In this book, all the major and frontier topics in the field of document analysis are brought together into a single volume creating a unique reference source.
Highlights include:

The motion of any body depends both on its characteristics and the forces acting on it. Although taking into account all possible properties makes the equations too complex to solve, sometimes it is possible to consider only the properties that have the greatest in?uence on the motion. Models of ideals bodies, which contain only the most relevant properties, can be studied using the tools of mathematical physics. Adding more properties into a model makes it more realistic, but it also makes the motion problem harder to solve. In order to highlight the above statements, let us ?rst suppose that a systemS ofN unconstrainedbodiesC ,i=1,. . . ,N,issu?cientlydescribed i by the model of N material points whenever the bodies have negligible dimensions with respect to the dimensions of the region containing the trajectories. ThismeansthatallthephysicalpropertiesofC thatin?uence i the motion are expressed by a positive number, themass m , whereas the i position of C with respect to a frame I is given by the position vector i r (t) versus time. To determine the functionsr (t), one has to integrate the i i following system of Newtonian equations: m¨ r =F ?f (r ,. . . ,r ,r ? ,. . . ,r ? ,t), i i i i 1 N 1 N i=1,

Mathematical modeling of human physiopathology is a tremendouslyambitioustask. It encompasses the modeling of most diverse compartments such as the cardiovaslar,respiratory,skeletalandnervoussystems,aswellasthemechanicalandbioch- ical interaction between blood ?ow and arterial walls, and electrocardiac processes and electric conduction in biological tissues. Mathematical models can be set up to simulate both vasculogenesis (the aggregation and organization of endothelial cells dispersed in a given environment) and angiogenesis (the formation of new vessels sprouting from an existing vessel) that are relevant to the formation of vascular networks, and in particular to the description of tumor growth. The integration of models aimed at simulating the cooperation and interrelation of different systems is an even more dif?cult task. It calls for the setting up of, for instance, interaction models for the integrated cardio-vascular system and the interplay between the central circulation and peripheral compartments, models for the mid-to-long range cardiovascular adjustments to pathological conditions (e.g., to account for surgical interventions, congenital malformations, or tumor growth), models for integration among circulation, tissue perfusion, biochemical and thermal regulation, models for parameter identi?cation and sensitivity analysis to parameter changes or data uncertainty – and many others.

Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced.

The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo­ rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid­ ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar­ ticles in which the main interest is the application to con­ crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.

In 1924 the firm of Julius Springer published the first volume of Methods of Mathematical Physics by Richard Courant and David Hilbert. In the preface, Courant says this: Since the seventeenth century, physical intuition has served as a vital source for mathematical problems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from the roots of mathematics in intuition, have concentrated on refinement and emphasized the postulational side of mathematics, and at times have overlooked the unity of their science with physics and other fields.

Mathematica is today’s most advanced technical computing system. It features a rich programming environment, two- and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface, and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.

Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.

Based on chaos theory two very important points are clear: (I) random­ looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre­ diction, and noise reduction-have been discussed in workshops and ar­ ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap­ plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest.

This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

This book examines the geometrical notion of orthogonality, and shows how to use it as the primitive concept on which to base a metric structure in affine geometry. The subject has a long history, and an extensive literature, but whatever novelty there may be in the study presented here comes from its focus on geometries hav­ ing lines that are self-orthogonal, or even singular (orthogonal to all lines). The most significant examples concern four-dimensional special-relativistic spacetime (Minkowskian geometry), and its var­ ious sub-geometries, and these will be prominent throughout. But the project is intended as an exercise in the foundations of geome­ try that does not presume a knowledge of physics, and so, in order to provide the appropriate intuitive background, an initial chapter has been included that gives a description of the different types of line (timelike, spacelike, lightlike) that occur in spacetime, and the physical meaning of the orthogonality relations that hold between them. The coordinatisation of affine spaces makes use of constructions from projective geometry, including standard results about the ma­ trix represent ability of certain projective transformations (involu­ tions, polarities). I have tried to make the work sufficiently self­ contained that it may be used as the basis for a course at the ad­ vanced undergraduate level, assuming only an elementary knowledge of linear and abstract algebra.

Prolog is important as one of the major programming languages. Beginning with a chapter on logic (which makes the book particularly useful to undergraduate students), Prolog for Computer Science provides a comprehensive tutorial that assumes no prior knowledge of programming. There are lots of realistic examples and case-studies, including an English-Dutch translator.

In many applications, e.g., bioinformatics, web access traces, system u- lization logs, etc., the data is naturally in the form of sequences. It has been of great interests to analyze the sequential data to find their inherent char- teristics. The sequential pattern is one of the most widely studied models to capture such characteristics. Examples of sequential patterns include but are not limited to protein sequence motifs and web page navigation traces. In this book, we focus on sequential pattern mining. To meet different needs of various applications, several models of sequential patterns have been proposed. We do not only study the mathematical definitions and application domains of these models, but also the algorithms on how to effectively and efficiently find these patterns.