On plateaued functions, linear structures and permutation polynomials

We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some applications of our new notion of linear translator to the construction of permutation polynomials. Furthermore, we give explicit classes of permutation polynomials over Fqn using some properties of Fq and some conditions of 2011, Akbary, Ghioca and Wang

Variation in sperm morphometry and sperm competition among barn swallow (Hirundo rustica) populations

Spermatozoa vary greatly in size and shape among species across the animal kingdom. Postcopulatory sexual selection is thought to be the major evolutionary force driving this diversity. In contrast, less is known about how sperm size varies among populations of the same species. Here, we investigate geographic variation in sperm size in barn swallows Hirundo rustica, a socially monogamous passerine with a wide Holarctic breeding distribution. We included samples from seven populations and three subspecies: five populations of ssp. rustica in Europe (Czech, Italy, Norway, Spain, and Ukraine), one population of ssp. transitiva in Israel, and one population of ssp. erythrogaster in Canada. All sperm traits (head length, midpiece length, tail length, and total length) varied significantly among populations. The variation among the European rustica populations was much lower than the differences among subspecies, indicating that sperm traits reflect phylogenetic distance. We also performed a test of the relationship between the coefficient of between-male variation in total sperm length and extrapair paternity levels across different populations within a species. Recent studies have found a strong negative relationship between sperm size variation and extrapair paternity among species. Here, we show a similar negative relationship among six barn swallow populations, which suggests that the variance in male sperm length in a population is shaped by the strength of stabilizing postcopulatory sexual selection