Symmetry

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication. Full article

In this paper, an asymmetric regression model for censored non-negative data based on the centred exponentiated log-skew-normal and Bernoulli distributions mixture is introduced. To connect the discrete part with the continuous distribution, the logit link function is used. The parameters of the model are estimated by using the likelihood maximum method. The score function and the information matrix are shown in detail. Antibody data from a study of the measles vaccine are used to illustrate applicability of the proposed model, and it was found the best fit to the data with respect to an others models used in the literature. Full article

In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means of the main entropy-like measures of their associated Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, the Rényi and Shannon entropies, and their corresponding spreading lengths are analytically expressed in terms of the degree and the parameter(s) of the orthogonality weight function. These entropic quantities are closely related to the gradient functional (Fisher) and the ${\mathfrak{L}}_q$-norms (Rényi, Shannon) of the polynomials. In addition, the degree asymptotics for these entropy-like functionals of the three canonical families of HPOs (i.e., Hermite, Laguerre, and Jacobi polynomials) are given and briefly discussed. Finally, a number of open related issues are identified whose solutions are both physico-mathematically and computationally relevant. Full article

As part of his explication of the epistemological error made in separating thinking from its ecological context, Bateson distinguished counts from measurements. With no reference to Bateson, the measurement theory and practice of Benjamin Wright also recognizes that number and quantity are different logical types. Describing the confusion of counts and measures as schizophrenic, like Bateson, Wright, a physicist and certified psychoanalyst, showed mathematically that convergent stochastic processes informing counts are predictable in ways that facilitate methodical measurements. Wright’s methods experimentally evaluate the complex symmetries of nonlinear and stochastic numeric patterns as a basis for estimating interval quantities. These methods also retain connections with locally situated concrete expressions, mediating the data display by contextualizing it in relation to the abstractly communicable and navigable quantitative unit and its uncertainty. Decades of successful use of Wright’s methods in research and practice are augmented in recent collaborations of metrology engineers and psychometricians who are systematically distinguishing numeric counts from measured quantities in new classes of knowledge infrastructure. Situating Wright’s work in the context of Bateson’s ideas may be useful for infrastructuring new political, economic, and scientific outcomes. Full article

Atmospheric turbulence significantly degrades image quality. A blind image deblurring algorithm is needed, and a favorable image prior is the key to solving this problem. However, the general sparse priors support blurry images instead of explicit images, so the details of the restored images are lost. The recently developed priors are non-convex, resulting in complex and heuristic optimization. To handle these problems, we first propose a convex image prior; namely, maximizing L1 regularization (ML1). Benefiting from the symmetrybetween ML1 and L1 regularization, the ML1 supports clear images and preserves the image edges better. Then, a novel soft suppression strategy is designed for the deblurring algorithm to inhibit artifacts. A coarse-to-fine scheme and a non-blind algorithm are also constructed. For qualitative comparison, a turbulent blur dataset is built. Experiments on this dataset and real images demonstrate that the proposed method is superior to other state-of-the-art methods in blindly recovering turbulent images. Full article

We review the general theory of the Jacobi last multipliers in geometric terms and then apply the theory to different problems in integrability and the inverse problem for one-dimensional mechanical systems. Within this unified framework, we derive the explicit form of a Lagrangian obtained by several authors for a given dynamical system in terms of known constants of the motion via a Jacobi multiplier for both autonomous and nonautonomous systems, and some examples are used to illustrate the general theory. Finally, some geometric results on Jacobi multipliers and their use in the study of Hojman symmetry are given. Full article

In a one-flavor NJL model with a finite temperature, chemical potential, and external magnetic field, the self-energy of the quark propagator contains more condensates besides the vacuum condensate. We use Fierz identity to identify the self-energy and propose a self-consistent analysis to simplify it. It turns out that these condensates are related to the chiral separation effect and spin magnetic moment. Full article

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM. Full article

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization. Full article

Correlations and clustering are of great importance in the study of the Nuclear Equation of State. Information on these items/aspects can be obtained using heavy-ion reactions which are described by dynamical theories. We propose a dataset that will be useful for improving the description of light cluster production in transport model approaches. The dataset combines published and new data and is presented in a form that allows direct comparison of the experiment with theoretical predictions. The dataset is ranging in bombarding energy from 32 to 1930 A MeV. In constructing this dataset, we put in evidence the existence of a change in the light cluster production mechanism that corresponds to a peak in deuteron production. Full article

There is a substantial strand of literature about ranking the subsets of a set of alternatives, usually referred to as opportunity sets. We investigate a model that is dependent on the preference of a grand set of alternatives. In this framework, the indirect-utility criterion ranks the opportunity sets by the following rule: a subset A is weakly preferred to another subset B if and only if A contains at least one preference maximizing element from $A\cup B$. This criterion leads to the indifference of each subset of alternatives to a singleton; symmetry appears at this stage, as the property holds true for any one of the maximizers in A. Conversely, suppose that a ranking of opportunity sets satisfies the property that each opportunity set is indifferent to a singleton contained within it. Then, we prove that such a ranking must use a generalized form of the indirect-utility criterion, where maximization is applied to a selection of the alternatives. Altogether, these results produce a characterization of the advised indirect-utility criterion for ranking opportunity sets. Full article

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters. Full article