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26
OrderPreserving Symmetric Encryption
"... We initiate the cryptographic study of orderpreserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD ’04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard securi ..."
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We initiate the cryptographic study of orderpreserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD ’04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosenplaintext attack (INDCPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look “asrandomaspossible ” subject to the orderpreserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random orderpreserving function and the hypergeometric probability distribution. In particular, it makes blackbox use of an efficient sampling algorithm for the latter. 1
A Rejection Technique for sampling from TConcave Distributions
 ACM Transactions on Mathematical Software
, 1994
"... : A rejection algorithm  called transformed density rejection  that uses a new method for constructing simple hat functions for an unimodal, bounded density f is introduced. It is based on the idea to transform f with a suitable transformation T such that T (f(x)) is concave. f is then called T ..."
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: A rejection algorithm  called transformed density rejection  that uses a new method for constructing simple hat functions for an unimodal, bounded density f is introduced. It is based on the idea to transform f with a suitable transformation T such that T (f(x)) is concave. f is then called T concave and tangents of T (f(x)) in the mode and in a point on the left and right side are used to construct a hat function with tablemountain shape. It is possible to give conditions for the optimal choice of these points of contact. With T = \Gamma1= p x the method can be used to construct a universal algorithm that is applicable to a large class of unimodal distributions including the normal, beta, gamma and tdistribution. AMS Subject Classification: 65C10, 68C25. CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation General Terms: Algorithms Additional Key Words and Phrases: Rejection method, logconcave distributions, universal method 1....
A Universal Generator for Discrete LogConcave Distributions
 Computing
, 1994
"... : We give an algorithm that can be used to sample from any discrete logconcave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast fo ..."
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Cited by 9 (3 self)
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: We give an algorithm that can be used to sample from any discrete logconcave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete logconcave distributions and not much slower than algorithms designed for a single distribution. AMS Subject Classification: 65C10, 68C25. Key Words: Random number generation, logconcave distributions, rejection method, simulation. 1. Introduction A discrete distribution on the integers is called logconcave if the probabilities p k satisfy p 2 k p k\Gamma1 p k+1 for all k. Most of the classical discrete distributions like the binomial, Poisson, negative binomial and hypergeometric distributions are of this type (the only non logconcave distribution that has a chapter of its own in [9] is the logarithmic series distribution). Among the less often used logconcave di...
Monte Carlo Algorithms for HardyWeinberg Proportions
 Duke University
, 2003
"... this paper. Slow and fast direct generation of random variates Given that we derived in (2) from the uniform permutation on 2N alleles, we can generate a random variate directly from by rst generating a random permutation of the 2N alleles and then just counting the frequencies f ij directly. We ..."
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Cited by 6 (2 self)
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this paper. Slow and fast direct generation of random variates Given that we derived in (2) from the uniform permutation on 2N alleles, we can generate a random variate directly from by rst generating a random permutation of the 2N alleles and then just counting the frequencies f ij directly. We will refer to this as the naive Monte Carlo method for this problem. At rst glance this appears to be an eective method, but closer examination reveals that it is actually an exponential algorithm. Generation of the permutation of 2N elements requires 2N space and 2N draws of random uniforms. We are only interested in m choose 2 or (m ) dierent frequencies, but N might be exponentially large in the size of the problem instance. Hence directly forming the permutation is actually an exponential algorithm for the problem
Sampling From Discrete And Continuous Distributions With CRand
 In Simulation and
, 1992
"... CRAND is a system of TurboC routines and functions intended for use on microcomputers. It contains uptodate random number generators for more than thirty univariate distributions. For some important distributions the user has the choice between extremely fast but rather complicated method ..."
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CRAND is a system of TurboC routines and functions intended for use on microcomputers. It contains uptodate random number generators for more than thirty univariate distributions. For some important distributions the user has the choice between extremely fast but rather complicated methods and somewhat slower but also much simpler procedures. Menu driven demo programs allow to test and analyze the generators with regard to speed and quality of the output. 1.
The Patchwork Rejection Technique for Sampling from Unimodal Distributions
, 1998
"... We report on both theoretical developments of and computational experience with the patchwork rejection technique as studied in [20] and [21]. The basic approach is due to Minh [13] who suggested a special sampling method for the gamma distribution. Its general objective is to rearrange the area bel ..."
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We report on both theoretical developments of and computational experience with the patchwork rejection technique as studied in [20] and [21]. The basic approach is due to Minh [13] who suggested a special sampling method for the gamma distribution. Its general objective is to rearrange the area below the density or histogram f(x) in the body of the distribution by certain point reflections such that variates may be generated efficiently within a large center interval. This is carried out via uniform hat functions combined with minorizing rectangles for immediate acceptance of one transformed uniform deviate. The remaining tails of f(x) are covered by exponential functions. Experiments show that patchwork rejection algorithms are in general faster than its competitors at the cost of higher setup times. Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation; G.3 [Probability and Statistics]: Statistical Software; I.6.1 [Simulation and Modeling ]: Simulation Theory General Terms: Random Variate Transformations, Algorithms, Stochastic Simulation Additional Key Words and Phrases: Random variate generation, patchwork rejection, sampling techniques, unimodal distributions 1
Corresponding author:
, 707
"... 1 Abstract: In a recent article, Desai and Fisher (2007) proposed a new method to calculate the speed of adaptation in asexual populations. The main idea behind their method is that the speed of adaptation is determined by the dynamics of the stochastic edge of the population, that is, by the emerge ..."
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1 Abstract: In a recent article, Desai and Fisher (2007) proposed a new method to calculate the speed of adaptation in asexual populations. The main idea behind their method is that the speed of adaptation is determined by the dynamics of the stochastic edge of the population, that is, by the emergence and subsequent establishment of rare mutants that exceed the fitness of all sequences currently present in the population. They perform an elaborate stochastic calculation of the mean time until a new class of mutants has been established, which leads them to a prediction of the speed at which the population adapts. Their result, however, is at variance with previous work on the same model (Rouzine et al. 2003 and its recent upgrade Rouzine et al. 2007), which is based on the same main idea but uses a rather different approach to predict the adaptation speed. Here, we substantially extend Desai and Fisher’s analysis of the dynamics at the stochastic edge. First, we rederive their result more carefully using the same basic approach, and point out the approximations made. Then, we argue that some of these approximations are too coarse, for example the method of backextrapolation of the bestfit class’s dynamics. We suggest alternative assumptions, which lead us to a different result compatible with the findings of Rouzine et al. (2003, 2007). Finally, we compare the accuracy of both results with numerical simulations.
DOI: 10.1111/j.15410420.2005.00418.x Monte Carlo Algorithms for Hardy–Weinberg Proportions
, 2006
"... Summary. The Hardy–Weinberg law is among the most important principles in the study of biological systems (Crow, 1988, Genetics 119, 473–476). Given its importance, many tests have been devised to determine whether a finite population follows Hardy–Weinberg proportions. Because asymptotic tests can ..."
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Summary. The Hardy–Weinberg law is among the most important principles in the study of biological systems (Crow, 1988, Genetics 119, 473–476). Given its importance, many tests have been devised to determine whether a finite population follows Hardy–Weinberg proportions. Because asymptotic tests can fail, Guo and Thompson (1992, Biometrics 48, 361–372) developed an exact test; unfortunately, the Monte Carlo method they proposed to evaluate their test has a running time that grows linearly in the size of the population N. Here, we propose a new algorithm whose expected running time is linear in the size of the table produced, and completely independent of N. In practice, this new algorithm can be considerably faster than the original method.
Contents
, 2010
"... This package provides tools to compute densities, mass functions, distribution functions and their inverses, and reliability functions, for various continuous and discrete probability distributions. It also offers facilities for estimating the parameters of some distributions from ..."
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This package provides tools to compute densities, mass functions, distribution functions and their inverses, and reliability functions, for various continuous and discrete probability distributions. It also offers facilities for estimating the parameters of some distributions from
General Classes 5
, 2010
"... This package implements random number generators from various standard distributions. It also provides an interface to the C package UNURAN. CONTENTS ..."
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This package implements random number generators from various standard distributions. It also provides an interface to the C package UNURAN. CONTENTS