Positive Time Delays Research Articles

Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds

The requirement that particles propagate causally on non-trivial backgrounds implies interesting constraints on higher-derivative operators. This work is part of a systematic study of the positivity bounds derivable from time delays on shockwave backgrounds. First, we discuss shockwaves in field theory, which are infinitely boosted Coulomb-like field configurations. We show how a positive time delay implies positivity of four-derivative operators in scalar field theory and electromagnetism, consistent with the results derived using dispersion relations, and we comment on how additional higher-derivative operators could be included.We then turn to gravitational shockwave backgrounds. We compute the infinite boost limit of Reissner-Nordström black holes to derive charged shockwave backgrounds. We consider photons traveling on these backgrounds and interacting through four-derivative corrections to Einstein-Maxwell theory. The inclusion of gravity introduces a logarithmic term into the time delay that interferes with the straightforward bounds derivable in pure field theory, a fact consistent with CEMZ and with recent results from dispersion relations. We discuss two ways to extract a physically meaningful quantity from the logarithmic time delay — by introducing an IR cutoff, or by considering the derivative of the time delay — and comment on the bounds implied in each case. Finally, we review a number of additional shockwave backgrounds which might be of use in future applications, including spinning shockwaves, those in higher dimensions or with a cosmological constant, and shockwaves from boosted extended objects.

Is biomedical research self-correcting? Modelling insights on the persistence of spurious science.

The reality that volumes of published biomedical research are not reproducible is an increasingly recognized problem. Spurious results reduce trustworthiness of reported science, increasing research waste. While science should be self-correcting from a philosophical perspective, that in insolation yields no information on efforts required to nullify suspect findings or factors shaping how quickly science may be corrected. There is also a paucity of information on how perverse incentives in the publishing ecosystem favouring novel positive findings over null results shape the ability of published science to self-correct. Knowledge of factors shaping self-correction of science remain obscure, limiting our ability to mitigate harms. This modelling study introduces a simple model to capture dynamics of the publication ecosystem, exploring factors influencing research waste, trustworthiness, corrective effort and time to correction. Results from this work indicate that research waste and corrective effort are highly dependent on field-specific false positive rates and time delays to corrective results to spurious findings are propagated. The model also suggests conditions under which biomedical science is self-correcting and those under which publication of correctives alone cannot stem propagation of untrustworthy results. Finally, this work models a variety of potential mitigation strategies, including researcher- and publisher-driven interventions.

Sub-barrier recollisions and the three classes of tunneling time delays in strong-field ionization

Tunneling ionization is characterized by a negative time delay, observed asymptotically as a specific shift of the photoelectron momentum distribution, which is caused by the interference of the sub-barrier recolliding and direct ionization paths. In contrast, a \textit{Gedankenexperiment} following the peak of the wavefunction shows a positive tunneling time delay at the tunnel exit, considering only the direct ionization path. In this paper, we investigate the effects of sub-barrier recollisions on the time delay pattern at the tunnel exit. We conclude that the interference of the direct and recolliding trajectories decreases the tunneling time delay at the exit by the value equal to the asymptotic time delay maintaining, however, its sizeable positive value. Finally, we discuss the recent experiment [Light: Science \& Applications 11, 1 (2022)] addressing the tunneling time in a modified two-color attoclock setup. The analysis of the experimental findings with our theoretical model indicates the physical necessity to introduce a new time characteristic for tunneling ionization -- the time delay describing the initiation of the tunneling wave packet.

Time-delay feedback control of an axially moving nanoscale beam with time-dependent velocity

The paper is concerned with the nonlinear subharmonic resonance of an axially moving nanoscale beam with time-dependent velocity controlled by displacement and velocity time delay. To gain a thorough understanding of the system, the frequency response equation is first obtained using the multiple scales method. The stable intervals of the system's zero and non-zero solutions, as well as the necessary and sufficient conditions for Hopf bifurcation are specified. Then, the effects of nonlocal parameter, displacement feedback gain coefficient, velocity feedback gain coefficient, displacement and velocity time delay on the system's dynamic behaviors are discussed. The analysis demonstrates that the nonlocal parameters can not only reduce the amplitude of the system, but also change the stable regions of the non-zero solution. Furthermore, the time delay parameters can affect the number, amplitude, and stability of non-zero solutions. If the time delay parameters are chosen within the optimal value range, both positive and negative time delay feedback can effectively control system stability. These research results will serve as a theoretical reference for the design and optimization of axially moving nanostructures.

Stability Analysis of Delayed COVID-19 Models

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB.

Dynamical analysis of a delayed p53 oscillator model with p53-Mdm2 positive feedback

The p53 oscillator is an essential cell fate controller after DNA damage. In general, the delayed p53-Mdm2 negative feedback loop is thought to be the foundational structure responsible for p53 oscillations. However, it is experimentally found that Mdm2 also has a positive effect on p53. Therefore, we redevelop a p53 model to investigate the effect of the p53-Mdm2 positive feedback loop and time delay on p53 oscillations. To study the effect of delay on the Hopf bifurcation, we analyze the characteristic equation of the linearized system and apply the central manifold method to determine the properties of the Hopf bifurcation. The theoretical results are proved numerically. Furthermore, we reveal that the delay induces not only oscillatory birth but also oscillatory death, depending on the parameters in the positive feedback. Finally, considering the biological background, we discuss the effects of the p53-Mdm2 positive feedback parameters on the amplitude of p53 oscillations. This work may be helpful for artificially altering p53 dynamics and even cell fate.

Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay

As the novel coronavirus pandemic has spread globally since 2019, most countries in the world are conducting vaccination campaigns. First, based on the traditional SIR infectious disease model, we introduce a positive feedback mechanism associated with the vaccination rate, and consider the time delay from antibody production to antibody disappearance after vaccination. We establish an UVaV model for COVID-19 vaccination with a positive feedback mechanism and time-delay. Next, we verify the existence of the equilibrium of the formulated model and analyze its stability. Then, we analyze the existence of the Hopf bifurcation, and use the multiple time scales method to derive the normal form of the Hopf bifurcation, further determining the direction of the Hopf bifurcation and the stability of the periodic solution of the bifurcation. Finally, we collect the parameter data of some countries and regions to determine the reasonable ranges of multiple parameters to ensure the authenticity of simulation results. Numerical simulations are carried out to verify the correctness of the theoretical results. We also give the critical time for controllable widespread antibody failure to provide a reference for strengthening vaccination time. Taking two groups of parameters as examples, the time of COVID-19 vaccine booster injection should be best controlled before 38.5 weeks and 35.3 weeks, respectively. In addition, study the impact of different expiration times on epidemic prevention and control effectiveness. We further explore the impact of changes in vaccination strategies on trends in epidemic prevention and control effectiveness. It could be concluded that, under the same epidemic vaccination strategy, the existence level of antibody is roughly the same, which is consistent with the reality.

A SIQRB delayed model for cholera and optimal control treatment

We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a L1 type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite - Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.

Stability and optimal control of a delayed HIV/AIDS-PrEP model

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, and analyze the impact of this delay on the number of individuals with HIV infection. We prove the existence and stability of two equilibrium points, for any positive time delay. After, an optimal control problem with state and control delays is proposed and analyzed, where the aim is to find the optimal strategy for PrEP implementation that minimizes the number of individuals with HIV infection, with minimal costs. Different scenarios are studied, for which the solutions derived from the Minimum Principle for Multiple Delayed Optimal Control Problems change depending on the values of the time delays and the weights constants associated with the number of HIV infected individuals and PrEP. We observe that changes on the weights constants can lead to a passage from <i>bang-singular-bang</i> to <i>bang-bang</i> extremal controls.</p>

Thickness-dependent IR distortion from bulk absorption and refraction and its effects on broadband sum frequency generation spectroscopy

In the characterization of buried interfaces with sum frequency generation spectroscopy (SFG), the bulk thickness-dependent IR distortion effects on delay-dependent SFG spectra were identified: Around time zero, the SFG signal intensity reduced with the film thickness increasing while the overall spectral shape sustained; at positive time delays, bulk refraction ruled, and the distorted SFG spectral shape showed similar features as resonant SFG bands of surface molecular species. Both linear and nonlinear refraction effects were observed based on the delay-dependent and film thickness-dependent results. These results provide useful implications for spectral interpretation for in situ SFG spectroscopy of buried interfaces.

MRI-related anxiety can induce slow BOLD oscillations coupled with cardiac oscillations

ObjectiveAlthough about 1–2% of MRI examinations must be aborted due to anxiety, there is little research on how MRI-related anxiety affects BOLD signals in resting states. MethodsWe re-analyzed cardiac beat-to beat interval (RRI) and BOLD signals of 23 healthy fMRI participants in four resting states by calculation of phase-coupling in the 0.07–0.13 Hz band and determination of positive time delays (pTDs; RRI leading neural BOLD oscillations) and negative time delays (nTDs; RRI lagging behind vascular BOLD oscillations). State anxiety of each subject was assigned to either a low anxiety (LA) or a high anxiety (HA, with most participants exhibiting moderate anxiety symptoms) category based on the inside scanner assessed anxiety score. ResultsAlthough anxiety strongly differed between HA and LA categories, no significant difference was found for nTDs. In contrast, pTDs indicating neural BOLD oscillations exhibited a significant cumulation in the high anxiety category. ConclusionsFindings may suggest that vascular BOLD oscillations related to slow cerebral blood circulation are of about similar intensity during low/no and elevated anxiety. In contrast, neural BOLD oscillations, which might be associated with a central rhythm generating mechanism (pacemaker-like activity), appear to be significantly intensified during elevated anxiety. SignificanceThe study provides evidence that fMRI-related anxiety can activate a central rhythm generating mechanism very likely located in the brain stem, associated with slow neural BOLD oscillation.

Macroscopic transient absorption in a V-type three-level system

Despite the wide employment of transient absorption spectroscopy in capturing fast-evolving dynamics, the experiments lack further exploration of macroscopic effects beyond the single-atom response. Here, the absorbance of Rb atoms excited and coupled by two near-infrared pulses with a variable interpulse delay is studied both experimentally and theoretically, from the limit of a dilute-gas medium into high-density cases. Our results reveal that with increasing atomic density, the absorption lines are broadened with substructures emerging therein. However, the spectral evolutions are rather distinctive for positive and negative time delays, pointing toward different mechanisms behind them. As a distinguishing characteristic of the V-type levels, delay-dependent oscillations are entwined and complicate the resulting profiles considerably. The obtained intensity- and density-controlled line shapes are well reproduced based on the density matrix theory with the inclusion of pulse propagation. We believe these observations will not only play a crucial role in studying strong-field dynamics in dense systems, but could also serve as key ingredients for optical pulse shaping.

Ultrafast time delay as a control parameter in resonant ionization by two XUV ultrashort pulses

We predict quantitatively that it is possible to use few-femtosecond positive or negative time delays, between two XUV Gaussian few-femtosecond pulses of moderate intensities and central frequencies and in order to control the probability of ionization at clearly defined exit energies corresponding to the sums of photon frequencies (), (), and ( or ). The phenomenon is demonstrated quantitatively by obtaining and using nonperturbative solutions of the time-dependent Schrödinger equation for a time-dependent scheme involving the process of two-photon resonant ionization of Helium via the (58.4 nm) and (52.22 nm) excited states. The calculations used wavefunctions which are state-specific for the discrete spectrum, (up to the Rydberg state), as well as for the energy-normalized continuous spectrum, (up to 2.0 a.u. above threshold with angular momenta = 0, 1, 2, 3, 4). For this system, using as a control knob, the effects on the photoelectron spectrum of the combination of the transition amplitudes via the two paths and their interference are determined clearly for pulses with field-cycles ranging from about 15 to about 80 cycles. The analysis has included the comparison of the nonperturbative results, obtained by implementing the state-specific expansion approach, with those obtained from the application of second order time-dependent perturbation theory with two Gaussian pulses of finite duration.

Rossby Waves Detection in the CO2 and Temperature Multilayer Climate Network

AbstractIncreasing atmospheric carbon dioxide (CO2) is the main factor of global warming. Carbon satellites have proven that CO2 concentrations have nonuniform spatio‐temporal distributions. The relationship between unevenly distributed CO2 and global surface air temperature (SAT) is seldom known. The success of complex networks provides an opportunity to address this issue. This paper proposes a multilayer climate network approach to identify the impacts of nonuniform CO2 on SAT. The results show that the probability density function (PDF) of degrees, weighted degrees, and link lengths follows power‐law distributions. A large fraction of strong correlation links resides in proximal distance (smaller than 2,000 km), indicating that CO2 nodes are strongly connected to the surrounding SAT nodes. The enhanced distributions of large positive weights, time delays, and degree patterns are all consistent with the properties of Rossby waves. This framework can be useful for predicting future climate changes and policy‐making for carbon reduction.

Transition induce by positive and negative time delay feedback in active Brownian particles

In this paper, we investigate the dynamical properties of active Brownian particles (ABPs) in the Schweitzer–Ebeling–Tilch (SET) model with time delay feedback which is driven by external and internal noises. The effects of time delay feedback, external and internal noises on the stationary probability distribution (SPD) and the mean first passage time (MFPT) of the ABPs are discussed, respectively. The results are shown as following: (i) the intensity of time delay feedback (K) can induce the transition between bimodal to unimodal states in the motion of a particle on the SPD, and the time delay can enhance the impacts of the intensity of time delay feedback K inducing transitions from the two stable states (ii) the MFPT as function of the noise strengths shows a maximum, which implies the signature of noise-enhanced stability (NES) phenomenon of the velocity v− in the ABPs for SET model. The positive or negative time delay feedback can enhance or weaken the stability of the motion of the ABPs.

Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay

We study scalar delay equations \begin{document}$ \dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2)) $\end{document} with odd nonlinearity $ f $, real nonzero parameters $ \lambda, \, b $, and two positive time delays $ 1, \ p/2 $. We assume supercritical Hopf bifurcation from $ x \equiv 0 $ in the well-understood single-delay case $ b = \infty $. Normalizing $ f' (0) = 1 $, branches of constant minimal period $ p_k = 2\pi/\omega_k $ are known to bifurcate from eigenvalues $ i\omega_k = i(k+\tfrac{1}{2})\pi $ at $ \lambda_k = (-1)^{k+1}\omega_k $, for any nonnegative integer $ k $. The unstable dimension of these rapidly oscillating periodic solutions is $ k $, at the local branch $ k $. We obtain stabilization of such branches, for arbitrarily large unstable dimension $ k $, and for, necessarily, delicately narrow regions $ \mathcal{P} $ of scalar control amplitudes $ b < 0 $.For $ p $: = $ p_k $ the branch $ k $ of constant period $ p_k $ persists as a solution, for any $ b\neq 0 $. Indeed the delayed feedback term controlled by $ b $ vanishes on branch $ k $: the feedback control is noninvasive there. Following an idea of Pyragas [30], we seek parameter regions $ \mathcal{P} = (\underline{b}_k, \overline{b}_k) $ of controls $ b \neq 0 $ such that the branch $ k $ becomes stable, locally at Hopf bifurcation. We determine rigorous expansions for $ \mathcal{P} $ in the limit of large $ k $. Our analysis is based on a 2-scale covering lift for the slow and rapid frequencies involved.These results complement earlier results in [8] which required control terms \begin{document}$ b^{-1} (x(t-\vartheta) + x(t-\vartheta -p/2)) $\end{document} with a third delay $ \vartheta $ near 1.

Stability of switched positive linear time‐delay systems

In this study, the authors analyse the stability of switched positive linear time-delay systems. By developing a novel multiple discontinuous co-positive Lyapunov–Krasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under mode-dependent average dwell time switching. Moreover, under average dwell time switching, the corresponding stability conditions are also proposed. It is shown that their results can obtain smaller lower bounds on dwell time. Finally, simulation results are given to show the effectiveness of their methods.

Gain and phase margins-based delay margin computation of load frequency control systems using Rekasius substitution

This paper investigates the effect of gain and phase margins (GPMs) on stability delay margin of a two-area load frequency control (LFC) system with constant communication delay. A gain-phase margin tester (GPMT) is introduced to the LFC system as to take into GPMs in delay margin computation. A frequency domain exact method, Rekasius substitution, is proposed to compute the GPMs-based stability delay margins. The method aims to calculate all possible purely complex roots of the characteristic equation for a finite positive time delay. The approach first transforms the characteristic polynomial of the LFC system with transcendental terms into a regular polynomial. Routh-Hurwitz stability criterion is then implemented to compute the purely imaginary roots with the crossing frequency and stability delay margin. For a wide range of proportional–integral controller gains and GPMs, time delay values at which LFC system is both stable and has desired stability margin measured by GPMs are computed. The accuracy of complex roots and delay margins are verified by using an independent algorithm, the quasi-polynomial mapping-based root finder and time-domain simulations. Simulation studies indicate that delay margins must be determined considering GPMs to have a better dynamic performance in term of fast damping of oscillations, less overshoot and settling time.

Optical/X-ray correlations during the V404 Cygni June 2015 outburst

Context. We present a multiwavelength analysis of the simultaneous optical and X-ray light curves of the microquasar V404 Cyg during the June 2015 outburst. Aims. We have performed a comprehensive analysis of all the INTEGRAL/IBIS, JEM–X, and OMC observations during the brightest epoch of the outburst, along with complementary NuSTAR, AAVSO, and VSNET data, to examine the timing relationship between the simultaneous optical and X-ray light curves, in order to understand the emission mechanisms and physical locations. Methods. We have identified all optical flares that have simultaneous X-ray observations, and performed a cross-correlation analysis to estimate the time delays between the optical and soft and hard X-ray emission. We also compared the evolution of the optical and X-ray emission with the hardness ratios. Results. We have identified several types of behaviour during the outburst. On many occasions, the optical flares occur simultaneously with X-ray flares, but at other times, positive and negative time delays between the optical and X-ray emission are measured. Conclusions. We conclude that the observed optical variability is driven by different physical mechanisms, including reprocessing of X-rays in the accretion disc and/or the companion star, interaction of the jet ejections with surrounding material or with previously ejected blobs, and synchrotron emission from the jet.

MRI-related anxiety in healthy individuals, intrinsic BOLD oscillations at 0.1 Hz in precentral gyrus and insula, and heart rate variability in low frequency bands.

Participation in magnetic resonance imaging (MRI) scanning is associated with increased anxiety, thus possibly impacting baseline recording for functional MRI studies. The goal of the paper is to elucidate the significant hemispheric asymmetry between blood-oxygenation-level-dependent (BOLD) signals from precentral gyrus (PCG) and insula in 23 healthy individuals without any former MRI experience recently published in a PLOSONE paper. In addition to BOLD signals state anxiety and heart rate variability (HRV) were analyzed in two resting state sessions (R1, R2). Phase-locking and time delays from BOLD signals were computed in the frequency band 0.07–0.13 Hz. Positive (pTD) and negative time delays (nTD) were found. The pTD characterize descending neural BOLD oscillations spreading from PCG to insula and nTD characterize ascending vascular BOLD oscillations related to blood flow in the middle cerebral artery. HRV power in two low frequency bands 0.06–0.1 Hz and 0.1–0.14 Hz was computed. Based on the anxiety change from R1 to R2, two groups were separated: one with a strong anxiety decline (large change group) and one with a moderate decline or even anxiety increase (small change group). A significant correlation was found only between the left-hemispheric time delay (pTD, nTD) and anxiety change, with a dominance of nTD in the large change group. The analysis of within-scanner HRV revealed a pronounced increase of low frequency power between both resting states, dominant in the band 0.06–0.1 Hz in the large change group and in the band 0.1–0.14 Hz in the small change group. These results suggest different mechanisms related to anxiety processing in healthy individuals. One mechanism (large anxiety change) could embrace an increase of blood circulation in the territory of the left middle cerebral artery (vascular BOLD) and another (small anxiety change) translates to rhythmic central commands (neural BOLD) in the frequency band 0.1–0.14 Hz.