A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

Computing tasks may often be posed as optimization problems.The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable.State-of-the-art methods for solving these problems typically only guarantee convergence to local minima.This work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective function.The core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing parameters.Gradients of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi equation.Our numerical examples illustrate global convergence.

Task Offloading in Edge Computing Using GNNs and DQN

In a network environment composed of different types of computing centers that can be divided into different layers(clod,edge layer,and others),the interconnection between them offers the possibility of peer-to-peer task offloading.For many resource-constrained devices,the computation of many types of tasks is not feasible because they cannot support such computations as they do not have enough available memory and processing capacity.In this scenario,it is worth considering transferring these tasks to resource-rich platforms,such as Edge Data Centers or remote cloud servers.For different reasons,it is more exciting and appropriate to download various tasks to specific download destinations depending on the properties and state of the environment and the nature of the functions.At the same time,establishing an optimal offloading policy,which ensures that all tasks are executed within the required latency and avoids excessive workload on specific computing centers is not easy.This study presents two alternatives to solve the offloading decision paradigm by introducing two well-known algorithms,Graph Neural Networks(GNN)and Deep Q-Network(DQN).It applies the alternatives on a well-known Edge Computing simulator called PureEdgeSimand compares them with the two defaultmethods,Trade-Off and Round Robin.Experiments showed that variants offer a slight improvement in task success rate and workload distribution.In terms of energy efficiency,they provided similar results.Finally,the success rates of different computing centers are tested,and the lack of capacity of remote cloud servers to respond to applications in real-time is demonstrated.These novel ways of finding a download strategy in a local networking environment are unique as they emulate the state and structure of the environment innovatively,considering the quality of its connections and constant updates.The download score defined in this research is a crucial feature for determining the quality of a download path in the GNN training process and has not previously been proposed.Simultaneously,the suitability of Reinforcement Learning(RL)techniques is demonstrated due to the dynamism of the network environment,considering all the key factors that affect the decision to offload a given task,including the actual state of all devices.

A Review of Lightweight Security and Privacy for Resource-Constrained IoT Devices

The widespread and growing interest in the Internet of Things(IoT)may be attributed to its usefulness in many different fields.Physical settings are probed for data,which is then transferred via linked networks.There are several hurdles to overcome when putting IoT into practice,from managing server infrastructure to coordinating the use of tiny sensors.When it comes to deploying IoT,everyone agrees that security is the biggest issue.This is due to the fact that a large number of IoT devices exist in the physicalworld and thatmany of themhave constrained resources such as electricity,memory,processing power,and square footage.This research intends to analyse resource-constrained IoT devices,including RFID tags,sensors,and smart cards,and the issues involved with protecting them in such restricted circumstances.Using lightweight cryptography,the information sent between these gadgets may be secured.In order to provide a holistic picture,this research evaluates and contrasts well-known algorithms based on their implementation cost,hardware/software efficiency,and attack resistance features.We also emphasised how essential lightweight encryption is for striking a good cost-to-performance-to-security ratio.

Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis

A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.

Intelligent diagnosis of atrial septal defect in children using echocardiography with deep learning

Background Atrial septal defect(ASD)is one of the most common congenital heart diseases.The diagnosis of ASD via transthoracic echocardiography is subjective and time-consuming.Methods The objective of this study was to evaluate the feasibility and accuracy of automatic detection of ASD in children based on color Doppler echocardiographic static images using end-to-end convolutional neural networks.The proposed depthwise separable convolution model identifies ASDs with static color Doppler images in a standard view.Among the standard views,we selected two echocardiographic views,i.e.,the subcostal sagittal view of the atrium septum and the low parasternal four-chamber view.The developed ASD detection system was validated using a training set consisting of 396 echocardiographic images corresponding to 198 cases.Additionally,an independent test dataset of 112 images corresponding to 56 cases was used,including 101 cases with ASDs and 153 cases with normal hearts.Results The average area under the receiver operating characteristic curve,recall,precision,specificity,F1-score,and accuracy of the proposed ASD detection model were 91.99,80.00,82.22,87.50,79.57,and 83.04,respectively.Conclusions The proposed model can accurately and automatically identify ASD,providing a strong foundation for the intelligent diagnosis of congenital heart diseases.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

Hybridization of Fuzzy and Hard Semi-Supervised Clustering Algorithms Tuned with Ant Lion Optimizer Applied to Higgs Boson Search

This paper focuses on the unsupervised detection of the Higgs boson particle using the most informative features and variables which characterize the“Higgs machine learning challenge 2014”data set.This unsupervised detection goes in this paper analysis through 4 steps:(1)selection of the most informative features from the considered data;(2)definition of the number of clusters based on the elbow criterion.The experimental results showed that the optimal number of clusters that group the considered data in an unsupervised manner corresponds to 2 clusters;(3)proposition of a new approach for hybridization of both hard and fuzzy clustering tuned with Ant Lion Optimization(ALO);(4)comparison with some existing metaheuristic optimizations such as Genetic Algorithm(GA)and Particle Swarm Optimization(PSO).By employing a multi-angle analysis based on the cluster validation indices,the confusion matrix,the efficiencies and purities rates,the average cost variation,the computational time and the Sammon mapping visualization,the results highlight the effectiveness of the improved Gustafson-Kessel algorithm optimized withALO(ALOGK)to validate the proposed approach.Even if the paper gives a complete clustering analysis,its novel contribution concerns only the Steps(1)and(3)considered above.The first contribution lies in the method used for Step(1)to select the most informative features and variables.We used the t-Statistic technique to rank them.Afterwards,a feature mapping is applied using Self-Organizing Map(SOM)to identify the level of correlation between them.Then,Particle Swarm Optimization(PSO),a metaheuristic optimization technique,is used to reduce the data set dimension.The second contribution of thiswork concern the third step,where each one of the clustering algorithms as K-means(KM),Global K-means(GlobalKM),Partitioning AroundMedoids(PAM),Fuzzy C-means(FCM),Gustafson-Kessel(GK)and Gath-Geva(GG)is optimized and tuned with ALO.

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.

THE METHOD OF MULTIPLE SCALES APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A TRUNCATED SHALLOW SPHERICAL SHELL OF VARIABLE THICKNESS WITH THE LARGE GEOMETRICAL PARAMETER

Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.

Intermittent Control for Fixed-Time Synchronization of Coupled Networks

Dear Editor, This letter deals with fixed-time synchronization(Fd-TS) of complex networks(CNs) under aperiodically intermittent control(AIC)for the first time. The average control rate and a new Lyapunov function are proposed to overcome the difficulty of dealing with fixedtime stability/synchronization of CNs for AIC.

Novel Analysis of Two Kinds Hybrid Models in Ferro Martial Inserting Variable Lorentz Force Past a Heated Disk:An Implementation of Finite Element Method

In this article,the rheology of Ferro-fluid over an axisymmetric heated disc with a variable magnetic field by considering the dispersion of hybrid nanoparticles is considered.The flow is assumed to be produced by the stretching of a rotating heated disc.The contribution of variable thermophysical properties is taken to explore themomentum,mass and thermal transportation.The concept of boundary layermechanismis engaged to reduce the complex problem into a simpler one in the form of coupled partial differential equations system.The complex coupled PDEs are converted into highly nonlinear coupled ordinary differential equations system(ODEs)and the resulting nonlinear flow problem is handled numerically.The solution is obtained via finite element procedure(FEP)and convergence is established by conducting the grid-independent survey.The solution of converted dimensionless problem containing fluid velocity,temperature and concentration field is plotted against numerous involved emerging parameters and their impact is noted.From the obtained solution,it is monitored that higher values of magnetic parameter retard the fluid flow and escalating values of Eckert number results in to enhance temperature profile.Ferro-fluid flow and heat energy for the case of the Yamada Ota hybrid model are higher than for the case of the Hamilton Crosser hybrid model.Developing a model is applicable to the printing process,electronic devices,temperature measurements,engineering process and food-making process.The amount of mass species is reduced vs.incline impacts of chemical reaction and Schmidt parameter.

(α,γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties

Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation.The governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity transformation.The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software.It was found that dual solutions exist for the shrinking parameter values up to a certain range.The numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the literature.The governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and analyzed.The variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field parameters.It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

Hydrocephalic cerebrospinal fluid flowing rotationally with pulsatile boundaries:A mathematical simulation of the thermodynamical approach

To study the kinematics of flow rate and ventricular dilatation,an analytical perturbation approach of hydrocephalus has been devised.This research provides a comprehensive investigation of the characteristics of cerebrospinal fluid(CSF)flow and pressure in a hydrocephalic patient.The influence of hydrocephalic CSF,flowing rotationally with realistic dynamical characteristics on pulsatile boundaries of subarachnoid space,was demonstrated using a nonlinear controlling system of CSF.An analytical perturbation method of hydrocephalus has been developed to investigate the biomechanics of fluid flow rate and the ventricular enlargement.In this paper presents a detailed analysis of CSF flow and pressure dynamics in a hydrocephalic patient.It was elaborated with a nonlinear governing model of CSF to show the influence of hydrocephalic CSF,flowing rotationally with realistic dynamical behaviors on pulsatile boundaries of subarachnoid space.In accordance with the suggested model,the elasticity factor changes depending on how much a porous layer,in this case the brain parenchyma,is stretched.It was improved to include the relaxation of internal mechanical stresses for various perturbation orders,modelling the potential plasticity of brain tissue.The initial geometry that was utilised to create the framework of CSF with pathological disease hydrocephalus and indeed the output of simulations using this model were compared to the actual progression of ventricular dimensions and shapes in patients.According to this observation,the non-linear and elastic mechanical phenomena incorporated into the current model are probably true.Further modelling of ventricular dilation at a normal pressure may benefit from the existence of a valid model whose parameters approximate genuine mechanical characteristics of the cerebral cortex.

Classification of Nonlinear Confusion Component Using Hybrid Multi-Criteria Decision Making

In today’s digital world,the most inevitable challenge is the protection of digital information.Due to the weak confidentiality preserving techniques,the existing world is facing several digital information breaches.To make our digital data indecipherable to the unauthorized person,a technique forfinding a crypto-graphically strong Substitution box(S-box)have presented.An S-box with sound cryptographic assets such as nonlinearity(NL),strict avalanche criterion(SAC),bit independence criteria(BIC),bit independence criteria of nonlinearity(BIC-NL),Bit independence criteria of Strict avalanche criteria(BIC-SAC),and Input/output XOR is considered as the robust S-box.The Decision-Making Trial and Evaluation Laboratory(DEMATEL)approach of multi-criteria decision making(MCDM)is proposed forfinding the interrelation among cryptographic properties.A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis(MOORA)is applied for the best S-box selection.A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria,entro-py weight assigning,and MOORA ranking scheme.The combination of these three methods provides a fast selection procedure for the secure confusion com-ponent.The offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.

Effects of Different Feedback Conditions on Sensorimotor Adaptation Revealed in a Mirror Reversal Paradigm

Humans are able to overcome sensory perturbations imposed on their movements through motor learning. One of the key mechanisms to accomplish this is sensorimotor adaptation, an implicit, error-driven learning mechanism. Past work on sensorimotor adaptation focused mainly on adaptation to rotated visual feedback—A paradigm known as visuomotor rotation. Recent studies have shown that sensorimotor adaptation can also occur under mirror-reversed visual feedback. In visuomotor rotation, sensorimotor adaptation can be driven by both endpoint and online feedback [1] [2]. However, it’s not been clear whether both kinds of feedback can similarly drive adaptation under a mirror reversed perturbation. We performed a study to establish what kinds of feedback can drive adaptation under mirror reversal. In the first two conditions, the participants were asked to ignore visual feedback. In the first condition, we provided mirror reversed online feedback and endpoint feedback. We reproduced previous findings showing that online feedback elicited adaptation under mirror reversal. In a second condition, we provided mirror reversed endpoint feedback. However, in the second condition, we found that endpoint feedback alone failed to elicit adaptation. In a third condition, we provided both types of feedback at the same time, but in a conflicting way: endpoint feedback was non-reversed while online feedback was mirror reversed. The participants were asked to ignore online visual feedback and try to hit the target with help from veridical endpoint feedback. In the third condition, in which veridical endpoint feedback and mirror reversed online feedback were provided, adaptation still occurred. Our results showed that endpoint feedback did not elicit adaptation under mirror reversal but online feedback did. This dissociation between effects of endpoint feedback and online feedback on adaptation under mirror reversal suggests that adaptation under these different kinds of feedback might in fact operate via distinct mechanisms.

Deep bed filtration model for cake filtration and erosion

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.