Boundedness in the higher-dimensional quasilinear chemotaxis-growth system with indirect attractant production

This paper deals with the following quasilinear chemotaxis-growth system

in a smoothly bounded domain $\Omega ?{\mathbb{R}}^n(n\ge 3)$ under zero-flux boundary conditions. The parameters $\mu ,\delta$ and $\tau$ are positive and the diffusion function $D\left(u\right)$ is supposed to generalize the prototype $D\left(u\right)\ge D_0{u}^{\theta }$ with $D_0>0$ and $\theta \in \mathbb{R}$. Under the assumption $\theta >1?\frac{4}{n}$, it is proved that whenever $\mu >0$, $\tau >0$ and $\delta >0$, for any given nonnegative and suitably smooth initial data ($u_0$, $v_0$, $w_0$) satisfying $u_0?0$, the corresponding initial–boundary problem possesses a unique global solution which is uniformly-in-time bounded. The novelty of the paper is that we use the boundedness of the $\left|\right|v(?,t)|{|}_{W^{1,s}\left(\Omega \right)}$ with $s\in [1,\frac{2n}{n?2})$ to estimate the boundedness of $\left|\right|?v(?,t)|{|}_{L^{2q}\left(\Omega \right)}(q>1)$. Moreover, the result in this paper can be regarded as an extension of a previous consequence on global existence of solutions by Hu et al. (2016) under the condition that $D\left(u\right)\equiv 1$ and $n=3$.     

Global asymptotic stability of steady states in a chemotaxis-growth system with singular sensitivity

This paper deals with a fully parabolic chemotaxis-growth system with singular sensitivity

under homogeneous Neumann boundary conditions in a smooth bounded domain $\Omega ?{\mathbb{R}}^2$, where the parameters $\chi ,\mu >0$ and $r\in \mathbb{R}$. Global existence and boundedness of solutions to the above system were established under some suitable conditions by Zhao and Zheng (2017). The main aim of this paper is further to show the large time behavior of global solutions which cannot be derived in the previous work.     

Dynamics and simulations of a logistic model with impulsive perturbations in a random environment

A stochastic logistic model with Markovian switching and impulsive perturbations is proposed and investigated. Firstly, we show that this model has a global and positive solution. Then we establish the sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence of the solution. The critical value between weak persistence and extinction is obtained. Afterwards we study some asymptotic properties of this model. The lower- and the upper-growth rates of the positive solution are investigated. The superior limit of the average in time of the sample path of the solution is also estimated. Finally, some simulation figures are introduced to illustrate the main results.     

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also eiven.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.     

Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors

When continuous predictors are present, classical Pearson and deviance goodness-of-fit tests to assess logistic model fit break down. The Hosmer-Lemeshow test can be used in these situations. While simple to perform and widely used, it does not have desirable power in many cases and provides no further information on the source of any detectable lack of fit. Tsiatis proposed a score statistic to test for covariate regional effects. While conceptually elegant, its lack of a general rule for how to partition the covariate space has, to a certain degree, limited its popularity. We propose a new method for goodness-of-fit testing that uses a very general partitioning strategy (clustering) in the covariate space and either a Pearson statistic or a score statistic. Properties of the proposed statistics are discussed, and a simulation study demonstrates increased power to detect model misspecification in a variety of settings. An application of these different methods on data from a clinical trial illustrates their use. Discussions on further improvement of the proposed tests and extending this new method to other data situations, such as ordinal response regression models are also included.     

Stability of an equilibrium state in a multiinfectious-type SIS model on a truncated network

In a homogeneous constant population, the basic SIS model potentially has an epidemic equilibrium state with global asymptotic stability since it can be reduced to the logistic equation. On the basic SIS model with a nonhomogeneous constant population, viewed as a multitype SIS model, the global or local asymptotic stability of an epidemic equilibrium state has also been studied.^1–4 However, this kind of analysis in other models with nonhomogeneous populations has rarely been developed, even though the corresponding models with homogeneous populations are well known. In addition, recent studies of complex networks have revealed that heterogeneity of the link number of vertices drastically changes the epidemic thresholds.^5–9 For these reasons, figuring out the roles of heterogeneity is a major topic in epidemic modeling. Here, we consider a multiinfectious-type SIS model on a network, and show the (local or global) asymptotic stability of an epidemic equilibrium state whenever it exists. This work was presented in part at the 11th International Symposium of Artificial Life and Robotics, Oita, Japan, January 23–25, 2006     

Introducing a new open source GIS user interface for the SWAT model

The Soil and Water Assessment Tool (SWAT) model is a robust watershed modeling tool. It typically uses the ArcSWAT interface to create its inputs. ArcSWAT is public domain software which works in the licensed ArcGIS environment. The aim of this paper was to develop an open source user interface for the SWAT model. The interface, QSWAT, is written in the Python programming language and uses various functionalities of the open source geographic information system, QGIS. The current interface performs similar functions to ArcSWAT, but with additional enhanced features such as merging small subbasins and static and dynamic visualization of outputs. The interface is demonstrated through a case study in the Gumera watershed in the Lake Tana basin of Ethiopia, where it showed a successful performance. QSWAT will be a valuable tool for the SWAT scientific community, with improved availability and functionality compared with other options for creating SWAT models.     

Asymptotic stabilization of the position of a rigid body with fixed point without velocity measurements

The problem of stabilization of a rigid body with a fixed point in reference to its velocity and position is considered. It is assumed that the rigid body is controlled by three external torques. The proposed controlling torques need neither the measurements of the velocity nor the information about the inertial parameters. Such a control may be realized by the on-line solution of the auxiliary differential equations.The stability of the closed loop nonlinear system is established by means of the Lyapunov function and Barbashin's theorem. The proposed control may be applied to stabilize the satellites controlled by the reactive jets.     

A new parameter estimate in singular perturbations

A new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system. General time-invariant systems with a single small parameter are considered. The paper employs a Riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics. An application of the Brouwer fixed point theorem to the Riccati equation and of Liapunov's direct method to the fast and slow subsystems results in the desired upper bound. Computation of the estimate requires only the solution of two Liapunov matrix equations.     

A closed-loop logistic model with a spanning-tree based genetic algorithm

Due to the problem of global warming, the green supply chain management, in particular, closed-loop logistics, has drawn the attention of researchers. Although there were logistics models that were examined in the literatures, most of them were case based and not in a closed-loop. Therefore, they lacked generality and could not serve the purposes of recycling, reuse and recovery required in a green supply chain. In this study, the integration of forward and reverse logistics was investigated, and a generalized closed-loop model for the logistics planning was proposed by formulating a cyclic logistics network problem into an integer linear programming model. Moreover, the decisions for selecting the places of manufactories, distribution centers, and dismantlers with the respective operation units were supported with the minimum cost. A revised spanning-tree based genetic algorithm was also developed by using determinant encoding representation for solving this NP model. Numerical experiments were presented, and the results showed that the proposed model and algorithms were able to support the logistic decisions in a closed-loop supply chain efficiently and accurately.

Statement of scope and purposes

This study concerns with operations of 3R in the green supply chain logistics and the location selection optimization. Based on ‘cradle to cradle’ principle of a green product, a “closed-loop” structure of a network was proposed in order to integrate the environmental issues into a traditional logistic system. Due to NP-hard nature of the model, a Genetic Algorithm, which is based on spanning tree structure was developed. Test problems from the small size for accuracy to the large scale for efficiency have been demonstrated with comparison. The promising results have shown the applicability of the proposed model with the solution procedure.     

A robust control approach to stabilization of networked control systems with time-varying delays

The stabilization problem is studied for networked control systems (NCSs) with time-varying delay that may be larger than one sampling period. By considering state feedback controllers, the closed-loop NCS is described as a switched delay system, which is then represented as an interconnected feedback system. A sufficient BIBO stability condition is derived for the closed-loop NCS by using the small gain theorem and the average dwell time technique. Design procedures for the BIBO stabilizing controllers are also presented. An example is given to demonstrate the effectiveness of the proposed method.     

Stability analysis for a fractional differential model of HIV infection of CD4 T-cells with time delay

In this paper, we introduce fractional-order derivatives into a model of HIV infection of CD4⁺ T-cells with time delay. We deal with the stability of both the viral free equilibrium and the infected equilibrium. Criteria are given to ensure that both the equilibria are asymptotically stable for all delay under some conditions. Numerical simulations are carried out to illustrate the results.     

A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.     

Permanence and global stability for a two-species cooperative system with time delays in a two-patch environment

A two-species nonautonomous delayed system is considered. The system models two-population dispersal between two patches in a heterogeneous environment. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are established for global stability of the system.     

Global stabilization of a chain of integrators with input saturation and disturbances: A new approach

In this article, we solve the problem of global stabilization for a chain of integrators in the presence of input saturation and disturbances. A novel and elegant approach to solve this problem, in the absence of disturbances, was proposed by Teel (1992) using saturation functions and coordinate transformation. With Teel’s work as a foundation, many results have been proposed to improve the performance of controllers for a chain of integrators. Naturally, all such approaches also inherited the limitations of Teel’s approach. Most importantly, in the presence of uncertainties and disturbances, the transformation introduced in Teel (1992) would considerably shrink the region where the controller is unsaturated and, severely limit the level of uncertainties and disturbances which can be tolerated. In order to overcome these difficulties, a conceptually different approach which does not rely on the coordinate transformation is presented in this work. Specifically, modified saturation functions are directly applied to the tracking error of actual states as opposed to transformed fictitious states to develop a globally stable controller. The proposed controller is less conservative in terms of the level of uncertainties and disturbances which can be handled. In addition, arbitrarily good disturbance rejection in the unsaturated region can be achieved theoretically. Comparative simulation studies performed on a third order integrator chain verified the effectiveness of the proposed scheme.     

A strategic analysis for successful open source software utilization based on a structural equation model

Commercial software companies face many challenges when competing in today’s fast moving and competitive industry environment. Recently, the use of open source software (OSS) has been proposed as a possible way to address those challenges. OSS provides many benefits, including high-quality software and substantial profits. Nevertheless, OSS has not been effectively utilized in real business. The purpose of this paper is to find what affects the utilization of OSS. For this study, we propose a structural equation model (SEM) to analyze the relationships between the quality factors based on ISO/IEC 9126 and OSS utilization. In addition, we suggest an open source software utilization index (OSSUI) based on the proposed SEM. The results provide us with the controllable feedback information to improve user (programmer) satisfaction during OSS utilization.     

A new algorithm to maintain lateral stabilization during the running gait of a quadruped robot

This paper presents a new uncoupled controller (based on a Kinetic Momentum Management Algorithm, KMMA) which allows a quadrupedal robot, whose operation is simple and fast, to run using a symmetrical gait patterns in a wide variety of scenarios. It consists of two tasks: calculating the lateral position and speed of the fore swinging leg when it next makes contact with the ground; and controlling the roll angle by mean of inertia forces using the stance legs.The KMMA provides the benefits of modulation and the synchronization typically presented in CPG (Central Pattern Generation) models. Furthermore, it is able to maintain the locomotion parameters (such as stroke frequency of gait pattern) when the robot runs in a highly disturbed environment, thus resulting in a lower energy consumption. Additionally, the uncoupled scheme of the leg makes the operation computationally cheap, thus avoiding the use of a Virtual Actuator Control or a Hybrid Zero Dynamics.The performance of the KMMA has been verified by means of co-simulation (using ADAMS and MATLAB) with a highly realistic model of a quadruped robot with uncoupled legs. The performance of the algorithm has been tested in different situations in which the following variables have been varied: frontal velocity, turning ratio, payload, external disturbances and terrain slope. Successful results in terms of stability, energy efficiency, and adaptability to a complex locomotion environment have been obtained.     

A new small‐gain theorem with an application to the stabilization of the chemostat

New small‐gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small‐gain results usually utilize to prove stability properties. The results allow the application of the small‐gain perspective to various systems that satisfy less‐demanding stability notions than the input‐to‐output stability property. The robust global feedback stabilization problem of an uncertain time‐delayed chemostat model is solved by means of the new small‐gain results. Copyright © 2011 John Wiley & Sons, Ltd.     

A hybrid data fusion approach with twin CNN architecture for enhancing image source identification in IoT environment

With the proliferation of digital devices in internet of things (IoT) environment featuring advanced visual capabilities, the task of Image Source Identification (ISI) has become increasingly vital for legal purposes, ensuring the verification of image authenticity and integrity, as well as identifying the device responsible for capturing the original scene. Over the past few decades, researchers have employed both traditional and machine-learning methods to classify image sources. In the current landscape, data-driven approaches leveraging deep learning models have emerged as powerful tools for achieving higher accuracy and precision in source prediction. The primary focus of this research is to address the complexities arising from diverse image sources and variable quality in IoT-generated multimedia data. To achieve this, a Hybrid Data Fusion Approach is introduced, leveraging multiple sources of information to bolster the accuracy and robustness of ISI. This fusion methodology integrates diverse data streams from IoT devices, including metadata, sensor information, and contextual data, amalgamating them into a comprehensive data set for analysis. This study introduces an innovative approach to ISI through the implementation of a Twin Convolutional Neural Network Architecture (TCA) aimed at enhancing the efficacy of source classification. In TCA, the first CNN architecture, referred to as DnCNN, is employed to eliminate noise from the original data set, generating 256 × 256 patches for both training and testing. Subsequently, the second CNN architecture is employed to classify images based on features extracted from various convolutional layers using a 3 × 3 filter, thereby enhancing prediction efficiency. The proposed model demonstrates exceptional accuracy in effectively classifying image sources, showcasing its potential as a robust solution in the realm of ISI.