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148
Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance
, 2001
"... The number of steps any classical computer requires in order to find the prime factors of an ldigit integer N increases exponentially with l, at least using algorithms [1] known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying th ..."
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Cited by 150 (4 self)
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The number of steps any classical computer requires in order to find the prime factors of an ldigit integer N increases exponentially with l, at least using algorithms [1] known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying
Digit functions of integer sequences
 Fibonacci Q
, 1984
"... It was noticed by Benford [1] that the first nonzero digit in certain sets of real numbers is not uniformly distributed among the integers 1 through 9; in fact, the probability that this first, leftmost digit equals 3 is equal to log10(l + 3 " 1). He extended the analysis to the frequency of di ..."
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Cited by 1 (0 self)
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It was noticed by Benford [1] that the first nonzero digit in certain sets of real numbers is not uniformly distributed among the integers 1 through 9; in fact, the probability that this first, leftmost digit equals 3 is equal to log10(l + 3 " 1). He extended the analysis to the frequency
Fast OnLine Integer Multiplication
 PROC. 5TH ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1974
"... A Turing machine multiplies binary integers onZine if it receives its inputs loworder digits first and produces the jth digit of the product before reading in the (j+l)st digits of the two inputs. We present a general method for converting any offline multiplication algorithm which forms the prod ..."
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Cited by 12 (1 self)
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A Turing machine multiplies binary integers onZine if it receives its inputs loworder digits first and produces the jth digit of the product before reading in the (j+l)st digits of the two inputs. We present a general method for converting any offline multiplication algorithm which forms
Circuits for Integer Factorization: A Proposal
, 2001
"... The number eld sieve takes time L 1:901+o(1) on a generalpurpose computer with L 0:950+o(1) bits of memory; here L is a particular subexponential function of the input size. It takes the same time on a parallel trialdivision machine, such as Cracker or TWINKLE, of size L 0:950+o(1) . It t ..."
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Cited by 7 (0 self)
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) . It takes time only L 1:185+o(1) on a machine of size L 0:790+o(1) explained in this paper. This reduction of total cost from L 2:852+o(1) to L 1:976+o(1) means that a ((3:009 +o(1))d)digit factorization with the new machine has the same cost as a ddigit factorization with previous machines
ON THE REPRESENTATION OF FIBONACCI AND LUCAS NUMBERS IN AN INTEGER BASES
"... Abstract. Résumé. Nous présentons plusieurs théorèmes sur l’écriture des nombres entiers dans deux bases indépendantes. Nous dressons la liste complète des nombres de Fibonacci et des nombres de Lucas qui s’écrivent en binaire avec au plus quatre chiffres 1. Abstract. We discuss various results on t ..."
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Cited by 1 (1 self)
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on the representation of integers in two unrelated bases. We give the complete list of all the Fibonacci numbers and of all the Lucas numbers which have at most four digits 1 in their binary representation. 1.
REPRESENTATION OF NUMBERS WITH NEGATIVE DIGITS AND MULTIPLICATION OF SMALL INTEGERS
, 1999
"... The usual way to multiply numbers in binary representation runs as follows: To compute mn, copy n to x. Multiply x by two. If the last digit of m is 1, then add n to x. Now delete the last digit of m. Repeat until m = 1, then x = mn. Since multiplication by 2 needs almost no time, the running time ..."
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The usual way to multiply numbers in binary representation runs as follows: To compute mn, copy n to x. Multiply x by two. If the last digit of m is 1, then add n to x. Now delete the last digit of m. Repeat until m = 1, then x = mn. Since multiplication by 2 needs almost no time, the running
#A16 INTEGERS 14 (2014) ON GENERALIZED ADDITION CHAINS
"... Given integers d 1, and g 2, a gaddition chain for d is a sequence of integers a0 = 1, a1, a2,..., ar1, ar = d where ai = aj1 +aj2 + · · ·+ajk, with 2 k g, and 0 j1 j2 · · · jk i 1. The length of a gaddition chain is r, the number of terms following 1 in the sequence. We denote by l ..."
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Given integers d 1, and g 2, a gaddition chain for d is a sequence of integers a0 = 1, a1, a2,..., ar1, ar = d where ai = aj1 +aj2 + · · ·+ajk, with 2 k g, and 0 j1 j2 · · · jk i 1. The length of a gaddition chain is r, the number of terms following 1 in the sequence. We denote
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 5(3) (2005), #A07 IRREGULARITIES OF DISTRIBUTION OF DIGITAL
"... In this paper, as an application of our recent results to appear elsewhere [5], we compare digital (0, 1)sequences generated by nonsingular upper triangular matrices in arbitrary prime bases to van der Corput sequences and show these last ones are the worst distributed with respect to the star dis ..."
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discrepancy, the extreme discrepancy, the L2discrepancy and the diaphony. Moreover, we obtain digital (0, 1)sequences in arbitrary prime bases with very good extreme discrepancy, quite comparable to the best generalized van der Corput sequences already found in preceding studies ([2] and [4]). 1
A TwoStep Estimation Procedure and a GoodnessofFit Test for Spatial Extremes Models
"... Parametric maxstable processes are increasingly used to model spatial extremes. Since the dependence structure is specified for block maxima, the data used for inference are block maxima from all sites. To improve the estimation efficiency, we propose a twostep approach with composite likelihood t ..."
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Parametric maxstable processes are increasingly used to model spatial extremes. Since the dependence structure is specified for block maxima, the data used for inference are block maxima from all sites. To improve the estimation efficiency, we propose a twostep approach with composite likelihood that utilizes sitewise daily records in addition to block maxima. Besides the parameter estimation, there is no formal model checking and diagnosis method for spatial extremes modeling yet. Model diagnosis in practice has been informal and mostly based on visual checking tools such as residual plot and quantilequantile plot. We proposed a goodnessoffit test for maxstable processes based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function. The proposed twostep procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal parameters with an independence Likelihood by ignoring the spatial dependence. Given ithe marginal parameter estimates, the second step estimates the dependence parameters
A LOWPOWER MINIMUM DISTANCE lDSEARCH ENGINE USING HYBRID DIGITAL/ANALOG CIRCUIT TECHNIQUES
"... This Minimum Distance IDSearch Engine (MDSE) realizes the patternmatching hardware accelerator for the portable multimedia and intelligent processing systems. The chip executes highly parallel computation of L,norms between an input key and stored multiple reference records, and search of the mi ..."
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This Minimum Distance IDSearch Engine (MDSE) realizes the patternmatching hardware accelerator for the portable multimedia and intelligent processing systems. The chip executes highly parallel computation of L,norms between an input key and stored multiple reference records, and search
Results 1  10
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148