This book provides a comprehensive presentation of a recently introduced framework, named "probabilistic indexing" (PrIx), for searching text in large collections of document images and other related applications. It fosters the development of new search engines for effective information retrieval from manuscripts which, however, lack the electronic text (transcripts) that would typically be required for such search and retrieval tasks.

The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob­ lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom­ pleteness".

In the fall of 1999, I was asked to teach a course on computer intrusion detection for the Department of Mathematical Sciences of The Johns Hopkins University. That course was the genesis of this book. I had been working in the field for several years at the Naval Surface Warfare Center, in Dahlgren, Virginia, under the auspices of the SHADOW program, with some funding by the Office of Naval Research. In designing the class, I was concerned both with giving an overview of the basic problems in computer security, and with providing information that was of interest to a department of mathematicians. Thus, the focus of the course was to be more on methods for modeling and detecting intrusions rather than one on how to secure one's computer against intrusions. The first task was to find a book from which to teach. I was familiar with several books on the subject, but they were all at either a high level, focusing more on the political and policy aspects of the problem, or were written for security analysts, with little to interest a mathematician. I wanted to cover material that would appeal to the faculty members of the department, some of whom ended up sitting in on the course, as well as providing some interesting problems for students. None of the books on the market at the time had an adequate discussion of mathematical issues related to intrusion detection.

Learn the answers to 30 cutting-edge questions in machine learning and AI and level up your expertise in the field.

It started with image processing in the sixties. Back then, it took ages to digitize a Landsat image and then process it with a mainframe computer. Pro- cessing was inspired on the achievements of signal processing and was still very much oriented towards programming.

This textbook provides a comprehensive, thorough and up-to-date treatment of topics of mathematics that an engineer and scientist would need, at the basic levels that contents of engineering and sciences are built by. For this purpose, natural readers would be junior and senior undergraduate students, who normally have the content of this book under different names on their degree plans. Also, engineers and scientists will benefit from this book since the book is a comprehensive volume for such audiences.

Maths 100 Ideas in 100 Words offers the essential facts at your fingertips, satisfying your mathematical curiosity and helping you to understand the biggest concepts in maths in concise, 100-word summaries.