Explicit Time Delay Research Articles

Optimal dormancy strategies in fluctuating environments given delays in phenotypic switching

Organisms have evolved different mechanisms in response to periods of environmental stress, including dormancy – a reversible state of reduced metabolic activity. Transitions to and from dormancy can be random or induced by changes in environmental conditions. Prior theoretical work has shown that stochastic transitioning between active and dormant states at the individual level can maximize fitness at the population level. However, such theories of ‘bet-hedging’ strategies typically neglect certain physiological features of transitions to dormancy, including time lags to gain protective benefits. Here, we construct and analyze a dynamic model that couples stochastic changes in environmental state with the population dynamics of organisms that can initiate dormancy after an explicit time delay. Stochastic environments are simulated using a multi-state Markov chain through which the mean and variance of environmental residence time can be adjusted. In the absence of time lags (or in the limit of very short lags), we find that bet-hedging strategy transition probabilities scale inversely with the mean environmental residence times, consistent with prior theory. We also find that increasing delays in dormancy decreases optimal transitioning probabilities, an effect that can be influenced by the correlations of environmental noise. When environmental residence times – either good or bad – are uncorrelated, the maximum population level fitness is obtained given low levels of transitioning between active and dormant states. However when environmental residence times are correlated, optimal dormancy initiation and termination probabilities increase insofar as the mean environmental persistent time is longer than the delay to reach dormancy. We also find that bet hedging is no longer advantageous when delays to enter dormancy exceed the mean environmental residence times. Altogether, these results show how physiological limits to dormancy and environmental dynamics shape the evolutionary benefits and even viability of bet hedging strategies at population scales.

Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements.

The mathematical modeling of the human smooth pursuit system from eye-tracking data is considered. Recently developed algorithms for the estimation of Volterra-Laguerre (VL) models with explicit time delay are applied in continuous and discrete time formulations to experimental data collected from Parkinsonian patients in different medication states and healthy controls. The discrete VL model with an explicit time delay and the method for its estimation are first introduced in this paper. The estimated parameters of a second-order VL model are shown to capture the ocular dynamics both in health and disease. The possibility of including the estimated time delay, along with the VL kernel parameters, into the set of the model parameters is explored. The results obtained in continuous VL modeling are compared with those in discrete time to discern the effects due to the sampling enforced by the eye tracker used for data acquisition.

Stability analysis of a logistic growth epidemic model with two explicit time-delays, the nonlinear incidence and treatment rates

Stability analysis of a logistic growth epidemic model with two explicit time-delays, the nonlinear incidence and treatment rates

Neural network aided approximation and parameter inference of non-Markovian models of gene expression

Non-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

Direction-selective motion discrimination by traveling waves in visual cortex.

The majority of neurons in primary visual cortex respond selectively to bars of light that have a specific orientation and move in a specific direction. The spatial and temporal responses of such neurons are non-separable. How neurons accomplish that computational feat without resort to explicit time delays is unknown. We propose a novel neural mechanism whereby visual cortex computes non-separable responses by generating endogenous traveling waves of neural activity that resonate with the space-time signature of the visual stimulus. The spatiotemporal characteristics of the response are defined by the local topology of excitatory and inhibitory lateral connections in the cortex. We simulated the interaction between endogenous traveling waves and the visual stimulus using spatially distributed populations of excitatory and inhibitory neurons with Wilson-Cowan dynamics and inhibitory-surround coupling. Our model reliably detected visual gratings that moved with a given speed and direction provided that we incorporated neural competition to suppress false motion signals in the opposite direction. The findings suggest that endogenous traveling waves in visual cortex can impart direction-selectivity on neural responses without resort to explicit time delays. They also suggest a functional role for motion opponency in eliminating false motion signals.

Maintenance in Mathematics for Individuals with Intellectual Disability: A Systematic Review of Literature

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. The researchers in this study reviewed all studies from 1975 to 2018 that involved teaching mathematics to individuals with intellectual disability. A total of 135 studies met inclusion criteria, but only 53 studies involved a maintenance phase (39.2%). Among the 53 studies, only 22 were included for the final analysis, after evaluating their methodological rigor. In those 22 studies, there was no consensus among researchers on the standards for conducting a maintenance phase (i.e., latency between intervention and maintenance phases, length of maintenance phase, number of maintenance sessions). Further, in the studies which included a maintenance phase, the most widely taught mathematical content was numbers and operations. All studies employed intervention packages which included more than one instructional method and/or materials and the most widely used instructional method was prompting while the most widely used instructional materials were visual supports and manipulatives. The results suggest that prompting is an evidence-based practice for individuals with intellectual disability in supporting maintenance, while explicit instruction, time delay, feedback, and instructional sequence (e.g., the virtual-representational-abstract instructional sequence) are potentially evidence-based practice for individuals with intellectual disability.

Impact of delays on effectiveness of contact tracing strategies for COVID-19: a modelling study

SummaryBackgroundIn countries with declining numbers of confirmed cases of COVID-19, lockdown measures are gradually being lifted. However, even if most physical distancing measures are continued, other public health measures will be needed to control the epidemic. Contact tracing via conventional methods or mobile app technology is central to control strategies during de-escalation of physical distancing. We aimed to identify key factors for a contact tracing strategy to be successful.MethodsWe evaluated the impact of timeliness and completeness in various steps of a contact tracing strategy using a stochastic mathematical model with explicit time delays between time of infection and symptom onset, and between symptom onset, diagnosis by testing, and isolation (testing delay). The model also includes tracing of close contacts (eg, household members) and casual contacts, followed by testing regardless of symptoms and isolation if testing positive, with different tracing delays and coverages. We computed effective reproduction numbers of a contact tracing strategy (RCTS) for a population with physical distancing measures and various scenarios for isolation of index cases and tracing and quarantine of their contacts.FindingsFor the most optimistic scenario (testing and tracing delays of 0 days and tracing coverage of 100%), and assuming that around 40% of transmissions occur before symptom onset, the model predicts that the estimated effective reproduction number of 1·2 (with physical distancing only) will be reduced to 0·8 (95% CI 0·7–0·9) by adding contact tracing. The model also shows that a similar reduction can be achieved when testing and tracing coverage is reduced to 80% (RCTS 0·8, 95% CI 0·7–1·0). A testing delay of more than 1 day requires the tracing delay to be at most 1 day or tracing coverage to be at least 80% to keep RCTS below 1. With a testing delay of 3 days or longer, even the most efficient strategy cannot reach RCTS values below 1. The effect of minimising tracing delay (eg, with app-based technology) declines with decreasing coverage of app use, but app-based tracing alone remains more effective than conventional tracing alone even with 20% coverage, reducing the reproduction number by 17·6% compared with 2·5%. The proportion of onward transmissions per index case that can be prevented depends on testing and tracing delays, and given a 0-day tracing delay, ranges from up to 79·9% with a 0-day testing delay to 41·8% with a 3-day testing delay and 4·9% with a 7-day testing delay.InterpretationIn our model, minimising testing delay had the largest impact on reducing onward transmissions. Optimising testing and tracing coverage and minimising tracing delays, for instance with app-based technology, further enhanced contact tracing effectiveness, with the potential to prevent up to 80% of all transmissions. Access to testing should therefore be optimised, and mobile app technology might reduce delays in the contact tracing process and optimise contact tracing coverage.FundingZonMw, Fundação para a Ciência e a Tecnologia, and EU Horizon 2020 RECOVER.

A New Model For Endocrine Glucose-Insulin Regulatory System

To gain insight into complex biological endocrine glucose-insulin regulatory system where the interactions of components of the metabolic system and time-delay inherent in the biological system give rise to complex dynamics. The modeling has increased interest and importance in physiological research and enhanced the medical treatment protocols. This brief contains a new model using time delay differential equations, which give an accurate result by utilizing two explicit time delays. The bifurcation analysis has been conducted to find the main system parameters bifurcation values and corresponding system behaviors. The results found consistent with the biological experiments results.

FPGA implementation of adaptive time delay estimation for real‐time near‐field electromagnetic ranging

SummaryThe near‐field electromagnetic ranging systems exploit the near‐field phase behavior of low frequency signals for indoor real‐time ranging. Conventionally, phase detector is used to determine the phase of electric and magnetic fields. Subsequently, the phase difference is used to estimate a distance value. In adaptive time delay estimation approach, the time delay between electric and magnetic signals is used instead of phase difference for an estimation. This method does not require a priori knowledge of the transmitting signals and can obtain better performance in low signal‐to‐noise ratio environment. In this paper, we propose a digital near‐field electromagnetic ranging system design and implement it on field‐programmable gate array. This system is composed of time delay estimator, frequency estimator, and received signal strength indicator. A maximum correntropy criterion–based explicit time delay estimation algorithm with a delay in the coefficient update is implemented to estimate the time delay in real time. The fast Fourier transform and received signal strength indicator modules determine the signal frequency and the signal strength received, respectively. Our experimental results indicate that the delayed maximum correntropy criterion–based explicit time delay estimation algorithm has fast convergence rate and good steady‐state performance in an impulsive noise environment.

Adaptive Noise Cancellation Based on Time Delay Estimation for Low Frequency Communication

Low frequency communication, taking advantage of the features of low frequency electromagnetic signals in near field, is widely used in through-the-earth (TTE) wireless applications. However, the low frequency non-Gaussian noise severely limits the communication performance. In this paper, an adaptive noise cancellation algorithm based on time delay estimation (ANC-TDE) and maximum correntropy criterion (MCC) is proposed. The explicit time delay estimation algorithm based on MCC (MCC-ETDE) is used to estimate the time-varying delay and the noise correlationship between the primary input and reference inputs. With a reference noise selected and time delay compensated, the non-Gaussian noise is canceled by adaptive filter based on MCC. The proposed algorithm is implemented on field programmable gate array (FPGA) and the performance is evaluated by simulation and experiment. As shown in the results, the ANC-TDE algorithm can reduce the complexity of ANC filter and adaptively compensate the varied time delay between the primary input and reference input. With the time delay compensated, the ANC-TDE algorithm has better performance in non-Gaussian noise environment and is more suitable for real-time systems.

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks.

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations without an explicit time delay. We show that this discrepancy is due to a voltage-dependent spike-synchronization mechanism inherent in networks of spiking neurons which is not captured by standard firing rate equations. Here we investigate an exact low-dimensional description for a network of heterogeneous canonical Class 1 inhibitory neurons which includes the sub-threshold dynamics crucial for generating synchronous states. In the limit of slow synaptic kinetics the spike-synchrony mechanism is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inputs are also slow. However, even in this limit synchronous spiking can be elicited by inputs which fluctuate on a time-scale of the membrane time-constant of the neurons. Our meanfield equations therefore represent an extension of the standard Wilson-Cowan equations in which spike synchrony is also correctly described.

Oscillatory dynamics of p38 activity with transcriptional and translational time delays

Recent experimental evidence reports that oscillations of p38 MAPK (p38) activity would efficiently induce pro-inflammatory gene expression, which might be deleterious to immune systems and may even cause cellular damage and apoptosis. It is widely accepted now that transcriptional and translational delays are ubiquitous in gene expression, which can typically result in oscillatory responses of gene regulations. Consequently, delay-driven sustained oscillations in p38 activity (p38*) could in principle be commonplace. Nevertheless, so far the studies of the impact of such delays on p38* have been lacking both experimentally and theoretically. Here, we use experimental data to develop a delayed mathematical model, with the aim of understanding how such delays affect oscillatory behaviour on p38*. We analyze the stability and oscillation of the model with and without explicit time delays. We show that a sufficiently input stimulation strength is prerequisite for generating p38* oscillations, and that an optimal rate of model parameters is also essential to these oscillations. Moreover, we find that the time delays required for transcription and translation in mitogen-activated protein kinase phosphatase-1 (MKP-1) gene expression can drive p38* to be oscillatory even when the concentration of p38* level is at a stable state. Furthermore, the length of these delays can determine the amplitude and period of the oscillations and can enormously extend the oscillatory ranges of model parameters. These results indicate that time delays in MKP-1 synthesis are required, albeit not sufficient, for p38* oscillations, which may lead to new insights related to p38 oscillations.

An Iteration-Based Variable Step-Size Algorithm for Joint Explicit Adaptation of Time Delay

By using an adaptive technique similar to the joint explicit time delay estimator, a novel variable step-size algorithm is derived. This algorithm employs the iteration time to control the step-size update and its respective performance analysis is also given. It is also proved that the proposed algorithm efficiently improves the convergence speed and the delay variance with only increasing a little computational cost compared to the conventional adaptive time delay estimation algorithm.

A New Adaptive Subsample ETDE for Large‐Range Time‐Varying Delay Estimation Using Low‐Order Interpolators

We present a new adaptive subsample Explicit time delay estimator (ETDE) that is well suitable for determining and tracking the large-range time-varying delay between two noisy bandlimited signals only using low-order interpolators. Unlike conventional ETDE where a Fractional delay filter (FDF) is used, the new ETDE is based on a novel on-line interpolator which has the ability to optimally synthesize any continuously variable nonintegral sample delay. The theoretical derivations for our proposed on-line interpolator and the new ETDE algorithm are provided. Simulations are presented to evaluate the performance of the new estimator and to compare the performance with other estimators. Simulation results show that the new ETDE significantly outperforms FDF-based ETDE when the delay is large or varies in a large range, and the same filter orders are used.

An Adaptive Time Delay Estimator Based on ETDE Algorithm with Noisy Measurements

We address the problem of adaptive time delay estimation with noisy measurements. We develop a computationally efficient adaptive time delay estimator based on Explicit time delay estimation (ETDE) algorithm, by applying the unbiased impulse response estimation approach. In this algorithm, a weighted error function is derived, and the time delay is explicitly parameterized in the filter coefficients and iteratively updated directly by utilizing the modified error function. Simulations validate the performance of the proposed algorithm for colored input and low signal-to-noise ratio scenarios.

Explicit expression-based practical model predictive control implementation for large-scale structures with multi-input delays

In this paper, two practical model predictive control (MPC) implementation algorithms with multi-input delay (NFMPCMID1 and NFMPCMID2) are developed in discrete-time formulation for vibration control of large-scale structures. By introducing a particular augmented state vector, the controlled dynamic equation with multi-input delay is transformed into the standard form without any explicit time delay. Because of no approximation for multi-input delay involved, the system performance and stability are easily guaranteed. In order to solve the computation efficiency and memory requirement for large-scale structure, a novel explicit expression form of Newmark-β method is derived, from which the future states can be easily predicted without computing matrix exponential and its integration. By applying this explicit expression form into MPC, the control input of NFMPCMID1 method can be computed by some matrix–matrix multiplications, and also the control input of NFMPCMID2 method can be computed just by two off-line transient analyses and one on-line transient analysis at every sampling instant on the structure. For no computation of matrix exponential and its integration in NFMPCMID1 and NFMPCMID2 methods, the off-line computation efficiency is greatly improved, and the memory requirement is greatly reduced, especially for the NFMPCMID2 method. In additional, due to the small amount of on-line computation, the on-line computation efficiency is also guaranteed. At last, the stability, feasibility and efficiency of the proposed methods are verified by several typical numerical examples.

An enhanced mixed modulated Lagrange explicit time delay estimator with noisy input

The mixed modulated Lagrange explicit time delay estimation (MMLETDE) algorithm provides an efficient time delay estimation between narrowband or sinusoidal signals. However, it does not explicitly consider the additive measurement noise at the input, which actually exists in practice. Aiming at this issue, an enhanced MMLETDE algorithm is proposed for noisy inputs based on the unbiased impulse response estimation technique, assuming that the noise power ratio is known a priori. Simulation results show that for narrowband signals or sinusoids over a wide frequency range, the proposed algorithm with a small filter order performs well in moderate and high noise scenarios.

Stability analysis in a car-following model with reaction-time delay and delayed feedback control

The delayed feedback control in terms of both headway and velocity differences has been proposed to guarantee the stability of a car-following model including the reaction-time delay of drivers. Using Laplace transformation and transfer function, the stable condition is derived and appropriate choices of time delay and feedback gains are designed to stabilize traffic flow. Meanwhile, an upper bound on explicit time delay is determined with respect to the response of desired acceleration. To ensure the string stability, the explicit time delay cannot over its upper bound. Numerical simulations indicate that the proposed control method can restraint traffic congestion and improve control performance.

Active Control Experiment Study of a Flexible Beam with Multiple Time Delays

In this paper, active control for vibration of a flexible beam with multiple time delays is studied numerically and experimentally. Piezoelectric (PZT) patches are used as actuators, and foil gauges were used as sensors. Firstly the motion equation of a flexible beam with multiple time delays and Piezoelectric patches is presented and written into a state space form. Then the state equation is discretized and transformed into a standard form without any explicit time delay by a particular augmentation for state variables. So time-delay controller could be designed based on the standard state equation using the discrete active control method. Finally, numerical and experimental studies are presented to verify the validity of the time-delay processing method using the discrete optimal control method and the discrete variable structure control method, respectively. An experimental setup is constructed using DSP TMS320F2812. The numerical and experimental results show that the proposed time-delay controller is effective in suppressing the beam vibration. It is also applicable to both shortand longtime delays.

Fractional time delay estimation algorithm based on the maximum correntropy criterion and the Lagrange FDF

In this paper, a novel algorithm for fractional time delay estimation is proposed. It is based on the maximum correntropy criterion and the Lagrange fractional delay filter (FDF). The instantaneous correntropy is introduced to measure the similarity between received signals and estimated ones in the proposed algorithm. It leads to an effective performance under both Gaussian and impulsive noises. The performances, including the convergence of the algorithm and the variance of the time delay estimation, are theoretically analyzed. Simulations demonstrate that the time delay estimation precision of the proposed algorithm is higher than that utilizing the mixed modulated Lagrange explicit time delay estimation (MMLETDE) especially under low generalized signal-to-noise ratio (GSNR).