Small Delay Research Articles

Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE

We consider functional differential equations (FDEs) which are perturbations of smooth ordinary differential equations (ODEs). The FDE can involve multiple state-dependent delays, distributed delays, or implicitly defined delays (forward or backward). We show that, under some mild assumptions on the perturbation, if the ODE has a nondegenerate periodic orbit, then the FDE has a smooth periodic orbit. Moreover, when the perturbation depends on some parameters, we get smooth dependence of the periodic orbit and its frequency on the parameters with high regularity.The method can also be applied to treat equations with small delays appearing in electrodynamics and FDEs which are perturbations of some evolutionary partial differential equations (PDEs).The proof consists in solving functional equations satisfied by the parameterization of the periodic orbit and the frequency using a fixed-point approach. We do not need to consider the smoothness of the evolution or even the phase space of the FDEs.

A Simulation Model to Evaluate the Potential Impact of Disease-Modifying Treatments on Burden of Illness in Alzheimer's Disease.

Alzheimer's disease (AD) is a progressive neurodegenerative disease that places a substantial burden on patients, caregivers, and society. The advent of disease-modifying treatments (DMTs) would represent a major advancement in the management of AD, particularly in early AD. It is important to understand the potential value of these therapies to individuals and society. A modeling framework was developed to estimate the potential clinical and economic burden of AD in the USA by simulating the impact, relative to that of usual care, of a DMT with hypothesized availability beginning from 2022. The model assessed AD epidemiology, disease progression, and burden of illness from 2020 to 2050. Model outcomes included the total number of Americans with mild cognitive impairment (MCI) due to AD and mild, moderate, or severe AD dementia in community or residential care settings and their associated care costs, including direct medical and non-medical costs for healthcare resource use and indirect costs for caregiving. A hypothetical DMT was compared to the usual care under different effect scenarios based on delay in onset of AD (1, 3, and 5years) and DMT uptake (25%, 50%, and 100%). A delay in the onset of AD by 5years would reduce the prevalence of AD in 2050 by 6%, 12%, and 25%, resulting in savings of $0.783, $1.566, and $3.132 trillion from 2022 to 2050 for the 25%, 50%, and 100% uptake scenarios, respectively. This analysis demonstrated that DMTs that provide even small delays in the onset of AD can lead to an increase in disease-free years and sizable savings in the cost of care, providing significant benefits to patients, caregivers, and society.

A CAN Bus Security Testbed Framework for Automotive Cyber-Physical Systems

The popularization of electronic devices and the enrichment of external interfaces have increased the attack surface of the automotive cyber-physical system (CPS). As a vital part of the CPS, the controller area network (CAN) is more vulnerable to security threats due to the lack of corresponding security protection mechanisms. This kind of security problem has also attracted extensive attention from academia and industry. Researchers have proposed numerous intrusion detection models for the in-vehicle CAN bus, solving some security problems to a certain extent. However, vehicle manufacturers seldom disclose the internal details of vehicle ECUs due to safety concerns. Thus, it is difficult for researchers to investigate the operation mechanism of the bus. Meanwhile, there is a risk of personal safety in completing attack experiments on real vehicles, which can also lead to the lack and diversification of in-vehicle network data, especially the data of attack behavior. Based on real vehicle data, an open, adaptable, and low-risk CAN bus security testbed framework in the automotive CPS is proposed in this study, aiming to enrich the operation data of the CAN bus and enhance the personal safety of researchers. Besides, the delay of the testbed sending and receiving periodic and aperiodic CAN messages is theoretically explored. The results demonstrate that the generated timestamp in the dataset is mainly associated with the timestamp of the real vehicle data and that the transmission and collection of time series data are completed by Algorithm 1 and Algorithm 2. In the evaluation of the security testbed, the stability of the security testbed is studied from the two indicators of delay and packet loss rate. The experiment reveals that the testbed has a small relative delay difference and a low packet loss rate. Moreover, the DTW algorithm is employed to calculate the distance between the real vehicle and the testbed, and the experimental results demonstrate that the testbed is featured with high similarity and simulation.

A Pulse Delay Control Method by External Trigger to Underwater Illumination

Aiming at the problem of high precision pulse synchronization control in digital signal processing, we proposed an external trigger synchronization control method by double-layer hierarchical delay. The method consists of hardware circuit and control algorithm. The hardware circuit employs the main control unit and the digital delay unit, in which the main control unit makes the coordination between the digital delay unit and the peripheral circuit, and the two-layer digital delay unit performs multiple fixed period delay operation according to the instruction of the main control unit. The control algorithm adopts the two-layer hierarchical control mode, decomposes the total delay time according to the two-layer delay precision, and performs the combined delay in the two-layer digital delay unit successively. The delay result achieves a fixed delay of less than 40 ns, a delay step of 0.25 ns and a delay range of less than 1000 ns. The method adopts the combination of hardware and software to realize the external trigger double-layer hierarchical delay synchronization control, which has the characteristics of high delay step and pulse width adjustment accuracy and small cumulative delay error. It is suitable for the application scenarios of lidar echo signal and ultra-wide spectrum power source synthesis.

Spatial variation of crustal anisotropy in the Arunachal Himalaya inferred from splitting of local S waveforms

• A large spatial variability in crustal deformation is found beneath the western and eastern parts of the Arunachal Himalaya. • Small delay times and large scattering in the fast axis of anisotropy characterize the western part. • Crustal anisotropy beneath the western part is due to a combination of structure- and stress-induced mechanisms. • Correlation of local S and XK(K)S measurements in the central part suggests coherent deformation. • Combined delay times from the central and eastern parts show a correlation with depth. Shear wave anisotropy of the crust beneath the Arunachal Himalaya is investigated by analysing the splitting of steeply incident (i c ≤ 45°) direct S-phases of 396 local earthquakes, recorded at 32 stations. The 76 well constrained splitting measurements reveal that the delay times between fast and slow waves range from 0.02 to 0.30 s, clustered around 0.07 s. A large variation in the orientation of fast polarization directions (FPDs) is found. The smallest delay times (mostly < 0.10 s) and large variation in the orientation of FPDs are found at stations located in the western part of the Arunachal Himalaya. This is likely associated with heterogeneities in the lithological properties and a combined effect of stress-induced and structure-induced anisotropy. For a small crustal block in the central part of Arunachal, the FPDs are parallel to the strike of the Himalayan arc and are associated with structure-induced anisotropy. In this region, the FPDs representing the upper mantle are also found to be parallel to the strike of the Himalayan arc, suggesting a coherent deformation. In the eastern part, a variation in the FPDs is observed from north to south, being parallel to the strike of the Siang river in the former and mostly parallel to the average maximum horizontal stress in the latter. The delay times show a correlation with depth when the observations in the central and eastern parts of the Arunachal Himalaya are combined.

Delay-induced directional switches and mean switching time in swarming systems

Coordinated directional switches often emerge in moving biological groups replete with individual-level interactions. Recent self-propelled particles models can somewhat mimic the patterns of directional switches, but they usually do not include the effects of time delays in the interactions. Here, we focus on investigating the influence of time-delay interactions on the collective motion of swarming locusts, an experimentally well-studied system that exhibits ordered switches between clockwise and counterclockwise movement. We show, both analytically and numerically, that time delays of different types can affect the directional switches. Specifically, for the sufficiently small response delay, increasing the transmission delay can increase the mean switching time, while, for the large response delay, increasing the transmission delay may destroy the ordered directional switches. Our results decipher the role of time-delay interactions in the collective motion, which could be beneficial to the design of collective intelligent devices.

Adaptive Lag Smoother for State Estimation.

Fixed-lag smoothing has been used across different disciplines for offline analysis in many applications. With rising computational power and parallel processing architectures, fixed-lag smoothers are increasingly integrated into online processing system with small delays. This delay is directly related to the lag-length used in system design, which needs to be chosen appropriately. In this work, an adaptive approach is devised to choose an appropriate lag-length that provides a good trade-off between accuracy and computational requirements. The analysis shown in this paper for the error dynamics of the fixed-lag smoother over the lags helps in understanding its saturation over increasing lags. In order to provide the empirical results, simulations are carried out over a second-order Newtonian system, single-axis attitude estimation, Van der Pol’s oscillator, and three-axis attitude estimation. The simulation results demonstrate the performance achieved with an adaptive-lag smoother as compared to a fixed-lag smoother with very high lag-length.

Periodic delay orbits and the polyfold implicit function theorem

We consider differential delay equations of the form \partial_tx(t) = X_{t}(x(t - \tau)) in \mathbb{R}^n , where (X_t)_{t\in S^1} is a time-dependent family of smooth vector fields on \mathbb{R}^n and \tau is a delay parameter. If there is a (suitably non-degenerate) periodic solution x_0 of this equation for \tau=0 , that is without delay, there are good reasons to expect existence of a family of periodic solutions for all sufficiently small delays, smoothly parametrized by \tau . However, it seems difficult to prove this using the classical implicit function theorem, since the equation above, considered as an operator, is not smooth in the delay parameter. In this paper, we show how to use the M-polyfold implicit function theorem by Hofer–Wysocki–Zehnder (2009, 2021) to overcome this problem in a natural setup.

Next generation QCA technology based true random number generator for cryptographic applications

The penchant for almost all modern-day devices is high data and communication security. To achieve the highest standard of security, hardware-based encryption architectures like true random number generators (TRNG) and physically unclonable functions (PUF) supersede attack deterrence to any known software-based cryptography algorithm. The keys generated are random and unpredictable. This paper proposes a new architecture for TRNG in quantum-dot cellular automata (QCA) technology using feedback and feed-forward D flip-flop arrangement with small delay defects. A new optimized negative edge-triggered D flip-flop is presented using only 25-QCA cells. This unique and carefully curated TRNG structure ensures the generated output bits are highly unpredictable and truly random in behavior. Furthermore, 15 statistical tests designed for random number generators are performed. These test results validate the random nature of the generated outputs and unpredictable behavior of the proposed TRNG design. The energy dissipation analysis shows a significant improvement of 49.6% for energy dissipation per bit compared to existing designs.

GEPDFs: Path Delay Faults Based on Two-Cycle Gate-Exhaustive Faults

Path delay faults model small delay defects that affect the operation of the circuit when they accumulate along a path. For lines on a path, the propagation conditions can be related to those of transition faults. Two-cycle defect-aware, cell-aware and gate-exhaustive faults model delay defects with more complex activation conditions than transition faults. This article observes that detecting gate-exhaustive faults along a path results in the detection of small delay defects with more complex activation conditions than transition faults. Such path delay faults are referred to as gate-exhaustive path delay faults. This article defines gate-exhaustive path delay faults and describes a path selection procedure to support test generation. The experimental results for benchmark circuits demonstrate the possibility of detecting gate-exhaustive path delay faults.

Combined head accelerometry and EEG improves the detection of respiratory-related cortical activity during inspiratory loading in healthy participants.

Mechanical ventilation is a highly utilized life‐saving tool, particularly in the current era. The use of EEG in a brain–ventilator interface (BVI) to detect respiratory discomfort (due to sub‐optimal ventilator settings) would improve treatment in mechanically ventilated patients. This concept has been realized via development of an EEG covariance‐based classifier that detects respiratory‐related cortical activity associated with respiratory discomfort. The aim of this study was to determine if head movement, detected by an accelerometer, can detect and/or improve the detection of respiratory‐related cortical activity compared to EEG alone. In 25 healthy participants, EEG and acceleration of the head were recorded during loaded and quiet breathing in the seated and lying postures. Detection of respiratory‐related cortical activity using an EEG covariance‐based classifier was improved by inclusion of data from an Accelerometer‐based classifier, i.e. classifier ‘Fusion’. In addition, ‘smoothed’ data over 50s, rather than one 5 s window of EEG/Accelerometer signals, improved detection. Waveform averages of EEG and head acceleration showed the incidence of pre‐inspiratory potentials did not differ between loaded and quiet breathing, but head movement was greater in loaded breathing. This study confirms that compared to event‐related analysis with >5 min of signal acquisition, an EEG‐based classifier is a clinically valuable tool with rapid processing, detection times, and accuracy. Data smoothing would introduce a small delay (<1 min) but improves detection results. As head acceleration improved detection compared to EEG alone, the number of EEG signals required to detect respiratory discomfort with future BVIs could be reduced if head acceleration is included.

IoT Based Smart Street Lights Empowered by Piezoelectric Sensors

The power generated from piezo plates is connected to the lead acid battery which is rechargeable battery and supply the energy to the street light under two conditions first is the LDR should be detect a dark condition and the ultrasonic sensor should detect any human being or vehicle passes on the roadways under these conditions with a small delay and automatic turn on the street light with full brightness and as human being or vehicles go away from that location the street lights come back to low brightness mode. During daylight the LDR detects a full bright light due to this this circuit is in the disable state and no question of turning any of the straight light during day time the microcontroller is programmed for the ultrasonic sensor which sense the object or human being and triggers the output relay to enable or disable the time based operation of the street lights.

Mixed-Flow Load-Balanced Scheduling for Software-Defined Networks in Intelligent Video Surveillance Cloud Data Center

As the large amount of video surveillance data floods into cloud data center, achieving load balancing in a cloud network has become a challenging problem. Meanwhile, we hope the cloud data center maintains low latency, low consumption, and high throughput performance when transmitting massive amounts of data. OpenFlow enables a software-defined solution through programing to control the scheduling of data flow in the cloud data center. However, the existing scheduling algorithm of the data center cannot cope with the congestion of the network center effectively. Even for some dynamic scheduling algorithms, adjustments can only be made after congestion occurs. Hence, we propose a proactive and dynamically adjusted mixed-flow load-balanced scheduling (MFLBS) algorithm, which not only takes into account the different sizes of flows in the network but also maintains maximum throughput while balancing the load. In this paper, the MFLBS problem was formulated, along with a set of heuristic algorithms for real-time feedback and adjustment. Experiments with mesh and tree network models show that our MFLBS is significantly better than other dynamic scheduling algorithms, including one-hop DLBS and static scheduling algorithm FCFS. The MFLBS algorithm can effectively reduce the delay of small flows and average delay while maintaining high throughput.

Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries and time-delayed feedback

The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries and time-delayed feedback is investigated. Firstly, by introducing an asymmetric factor into UPBSR potential, three kinds of asymmetries are constructed, i.e., well-depth asymmetry (WDA), well-width asymmetry (WWA), and both well-depth and well-width asymmetry (BDWA). Then, by using two-state theory and small delay approximation, the output signal-to-noise ratio (SNR) is derived to analyze the behavior of SR. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, as an intermediate result in the calculation of the SNR, the mean first passage time (MFPT), is often used to discuss the transient properties of nonlinear systems. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the WDA dominates the three cases. In addition, the effect of feedback intensity on SR depends heavily on the asymmetric cases, it plays the opposite role in different asymmetric cases. In contrast, the effect of time delay is independent on the asymmetric cases, which always exhibits an improvement of SR noise immunity. As for MFPT analysis, the small γ and β are conducive to the transition of the particles between potential wells, while τ almost has no effect on the transition of particles.

New EU Strategy for Central Asia: Barriers for Its Successful Implementation

The European Union (EU) continues the line of cooperation with Central Asia. The 2007 strategy envisioned cooperation in areas ranging from environmental and energy to security, human rights and the rule of law. It was accepted for a ten-year term and it was replaced by another strategy with a small delay 12 years later. The new EU strategy for Central Asia, adopted in 2019, is an updated version of the 2007 strategy. This 2007 version was sharply criticized, on the one hand, due to the lack of clear goals, and on the other hand, because of the seemingly important, but in fact, marginal topics from the point of view of the Central Asian countries. The EU was criticized for its weak foreign policy, indecision and prioritization of secondary issues not only from outside, but also by member states. There is no doubt that the new Strategy has been supplemented and new areas of cooperation have been added. Nevertheless, to our minds, there are some inhibiting factors that interfere with the full success of the Strategy. Thus, the article focuses not on the success or the most positive aspects of the EU new Strategy for CA, but on defining the obstacles for its full development. Key words: Central Asia, cooperation, EU, strategy studies, security

Stability analysis of hybrid stochastic delayed Cohen-Grossberg neural networks with Lévy noise and Markov switching

The almost sure exponential stability for hybrid stochastic delayed Cohen-Grossberg neural networks with Lévy noise and Markov switching (SDCGNNs-LN-MS) is investigated in the article. Taking full advantage of stationary distribution and by constructing a special Lyapunov function, we get the almost sure exponential stability standard via linear matrix inequality (LMI) for nominal hybrid stochastic system (HSS) without imposing system stability condition. Based on this, we explore the almost sure exponential stability for underlying SDCGNNs-LN-MS according to the comparison principle for sufficiently small time delay τ and an implicit lower bound for τ is provided. Finally, the validity of results is demonstrated by an example.

Effects of Driving Style on Energy Consumption and CO2 Emissions

The tractive force developed by energy consumption (EC) in a car engine produces its acceleration and sustains the motion against velocity dependent resistance forces. In internal combustion engines, fuel burning entails pollutant emissions (PE) released into the atmosphere. In vehicular traffic, EC and PE depend on the driving style. This paper assumed that the transition rules in a traffic cellular automata (TCA) represent a driving style, and its effect on EC and PE in TCA is studied. Extending empirical relationships, we proposed models to estimate EC and PE in TCA from the velocity and acceleration distributions, which we obtained by computer simulations for three well-known TCA. The Nagel-Schreckenberg (NS) and Fukui-Ishibashi (FI) models, and a variant (NS+FI) defined by combining the NS and FI rules, were considered. The FI driving style revealed EC and CO2 emission rates dependent on the stochastic delay (p) only for low vehicular densities. We also detected that the larger EC and CO2 emission rates were 45.4 kW and 26.7 g/s with no dependence on p. With NS and NS+FI driving styles, the larger energy consumption and CO2 emission rates occurred for small stochastic delays, 18.4 kW and 6.6 g/s and 61.1kW and 30.2 g/s for p = 0.2. On average, for NS, FI, and NS+FI models (p = 0.2), we obtained energy consumptions of 1.88, 2.60, and 2.76 MJ/km, fuel consumptions of 0.08, 0.12, and 0.13 L/km, and CO2 emissions of 0.158, 0.460, and 0.562 kgCO2/km. Our results agree with those (3.37 MJ/km and 0.235 kgCO2/km) of petrol combustion car engines at 10 km/L. This work may help in designing flow and driving style scenarios to optimize vehicular traffic EC and reduce PE.

Reduced oviposition period promotes blowfly population extinction in Nicholson’s model

ABSTRACT Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson’s model describes the population dynamics of the Australian blowfly (Lucilia Cuprina). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, Lucilia Sericata, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: L. Sericata prefers warmer months, thus in summer, while L. Cuprina is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.

Virtual double-well potential for an underdamped oscillator created by a feedback loop

Virtual potentials are a very elegant, precise and flexible tool to manipulate small systems and explore fundamental questions in stochastic thermodynamics. In particular double-well potentials have applications in information processing, such as the demonstration of Landauer’s principle. Nevertheless, virtual double-well potentials had never been implemented in underdamped systems. In this article, we detail how to face the experimental challenge of creating a feedback loop for an underdamped system (exploring its potential energy landscape much faster than its over-damped counterpart), in order to build a tunable virtual double-well potential. To properly describe the system behavior in the feedback trap, we express the switching time in the double-well for all barrier heights, combining for the first time Kramer’s description, valid at high barriers, with an adjusted model for lower ones. We show that a small hysteresis or delay of the feedback loop in the switches between the two wells results in a modified velocity distribution, interpreted as a cooling of the kinetic temperature of the system. We successfully address all issues to create experimentally a virtual potential that is statistically indistinguishable from a physical one, with a tunable barrier height and energy step between the two wells.

Interval observer-based supervision of nonlinear networked control systems

Networked control system (NCS) is a multidisciplinary area that attracts increasing attention today. In this paper, we deal with remote supervision of a nonlinear networked control systems class subject to network imperfections. Different from many existing researches that consider only the problem of small and/or constant communication delays, we focus on large and time-varying network delays problem in both measurement and control channels. The proposed method is a set-membership estimation-based predictor approach computing a guaranteed set of admissible state values when the uncertainties (i.e. measurement noises and system disturbances) are considered unknown but bounded with a priori known bounds. The state prediction strategy is used to compensate the effect of transmission delays. Finally, the theoretical results are validated through a numerical example.