Dynamical behavior of recurrent neural networks with different external inputs

The main aim of this paper is to study the dynamics of a recurrent neural networks with different input currents in terms of asymptotic point. Under certain circumstances, we studied the existence, the uniqueness of bounded solutions and their homoclinic and heteroclinic motions of the considered system with rectangular currents input. Moreover, we studied the unpredictable behavior of the continuous high-order recurrent neural networks and the discrete high-order recurrent neural networks. Our method was primarily based on Banach’s fixed-point theorem, topology of uniform convergence on compact sets and Gronwall inequality. For the demonstration of theoretical results, we give examples and their numerical simulations.

Estimation of the critical points of an epidemic by means of a logistic growth model

Epidemiological models have become a very important tool in understanding an epidemic’s development, mainly because they help researchers find more efficient strategies in their fight against its spread. Several models have been proposed up to now: some use fractional calculus to solve differential equations while others use applications from other areas such as predatorprey models. The SIR and SEIR models, among others, mainly focus on the variable response and on epidemiological parameters such as the basic reproduction number (R0) and infection rate per unit of time, nevertheless they do not focus on the variable ‘time’. We propose the use of the variable time, as the main variable, by using a reparametrization in the logistic model since it will lead to the understanding of the epidemic as it goes along the time. Moreover, this model is important because it allows the estimation of the points of acceleration and deceleration, the point of maximum growth and the asymptotic point of the epidemic. This is only possible by getting an stable epidemic curve with an ‘S’ shape. In this work we use the variable ‘accumulated cases’ of COVID-19 of China and Italy and point out the main socioeconomic facts that occurred in each period of the estimated critical points from the logistic growth model.

Estimating the critical points of an epidemic: An application of non-epidemiological logistic growth model for COVID-19

Epidemiological models have become a very important tool in understanding an epidemic development, mainly because they help researchers in finding good and new strategies in their fight against its spread. Several models have been proposed up to now, some are mathematical others apply models from other areas. The SIR and SEIR among others, mainly focus on the variable response and on epidemiological parameters as the basic reproduction number (R0) and infection rate per unit of time, nevertheless they do not focus on the variable ‘time’. We propose the use of the variable time using the logistic model as it is generally used to describe the growth of animals. This model is important because it allows the estimation of the points of acceleration and deceleration, the point of maximum growth and the asymptotic point of the epidemic. This is only possible when the epidemic curve is stable and has an ‘S’ shape. In this work we use the variable ‘accumulated cases’ of China and Italy and point out the main socioeconomic facts that occurred in each period of the estimated critical points from the logistic growth model.

Viscoacoustic anisotropic wave equations

The wave equation plays a central role in seismic modeling, processing, imaging and inversion. Incorporating attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic forward and inverse modeling in attenuating anisotropic media. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. We have developed a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also obtain the viscoacoustic wave equations for transverse isotropy as a special case. The viscoacoustic orthorhombic wave equations are flexible for multiple viscoacoustic models. We take into account the classic visocoacoustic models such as the Kelvin-Voigt, Maxwell, standard-linear-solid and Kjartansson models, and we derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic point-source solution of the scalar wave equation. Numerical examples indicate a comparison of the acoustic waveforms excited by a point source in the viscoacoustic orthorhombic models and the corresponding nonattenuating model, and the effect of the attenuation anisotropy on the acoustic waveforms.

On a q-Analog of a Singularly Perturbed Problem of Irregular Type with Two Complex Time Variables

The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the - 1 -branch of Lambert W function, which turns out to be crucial.

Short Communication: Population dynamics of double-spined rock lobster (Panulirus penicillatus Olivier, 1791) in Southern Coast of Yogyakarta

Larasati RF, Suadi, Setyobudi E. 2018. Short Communication: Population dynamics of double-spined rock lobster (Panulirus penicillatus Olivier, 1791) in Southern Coast of Yogyakarta. Biodiversitas 19: 337-342. The southern coast of Yogyakarta, Indonesia, near to the Indian Ocean borders is a preferable habitat for lobster. Double-spined rock lobster (Panulirus penicillatus) is one of the prevalent species caught by fishermen. However the increased number of capture activities had an effect on the sustainability of global lobster fisheries. In order to sustain these fisheries resource, the preservation management of lobster should include wild stock assessments. Currently, the effect of fishing pressures on populations of P. penicillatus is limited. The objective of this research was to identify several factors affecting lobster population in terms of growth (carapace length (CL) and mass), recruitment, mortality rates, and exploitation rates in this species. Results showed that double-spined rock lobster had a longer size (CL) (45.2-55.1 mm) than that of females (55.2 mm-65.1 mm). While the growth rate (K) of males lobster is 0.85 year-¹ and its CL reached an asymptotic point at 125 mm (12 years old). Growth rate of females double-spined rock lobster was 0.55 year-¹ and its CL reached an asymptotic point at 125.5 mm (15 years old). The total estimation of mortality rates of double-spined rock lobster was 2.46, wherein 2.56 year-¹ for males and females, respectively. The estimated values of M were 1.08, 0.81 year-¹ for males and females, respectively while the respective values of F were 1.38 year-¹ and 1.75 year-¹ for males and females. The exploitation rate of males was 0.56 and females was 0.68. It has exceeded the optimal level (0.5) and reached overfishing value. Based on these results, it suggest that the time management of fishing activities such as by several approaches including the restricted time of fishing activity in spawning and recruitment season, the management of catching effort by the development of environment-friendly fishing gear, and the development of the lobster hatchery to reproduce and maintain their population naturally.

Selection Corrected Statistical Inference for Region Detection with High-throughput Assays

Scientists use high-dimensional measurement assays to detect and prioritize regions of strong signal in a spatially organized domain. Examples include finding methylation enriched genomic regions using microarrays and identifying active cortical areas using brain-imaging. The most common procedure for detecting potential regions is to group together neighboring sites where the signal passed a threshold. However, one needs to account for the selection bias induced by this opportunistic procedure to avoid diminishing effects when generalizing to a population. In this paper, we present a model and a method that permit population inference for these detected regions. In particular, we provide non-asymptotic point and confidence interval estimates for mean effect in the region, which account for the local selection bias and the non-stationary covariance that is typical of these data. Such summaries allow researchers to better compare regions of different sizes and different correlation structures. Inference is provided within a conditional one-parameter exponential family for each region, with truncations that match the constraints of selection. A secondary screening-and-adjustment step allows pruning the set of detected regions, while controlling the false-coverage rate for the set of regions that are reported. We illustrate the benefits of the method by applying it to detected genomic regions with differing DNA-methylation rates across tissue types. Our method is shown to provide superior power compared to non-parametric approaches.

EMERGENCE OF MULTI-CLUSTER CONFIGURATIONS FROM ATTRACTIVE AND REPULSIVE INTERACTIONS

We discuss a first-order Cucker–Smale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

TOPOLOGY OF ENTANGLEMENT EVOLUTION OF TWO QUBITS

The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described by the function n(t), where n is the 15-dimensional polarization vector. This representation is particularly useful because the components of n are direct physical observables, there is a meaningful notion of orthogonality, and the concurrence C can be computed for any point in the space. We analyze the topology of the space S of separable states (those having C = 0), and the often lower-dimensional linear dynamical subspace D that is characteristic of a specific physical model. This allows us to give a rigorous characterization of the four possible kinds of entanglement evolution. Which evolution is realized depends on the dimensionality of D and of D∩S, the position of the asymptotic point of the evolution, and whether or not the evolution is "distance-Markovian", a notion we define. We give several examples to illustrate the general principles, and to give a method to compute critical points. We construct a model that shows all four behaviors.