An efficient numerical approach for singularly perturbed time delayed parabolic problems with two-parameters

OBJECTIVES

The main objective of this work is to design an efficient numerical scheme is proposed for solving singularly perturbed time delayed parabolic problems with two parameters.

RESULTS

The scheme is constructed via the implicit Euler and non-standard finite difference method to approximate the time and space derivatives, respectively. Besides, to enhance the accuracy and order of convergence of the method Richardson extrapolation technique is employed. Intensive numerical experimentation has been done on some model examples. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence( Δ t ) 2 + h 2 .

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.

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 (V ˙ E ), oxygen uptake (V ˙ O 2 ), and heart rate ( f H ) were assessed sinusoid-by-sinusoid. Blood lactate ([La-]) and rate of perceived exertion (RPE) were determined at each sinusoid.

RESULTS

V ˙ O 2 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 forV ˙ O 2 tD up and tD down, respectively; P < 0.01), with unchanged tDs.V ˙ O 2 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 lowerV ˙ O 2 AMP in CPex. The asymmetries in CPex suggest progressive decline of muscle phosphocreatine concentration, leading to fatigue, as witnessed by RPE.

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.

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.

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.