[en] In this work, we show that the prime numbers follow a multiscale distribution. Indeed they can be classified thanks to tree structures, which are expressed in terms of two maximal subsets of N and using multilayer selection rules, acting on these sets of prime candidates. Consequently, the prime numbers follow a specific deterministic rules. Indeed, a numeric accelerator for generating primes can be realized in terms of the above mentioned specific rules. From the comparison with the Fibonacci numbers a beautiful harmony comes in terms of the Golden Mean which is relevant to high energy physics and E-Infinity theory too.

[en] Starting from the result that the prime distribution is deterministic, we show in its maximal reduced form, the set of prime numbers P. This set can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The asymptotic behaviour is considered too. We go head towards an optimized algorithm to generate primes, whose computational complexity is C(n) element of O(n). In addition a pre-computed algorithm is also considered and its computational complexity C(n) element of O(1).

[en] We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an Ultimatum Game in complex networks. Specifically, players of three types are considered: (a) empathetic, whose aspiration levels, and offers, are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration levels, and offers, are independent. We analyze the asymptotic behavior of pure populations with different topologies using two kinds of strategic update rules: natural selection, which relies on replicator dynamics, and social penalty, inspired by the Bak–Sneppen dynamics, in which players are subject to a social selection rule penalizing not only the less fit individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies

[en] We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution density testing with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved

[en] If a glueball can decay into pairs of pseudoscalar mesons, then rather general arguments on flavour symmetry breaking imply that BR(G → ηη)> 1/2 BR(G → K⁺K^-) BR(G → ηη') < 1/2 BR(G → η'η'). The significance of KK* decays is also discussed

[en] A continuous kinetic function approach is proposed for analyzing the experimental decay curves. In the case of purely exponential behaviour, the values of kinetic function are the same at different ages of the investigated radionuclide. The deviation from main decay curve could be found by a comparison of experimental kinetic function values with those obtained in purely exponential case. (author). 12 refs

[en] Reactions of antiproton annihilation which are forbidden on a free nucleon but allowed on a bound nucleon, are considered. Investigation of these reactions is shown to be essential in clarifying the role of non-nucleonic degrees of freedom in the nuclei. It is also shown to be a good tool for search for exotic resonances. 20 refs., 4 figs., 2 tabs

[en] Using the connection with the Frobenius manifold (FM) structure, we study the matrix model description of minimal Liouville gravity (MLG) based on the Douglas String equation. Our goal is to find an exact discrete formulation of the $(q,p)$ MLG model that intrinsically contains information about the conformal selection rules. We discuss how to modify the FM structure appropriately for this purposes. We propose a modification of the construction for Lee–Yang series involving the $A_{p-<!--\; ???\; -->1}$ algebra instead of the previously used A₁ algebra. With the new prescription, we calculate correlators on the sphere up to four points and find full agreement with the continuous approach without using resonance transformations. (fast track communication)

[en] Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within a special class of differential dynamical systems. The general properties of connecting curves are derived and selection rules stated. Examples are presented to illustrate these properties for dynamical systems of dimension n = 3, 4, 5. (paper)

[en] A total of 71,518 days open (DO) and number of services per conception (NSC) records of 28,523 Iranian Holstein cows were analysed by random regression model. Akaike’s information criterion and likelihood ratio test suggested that a model with quadratic Legendre polynomials for additive genetic and permanent environmental was best. Heritability in different parities ranged from 0.103 to 0.045 in first parity and 0.054 to 0.030 in sixth parity for DO and NSC, respectively. Estimated genetic correlations between parities decreased continuously with increasing distance between parities for both DO and NSC. The first eigenfunction explained 89.99% and 97.22 % of the total genetic variance of DO and NSC, while the second eigenfunction accounted 6.24% and 3.18%, respectively. Different selection indices were constructed for DO and NSC. Genetic response to improve overall fertility was greater when the index included the first eigenvector than the response obtained from indices excluding it. Similar genetic gains were obtained from the first eigenvector, which had a nearly flat associated eigenfunction along lactations and from selection by the intercept of the random regression. The first eigenvector indices were responsible of changes in the level of DO and NSC in a similar manner for all parities, without altering the shape of the response curve across parities. The second and third eigenvector indices modified the shape of this curve but the improvement in genetic gains by including them in the selection index were small (DO) or negligible (NSC) due to the small amount of variability associated with these components.