相关论文: Bad witnesses for a composite number

The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number…

We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…

Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…

Given a predictor of outcome derived from a high-dimensional dataset, pre-validation is a useful technique for comparing it to competing predictors on the same dataset. For microarray data, it allows one to compare a newly derived predictor…

We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…

This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system…

Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…

We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of…

Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary…

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

We investigate one-dimensional families of diagonal forms, considering the evolution of the asymptotic formula and error term. We then discuss properties of the average asymptotic formula obtained. The subsequent second moment analysis…

Let $L/K$ be a Galois extension of number fields. The problem of counting the number of prime ideals $\mathfrak p$ of $K$ with fixed Frobenius class in $\mathrm{Gal}(L/K)$ and norm satisfying a congruence condition is considered. We show…

We compute the associated prime ideals of the normalization modulo the ring, and establish connections between different types of generalizations (resp. specializations) of the normalization. This has some applications. For example, we…

The Frobenius primality test is based on the properties of the Frobenius automorphism of the quadratic extension of the residue field. Although it is probabilistic, we show that is "very rarely wrong". To date there are no counterexamples…

Bivariate count models having one marginal and the other conditionals being of the Poissons form are called pseudo-Poisson distributions. Such models have simple exible dependence structures, possess fast computation algorithms and generate…

In this paper we generalize the classical Proth's theorem for integers of the form $N=Kp^n+1$. For these families, we present a primality test whose computational complexity is $\widetilde{O}(\log^2(N))$ and, what is more important, that…

Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most "natural" generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the mathematical…

Relational probabilistic models have the challenge of aggregation, where one variable depends on a population of other variables. Consider the problem of predicting gender from movie ratings; this is challenging because the number of movies…