Delay estimation for cortical-muscular interaction with wavelet coherence time lag

BACKGROUND

Cortico-muscular coherence (CMC) between the cerebral cortex and muscle activity is an effective tool for studying neural communication in the motor control system. To accurately evaluate the coherence between electroencephalogram (EEG) and electromyogram (EMG) signals, it is necessary to accurately calculate the time delay between physiological signals to ensure signal synchronization.

NEW METHOD

We proposed a new delay estimation method, named wavelet coherence time lag (WCTL) and the significant increase areas (SIA) index as a measure of the specific region enhancement effect of the magnitude squared coherence (MSC) image.

RESULTS

The grip strength level had a small effect on the information transmission time from the cortex to the muscles, while the transmission time from the cortex to different muscle channels was different for the same task. A positive correlation was found between the grip strength level and the SIA index on the β band of C3-B and the α and β bands of C3-FDS.

COMPARISON WITH EXISTING METHOD

The WCTL method was found to accurately calculate the delay time even when the number of repeated segments was low in a simple motor control model, and the results were more accurate than the rate of voxels change (RVC) and CMC with time lag (CMCTL) methods.

CONCLUSIONS

The WCTL is an effective method for detecting the transmission time of information between the cortex and muscles, laying the foundation for future rehabilitation treatment for stroke patients.

Calculating and analyzing time delay in zigzag graphene nanoscrolls based complementary metal-oxide-semiconductors

Graphene Nano Scrolls (GNSs) and Zigzag graphene nanoscrolls (ZGNSs) are semi-one-dimensional materials with exceptional electrical and optical properties, making them attractive to be used in nanoelectronics and complementary metal-oxide-semiconductor (CMOS) technology. With in CMOS device technology, time delay is a crucial issue in the design and implementation of CMOS based ZGNSs. Current paper focus is on ZGNSs application in the channel area of metal-oxide-semiconductor field-effect transistors (MOSFETs) in CMOS technology. We studied analytically, the importance of different parameters on time delay reduction, resulting in faster switching and higher frequency in integrated circuits (ICs). The results of this research demonstrates that, the ZGNS-based CMOS proves considerable variations in the current due to the geometrical parameters, such as chirality number, channel length, and nanoscroll length which can be engineered to produce faster ICs.

Impact of coronavirus pandemic on stock index: A polynomial regression with time delay

Motivation

Under contemporary market conditions in China, the stock index has been volatile and highly reflect trends in the coronavirus pandemic, but rare scientific research has been conducted to model the possible nonlinear relations between the two indicators. Added, on the advent that covid-related news in one time period impacts the stock market in another period, time delay can be an equally good predictor of the stock index but rarely investigated.

Objectives

To contribute to filling the gaps identified in existing research, this study models relationship between the stock market index and coronavirus pandemic by leveraging volatility in the stock market and covid data through time delay and best degree in a polynomial environment. The resultant optimal time delay and best degree model is used to derive a high-accuracy prediction of stock market index.

Novelty

In line with the possible relations, the novelty of this study is that it proposes, validates and implements polynomial regression with time delay to model nonlinear relationship between the stock index and covid.

Methods

This study utilizes high-frequency data from January 2020 to the first week of July 2022 to model the nonlinear relationship between the stock index, new covid cases and time delay under polynomial regression environment.

Findings

The empirical results show that time delay and new covid cases, when modelled in a polynomial environment with optimal degree and delay, do present better representation of the nonlinear relationship such predictors have with stock index for China. Relative to results from the polynomial regression without delay, the empirical evidence from the model with delay show that an optimal time delay of 17 weeks makes it possible to predict the stock index at high accuracy and record improvements of 16-fold or higher. The representative delay model is used to project for up to 17 weeks for future trends in the stock index.

Implication

The implication of the findings herein is that the prowess of the time delay polynomial regression is heavily dependent on instability in covid-related time trends and that researchers and decision-makers should consider modeling to cover for the unsteadiness in coronavirus cases to achieve better results.

Fractional-order electromagnetic modeling and identification for PMSM servo system

An accurate electromagnetic model is essential for an optimal controller tuning of the high-performance servo system. This paper proposes a fractional-order electromagnetic model of a permanent magnet synchronous motor (PMSM) servo system and an identification methodology of this model. The reason why the investigated electromagnetic model should be a fractional-order one is addressed with a detailed explanation. The influence of voltage source inverter nonlinearity, which may cause system identification error, is analyzed. An improved inverter nonlinearity model and compensation method are proposed to promote the accuracy of the model parameter identification. Compared with the existing typical electromagnetic models of the PMSM servo system, the current open-loop and closed-loop experiments prove that the proposed fractional-order electromagnetic model with time delay is more accurate for the actual physical system. The effectiveness of the proposed nonlinearity modeling and compensation scheme of the inverter is also verified on an experimental PMSM servo system.

Controllability on impulsive systems with delays in both input and impulse and its applications to multi-agent networks

This paper investigates the controllability of impulsive systems with input delay and impulse delay and its applications in multi-agent networks. We adopt the geometric and algebraic analytical tools to establish some easily verified controllability conditions for the considered system model. First, the analytic solution of the considered system is established on every impulsive interval by using ordinary differential equation theory. Then, according to the solution derived, some sufficient complete controllability criteria are developed to reveal the role of the Gramian matrices in different subintervals. By introducing a row matrix of different kinds of Gramian matrices, a complete controllability condition that is proved to be necessary and sufficient is further obtained. By using the relevant geometric matrix theory, the derived algebraic controllability condition is then converted to a geometric one. On other hand, we introduce a multi-agent network with delayed input and impulse and investigate its controllability. By resorting to graph theory and matrix theory, several factors affecting the controllability of the considered multi-agent networks are investigated, such as the topology structure, the inner coupling matrix, and the dynamics of each agent. Finally, two numerical examples are worked out to verify the derived controllability criteria.

Global dynamics of a time-delayed nonlocal reaction-diffusion model of within-host viral infections

In this paper, we study a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number R 0 and show that the infection-free steady state is globally asymptotically stable whenR 0 ≤ 1 , while the disease is uniformly persistent whenR 0 > 1 . In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of R 0 and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results, conduct sensitivity analysis, and investigate the impact of drugs on curtailing the spread of the viruses.

Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects

Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.

Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control

This paper mainly focuses on solving the global μ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize μ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to μ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov-Razumikhin, recursion, etc, some valid global μ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.

Energetics of sinusoidal exercise below and across critical power and the effects of fatigue

PURPOSE

Previous studies investigating sinusoidal exercise were not devoted to an analysis of its energetics and of the effects of fatigue. We aimed to determine the contribution of aerobic and anaerobic lactic metabolism to the energy balance and investigate the fatigue effects on the cardiorespiratory and metabolic responses to sinusoidal protocols, across and below critical power (CP).

METHODS

Eight males (26.6 ± 6.2 years; 75.6 ± 8.7 kg; maximum oxygen uptake 52.8 ± 7.9 ml·min-1·kg-1; CP 218 ± 13 W) underwent exhausting sinusoidal cycloergometric exercises, with sinusoid midpoint (MP) at CP (CPex) and 50 W below CP (CP-50ex). Sinusoid amplitude (AMP) and period were 50 W and 4 min, respectively. MP, AMP, and time-delay (tD) between mechanical and metabolic signals of expiratory ventilation ([Formula: see text]), oxygen uptake ([Formula: see text]), and heart rate ([Formula: see text]) were assessed sinusoid-by-sinusoid. Blood lactate ([La-]) and rate of perceived exertion (RPE) were determined at each sinusoid.

RESULTS

[Formula: see text] AMP was 304 ± 11 and 488 ± 36 ml·min-1 in CPex and CP-50ex, respectively. Asymmetries between rising and declining sinusoid phases occurred in CPex (36.1 ± 7.7 vs. 41.4 ± 9.7 s for [Formula: see text] tD up and tD down, respectively; P < 0.01), with unchanged tDs. [Formula: see text] MP and RPE increased progressively during CPex. [La-] increased by 2.1 mM in CPex but remained stable during CP-50ex. Anaerobic contribution was larger in CPex than CP-50ex.

CONCLUSION

The lower aerobic component during CPex than CP-50ex associated with lactate accumulation explained lower [Formula: see text] AMP in CPex. The asymmetries in CPex suggest progressive decline of muscle phosphocreatine concentration, leading to fatigue, as witnessed by RPE.

Attack estimation and state reconstruction for cyber-physical systems with state delay via reduced-order observer

This paper investigates the attack estimation and state reconstruction problem for linear cyber-physical systems with state delay and simultaneous sensor and actuator attacks. Reduced-order observer is designed for the augmented system to simultaneously estimate the actuator attack, sensor attack and the state of system. By adopting the double integral term into the Lyapunov-Krasovskii functional and decomposing the cross term, the delay-dependent results are obtained. The method proposed in this paper can accurately estimate the state, actuator and sensor attacks simultaneously without additional design. Compared with the previous method, the time delay information is fully utilized and the conservation is greatly reduced. Finally, the correctness of the results is verified by simulation.

Identification of Boolean control networks with time delay

This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods.

Dynamical analysis of a glucose-insulin regulatory system with insulin-degrading enzyme and multiple delays

This paper investigates the dynamics of a glucose-insulin regulatory system model that incorporates: (1) insulin-degrading enzyme in the insulin equation; and (2) discrete time delays respectively in the insulin production term, hepatic glucose production term, and the insulin-degrading enzyme. We provide rigorous results of our model including the asymptotic stability of the equilibrium solution and the existence of Hopf bifurcation. We show that analytically and numerically at a certain value the time delays driven stability or instability occurs when the corresponding model has an interior equilibrium. Moreover, we illustrate the oscillatory regulation and insulin secretion via numerical simulations, which show that the model dynamics exhibit physiological observations and more information by allowing parameters to vary. Our results may provide useful biological insights into diabetes for the glucose-insulin regulatory system model.

Uniformly convergent extended cubic B-spline collocation method for two parameters singularly perturbed time-delayed convection-diffusion problems

This work proposes a uniformly convergent numerical scheme to solve singularly perturbed parabolic problems of large time delay with two small parameters. The approach uses implicit Euler and the exponentially fitted extended cubic B-spline for time and space derivatives respectively. Extended cubic B-splines have advantages over classical B-splines. This is because for a given value of the free parameter [Formula: see text] the solution obtained by the extended B-spline is better than the solution obtained by the classical B-spline. To confirm the correspondence of the numerical methods with the theoretical results, numerical examples are presented. The present numerical technique converges uniformly, leading to the current study of being more efficient.

Feedback control strategy of networked multi-LSRMs system with semi-Markov topology switching and time delay

This paper studies the networked control system (NCS) with semi-Markov topology switching and network delay. The time delays of the system are considered in the measurement and control channels. The control channel is between the controller and the actuator, the measurement channel is between the sensor and the controller. The topology switching and the transition process among modes are described by semi-Markov sojourn-time probability density function and Markov transition probability matrix respectively. The mean square stability conditions for the networked multi-LSRMs system are obtained by constructing a new Lyapunov function. To ensure the σ-error mean square stability of the closed loop system, a state feedback controller is designed by combining the variation technique of inequalities and Lyapunov stability theory. Finally, several experiments results verify the effectiveness and rationality of the proposed control strategy.

Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The 0&lt;δ≤1 case

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.

The role of delay in vaccination rate on Covid-19

The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.

Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation

The emergence of a novel strain during a pandemic, like the current COVID-19, is a major concern to the healthcare system. The most effective strategy to control this type of pandemic is vaccination. Many previous studies suggest that the existing vaccine may not be fully effective against the new strain. Additionally, the new strain's late arrival has a significant impact on the disease dynamics and vaccine coverage. Focusing on these issues, this study presents a two-strain epidemic model in which the new strain appears with a time delay. We considered two vaccination provisions, namely preinfection and postinfection vaccinations, which are governed by human behavioral dynamics. In such a framework, individuals have the option to commit vaccination before being infected with the first strain. Additionally, people who forgo vaccination and become infected with the first train have the chance to be vaccinated (after recovery) in an attempt to avoid infection from the second strain. However, a second strain can infect vaccinated and unvaccinated individuals. People may have additional opportunities to be vaccinated and to protect themselves from the second strain due to the time delay. Considering the cost of the vaccine, the severity of the new strain, and the vaccine's effectiveness, our results indicated that delaying the second strain decreases the peak size of the infected individuals. Finally, by estimating the social efficiency deficit, we discovered that the social dilemma for receiving immunization decreases with the delay in the arrival of the second strain.

Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein

The COVID-19 pandemic has brought a serious threat to human life safety worldwide. SARS-CoV-2 virus mainly binds to the target cell surface receptor ACE2 (Angiotensin-converting enzyme 2 ) through the S protein expressed on the surface of the virus, resulting in infection of target cells. During this infection process, the target cell ACE2 receptor plays a very important mediating role. In this paper, a delay differential equation model containing the mediated effect of target cell receptor is established according to the mechanism of SARS-CoV-2 virus invasion of target cells, and the global stability of the infection-free equilibrium and the infected equilibrium of the model is obtained by using the basic reproduction number  ℛ 0  and constructing the appropriate Lyapunov functional. The expression of the basic reproduction number  ℛ 0  intuitively gives the dependence on the expression ratio of the target cell surface ACE2 receptor, which is helpful for the understanding of the mechanism of SARS-CoV-2 virus infection.

Structural basis of envelope and phase intrinsic coupling modes in the cerebral cortex

Intrinsic coupling modes (ICMs) can be observed in ongoing brain activity at multiple spatial and temporal scales. Two families of ICMs can be distinguished: phase and envelope ICMs. The principles that shape these ICMs remain partly elusive, in particular their relation to the underlying brain structure. Here we explored structure-function relationships in the ferret brain between ICMs quantified from ongoing brain activity recorded with chronically implanted micro-ECoG arrays and structural connectivity (SC) obtained from high-resolution diffusion MRI tractography. Large-scale computational models were used to explore the ability to predict both types of ICMs. Importantly, all investigations were conducted with ICM measures that are sensitive or insensitive to volume conduction effects. The results show that both types of ICMs are significantly related to SC, except for phase ICMs when using measures removing zero-lag coupling. The correlation between SC and ICMs increases with increasing frequency which is accompanied by reduced delays. Computational models produced results that were highly dependent on the specific parameter settings. The most consistent predictions were derived from measures solely based on SC. Overall, the results demonstrate that patterns of cortical functional coupling as reflected in both phase and envelope ICMs are both related, albeit to different degrees, to the underlying structural connectivity in the cerebral cortex.

Data-driven approach for time-delay estimation of industrial processes

An accurate estimate of time delay is of crucial importance for control tasks such as performance assessment and controller design. In this paper, a novel data-driven approach to time-delay estimation is developed for a process subject to industrial background disturbances, in which the closed-loop output data under the routine operating conditions is only required. The practical solutions are proposed to estimate the time delay based on the estimated impulse response of the closed loop that is estimated online by utilizing the output data. Without relying on system identification and any prior knowledge of the process as well, the time delay is estimated directly for a large time delayed process; while for a small time delayed process, the time delay is estimated by means of the stationarilized filter, the pre-filter and the loop filter. The effectiveness of the proposed approach is validated by various numerical and industrial examples including a distillation column, a petroleum refinery heating furnace and a ceramic dryer.

Passivity and passification of fractional-order memristive neural networks with time delays

A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.

Global stability of latency-age/stage-structured epidemic models with differential infectivity

In this paper, we first formulate a system of ODEs-PDE to model diseases with latency-age and differential infectivity. Then, based on the ways how latent individuals leave the latent stage, one ODE and two DDE models are derived. We only focus on the global stability of the models. All the models have some similarities in the existence of equilibria. Each model has a threshold dynamics for global stability, which is completely characterized by the basic reproduction number. The approach is the Lyapunov direct method. We propose an idea on constructing Lyapunov functionals for the two DDE and the original ODEs-PDE models. During verifying the negative (semi-)definiteness of derivatives of the Lyapunov functionals along solutions, a novel positive definite function and a new inequality are used. The idea here is also helpful in applying the Lyapunov direct method to prove the global stability of some epidemic models with age structure or delays.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Cost-effectiveness of improvement strategies for reperfusion treatments in acute ischemic stroke: a systematic review

BACKGROUND

Reducing delays along the acute stroke pathway significantly improves clinical outcomes for acute ischemic stroke patients eligible for reperfusion treatments. The economic impact of different strategies reducing onset to treatment (OTT) is crucial information for stakeholders in acute stroke management. This systematic review aimed to provide an overview on the cost-effectiveness of several strategies to reduce OTT.

METHODS

A comprehensive literature search was conducted in EMBASE, PubMed, and Web of Science until January 2022. Studies were included if they reported 1/ stroke patients treated with intravenous thrombolysis and/or endovascular thrombectomy, 2/ full economic evaluation, and 3/ strategies to reduce OTT. The Consolidated Health Economic Evaluation Reporting Standards statement was applied to assess the reporting quality.

RESULTS

Twenty studies met the inclusion criteria, of which thirteen were based on cost-utility analysis with the incremental cost-effectiveness ratio per quality-adjusted life year gained as the primary outcome. Studies were performed in twelve countries focusing on four main strategies: educational interventions, organizational models, healthcare delivery infrastructure, and workflow improvements. Sixteen studies showed that the strategies concerning educational interventions, telemedicine between hospitals, mobile stroke units, and workflow improvements, were cost-effective in different settings. The healthcare perspective was predominantly used, and the most common types of models were decision trees, Markov models and simulation models. Overall, fourteen studies were rated as having high reporting quality (79%-94%).

CONCLUSIONS

A wide range of strategies aimed at reducing OTT is cost-effective in acute stroke care treatment. Existing pathways and local characteristics need to be taken along in assessing proposed improvements.

IMC based robust PI/PID controllers for time-delayed inverse response processes

In the last decade, several works have been reported for stable and integrating processes to achieve a specified maximum sensitivity. Also, internal model control (IMC) is a popular controller design strategy as it has only one tuning parameter. IMC based controllers are available in literature for time-delayed inverse response processes but none of the reported works provide guidelines for selecting the tuning parameter. In the present work, IMC-PI/PID controllers for time-delayed inverse response processes are reported. To achieve a specified maximum sensitivity in the range of 1.4 to 2.0, set of tuning rules is proposed for the tuning parameter. Normalized form of the transfer functions are used in the present method which simplifies the design procedure. Novelty of the proposed approach is that the user can not only tune the tuning parameter for desired maximum sensitivity, but can also switch from smooth (M_s = 1.4) to tight (M_s = 2.0) control. Simulation results illustrate the effectiveness of the proposed tuning rules.

Dynamic analysis of rumor propagation model with media report and time delay on social networks

When a rumor appears on social networks, the media of relevant departments need reaction time to make an authoritative announcement. Considering the effects of the media report and time delay on a rumor spreading, and the different attitudes of individuals towards media reports. We proposed a susceptible-expose-infective-media-remover (SEIMR) rumor propagation model with media reports and time delay. Firstly, the basic reproduction number of the model is obtained. Secondly, the positivity, boundedness and existence of the solutions of the model are analyzed. Then, the local asymptotic stability of the rumor free equilibrium and the boundary equilibriums is proved, and the global asymptotic stability of the equilibriums is proved by constructing Lyapunov function when the time delay is zero. Besides, the prevention and control effects of the media report on rumor spreading and the effect of time delay are analyzed. The shorter time delay in media report and the greater the impact of the media report, the more effective the suppression of rumors will be. Finally, the accuracy of the theoretical results as well as the effects of different parameters of the model have been verified through numerical simulations, and the effectiveness of the SEIMR model has been verified via comparative experiments.

Guaranteed cost-based feedback control design for fractional-order neutral systems with input-delayed and nonlinear perturbations

Time delay in actuators is mainly caused by electrical and mechanical components. The effect is visible in the system response particularly when changing in the input command. Therefore, input delay is a problem in the control system design that must be taken into account. Besides, ignoring uncertainty in the dynamic models may compromise the controller design. Thus, how to mitigate the effect of this issue on the system stability and performance is a challenging topic. This article deals with the stabilization of fractional neutral systems considering input-delayed and nonlinear perturbations using the guaranteed cost-based feedback control technique. The main focus is to design the state- and output-feedback controllers to achieve a good performance. The stability criteria are formulated in the Lyapunov sense, which are described in terms of matrix inequalities. The proposed idea is validated using simulations.

A resilient outlier-resistant recursive filtering approach to time-delayed spatial-temporal systems with energy harvesting sensors

This paper is concerned with a resilient outlier-resistant recursive filtering problem for a class of time-delayed spatial-temporal systems (STSs) with energy harvesting sensors. We consider a situation that the sensors are able to harvest energy from external environments and consume certain energy when the measurements are transmitted to filters. When the energy of the sensor is insufficient to maintain the normal communication between the sensors and the filters, the measurement will be regarded as missing. For the sake of obtaining a satisfactory filtering performance, the innovations influenced by the measurement outliers is constrained by introducing a saturation function in the filter. Furthermore, the resilient issue of the designed recursive filter is considered to resist the fluctuations of the filter parameters. Under the effects of sensor energy constraints, measurement outliers as well as parameter fluctuations, a resilient outlier-resistant recursive filter is designed where an upper bound (UB) is first obtained on the filtering error covariance (FEC). Then, by resorting to a matrix recursive equation, such a UB is minimized by the filter gain matrix. Finally, we exhibit a numerical example to verify the effectiveness of the proposed resilient outlier-resistant recursive filter scheme for time-delayed STSs.

Finite-time bipartite synchronization of switched competitive neural networks with time delay via quantized control

This article tackles the finite-time bipartite synchronization (FTBS) of coupled competitive neural networks (CNNs) with switching parameters and time delay. Quantized control is utilized to achieve the FTBS at a small control cost and with limited channel resources. Since the effects of the time delay and switching parameters, traditional finite-time techniques cannot be directly utilized to the FTBS. By constructing a novel multiple Lyapunov functional (MLF), a sufficient criterion formulated by linear programming (LP) is established for the FTBS and the estimation of the settling time. To further improve the accuracy of the settling time, another MLF is designed by dividing the dwell time. With the aid of convex combination, a new LP is provided, which removes the requirement that the increment coefficient of the MLF at switching instants has to be larger than 1. In addition, to obtain the more precise settling time, an optimal algorithm is provided. Two numerical examples are put forward to demonstrate the reasonableness of the theoretical analysis.

There exists the "smartest" movement rate to control the epidemic rather than "city lockdown"

The emergency outbreak and spread of coronavirus disease 2019 (COVID-19) has left great damage to individuals over most of the world. Population mobility is the primary reason for the spread of the epidemic. A delayed stochastic epidemic susceptible-infected-recovered (SIR) model with Gaussian white noise is introduced. Compared with traditional models,this model is characterized by time delay, environmental noise and population mobility among municipalities with the convenient transportation network. The stochastic dynamic behavior of the SIR model is analyzed and the existence of the stochastic bifurcation of the system is proved. The effect of time delay and movement rate are investigated. Numerical simulations are performed to support the theoretical results. It is worth mentioning that the movement rate is not as low as possible and appropriate population mobility is conducive to alleviating the epidemic. Through simulation, we demonstrate the existence of the best movement rate named the "smartest" κ , which is helpful to control the epidemic. This model is also useful to prevent other infectious diseases.

Cell site analysis: Changes to networks with time

Cell service areas may change over time as sites or cells are adjusted, decommissioned or introduced, and there may have been changes between the time of calls and the analysis undertaken. The manner in which survey data is used as part of an analysis is of particular relevance as the data gathered may not reflect the state of the network at the time of calls and thus potentially mislead. Overlaying "historic" data (potentially generated before the calls) with "targeted" surveys (usually generated after the calls) may enable an assessment of possible network changes, or whether additional cells may also have served at a given location at a previous time. This paper outlines a case in which there was a significant time gap between the analysis of call data records and the date on which they were generated.

Simple internal model control based modified Smith predictor for integrating time delayed processes with real-time verification

Internal model control (IMC) tuned simple modified Smith predictor structure for integrating time delayed processes (IPTD) is reported here. Pole position at origin implies its non-self-regulating behaviour. Processes like distillation column, liquid supply to large storage tank, superheated steam flow to turbine etc. are usually found IPTD processes. Reported modified Smith predictor (MSP) design with multiple controllers is adequate to exhibit anticipated closed loop performance for IPTD processes. Tuning complexity of the reported multi-controller based structure is mitigated by the sole tuning parameter (closed loop time constant) obtained from IMC design. Proposed scheme shows considerable performance improvement during set point tracing by zero overshoot. Additionally, smooth as well as reasonably fast load recovery is ensured. Eminence of the reported scheme is established in terms of performance indices along with stability margins in assessment through recently reported modified Smith predictor techniques. Real-time evaluation of the proposed design is demonstrated on an indigenous set up of level control loop considered as IPTD process.

Tuning Generalized Predictive PI controllers for process control applications

Predictive PI (PPI) controllers have demonstrated to exceed traditional PID controllers when they are applied to systems with long delays. This work proposes a new controller structure and tuning that we call Generalized Predictive PI (GPPI) controller which provides greater design flexibility than PI and PPI strategies. To realize a fair comparison, the design and tuning rules for discrete PI and PPI controllers were developed using optimal arguments based on the root-locus, for critically damped response before a step change in the reference. Experimental results, using industrial equipment, have illustrated the tuning methodology and the performance of the proposed controller under real conditions. Flow and water level process in a laboratory flume were considered. For these processes, First Order Plus Time Delay (FOPTD) models are used. The GPPI control results are encouraging, reducing the settling time plus a very small overshoot before step change in the reference regarding the PI and PPI strategies, up to 41.03% for the flow control loop and up to 54.21% for the level control loop. The discrete analysis of the strategies in the Z plane was performed, allowing for a direct translation to recursive equations that can then be programmed into a Programmable Logic Controller (PLC), other industrial controllers such as Distributed Control Systems (DSC), or microcontrollers, such as Arduino, Raspberry or FPGA. This is an important result, since it demonstrates that the increased complexity of the proposed controller does not hamper its implementation in industrial controller systems. In this work, we used a Rockwell ControlLogix ^{\protect \relax \special {t4ht=®}} PLC with Structured Text programming language.

Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can shrink the Turing space, thereby inhibiting patterns from forming across large ranges of parameters. Such delays can also increase the time taken for pattern formation even when Turing instabilities occur. Here, we consider reaction-diffusion models incorporating fixed or distributed time delays, modelling the underlying stochastic nature of gene expression dynamics, and analyse these through a systematic linear instability analysis and numerical simulations for several sets of different reaction kinetics. We find that even complicated distribution kernels (skewed Gaussian probability density functions) have little impact on the reaction-diffusion dynamics compared to fixed delays with the same mean delay. We show that the location of the delay terms in the model can lead to changes in the size of the Turing space (increasing or decreasing) as the mean time delay, [Formula: see text], is increased. We show that the time to pattern formation from a perturbation of the homogeneous steady state scales linearly with [Formula: see text], and conjecture that this is a general impact of time delay on reaction-diffusion dynamics, independent of the form of the kinetics or location of the delayed terms. Finally, we show that while initial and boundary conditions can influence these dynamics, particularly the time-to-pattern, the effects of delay appear robust under variations of initial and boundary data. Overall, our results help clarify the role of gene expression time delays in reaction-diffusion patterning, and suggest clear directions for further work in studying more realistic models of pattern formation.

Parameter identification of Hammerstein-Wiener nonlinear systems with unknown time delay based on the linear variable weight particle swarm optimization

This paper deals with the parameter estimation of Hammerstein-Wiener (H-W) nonlinear systems which have unknown time delay. The linear variable weight particle swarm method is formulated for such time delay systems. This algorithm transforms the nonlinear system identification issue into a function optimization issue in the parameter space, then utilizes the parallel searching ability of the particle swarm optimization and the iterative identification technique to realize the simultaneous estimation of all parameters and the unknown time delay. Finally, parameters in the linear submodule, nonlinear submodule and the time delay are separated from the optimum parameter. Moreover, two illustrative examples are exhibited to evaluate the effectiveness of the proposed method. The simulation results demonstrate that the derived method has fast convergence speed and high estimation accuracy for estimating H-W systems with unknown time delay, and it is applied to the identification of the bed temperature systems.

Associative anticipatory learning and control of the cerebellar cortex based on the spike-timing-dependent plasticity of the parallel fiber-Purkinje cell synapses

Time delays are inevitable in the neural processing of sensorimotor systems; small delays can cause severe damage to movement accuracy and stability. It is strongly suggested that the cerebellum compensates for delays in neural signal processing and performs predictive control. Neural computational theories have explored concepts of the internal models of control objects-believed to avoid delays by providing internal feedback information-although there has been no clear relevance to neural processing. The timing-dependent plasticity of parallel fiber-Purkinje cell synapses is well known. The long-term depression of the synapse is observed when parallel fiber activation precedes climbing fiber activation within -50-300 ms, and is the greatest within 50-200 ms. This paper presents a theory that this temporal difference of 50-200 ms is the basis for an associative anticipation of as many milliseconds. Associative learning can theoretically connect an input signal to a desired signal; therefore, a 50-200 ms earlier input signal can be connected to a desired output signal through temporary asymmetric plasticity. After learning is completed, an input signal generates a desired output signal that appears 50-200 ms later. For the associative learning of temporally continuous signals, this study integrates the universal function approximation capability of the cerebellar cortex model and temporally asymmetric synaptic plasticity to create the theory of associative anticipatory learning of the cerebellum. The effective motor control of this learning is demonstrated by adaptively stabilizing an inverted pendulum with a delay similar to that done by humans.

Exponential synchronization of coupled neural networks under stochastic deception attacks

In this paper, the issue of synchronization is investigated for coupled neural networks subject to stochastic deception attacks. Firstly, a general differential inequality with delayed impulses is given. Then, the established differential inequality is further extended to the case of delayed stochastic impulses, in which both the impulsive instants and impulsive intensity are stochastic. Secondly, by modeling the stochastic discrete-time deception attacks as stochastic impulses, synchronization criteria of the coupled neural networks under the corresponding attacks are given. Finally, two numerical examples are provided to demonstrate the correctness of the theoretical results.

Stochastic COVID-19 SEIQ epidemic model with time-delay

In this work, we consider an epidemic model for corona-virus (COVID-19) with random perturbations as well as time delay, composed of four different classes of susceptible population, the exposed population, the infectious population and the quarantine population. We investigate the proposed problem for the derivation of at least one and unique solution in the positive feasible region of non-local solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function in the sense of delay-stochastic approach and the condition for the extinction of the disease is also established. Our obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been numerically simulated.

Quantization synchronization of chaotic neural networks with time delay under event-triggered strategy

This paper shows solicitude for the quantization synchronization of delayed chaotic master and slave neural networks under an dynamic event-triggered strategy. In virtue of a generalized Halanay-type inequality, a theoretical criterion for quasi-synchronization of master and slave neural networks is derived. Meanwhile, we can obtain an exact upper bound of synchronization error by using this criterion. Compared with output feedback controller with event triggering and quantization, the case where the controller only affected by quantization is also considered. Then, we exclude the Zeno behavior of the event-triggered controller. A sufficient criterion for the existence of the quantized output feedback controllers is also provided. A numerical example is cited to illustrate the efficiency of our theoretical criteria. In addition, some experiments of secure image communication are conducted under quasi-synchronization of master and slave neural networks.

Bilateral motion prediction and control for teleoperation under long time-varying delays

Bilateral controller design for the teleoperation system is studied in this paper based on a motion prediction approach. To compensate the known long time-varying delays, novel predictors are presented to reconstruct the positions and velocities of robots on both sides through using the delayed measurements. The proposed predictors consist of several sub-predictors in a cascade structure, each of which is to predict the states of the previous one. The estimations of the actual states can be obtained from the last sub-predictor. New prediction horizons of each sub-observers are designed to cope with the time-varying fractions of the time delay. Then through applying the predicted results, bilateral predictive controller is designed for the teleoperation. The errors of both position tracking and prediction can converge into the bounded regions under several sufficient conditions of the control gains, which are obtained by using the Lyapunov-Krasovskii approach. The effective capacity of the presented method can be verified through comparative simulations.

Stability behavior of a two-susceptibility SHIR epidemic model with time delay in complex networks

Taking two susceptible groups into account, we formulate a modified subhealthy-healthy-infected-recovered (SHIR) model with time delay and nonlinear incidence rate in networks with different topologies. Concretely, two dynamical systems are designed in homogeneous and heterogeneous networks by utilizing mean field equations. Based on the next-generation matrix and the existence of a positive equilibrium point, we derive the basic reproduction numbers R 0 1 and R 0 2 which depend on the model parameters and network structure. In virtue of linearized systems and Lyapunov functions, the local and global stabilities of the disease-free equilibrium points are, respectively, analyzed when R 0 1 < 1 in homogeneous networks and R 0 2 < 1 in heterogeneous networks. Besides, we demonstrate that the endemic equilibrium point is locally asymptotically stable in homogeneous networks in the condition of R 0 1 > 1 . Finally, numerical simulations are performed to conduct sensitivity analysis and confirm theoretical results. Moreover, some conjectures are proposed to complement dynamical behavior of two systems.

Vaccination control of an epidemic model with time delay and its application to COVID-19

This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number R 0 > 1 . The vaccination strategy is expressed as a state delayed feedback which is related to the current and previous state of the epidemic model, and makes the model become a linear system in new coordinates. For the presence and absence of vaccination control, we investigate the nonnegativity and boundedness of the model, respectively. We obtain some sufficient conditions for the eigenvalues of the linear system such that the nonnegativity of the epidemic model can be guaranteed when the vaccination strategy is applied. In addition, we study the stability of disease-free equilibrium when R 0 < 1 and the persistent of disease when R 0 > 1 . Finally, we use the obtained theoretical results to simulate the vaccination strategy to control the spread of COVID-19.

The effect of pre-analytical handling on the stability of fractalkine, monocyte chemoattractant protein 1 (MCP1), interleukin 6 and interleukin 8 in samples of human cerebrospinal fluid

Cytokine networks in cerebrospinal fluid (CSF) are important to our understanding of several neuroinflammatory diseases. Knowledge about optimal handling of samples is limited but important to minimize bias and reduce costs in CSF biomarker studies. The aim of this study was to examine the effect of storage temperature and time delay from CSF sample collection until freezing on the concentration of 11 different cytokines thought to be associated with chronic pain. CSF samples from 21 individuals undergoing hip or knee arthroplasty under spinal anesthesia were divided between two tubes. One tube was stored and centrifuged (within 30 min) at room temperature, and one tube was stored in ice water and centrifuged (within 30 min) at 4 °C. Each tube was split into six vials that were frozen at -80 °C, 0.5, 1, 2, 3, 4, or 5 h after collection. Cytokines were analyzed using a multiplex panel. A random effect panel data regression was conducted for each biomarker including the variables of storage temperature until freezing and time delay. Four cytokines had detectable levels: Fractalkine, monocyte chemoattractant protein 1(MCP-1), interleukine 6 (IL-6), and interleukine 8 (IL-8). There was no significant effect of storage temperature and time delay on MCP-1, IL-6, or IL-8 concentrations. Fractalkine concentration showed no clear trend. No concentration differences were observed between samples kept in ice water and those at room temperature except at the 3-h time point, and there was no overall significant effect of time delay on fractalkine concentration. We found no clear effect of storage temperature and time delay up to five hours from sample collection until freezing on the CSF concentrations of fractalkine, MCP-1, IL-6, or IL-8.

Mathematical modeling and analysis for controlling the spread of infectious diseases

In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.

Simplified filtered Smith predictor for high-order dead-time processes

This paper proposes a control structure suitable for high-order non-minimum phase (NMP) processes. In general, dead-time compensators (DTCs) firstly predict the process output with zero error at a steady-state and then a primary controller with an integrator is designed based on the delay-free model. The main advantage of the proposed structure is that the primary controller is only a state feedback gain with no integrators. This leads to fewer parameters to tune and lower order filters, while a robustness filter is used to reject disturbances and guarantee zero error at a steady state. Simulation results show better or equivalent performance compared to other recently published works, even kept the controller design simplicity.

Dynamics of a stage-structured SI model for food adulteration with media-induced response function

In this work, an eco-epidemic predator-prey model with media-induced response function for the interaction of humans with adulterated food is developed and studied. The human population is divided into two main compartments, namely, susceptible and infected. This system has three equilibria; trivial, disease-free and endemic. The trivial equilibrium is forever an unstable saddle position, while the disease-free state is locally asymptotically stable under a threshold of delay parameter τ as well as R 0 < 1 . The sufficient conditions for the local stability of the endemic equilibrium point are further explored when min { R 0 , R 0 ∗ } > 1 . The conditions for the occurrence of the stability switching are also determined by taking infection delay time as a critical parameter, which concludes that the delay can produce instability and small amplitude oscillations of population masses via Hopf bifurcations. Further, we study the stability and direction of the Hopf bifurcations using the center manifold argument. Furthermore, some numerical simulations are conducted to validate our analytical findings and discuss their biological inferences. Finally, the normalized forward sensitivity index is used to perform the sensitivity analysis of R 0 and R 0 ∗ .

Regularity of kinematic data between single and dual-task treadmill walking in people with Parkinson's disease

BACKGROUND

Regularity, quantified by sample entropy (SampEn), has been extensively used as a gait stability measure. Yet, there is no consensus on the calculation process and variant approaches, e.g. single-scale SampEn with and without incorporating a time delay greater than one, multiscale SampEn, and complexity index, have been used to calculate the regularity of kinematic or kinetic signals. The aim of the present study was to test the discriminatory performance of the abovementioned approaches during single and dual-task walking in people with Parkinson's disease (PD).

METHODS

Seventeen individuals with PD were included in this study. Participants completed two walking trials that included single and dual-task conditions. The secondary task was word searching with twelve words randomly appearing in the participants' visual field. Trunk linear acceleration at sternum level, linear acceleration of the center of gravity, and angular velocity of feet, shanks, and thighs, each in three planes of motion were collected. The regularity of signals was computed using approaches mentioned above for single and dual-task conditions.

RESULTS

Incorporating a time delay greater than one and considering multiple scales helped better distinguish between single and dual-task walking. For all signals, the complexity index, defined as the summary of multiscale SampEn analysis, was the most efficient discriminatory index between single-task walking and dual-tasking in people with Parkinson's disease. Specifically, the complexity index of the trunk linear acceleration of the center of gravity distinguished between the two walking conditions in all three planes of motion.

CONCLUSIONS

The significant results observed across the 24 signals studied in this study are illustrative examples of the complexity index's potential as a gait feature for classifying different walking conditions.

Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method

As the COVID-19 epidemic has entered the normalization stage, the task of prevention and control remains very arduous. This paper constructs a time delay reaction-diffusion model that is closer to the actual spread of the COVID-19 epidemic, including relapse, time delay, home quarantine and temporal-spatial heterogeneous environment that affect the spread of COVID-19. These factors increase the number of equations and the coupling between equations in the system, making it difficult to apply the methods commonly used to discuss global dynamics, such as the Lyapunov function method. Therefore, we use the global exponential attractor theory in the infinite-dimensional dynamic system to study the spreading trend of the COVID-9 epidemic with relapse, time delay, home quarantine in a temporal-spatial heterogeneous environment. Using our latest results of global exponential attractor theory, the global asymptotic stability and the persistence of the COVID-19 epidemic are discussed. We find that due to the influence of relapse in the in temporal-spatial heterogeneity environment, the principal eigenvalue λ * can describe the spread of the epidemic more accurately than the usual basic reproduction number R 0 . That is, the non-constant disease-free equilibrium is globally asymptotically stable when λ * < 0 and the COVID-19 epidemic is persisting uniformly when λ * > 0 . Combine with the latest official data of the COVID-19 and the prevention and control strategies of different countries, some numerical simulations on the stability and global exponential attractiveness of the spread of the COVID-19 epidemic in China and the USA are given. The simulation results fully reflect the impact of the temporal-spatial heterogeneous environment, relapse, time delay and home quarantine strategies on the spread of the epidemic, revealing the significant differences in epidemic prevention strategies and control effects between the East and the West. The results of this study provide a theoretical basis for the current epidemic prevention and control.

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

In this paper, we analyze the complexity of an eco-epidemiological model for phytoplankton-zooplankton system in presence of toxicity and time delay. Holling type II function response is incorporated to address the predation rate as well as toxic substance distribution in zooplankton. It is also presumed that infected phytoplankton does recover from the viral infection. In the absence of time delay, stability and Hopf-bifurcation conditions are investigated to explore the system dynamics around all the possible equilibrium points. Further, in the presence of time delay, conditions for local stability are derived around the interior equilibria and the properties of the periodic solution are obtained by applying normal form theory and central manifold arguments. Computational simulation is performed to illustrate our theoretical findings. It is explored that system dynamics is very sensitive corresponding to carrying capacity and toxin liberation rate and able to generate chaos. Further, it is observed that time delay in the viral infection process can destabilize the phytoplankton density whereas zooplankton density remains in its old state. Incorporation of time delay also gives the scenario of double Hopf-bifurcation. Some control parameters are discussed to stabilize system dynamics. The effect of time delay on (i) growth rate of susceptible phytoplankton shows the extinction and double Hopf-bifurcation in the zooplankton population, (ii) a sufficiently large value of carrying capacity stabilizes the chaotic dynamics or makes the whole system chaotic with further increment.

Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay

COVID-19 comes out as a sudden pandemic disease within human population. The pandemic dynamics of COVID-19 needs to be studied in detail. A pandemic model with hierarchical quarantine and time delay is proposed in this paper. In the COVID-19 case, the virus incubation period and the antibody failure will cause the time delay and reinfection, respectively, and the hierarchical quarantine strategy includes home isolation and quarantine in hospital. These factors that affect the spread of COVID-19 are well considered and analyzed in the model. The stability of the equilibrium and the nonlinear dynamics is studied as well. The threshold value τ k of the bifurcation is deduced and quantitatively analyzed. Numerical simulations are performed to establish the analytical results with suitable examples. The research reveals that the COVID-19 outbreak may recur over a period of time, which can be helpful to increase the number of tested people with or without symptoms in order to be able to early identify the clusters of infection. And before the effective vaccine is successfully developed, the hierarchical quarantine strategy is currently the best way to prevent the spread of this pandemic.