Distributed Beamforming with Wirelessly Powered Relay Nodes

This paper studies a system where a set of $N$ relay nodes harvest energy from the signal received from a source to later utilize it when forwarding the source's data to a destination node via distributed beamforming. To this end, we derive (approximate) analytical expressions for the mean SNR at destination node when relays employ: i) time-switching based energy harvesting policy, ii) power-splitting based energy harvesting policy. The obtained results facilitate the study of the interplay between the energy harvesting parameters and the synchronization error, and their combined impact on mean SNR. Simulation results indicate that i) the derived approximate expressions are very accurate even for small $N$ (e.g., $N=15$), ii) time-switching policy by the relays outperforms power-splitting policy by at least $3$ dB.Comment: 4 pages, 3 figures, accepted for presentation at IEEE VTC 2017 Spring conferenc

Modulation mode detection and classification for in-vivo nano-scale communication systems operating in terahertz band

This paper initiates the efforts to design an intelligent/cognitive nano receiver operating in terahertz band. Specifically, we investigate two essential ingredients of an intelligent nano receiver—modulation mode detection (to differentiate between pulse-based modulation and carrier-based modulation) and modulation classification (to identify the exact modulation scheme in use). To implement modulation mode detection, we construct a binary hypothesis test in nano-receiver’s passband and provide closed-form expressions for the two error probabilities. As for modulation classification, we aim to represent the received signal of interest by a Gaussian mixture model (GMM). This necessitates the explicit estimation of the THz channel impulse response and its subsequent compensation (via deconvolution). We then learn the GMM parameters via expectation–maximization algorithm. We then do Gaussian approximation of each mixture density to compute symmetric Kullback–Leibler divergence in order to differentiate between various modulation schemes (i.e., ${M}$ -ary phase shift keying and ${M}$ -ary quadrature amplitude modulation). The simulation results on mode detection indicate that there exists a unique Pareto-optimal point (for both SNR and the decision threshold), where both error probabilities are minimized. The main takeaway message by the simulation results on modulation classification is that for a pre-specified probability of correct classification, higher SNR is required to correctly identify a higher order modulation scheme. On a broader note, this paper should trigger the interest of the community in the design of intelligent/cognitive nano receivers (capable of performing various intelligent tasks, e.g., modulation prediction, and so on)

Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots

On traveling wave solutions of an autocatalytic reaction–diffusion Selkov–Schnakenberg system

This paper investigates the analytical solutions of the autocatalytic reaction–diffusion Selkov–Schnakenberg system of coupled nonlinear PDEs mathematical perspective. This is a simple chemical reaction system that admits periodic solutions. The new families of exact solutions are derived which represent the autocatalyst and reactant of chemical concentrations. These exact solutions are obtained by using the technique namely as ϕ6-model expansion. Furthermore, the existence of these solutions is also discussed under different constraint conditions and variables of concentrations that are represented in hyperbolic, trigonometric, and rational forms. These results are new and effective in the physical phenomena of autocatalytic chemical reactions. For a better understanding of the physical interpretation of the solutions, the 3D and 2D graphs of some reported solutions are dispatched below for the different choices of parameters. Hence the physical description of our results may fruitful tool for investigating the further results for nonlinear wave problems in applied science

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R01. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note

Twelve-month observational study of children with cancer in 41 countries during the COVID-19 pandemic

Childhood cancer is a leading cause of death. It is unclear whether the COVID-19 pandemic has impacted childhood cancer mortality. In this study, we aimed to establish all-cause mortality rates for childhood cancers during the COVID-19 pandemic and determine the factors associated with mortality