This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) method their formation for reliable digital signal processing (DSP), transmission, data storage. The is obtained based on general positional (PNS) with conditions functions converting BNS a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, multivalued systems. G...

The binomial tree method, first proposed by Cox, Ross, and Rubinstein [Journal of Financial Economics, 7 (1979), pp. 229–263], is one of the most popular approaches to pricing options. By introducing an additional path-dependent variable, such methods can be readily extended to the valuation of path-dependent options. In this paper, using numerical analysis and the notion of viscosity solutions...

Motivation: An important property of a valid method for testing for differential expression is that the false positive rate should at least roughly correspond to the p-value cutoff, so that if 10,000 genes are tested at a p-value cutoff of 10−4, and if all the null hypotheses are true, then there should be only about 1 gene declared to be significantly differentially expressed. We tested this b...

In order to understand the role of crossover in differential evolution, theoretical analysis and comparative study of crossover in differential evolution are presented in this paper. Two new crossover methods, namely consecutive binomial crossover and non-consecutive exponential crossover, are designed. The probability distribution and expectation of crossover length for binomial and exponentia...

BACKGROUND The assessment of treatment success in clinical trials when multiple (repeated) doses (courses) are involved is quite common, for example, in the case of infertility treatment with assisted reproductive technology (ART), and medical abortion using misoprostol alone or in combination with mifepristone. Under these or similar circumstances, most researchers assess success using binomia...