Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

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Information Theory, Inference and Learning Algorithms

This paper introduces a new corpus of read English speech, suitable for training and evaluating speech recognition systems. The LibriSpeech corpus is derived from audiobooks that are part of the LibriVox project, and contains 1000 hours of speech sampled at 16 kHz. We have made the corpus freely available for download, along with separately prepared language-model training data and pre-built language models. We show that acoustic models trained on LibriSpeech give lower error rate on the Wall Street Journal (WSJ) test sets than models trained on WSJ itself. We are also releasing Kaldi scripts that make it easy to build these systems.

/pdf/librispeech-an-asr-corpus-based-on-public-domain-audio-books-gslbn35u4y.pdf

Librispeech: An ASR corpus based on public domain audio books

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.

/pdf/channel-coding-rate-in-the-finite-blocklength-regime-35xxh8quud.pdf

Channel Coding Rate in the Finite Blocklength Regime

We survey the current techniques to cope with the problem of string matching that allows errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices. We conclude with some directions for future work and open problems.

/pdf/a-guided-tour-to-approximate-string-matching-22fowlmq5b.pdf

A guided tour to approximate string matching

Ontologies tend to be found everywhere. They are viewed as the silver bullet for many applications, such as database integration, peer-to-peer systems, e-commerce, semantic web services, or social networks. However, in open or evolving systems, such as the semantic web, different parties would, in general, adopt different ontologies. Thus, merely using ontologies, like using XML, does not reduce heterogeneity: it just raises heterogeneity problems to a higher level. Euzenat and Shvaikos book is devoted to ontology matching as a solution to the semantic heterogeneity problem faced by computer systems. Ontology matching aims at finding correspondences between semantically related entities of different ontologies. These correspondences may stand for equivalence as well as other relations, such as consequence, subsumption, or disjointness, between ontology entities. Many different matching solutions have been proposed so far from various viewpoints, e.g., databases, information systems, and artificial intelligence. The second edition of Ontology Matching has been thoroughly revised and updated to reflect the most recent advances in this quickly developing area, which resulted in more than 150 pages of new content. In particular, the book includes a new chapter dedicated to the methodology for performing ontology matching. It also covers emerging topics, such as data interlinking, ontology partitioning and pruning, context-based matching, matcher tuning, alignment debugging, and user involvement in matching, to mention a few. More than 100 state-of-the-art matching systems and frameworks were reviewed. With Ontology Matching, researchers and practitioners will find a reference book that presents currently available work in a uniform framework. In particular, the work and the techniques presented in this book can be equally applied to database schema matching, catalog integration, XML schema matching and other related problems. The objectives of the book include presenting (i) the state of the art and (ii) the latest research results in ontology matching by providing a systematic and detailed account of matching techniques and matching systems from theoretical, practical and application perspectives.

Ontology Matching

Binary codes capable of correcting deletions, insertions and reversals

Binary codes capable of correcting deletions, insertions, and reversals

This paper contains a survey of association scheme theory (with its algebraic and analytical aspects) and of its applications to coding theory (in a wide sense). It is mainly concerned with a class of subjects that involve the central notion of the distance distribution of a code. Special emphasis is put on the linear programming method, inspired by the MacWilliams transform. This produces upper bounds for the size of a code with a given minimum distance, and lower bounds for the size of a design with a given strength. The most specific results are obtained in the case where the underlying association scheme satisfies certain well-defined "polynomial properties;" this leads one into the realm of orthogonal polynomial theory. In particular, some "universal bounds" are derived for codes and designs in polynomial type association schemes. Throughout the paper, the main concepts, methods, and results are illustrated by two examples that are of major significance in classical coding theory, namely, the Hamming scheme and the Johnson scheme. Other topics that receive special attention are spherical codes and designs, and additive codes in translation schemes, including Z/sub 4/-additive binary codes.

Association schemes and coding theory

We introduce and solve some new problems of efficient reconstruction of an unknown sequence from its versions distorted by errors of a certain type. These erroneous versions are considered as outputs of repeated transmissions over a channel, either a combinatorial channel defined by the maximum number of permissible errors of a given type, or a discrete memoryless channel. We are interested in the smallest N such that N erroneous versions always suffice to reconstruct a sequence of length n, either exactly or with a preset accuracy and/or with a given probability. We are also interested in simple reconstruction algorithms. Complete solutions for combinatorial channels with some types of errors of interest in coding theory, namely, substitutions, transpositions, deletions, and insertions of symbols are given. For these cases, simple reconstruction algorithms based on majority and threshold principles and their nontrivial combination are found. In general, for combinatorial channels the considered problem is reduced to a new problem of reconstructing a vertex of an arbitrary graph with the help of the minimum number of vertices in its metrical ball of a given radius. A certain sufficient condition for solution of this problem is presented. For a discrete memoryless channel, the asymptotic behavior of the minimum number of repeated transmissions which are sufficient to reconstruct any sequence of length n within Hamming distance d with error probability /spl epsiv/ is found when d/n and /spl epsiv/ tend to 0 as n/spl rarr//spl infin/. A similar result for the continuous channel with discrete time and additive Gaussian noise is also obtained.

Efficient reconstruction of sequences

Universal bounds for the cardinality of codes in the Hamming space F/sub r//sup n/ with a given minimum distance d and/or dual distance d' are stated. A self-contained proof of optimality of these bounds in the framework of the linear programming method is given. The necessary and sufficient conditions for attainability of the bounds are found. The parameters of codes satisfying these conditions are presented in a table. A new upper bound for the minimum distance of self-dual codes and a new lower bound for the crosscorrelation of half-linear codes are obtained. >

V.I. Levenshtein

Papers

Binary codes capable of correcting deletions, insertions and reversals

Binary codes capable of correcting deletions, insertions, and reversals

Association schemes and coding theory

Efficient reconstruction of sequences

Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces