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Typesetting Concrete Mathematics

by Donald E. Knuth - TUGBOAT , 1989
"... ... tried my best to make the book mathematically interesting, but I also knew that it would be typographically interesting-because it would be the first major use of a new typeface by Hermann Zapf, commissioned by the American Mathematical Society. This typeface, called AMS Euler, had been carefull ..."
Abstract - Cited by 661 (1 self) - Add to MetaCart
carefully digitized and put into METAFONT form by Stanford's digital typography students [a]; but it had not yet been "tuned up " for real applications. My new book served as an ideal test case, because (1) it involved a great variety of mathematical formulas; (2) I was highly motivated

An introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition

by Ming Li, Paul Vitanyi , 1997
"... This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission to reproduc ..."
Abstract - Cited by 2138 (120 self) - Add to MetaCart
This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission

A Simple Model of Capital Market Equilibrium with Incomplete Information

by Robert C. Merton - JOURNAL OF FINANCE , 1987
"... The sphere of modern financial economics encompases finance, micro investment theory and much of the economics of uncertainty. As is evident from its influence on other branches of economics including public finance, industrial organization and monetary theory, the boundaries of this sphere are both ..."
Abstract - Cited by 756 (2 self) - Add to MetaCart
are both permeable and flexible. The complex interactions of time and uncertainty guarantee intellectual challenge and intrinsic excitement to the study of financial economics. Indeed, the mathematics of the subject contain some of the most interesting applications of probability and optimization theory

Network Applications of Bloom Filters: A Survey

by Andrei Broder, Michael Mitzenmacher - INTERNET MATHEMATICS , 2002
"... A Bloomfilter is a simple space-efficient randomized data structure for representing a set in order to support membership queries. Bloom filters allow false positives but the space savings often outweigh this drawback when the probability of an error is controlled. Bloom filters have been used in ..."
Abstract - Cited by 522 (17 self) - Add to MetaCart
in database applications since the 1970s, but only in recent years have they become popular in the networking literature. The aim of this paper is to survey the ways in which Bloom filters have been used and modified in a variety of network problems, with the aim of providing a unified mathematical

Applications Of Circumscription To Formalizing Common Sense Knowledge

by John McCarthy - Artificial Intelligence , 1986
"... We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects o ..."
Abstract - Cited by 532 (12 self) - Add to MetaCart
general formalism called prioritized circumscription is briefly explored. 1 INTRODUCTION ANDNEW DEFINITION OF CIRCUMSCRIPTION (McCarthy 1980) introduces the circumscription method of nonmonotonic reasoning and gives motivation, some mathematical properties and some ex1 amples of its application

A tutorial on hidden Markov models and selected applications in speech recognition

by Lawrence R. Rabiner - PROCEEDINGS OF THE IEEE , 1989
"... Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical s ..."
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Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical

Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging

by Michael Lustig, David Donoho, John M. Pauly - MAGNETIC RESONANCE IN MEDICINE 58:1182–1195 , 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
Abstract - Cited by 538 (11 self) - Add to MetaCart
finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts

A quantitative description of membrane currents and its application to conduction and excitation in nerve

by A. L. Hodgkin, A. F. Huxley - Journal of Physiology , 1952
"... This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin, Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a-c). Its general object is to discu the results of the preceding papers (Part I), to put them into ..."
Abstract - Cited by 1924 (2 self) - Add to MetaCart
into mathematical form (Part II) and to show that they will account for con-duction and excitation in quantitative terms (Part III). PART I. DISCUSSION OF EXPERIMENTAL RESULTS The results described in the preceding papers suggest that the electrical behaviour of the membrane may be represented by the network shown

The University of Florida sparse matrix collection

by Timothy A. Davis - NA DIGEST , 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
Abstract - Cited by 536 (17 self) - Add to MetaCart
and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificially-generated matrices cannot meet, and is widely used by the sparse matrix algorithms community

A gentle tutorial on the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models

by Jeff A. Bilmes , 1997
"... We describe the maximum-likelihood parameter estimation problem and how the Expectation-form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) fi ..."
Abstract - Cited by 693 (4 self) - Add to MetaCart
We describe the maximum-likelihood parameter estimation problem and how the Expectation-form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2
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