We formulated a mechanistic model for the cancer-immune system associated with therapy. In this model, cancer is divided into two types: cancer that is sensitive to treatment (CST) and cancer that gradually acquires resistance to therapeutic agents (CRT). Cancer activates various mechanisms to evade the actions of therapeutic agents, including chemotherapy or targeted therapy. A positive response is

Multidimensional scaling (MDS) provides a possibility to present the multidimensional data visually. It is a very popular method of this class. MDS minimizes some stress functions. In this paper, the stress function and multidimensional scaling, in general, have been considered from the geometric point of view. The so-called Geometric MDS has been developed. The new interpretation of the stress allows

The connectivity is an important indicator to evaluate the robustness of a network. Many works have focused on connectivity-based reliability analysis for decades. As a generalization of connectivity, H-structure connectivity and H-substructure connectivity were proposed to evaluate the robustness of networks. In this paper, we investigate the H-structure connectivity and H-substructure connectivity

The classical Weierstrass transform is an isometric operator mapping elements of the weighted L2−space L2(R,exp(−x2/2)) to the Fock space. It has numereous applications in physics and applied mathematics. In this paper, we define an analogue version of this transform in discrete Hermitian Clifford analysis, where functions are defined on a grid rather than the continuous space. This new transform is

The non-linear anomalous diffusion in anisotropic media is using in various fields, e.g. in molecular dynamics, hydrology, financial systems, porous media analysis, etc. The Lie group method is developed to study the time-fractional diffusion equation with a source term in anisotropic media. As an application, the complete Lie group classification is performed up to the equivalence transformations

This paper focus on the event-triggered filter design problem for delayed discrete-time Markovian jump systems. Firstly, a new mode-dependent Lyapunov-Krasovskii functional is introduced, where more than one Lyapunov matrices are dependent on jumping modes. Secondly, sufficient conditions are established by employing the Lyapunov stability theory together with Wirtinger-based inequality, under which

The repercussion of understanding how waves propagate in poroelastic media is enormous. Poroelastic cylinders have been used in several applications of different fields. For example, geophysics, structural mechanics, medicine, aerodynamic, nanoscience, among others. This work, based on Biot viscosity-extended theory, investigates the torsional vibrations of infinite fully saturated, axial-symmetric

In this paper, we construct some directed strongly regular Cayley graphs on Dihedral groups, which generalizes some earlier constructions. We also characterize certain directed strongly regular Cayley graphs on Dihedral groups Dpα, where p is a prime and α ≥ 1 is a positive integer.

In this paper, we construct a mathematical model for a supply chain with computer aided digital manufacturing process. We show that the model exhibits various complicated behaviors including chaotic attractors. A stabilizing linear feedback controller is designed to stabilize the supply chain system. We move on to develop an active controller to synchronize two such systems. The design methodologies

We develop a mathematical model of the performance of a group of independent Bayesian searchers who are all seeking a common goal. In this context, the searchers do not directly interact with one another, but they may observe the behavior of nearby searchers and adjust their behavior accordingly. By modeling this system as an evolutionary game, an evolutionarily stable strategy is found for the percentage

By using the important concept of stoping distance of the LDPC codes, how to perform about the iterative decoding of the LDPC codes in binary erasure channels is analyzed. In this article, we introduce a class of LDPC codes designed on the premise of the symplectic space over finite fields. An important parameter of stopping distance is estimated mainly and the lower bound on the stopping distance

The memory-dependent derivative (MDD) is a new substitution for the fractional derivative (FD). It reflects the memory effect in a more distinct way. As an application, the representative heat diffusion process is remodeled with it. In fact, due to the existence of heat-conduction paradox, the time-space evolution mechanisms of this process are challenges to the modelers. The paradox cann’t be ascribed

This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination

In this paper, we prove the existence, stability and controllability results for fractional damped differential system with non-instantaneous impulses. The results are obtained by using Banach fixed-point theorem, nonlinear functional analysis, Mittag-Leffler matrix function and controllability Grammian matrix. At last, some numerical examples are given to illustrate the obtained theory.

Heat exchange and Fe3O4/water nanofluid flow behaviors into horizontal channel subjected to the effect of a magnetic field was studied numerically. The basic equations were solved using the finite volume method with the time-splitting algorithm. The results were represented by temperature field, streamlines, velocity field, averaged and normalized Nusselt numbers, for various nanoparticles volume fractions

In this paper, neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations. The error functions containing adjustable parameters (the weights) for the training sets are constructed. The range of learning rate is analyzed to ensure that the error decreases with respect to training times. Several numerical examples including numerical results and

In this paper, we aim at relaxing the boundedness condition for the input coefficient A of the Legendre random differential equation, to permit important unbounded probability distributions for A. We demonstrate that the formal solution constructed using the Fröbenius approach is indeed the mean square solution on the domain (−1,1), under mean fourth integrability of the initial conditions X0, X1 and

In this article, we will study the existence of the global and exponential attractors for the regularized Bénard equations with fractional Laplacian in the three-dimensional case. This system depends on three parameters β, γ and δ, which affect the regularity of the solution.

It has been generally recognized that most of the existing parametric filled function methods used for finding the global mininizer of unconstrained global optimization problems have computational weaknesses. In this paper, a new non parameter-filled function is proposed. This type of auxiliary function behaves as a bridge that can deliver one minimizer to another local minimizer, if one exists. To

This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity

The operator of double differentiation perturbed by the composition of the differentiation operator and a convolution one on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the convolution kernel from the spectrum both in a weighted L2-norm and in a weighted uniform norm. For this purpose, we successively prove uniform stability of each

The dynamics is studied of an infinite continuum system of jumping and coalescing point particles. In the course of jumps, the particles repel each other whereas their coalescence is free. Such models have multiple applications, e.g., in the theory of evolving ecological systems. As the equation of motion we take a kinetic equation, derived by a scaling procedure from the microscopic Fokker-Planck

We introduce a new spatial prisoner’s dilemma (SPD) model in which the so-called network reciprocity is enhanced more than in the conventional model. In addition to the usual binary strategies—perfect cooperator and perfect defector—we introduce “fence-sitters”, who either cooperate or defect with equal probability, as a third strategy. In regions with larger Stag-Hunt-type dilemmas but smaller Chicken-type

To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous computational cost. The method of multiple shooting, on the other hand, takes its place in between these two extremes. The computational cost of the algorithm is mostly

The combination of chemical, physical, electrical, and structural properties of the neurons has made them highly complex dynamical units. One of the best tools to deal with such high-level complexity is to study the neural spatiotemporal patterns. In this work, we have focused specifically on the spiral spatiotemporal pattern. Spirals make an important contribution to some of the cortical activities

Natural, forced and mixed convection heat transfer problems are solved by the meshless Method of Approximate Particular Solutions (MAPS). Particular solutions of Poisson and Stokes equations are employed to approximate temperature and velocity, respectively. The latter is used to obtained a closed expression for pressure particular solution. In both cases, the source terms are multiquadric radial basis

In this paper, the problem of simultaneously reconstructing the states and delays for nonlinear systems subject to input delays is studied. To relax some limitations of the classical Lipschitz condition, the one-sided Lipschitz and quadratically inner-bounded conditions are employed to handle nonlinearities. The control inputs are subject to bounded unknown time-varying delays. To deal with this open

This paper presents an edge preserving and tensor filtering method for diffusion tensor image. The main idea consists in using the Lα Riemannian centers of mass attached to the edge information estimated in the domain of the diffusion tensor so that the image edges not been smoothed in the filtering process. For α ∈ [1, 2], the method encompasses both the standard case of the Riemannian weighted mean

Transmission line displaying non-locality effects is modelled by considering the magnetic coupling of inductors in the series branch of Heaviside’s elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given non-local magnetic flux through the cross-inductivity kernel. Non-local telegrapher’s equations are derived as the continuum limit of corresponding

Because of its broad real-life application, community detection (in the realm of a complex network) is an attractive challenge to many researchers. However, current methods fail to reveal the full community structure and its formation process. Thus, here we present SIMGT, an effective and Scalable approach that detects overlapping communities: Integrating social identity Model and Game Theory. Inspired

This paper studies the cooperative output regulation (COR) problem of heterogeneous linear multi-agent systems (MAS)s based on two kinds of event-triggered control protocols under time-varying topologies. Firstly, a state feedback distributed control scheme is designed to achieve COR problem and eliminate Zeno behavior of the MASs with only intermittent communication between neighbors. The design of

For a given graph G, the Mostar index Mo(G) is the sum of absolute values of the differences between nu(e) and nv(e) over all edges e=uv of G, where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to u than to v and the number of vertices of G lying closer to v than to u. The degree sequence of a tree is the sequence of the degrees (in descending order) of the non-leaf vertices

This paper presents a numerical approximation technique to solve reaction-diffusion singularly-perturbed differential equation with robin-type boundary conditions. The proposed technique applies cubic splines to discretize the robin-boundary conditions and exponential splines to generate the solution of singularly perturbed differential equation at the internal nodes of a layer adapted grid. The layer

This paper is concerned with a kind of infinite horizon forward and backward stochastic difference equations (FBSDEs) with asymmetric information. The asymmetric information means that there exists two kinds of conditional expectations with respect to two different filtrations caused by the additive noise and the measurement packet dropout. The main contribution is to present the analytical solutions

Fractional differential equations have been studied due to their applications in modelling, and solved using various mathematical methods. Systems of fractional differential equations are also used, for example in the study of electric circuits, but they are more difficult to analyse mathematically. We present explicit solutions for several families of such systems, both homogeneous and inhomogeneous

This paper is dedicated to numerical computation of higher order derivatives in Simulink. In this paper, a new module has been implemented to achieve this purpose within the Simulink-based Infinity Computer solution, recently introduced by the authors. This module offers several blocks to calculate higher order derivatives of a function given by the arithmetic operations and elementary functions. Traditionally

This paper introduces a novel localized collocation Trefftz method (LCTM) for potential-based inverse electromyography (PIE). PIE is a noninvasive technique to calculate the internal electrical potentials from measured body surface electromyographic data, which can be considered as an inverse Cauchy problem with potential equation. In the proposed LCTM, the electrical potential at every node is expressed

In this paper, two different acceleration techniques for a deterministic DIRECT (DIviding RECTangles)-type global optimization algorithm, DIRECT-GLce, are considered. We adopt dynamic data structures for better memory usage in MATLAB implementation. We also study shared and distributed parallel implementations of the original DIRECT-GLce algorithm, and a distributed parallel version for the aggressive

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference

In an acquaintance society, reputation plays an important role in individuals’ activities. Especially when we face with collective decision-making, such as crowd-funding. The existence of reputation could stimulate cooperation. In this work, individuals’ reputation has been divided into being good, bad and medium according to their neighbors’ judgement. Considering people with different requirements

The role of incentive institutions on promoting cooperation in public goods game (PGG) has attracted much attention. Theoretical studies based on Nash equilibrium analysis predict that the punishment effect is often stronger than the reward effect. Although this result is confirmed by empirical studies, subjects do not always play these rational strategies. Recent experiments indicate that most subjects

In this paper, we propose a mathematical model, its numerical scheme, and some computational experiments for droplet evaporation. In order to model the evaporation, a classical Cahn–Hilliard equation with an interfacial evaporation mass flux term is proposed. An unconditionally gradient stable scheme is used to discretize the governing equation, and the multigrid method is applied to solve the resulting

This letter focus on the stability and explicit stationary density of a widely adopted stochastic single-species model. By taking advantage of Feller’s classification criteria, this letter verifies that there is a critical value Υ that characterizes the dynamical behaviors of the model, namely, if Υ > 0, then the model has a unique stationary probability distribution with an explicit density function;

In paper the nonlinear inverse problem of finding a control parameter in a space-time fractional diffusion equation with varying degrees of heterogeneity is investigated. An iterative method for finding an unknown control parameter is proposed. Under the maximal regularity condition respecting input data on the Bessel potential scale, the existence and uniqueness of a solution of such inverse problem

Mostly motivated by the crop field classification problem and the automated computational methodology for the extraction of agricultural fields with a uniform crop distribution from satellite data, we propose an indirect approach for the image segmentation which is based on the concept of a piecewise constant approximation of the slope-based vegetation indices. We discuss in detail the consistency

Several quaternion Fourier transforms have received considerable attention in the last years. In this paper, based on the symplectic decomposition of quaternions, we prove that the Hermite functions in the spherical basis are the eigenfunctions of the QFTs. The relationship with Radon transform, the real and complex Paley-Wiener theorem, as well as the sampling formula for the 2-sided QFT are established

The present paper is devoted to the study of discrete almost maximal regularity and stability of the difference schemes of nonhomogeneous fractional evolution equations. Using the discretization method of the fractional derivative proposed by Ashyralyev, which actually is the same as the Grünwald-Letnikov approximation for the fractional derivative, the discrete almost maximal regularity and stability

In this paper, the linearized backward Euler scheme for the transient Stokes equations with damping is presented, in which the velocity and pressure are approximated by the lowest-order Bernadi-Raugel rectangular element pair. Unconditional optimal error estimates of the velocity in the norms L∞(L2) and L∞(H1), and the pressure in the norm L∞(L2) are derived through the Stokes operator and the H−1-norm

Competitive neural networks have become increasingly popular since this kind of neural networks can better describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In this paper, we first propose fractional-order competitive neural networks with multiple time-varying-delay links and explore the global asymptotic stability of this class of neural networks. A novel and

This paper is related to the information theoretic learning methodology, whose goal is to quantify global scalar descriptors (e.g., entropy) of a given probability density function (PDF). In this context, the core concept is the information potential (IP) S[s](x):=∫Rps(t,x)dt, s > 0 of a PDF p(t, x) depending on a parameter x; it is naturally related to the Rényi and Tsallis entropies. We present several

A rational approximation (that is, approximation by a ratio of two polynomials) is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non-Lipschitz functions, where polynomial approximations are not efficient. We prove that the optimisation problems appearing in the best uniform rational approximation and its generalisation

This study develops a novel metaheuristic algorithm that is motivated by the behavior of jellyfish in the ocean and is called artificial Jellyfish Search (JS) optimizer. The simulation of the search behavior of jellyfish involves their following the ocean current, their motions inside a jellyfish swarm (active motions and passive motions), a time control mechanism for switching among these movements

This paper investigates the problem of fault estimation and sliding mode fault-tolerant control(FTC) for networked control systems with sensor faults under dynamic event-triggered scheme. First, the sensor faults are equivalent to virtual internal system faults in system by filtering, and dynamic event-triggered fault/state observer is designed to estimate the system state and fault at the same time

In this paper, static and dynamic output feedback controllers are designed for a class of switched nonlinear time-delay systems in the presence of exogenous disturbances and parameter uncertainties to achieve finite-time boundedness (FTB) of the closed-loop system. Moreover, an H∞ index is guaranteed with respect to the exogenous disturbances using auxiliary matrices and the average dwell time method

This work studies the asynchronous fault-tolerant sliding mode control for uncertain stochastic jumping systems subject to singular perturbations, in which the controller is assumed to be able to estimate the hidden system mode through a detector with a conditional probability via the hidden-Markov model. Additionally, in consideration of avoiding the system performance decreases generated by the actuator

In this paper, we present a numerical study of a mixed formulation of the bilateral obstacle problem with a non-homogeneous condition on the boundary. We define the discrete problem starting from the discretization, by the finite element method, of the mixed formulation, then we establish the convergence of the approximate solutions to the exact one. Next, we propose an iterative method based on an

A decomposition approach is used to discuss the stability of large-scale stochastic differential equations driven by G-Brownian motion (G-SDEs, in short). This method establishes the connection between the large-scale G-SDEs and the corresponding reference G-SDEs (which is also called the isolated subsystems). It is shown that large-scale G-SDEs are exponentially stable in mean square if and only if

This paper investigates the H∞ performance state estimation problem for static neural networks with time-varying delays. A parameter-dependent reciprocally convex inequality (PDRCI) is presented, which encompasses some existing results as its special cases. By dividing the estimation error of activation function into two parts, an improved Lyapunov-Krasovskii functional (LKF) is constructed, in which

Medical statistics reveal a significant dependence of hospitalized dengue patients on their age. We extend an ODE system governing dengue epidemics to a hyperbolic PDE system to incorporate age dependence. The equilibrium distributions are determined by the fixed points of the resulting integro-differential equation. The basic reproductive number is then characterized to define parameter regimes, where

Recent developments in shape analysis and retrieval play an important role in a wide variety of applications that potentially require matching of objects with different geometries. In shape classification, there is no natural way to represent an object but the similarity measure, distance between representations or descriptors, depends heavily on the strategy of computing optimal correspondences. In