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Two Applications of an Incomplete Additive Character Sum to Estimating Nonlinearity of Boolean Functions
"... Abstract. In recent years, several classes of Boolean functions with good cryptographic properties have been constructed by using univariate (or bivariate) polynomial representation of Boolean functions over finite fields. The estimation of an incomplete additive character sum plays an important ro ..."
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Abstract. In recent years, several classes of Boolean functions with good cryptographic properties have been constructed by using univariate (or bivariate) polynomial representation of Boolean functions over finite fields. The estimation of an incomplete additive character sum plays an important
THE FREQUENCY AND THE STRUCTURE OF LARGE CHARACTER SUMS
"... Abstract. Let M() denote the maximum of j∑nN (n)j for a given nonprincipal Dirichlet character (mod q), and let N denote a point at which the maximum is attained. In this article we study the distribution of M()= p q as one varies over characters (mod q), where q is prime, and investigate the lo ..."
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the location of N. We show that the distribution of M()= p q converges weakly to a universal distribution , uniformly throughout most of the possible range, and get (doubly exponential decay) estimates for 's tail. Almost all for which M() is large are odd characters that are 1pretentious. Now, M
Bayesian inference on phylogeny and its impact on evolutionary biology.
 Science
, 2001
"... 1 As a discipline, phylogenetics is becoming transformed by a flood of molecular data. These data allow broad questions to be asked about the history of life, but also present difficult statistical and computational problems. Bayesian inference of phylogeny brings a new perspective to a number of o ..."
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Cited by 235 (10 self)
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]). The posterior probability of a tree can be interpreted as the probability that the tree is correct. Inferences about the history of the group are then based on the posterior probability of trees. For example, the tree with the highest posterior probability might be chosen as the best estimate of phylogeny (1
A sumproduct estimate in finite fields, and applications
"... Abstract. Let A be a subset of a finite field F: = Z/qZ for some prime q. If F  δ < A  < F  1−δ for some δ> 0, then we prove the estimate A + A  + A · A  ≥ c(δ)A  1+ε for some ε = ε(δ)> 0. This is a finite field analogue of a result of [ESz1983]. We then use this estimate to ..."
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Cited by 75 (7 self)
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Abstract. Let A be a subset of a finite field F: = Z/qZ for some prime q. If F  δ < A  < F  1−δ for some δ> 0, then we prove the estimate A + A  + A · A  ≥ c(δ)A  1+ε for some ε = ε(δ)> 0. This is a finite field analogue of a result of [ESz1983]. We then use this estimate
A CLASS OF CHARACTER SUMS
"... Let p denote an odd prime, x a multiplicative character modulo p, (t real) and r,(x), r2(x) rational functions of x with integral coeficients. The P 1 character sum C *~(r,(x))e(r~(x)) has been estimated by Perel'muter [3]. m e ..."
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Let p denote an odd prime, x a multiplicative character modulo p, (t real) and r,(x), r2(x) rational functions of x with integral coeficients. The P 1 character sum C *~(r,(x))e(r~(x)) has been estimated by Perel'muter [3]. m e
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579,881