Pseudorandom bit generators play an essential role in high-security audio/video scrambling and addressing systems which allow pay-TV programs to be viewed only by authorized subscribers. This paper evaluated cryptographic strength of the bit generators proposed by the European Broadcast Unit and the Japan's Ministry of Posts and Telecommunications and some security weakness was found on the gen...

The "replicate histogram" is introduced as a simple diagnostic tool for describing the sampling distribution of a general statistic. It can be applied to virtually any statistic that has an asymptotic distribution, and, the data on which the statistic is computed may be serially or spatially dependent. The method is completely sample-based, requiring no theoretical analysis by the user, no know...

Under the condition that the design space is finite, new sufficient conditions for the strong consistency and asymptotic normality of the least-squares estimator in nonlinear stochastic regression models are derived. Similar conditions are obtained for the maximum-likelihood estimator in Bernoulli type experiments. Consequences on the sequential design of experiments are pointed out.

A supersimple theory eliminates hyperimaginaries. In particular, in a supersimple theory Lascar strong type is the same as strong type, and every strong type has a canonical base in C . It follows that the Amalgamation Theorem (Independence Theorem) holds for types over algebraically closed sets.

An odd prime p is called a Wieferich prime if 2p−1 ≡ 1 (mod p); alternatively, a Wilson prime if (p− 1)! ≡ −1 (mod p). To date, the only known Wieferich primes are p = 1093 and 3511, while the only known Wilson primes are p = 5, 13, and 563. We report that there exist no new Wieferich primes p < 4×1012 , and no new Wilson primes p < 5×108. It is elementary that both defining congruences above h...

Let ψm be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 ≤ m ≤ 11. We extend this by finding ψ12 and ψ13. We also present an algorithm to find all integers n ≤ B that are strong pseudoprimes to the first m prime bases; with a reasonable heuristic assumption we can show that it takes at most B2/3+o(1) time.

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estim...

Background: Preterm birth is a major contributor to neonatal and under-five mortality, and births at lower gestational ages (GA) contribute more to these statistics. Most developed countries have succeeded in improving survival at extremes of GA, while most developing countries like Nigeria still lag behind. The objective of this retrospective study was to document the...

The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes one-shock models, such as the EGARCH model of Nelson (1991), and two-shock models, such as the SV model of Taylor (1986). The variable of interest might not have finite fractional moment of an...