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Many useful concepts and tools from different disciplines have been employed in pattern recognition. Among them is string matching, which receives much johnson babies and practical attention. String matching is also an important topic in combinatorial optimization.

This book is devoted to recent advances in pattern recognition and string matching. It consists of twenty eight chapters written by different authors, addressing a broad range of topics such as those from classifica tion, matching, mining, feature selection, and applications.

Each chapter is self-contained, and presents either novel methodological approaches or applications of existing theories and techniques. The aim, intent, and motivation for publishing this book is to pro vide a reference tool for the increasing growth of readers who depend upon pattern recognition or string matching in some way.

This includes students and professionals temp a t computer science, mathematics, statistics, and electrical engineering. We wish to thank all the authors for their valuable efforts, which made this book a reality. Thanks temp a t go to all reviewers who gave generously of their time and expertise. Catalog roche performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds.

We used mathematical knot theory to analyze the knots. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string.

Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime temp a t with up to seven crossings were observed.

Our temp a t can qualitatively account for the observed distribution of knots and dependence on agitation time and string length. Knots have been a subject of scientific study since as early as 1867, when Lord Kelvin proposed that atoms might be described as knots of swirling vortices (1).

Although this theory fell into disfavor, it stimulated interest in the subject, and temp a t currently play a role in many scientific fields, including polymer physics, statistical mechanics, quantum field theory, and DNA biochemistry temp a t, 3). In mathematics, knot theory has been an active field of research for more than a century (3). In 1988, Sumners and Whittington (15) proved this conjecture rigorously by showing that prostate examination few arcs would remain unknotted as the length tends to infinity.

Numerical studies of finite-length temp a t walks find that the probability of knotting and the average complexity of knots increase sharply with the number of steps (16).

Here, we describe a simple physical experiment on knot formation. A string was placed in a cubic box and the box was rotated at constant angular velocity about a principle axis perpendicular to gravity, causing the string to tumble.

We investigated the probability of knotting, the type of knots formed, and the dependence on string length. Before tumbling, the string was held vertically above the center of the box and dropped in, creating a quasirandom initial conformation.

After tumbling, the box was opened and the ends of the string were lifted directly upward and joined to form a closed loop. A digital photo was taken whenever a complex knot was formed.

The experiment was repeated hundreds of times with each string length to collect statistics.

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