The minimum tree for a given zero-entropy period

We answer the following question: given any n∈ℕ, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en=s1s2…sk−∑i=2ksisi+1…sk, where n=s1s2…sk is the decomposition of n into a product of primes such that si≤si+1 for 1≤iperiodic orbit of period m with em>e, then the topological entropy of f is positive

Humeral development from neonatal period to skeletal maturity—application in age and sex assessment

The goal of the present study is to examine cross-sectional information on the growth of the humerus based on the analysis of four measurements, namely, diaphyseal length, transversal diameter of the proximal (metaphyseal) end of the shaft, epicondylar breadth and vertical diameter of the head. This analysis was performed in 181 individuals (90 ♂ and 91 ♀) ranging from birth to 25 years of age and belonging to three documented Western European skeletal collections (Coimbra, Lisbon and St. Bride). After testing the homogeneity of the sample, the existence of sexual differences (Student"s t- and Mann-Whitney U-test) and the growth of the variables (polynomial regression) were evaluated. The results showed the presence of sexual differences in epicondylar breadth above 20 years of age and vertical diameter of the head from 15 years of age, thus indicating that these two variables may be of use in determining sex from that age onward. The growth pattern of the variables showed a continuous increase and followed first- and second-degree polynomials. However, growth of the transversal diameter of the proximal end of the shaft followed a fourth-degree polynomial. Strong correlation coefficients were identified between humeral size and age for each of the four metric variables. These results indicate that any of the humeral measurements studied herein is likely to serve as a useful means of estimating sub-adult age in forensic samples.

Sexual foraging segregation in South American sea lions increases during the pre-breeding period in the La Plata River plume

Stable carbon and nitrogen isotopes in skin and bone of South American sea lions from Brazil and Uruguay were analysed to test the hypothesis that trophic overlap between the sexes is lower during the pre-breeding season than throughout the rest of the year. The isotopic values of skin and bone were used to infer the trophic relationships between the sexes during the pre-breeding period and year round, respectively. Prey species were also analysed to establish a baseline necessary for interpreting the stable isotope ratios of skin and bone. Standard ellipse areas, estimated using Bayesian inference in the SIBER routine of the SIAR package in R, suggested that males and females used a wide diversity of foraging strategies throughout the year and that no differences existed between the sexes. However, the diversity of foraging strategies was largely reduced during the pre-breeding period, with all the individuals of each sex adopting similar strategies, but with the two sexes differing considerably in stable isotope values and the ellipse areas of males and females not overlapping at all. Nevertheless, the results revealed a general increase in the consumption of pelagic prey by both sexes during the pre-breeding period. The progressive crowding of individuals in the areas surrounding the breeding rookeries during the pre-breeding period could lead to an increase in the local population density, which could explain the above reported changes.

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. The time till lysis (or latent period) is assumed to have an arbitrary distribution. We have carried out an optimization procedure, and we have found that the latent period corresponding to maximal fitness (i.e. maximal growth rate of the bacteriophage population) is of fixed length. We also study the dependence of the optimal latent period on the amount of susceptible bacteria and the number of virions released by a single infection. Finally, the evolutionarily stable strategy of the latent period is also determined as a fixed period taking into account that super-infections are not considered