[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] 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] 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] 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] In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed by Dong et al (2011 J. Math. Imag. Vis. 40 82–104) where an automated parameter selection rule for spatially varying parameters has been proposed. Their parameter selection rule, however, only applies if measured imaging data are defined in the image domain, e.g. for image denoising and image deblurring problems. By introducing an auxiliary variable in their model, we show here that this idea can indeed by extended to general inverse imaging problems such as tomographic reconstruction where measurements are not in the image domain. With a spatially varying regularization parameter, the new method can suppress artifacts due to limited data and noise while preserving more details. Using numerical simulations on synthetic and real data, we demonstrate the validity of the proposed approach and its effectiveness for computed tomography reconstruction, delivering reconstruction results that are significantly improved compared to the state-of-the-art. (special issue article)

[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)