test problems and a recent problem in intensity-modulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems.
Mathematical Analysis : Linear and Metric Structures and Continuity
The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.
Local Newforms for GSp(4)
Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).
Linear Algebra Thoroughly Explained
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering.
Limit Cycles of Differential Equations
Contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006.The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.
Les vérités du cancer : Partager l'information, installer la relation = The truths about cancer : Sharing information, building the relationship
Les médecins et les équipes soignantes perçoivent comme une nouvelle pression la nécessité de transmettre le diagnostic de cancer et de discuter des options thérapeutiques avec un patient qui n’est pas toujours prêt à s y confronter. Bien que l’on puisse saluer le partage de l’information et encourager la transparence, le médecin prend le risque du blocage de dialogue, d’une indifférence, au pire d’un traumatisme. L’idée d’une diminution d’un certain pouvoir médical s’insinue dans le « dispositif » d’annonce qui renvoie la clinique à des apprentissages techniques. Au contraire, certains médecins cherchent à s’inscrire dans un mouvement plus démocratique. Ils constatent que pour le malade, savoir n’est pas choisir, et que dans les cas difficiles, ils restent encore décideurs. Cet ouvrage fait le point sur les changements obtenus par les lois et leurs conséquences sur les pratiques et incite à une réflexion philosophique sur la vérité et les vérités des interlocuteurs de la scène médicale.
Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.
K-Theory : An Introduction
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory.
Kernel Based Algorithms for Mining Huge Data Sets : Supervised, Semi-supervised, and Unsupervised Learning
"Kernel Based Algorithms for Mining Huge Data Sets" is the first book treating the fields of supervised, semi-supervised and unsupervised machine learning collectively. The book presents both the theory and the algorithms for mining huge data sets by using support vector machines (SVMs) in an iterative way. It demonstrates how kernel based SVMs can be used for dimensionality reduction (feature elimination) and shows the similarities and differences between the two most popular unsupervised techniques, the principal component analysis (PCA) and the independent component analysis (ICA).
IUTAM Symposium on Computational Physics and New Perspectives in Turbulence ; Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, Nagoya University, Nagoya, Japan, September, 11-14, 2006
Leading experts in turbulence were brought together at this Symposium to exchange ideas and discuss, in the light of the recent progress in computational methods, new perspectives in our understanding of turbulence. The Symposium also fostered a vigorous interaction between those who pursue computations, and those concerned with developments in experiment and theory.
Complex Variables with Applications
Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. It explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination.
Complex Geometry : An Introduction
Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions.
Characteristics Finite Element Methods in Computational Fluid Dynamics
This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. The fluid dynamics equations are derived from basic thermo-mechanical principles and the multi-dimensional and infinite-directional upstream procedure is developed by combining a finite element discretization of a characteristics-bias system with an implicit Runge-Kutta time integration. For the computational solution of the Euler and Navier Stokes equations, the procedure relies on the mathematics and physics of multi-dimensional characteristics. As a result, the procedure crisply captures contact discontinuities, normal as well as oblique shocks, and generates essentially non-oscillatory solutions for incompressible, subsonic, transonic, supersonic, and hypersonic inviscid and viscous flows.
Blind Speech Separation
This is the first book to provide a cutting edge reference to the fascinating topic of blind source separation (BSS) for convolved speech mixtures. Through contributions by the foremost experts on the subject, the book provides an up-to-date account of research findings, explains the underlying theory, and discusses potential applications. The individual chapters are designed to be tutorial in nature with specific emphasis on an in-depth treatment of state of the art techniques. Blind Speech Separation is divided into three parts:Part 1 presents overdetermined or critically determined BSS. Here the main technology is independent component analysis (ICA). ICA is a statistical method for extracting mutually independent sources from their mixtures. Part 2 addresses underdetermined BSS, where there are fewer microphones than source signals. Here, the sparseness of speech sources is very useful; we can utilize time-frequency diversity, where sources are active in different regions of the time-frequency plane.Part 3 presents monaural BSS where there is only one microphone. Here, we can separate a mixture by using the harmonicity and temporal structure of the sources. We can build a probabilistic framework by assuming a source model, and separate a mixture by maximizing the a posteriori probability of the sources.
Bioelectricity : A Quantitative Approach
"The authors’ goal in producing this book was to provide an introductory text to electrophysiology, based on a quantitative approach. In attempting to achieve this goal, therefore, the authors have opened the book with a useful, and digestible, introduction to various aspects of the mathematics relevant to this field, including vectors, introduction to Laplace, Gauss’s theorem, and Green’s theorem. This book will be useful for students in medical physics and biomedical engineering wishing to enter the field of electrophysiological investigation. It will also be helpful for biologists and physiologists who wish to understand the mathematical treatment of the processes and signals at the center of the interesting interdisciplinary field.
Basic Probability Theory with Applications
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.
