Let’s assume , ,.., 1 , n k t t k = = , 0 , 0 ) 1 ( 1 1 = − − + = t n T k t tk ) ))( ( ( k k t X x ⋅ Φ = is a model of observed time series . ... 1 n x x Let’s call ξ as a basic process of the model. Levy processes with independent stationary increments have been considered as basic for models of time series (particularly financial) [1-4]. The next step in the development of the models is trans...

In this issue, a pair of studies (Levy et al. and Sanders et al.) identify several de novo copy-number variants that together account for 5%-8% of cases of simplex autism spectrum disorders. These studies suggest that several hundreds of loci are likely to contribute to the complex genetic heterogeneity of this group of disorders. An accompanying study in this issue (Gilman et al.), presents ne...

The role of various symmetries in the evaluation of splitting functions and coefficient functions is discussed. The scale invariance in hard processes is known to be a guiding tool to understand the dynamics. We discuss the constraints on splitting functions coming from various symmetries such as scale, conformal and supersymmetry. We also discuss the Drell-Levy-Yan relation among splitting and...