Time-delayed Version Research Articles

Filter bank temporally delayed CCA for uncalibrated SSVEP-BCI.

The uncalibrated brain-computer interface (BCI) system based on steady-state visual evoked potential (SSVEP) can omit the training process and is closer to the practical application. Filter bank canonical correlation analysis (FBCCA), as a classical approach of uncalibrated SSVEP-based BCI, extracts the fundamental and harmonic ingredients through filter bank decomposition. Nevertheless, this method fails to fully leverage the temporal feature of the signal. The paper suggested utilizing reconstructed data with temporal delay in the computation of the canonical correlation coefficient, and the different combinations of the time-delayed embedding and FBCCA were discussed. We selected the data from seven participants in the Benchmark dataset for parameter optimization and evaluated the method across all participants. The experimental results showed that only embedding the time-delayed version into the first subband (FBdCCA) was better than embedding it into all subbands (FBdCCA(all)), and the accuracy of FBdCCA surpassed that of FBCCA significantly. This suggests that the approach of time-delayed embedding can further enhance the performance of FBCCA.

Time-delayed single satellite quantum repeater node for global quantum communications

Global-scale quantum networking faces significant technical and scientific obstacles. Quantum repeaters (QRs) have been proposed to overcome the inherent direct transmission range limit through optical fiber. However, QRs are typically limited to a total distance of a few thousand kilometers and/or require extensive hardware overhead. Recent proposals suggest that strings of space-borne QRs with on-board quantum memories (QMs) are able to provide global coverage. Here, we propose an alternative to such repeater constellations using a single satellite with two QMs that effectively acts as a time-delayed version of a single QR node. By physically transporting stored qubits, our protocol improves long-distance entanglement distribution with reduced system complexity over previous proposals. We estimate the amount of secure key in the finite block regime and demonstrate an improvement of at least three orders of magnitude over prior single-satellite methods that rely on a single QM, while simultaneously reducing the necessary memory capacity similarly. We propose an experimental platform to realize this scheme based on rare-earth ion doped crystals with appropriate performance parameters. By exploiting recent advances in quantum memory lifetimes, we are able to significantly reduce system complexity while achieving high key rates, bringing global quantum networking closer to implementation.

A Deep Time Delay Filter for Cooperative Adaptive Cruise Control

Cooperative adaptive cruise control (CACC) is a smart transportation solution to alleviate traffic congestion and enhance road safety. The performance of CACC systems can be remarkably affected by communication time delays, and traditional control methods often compromise control performance by adjusting control gains to maintain system stability. In this paper, we present a study on the stability of a CACC system in the presence of time delays and highlight the trade-off between control performance and tuning controller gains to address increasing delays. We propose a novel approach incorporating a neural network module called the deep time delay filter (DTDF) to overcome this limitation. The DTDF leverages the assumption that time delays primarily originate from the communication layer of the CACC network, which can be subject to adversarial delays of varying magnitudes. By considering time-delayed versions of the car states and predicting the present (un-delayed) states, the DTDF compensates for the effects of communication delays. The proposed approach combines classical control techniques with machine learning, offering a hybrid control system that excels in explainability and robustness to unknown parameters. We conduct comprehensive experiments using various deep-learning architectures to train and evaluate the DTDF models. Our experiments utilize a robot platform consisting of MATLAB, Simulink, the Optitrack motion capture system, and the Qbot2e robots. Through these experiments, we demonstrate that when appropriately trained, our system can effectively mitigate the adverse effects of constant time delays and outperforms a traditional CACC baseline in control performance. This experimental comparison, to the best of the author’s knowledge, is the first of its kind in the context of a hybrid machine learning CACC system. We thoroughly explore initial conditions and range policy parameters to evaluate our system under various experimental scenarios. By providing detailed insights and experimental results, we aim to contribute to the advancement of CACC research and highlight the potential of hybrid machine learning approaches in improving the performance and reliability of CACC systems.

On the Krýlov–Bogoliúbov-Mitropólsky and Multiple Scales Methods for Analyzing a Time Delay Duffing–Helmholtz Oscillator

This study is divided into two important axes; for the first one, a new symmetric analytical (approximate) solution to the Duffing–Helmholtz oscillatory equation in terms of elementary functions is derived. The obtained solution is compared with the numerical solution using 4th Range–Kutta (RK4) approach and with the exact analytical solution that is obtained using elliptic functions. As for the second axis, we consider the time-delayed version for the same oscillator taking the impact of both forcing and damping terms into consideration. Some analytical approximations for the time delayed Duffing–Helmholtz oscillator are derived using two different perturbation techniques, known as Krylov–Bogoliubov–Mitropolsky method (KBMM) and the multiple scales method (MSM). Moreover, these perturbed approximations are analyzed numerically and compared with the RK4 approximations.

On the well-posedness of the "Bando-follow the leader" car following model and a time-delayed version

<abstract><p>In this contribution we study the "Bando-follow the leader" car-following model, a second order ordinary differential equation, for its well-posedness. Under suitable conditions, we provide existence and uniqueness results, and also bounds on the higher derivatives, i.e., velocity and acceleration. We then extend the result to the "reaction" delay case where the delay is instantiated in reacting on the leading vehicle's position and velocity. We prove that the solution of the delayed model converges to the undelayed when the delay converges to zero and present some numerical examples underlying the idea that it is worth looking in more details into delay as it might explain problems in traffic flow like "phantom shocks" and "stop and go" waves.</p></abstract>

Optimal transmission of messages in computer networks – an optimal control problem involving control-dependent time-delayed arguments

In this paper, we find the optimal transmission of messages in computer networks. This problem has been formulated as a nondelayed optimal control problem in several recent papers on TCP (transmission control protocol). Since the actual transmission of messages from origins to destinations should consist of both forward transmission delays of the buffers and latency of the links, we remodel the problem as a time-delayed optimal control problem consisting of both control-dependent time-delayed arguments and discrete time-delayed arguments. We then develop a modified control parameterization method for solving this time-delayed optimal control problem. The gradients of the new objective function and constraint functions generated by this modified control parametrization method are derived. A numerical example is solved by using the time-delayed version of the problem that we formulate, as well as the nondelayed version of the problem in the literature. Numerical results clearly illustrate the efficiency of the modified control parameterization method for solving both versions of this optimal transmission problem. Comparison of results of the two versions concerning the optimal transmission rates at the origins, the optimal output flow rates at the destination, and the queue sizes at the buffers are obtained. These comparison results clearly reflect how the optimal transmission of messages in computer networks in real life can be affected by both the forward transmission delays of the buffers and the latency of the links.

Blind Two-Dimensional Super-Resolution and Its Performance Guarantee

In this work, we study the problem of identifying the parameters of a linear system from its response to multiple unknown input waveforms. We assume that the system response, which is the only given information, is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the linear system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain randomness and concentration properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications such as radar imaging, image restoration, and indoor source localization. In this framework, we show that under a minimum separation condition between the time-frequency shifts, all the unknowns that characterize the linear system can be recovered precisely and with very high probability provided that a lower bound on the total number of the observed samples is satisfied. The proposed framework is based on 2D atomic norm minimization problem which is shown to be reformulated and solved efficiently via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided.

Reservoir Computing with Delayed Input for Fast and Easy Optimisation.

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

Andronov\u2013Hopf and Neimark\u2013Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov–Hopf bifurcations in the differential equations and Neimark–Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark–Sacker bifurcations are less than critical times for Andronov–Hopf bifurcations but converge to them as the time step of the discretization tends to zero.

Dynamics analysis of a delayed virus model with two different transmission methods and treatments

In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Math. Methods Med. 2015:758362, 2015). We show that the virus-free equilibrium is locally asymptotically stable if the basic reproduction number is smaller than one, and by regarding the time delay as a bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of the endemic equilibrium. Finally, we give some numerical simulations to illustrate the theoretical findings.

On regularity of stochastic convolutions of functional linear differential equations with memory

In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates on fundamental solutions which are time delay versions of those on $ C_0 $-semigroups. To this end, we develop a scheme of constructing the resolvent operators for the integrodifferential equations of Volterra type since the equation under investigation is of this type in each subinterval describing the segment of its solution. Then we apply these estimates to stochastic convolutions of our equations to obtain the desired regularity property.

Sound Quality Improvement for Hearing Aids in Presence of Multiple Inputs

Modern-day hearing aids are capable of receiving acoustic signals over a wireless link and also from the surroundings through the microphone. If the hearing aid receives input only from the acoustic environment, feedback cancellation proceeds according to the existing methodologies for bias reduction. However, the wirelessly received signal and the acoustic environment input, when emitted from the same source, can be very similar to each other or with a time-delayed version of each other, thereby having a high correlation between them. Both inputs can also be emitted from different sources and, thus, be less correlated with each other. In the aforementioned scenarios, acoustic confusion can occur for the user as the hearing aid receives both signals simultaneously. To improve the output signal quality and to reduce bias in an adaptive feedback cancellation system with a wirelessly received signal as well as an acoustic environment input, we propose a cost function, and the optimization of the feed-forward path and of the shaping filter for the wireless signal. The feed-forward path is designed to be a cascade of the required acoustic enhancement along with an FIR filter. We derive expressions for an optimum shaping filter and for an optimized feed-forward path. Improvement in loudspeaker output signal quality, normalized misalignment and maximum stable gain for each of the above-mentioned scenarios is assessed through numerical simulations.

Franson interferometry with a single pulse

In classical optics, interference occurs between two optical fields when they are indistinguishable from one another. The same holds true in quantum optics, where a particular experiment, the Franson interferometer, involves the interference of a photon pair with a time-delayed version of itself. The canonical version of this interferometer requires that the time delay be much shorter than the coherence length of the pump used to generate the photon pair, so as to guarantee indistinguishability. However, when this time delay is comparable to the coherence length, conventional wisdom suggests that interference visibility degrades significantly. In this work, though, we show that the interference visibility can be restored through judicious temporal post-selection. Utilizing correlated photon pairs generated by a pump whose pulsewidth (460 ps) is shorter than the interferometer’s time delay (500 ps), we are able to observe a fringe visibility of 97.4±4.3%. We believe this new method can be used for the encoding of high-dimensional quantum information in the temporal domain.

Using spatiotemporal source separation to identify prominent features in multichannel data without sinusoidal filters.

The number of simultaneously recorded electrodes in neuroscience is steadily increasing, providing new opportunities for understanding brain function, but also new challenges for appropriately dealing with the increase in dimensionality. Multivariate source separation analysis methods have been particularly effective at improving signal-to-noise ratio while reducing the dimensionality of the data and are widely used for cleaning, classifying and source-localizing multichannel neural time series data. Most source separation methods produce a spatial component (that is, a weighted combination of channels to produce one time series); here, this is extended to apply source separation to a time series, with the idea of obtaining a weighted combination of successive time points, such that the weights are optimized to satisfy some criteria. This is achieved via a two-stage source separation procedure, in which an optimal spatial filter is first constructed and then its optimal temporal basis function is computed. This second stage is achieved with a time-delay-embedding matrix, in which additional rows of a matrix are created from time-delayed versions of existing rows. The optimal spatial and temporal weights can be obtained by solving a generalized eigendecomposition of covariance matrices. The method is demonstrated in simulated data and in an empirical electroencephalogram study on theta-band activity during response conflict. Spatiotemporal source separation has several advantages, including defining empirical filters without the need to apply sinusoidal narrowband filters.

Blocker-Tolerant and High-Sensitivity $\Delta \Sigma $ Correlation Digitizer for Radar and Coherent Receiver Applications

In this paper, a coherent subsampling digitizer for pulsed Doppler radar systems is proposed. Prior to transmission, the radar system modulates the RF pulse with a known pseudorandom binary phase shift keying (BPSK) sequence. Upon reception, the radar digitizer uses a programmable sample-and-hold circuit to multiply the received waveform by a properly time-delayed version of the known a priori BPSK sequence. This operation demodulates the desired echo signal while suppressing the spectrum of all in-band noncorrelated interferers, making them appear as noise in the frequency domain. The resulting demodulated narrowband Doppler waveform is then subsampled at the IF frequency by a delta–sigma modulator. Because the digitization bandwidth within the delta–sigma feedback loop is much less than the input bandwidth to the digitizer, the thermal noise outside of the Doppler bandwidth is effectively filtered prior to quantization, providing an increase in signal-to-noise ratio (SNR) at the digitizer’s output compared with the input SNR. In this demonstration, a delta–sigma correlation digitizer is fabricated in a 0.18- $\mu \text{m}$ CMOS technology. The digitizer has a power consumption of 1.12 mW with an IIP3 of 7.5 dBm. The digitizer is able to recover Doppler tones in the presence of blockers up to 40 dBm greater than the Doppler tone.

Numerical Model of an Injection-Locked Wideband Frequency Modulator for Polar Transmitters

We present a numerical model of a wideband injection-locked frequency modulator used in a polar transmitter for 3G cellular radio application. At the heart of the system is a self-injection-locked oscillator with a programmable linear tuning range of up to 200 MHz at 4-GHz oscillation frequency. The oscillator is injection locked to a time-delayed version of its resonating voltage, and its frequency is modulated by manipulating the phase and amplitude of the injected current. The model is used to study the feasibility of the proposed system by analyzing the impact of various impairments in the auxiliary injection loop on the system performance. The model is written in MATLAB/SIMULINK, and the simulation output is analyzed by a vector signal analyzer in terms of 3GPP specifications. Based on the simulation results, key specifications for individual blocks in the system are determined. The key benefits of the presented modeling methodology are simplicity, efficiency, and portability.

A Digitally Controlled Injection-Locked Oscillator With Fine Frequency Resolution

We propose a digitally controlled injection-locked RF oscillator with an auxiliary loop as an alternative to the conventional capacitive fine-tuning of an LC-tank. The oscillator is injection locked to a time-delayed version of its resonating voltage and its frequency is modulated by manipulating the phase and amplitude of injected current. The injection strength can be programmed for the DCO step size to be as fine as 9 kHz at 4 GHz. Alternatively, with large injection strength, the tuning range can reach up to 200 MHz. The proposed oscillator is experimentally verified in TSMC 40 nm digital CMOS.

Effect of Multiple Fingers on Receiver Performance in CDMA Forward Link

Rake receiver can be implemented in any communication system, which has possibility of multipath components. Rake receiver can take advantage from these multipath components and combined all multipath components to achieve optimum result. The bit error rate (BER) performance of the Code Division Multiple Access (CDMA) cellular system based on IS-95 standard in the presence of an additive white Gaussian noise (AWGN) and interference has been investigated in this paper. The performance of the RAKE receiver is analysed considering of different number of fingers. The performance is evaluated under noise and interference for the CDMA forward link. Rake receiver is used in CDMA-based (Code Division Multiple Access) systems and can combine multipath components, which are time-delayed versions of the original signal transmission. Combining is done in order to improve the signal to noise ratio at the receiver and so reduced the BER. The BER has been studied for different numbers of Rake fingers.

Bifurcation analysis of a mathematical model for genetic regulatory network with time delays

In this paper, we aim to investigate the dynamics of a gene regulatory network which is a time-delayed version of the model proposed by Elowitz and Leibler [Nature 403 (2000) 335–338]. Based on the normal form theory and center-manifold reduction, Hopf bifurcations including the bifurcation direction and stability of the bifurcated periodic orbits are investigated. We also discuss effects of transcriptional rate and time delay on the amplitude and period of the oscillation of the network. It shows that variations of time delay or transcriptional rate can change the period and amplitude of the oscillation. More precisely, (i) the amplitude increases with small time delay, while the change of amplitude is not sensitive to relatively large time delay. However, the robustness of amplitudes is not true any more for the case of using the transcriptional rate as parameter, where amplitude always increases quickly and linearly with the transcriptional rate; (ii) the period of oscillation increases as the time delay increases, but it grows up initially as the transcriptional rate increases and then keeps unchanged to certain constant value, which implies that the robustness of period to the transcriptional rate variations occurs. Our numerical simulations also support the theoretical conclusions, namely both suggest that time delay and transcriptional rate can be used as control parameters in genetic regulatory networks.

Time-domain coherent anti-Stokes Raman scattering in terms of the time-delayed Yuratich equation.

We show that the increasingly popular nonlinear optical technique of time-domain coherent anti-Stokes Raman scattering (CARS), which is often viewed from the dynamical perspective of the semiclassical time-dependent third-order polarization, can also be studied by means of the time-delayed version of the Yuratich equation, so popular in traditional frequency-domain CARS. The method proves successful in explaining experimental results that are otherwise treated by means of numerical methods only.