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An FPGA Implementation of the Natural Logarithm Based on CORDIC Algorithm
, 2013
"... Abstract: In digital signal and image processing, it's very common to calculate the value of certain transcendental functions, such as natural logarithmic function. This study introduces the basic principles of the mode of calculation of the hyperbolic systems by using the CORDIC algorithm, th ..."
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Abstract: In digital signal and image processing, it's very common to calculate the value of certain transcendental functions, such as natural logarithmic function. This study introduces the basic principles of the mode of calculation of the hyperbolic systems by using the CORDIC algorithm
Natural logarithmic relationship between brain oscillators
, 2002
"... Behaviorally relevant brain oscillations relate to each other in a specific manner to allow neuronal networks of different sizes with wide variety of connections to cooperate in a coordinated manner. For example, thalamocortical and hippocampal oscillations form numerous frequency bands, which foll ..."
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follow a general rule. Specifically, the center frequencies and frequency ranges of oscillation bands with successively faster frequencies, from ultraslow to ultrafast frequency oscillations, form an arithmetic progression on the natural logarithmic scale. Due to mathematical properties of natural
Figure 1. Natural logarithms of LC50 values for
"... The use of an uncertainty factor (UF) to account for interspecies variation in risk assessment procedures for noncarcinogens is well known and implemented by regulatory agencies at the federal and state levels. The approach that has been widely adopted is to assume that humans may be 10fold more sen ..."
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The use of an uncertainty factor (UF) to account for interspecies variation in risk assessment procedures for noncarcinogens is well known and implemented by regulatory agencies at the federal and state levels. The approach that has been widely adopted is to assume that humans may be 10fold more sensitive than the animal model. This factor of 10 has become routinely adopted in essentially all risk assessment procedures involving animal model data for extrapolation. Despite the longstanding use of the interspecies UF of 10, only limited biological and/or toxicological justification for the interspecies UF has ever been put forth by any regulatory agency (1) or national advisory committee (e.g., National Academy of Sciences Safe Drinking Committee). The adoption of the 10fold factor appears to have been based on a combination of public health protection philosophy, practical/intuitive toxicological insights based J,
Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm
 Machine Learning
, 1988
"... learning Boolean functions, linearthreshold algorithms Abstract. Valiant (1984) and others have studied the problem of learning various classes of Boolean functions from examples. Here we discuss incremental learning of these functions. We consider a setting in which the learner responds to each ex ..."
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Cited by 773 (5 self)
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example according to a current hypothesis. Then the learner updates the hypothesis, if necessary, based on the correct classification of the example. One natural measure of the quality of learning in this setting is the number of mistakes the learner makes. For suitable classes of functions, learning
AN INFINITE SERIES FOR THE NATURAL LOGARITHM THAT CONVERGES THROUGHOUT ITS DOMAIN AND MAKES CONCAVITY TRANSPARENT
"... Abstract. The natural logarithm can be represented by an infinite series that converges for all positive real values of the variable, and which makes concavity patently obvious. Concavity of the natural logarithm is known to imply, among other things, the fundamental inequality between the arithmet ..."
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Abstract. The natural logarithm can be represented by an infinite series that converges for all positive real values of the variable, and which makes concavity patently obvious. Concavity of the natural logarithm is known to imply, among other things, the fundamental inequality between
1 A FIXEDPOINT IMPLEMENTATION OF THE NATURAL LOGARITHM BASED ON A EXPANDED HYPERBOLIC CORDIC ALGORITHM
"... his work presents a fixedpoint hardware implementation of the natural logarithm (ln) function. The natural logarithm approximation is based on a expanded hyperbolic CORDIC algorithm, which allows an efficient mapping of the logarithm function onto a VLSI or FPGA architecture, since the CORDIC algor ..."
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his work presents a fixedpoint hardware implementation of the natural logarithm (ln) function. The natural logarithm approximation is based on a expanded hyperbolic CORDIC algorithm, which allows an efficient mapping of the logarithm function onto a VLSI or FPGA architecture, since the CORDIC
Strengths and weaknesses of quantum computing
, 1996
"... Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both solv ..."
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Cited by 381 (10 self)
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Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both
On Clusterings: Good, Bad and Spectral
, 2003
"... We motivate and develop a natural bicriteria measure for assessing the quality of a clustering which avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have polylogarithmic worstcase guarantees under the new measure. The main result of the paper is the analysis of ..."
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Cited by 332 (11 self)
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We motivate and develop a natural bicriteria measure for assessing the quality of a clustering which avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have polylogarithmic worstcase guarantees under the new measure. The main result of the paper is the analysis
Results 1  10
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