Delay Distribution Research Articles

Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3

ABSTRACT The mass, spin, and merger rate distribution of the binary black holes (BBHs) across cosmic redshifts provide a unique way to shed light on their formation channel. Along with the redshift dependence of the BBH merger rate, the mass distribution of BBHs can also exhibit redshift dependence due to different formation channels and dependence on the metallicity of the parent stars. We explore the redshift dependence of the BBH mass distribution jointly with the merger rate evolution from the third gravitational wave (GW) catalogue GWTC-3 of the LIGO–Virgo–KAGRA collaboration. We study possible connections between peak-like features in the mass spectrum of BBHs and processes related to supernovae physics and time delay distributions. We obtain a preference for short-time delays between star formation and BBH mergers. Using a power-law form for the time delay distribution ($(t^{\rm min}_d)^{d}$), we find d < −0.7 credible at 90 per cent interval. The mass distribution of the BBHs could be fitted with a power-law form with a redshift-dependent peak feature that can be linked to the pair instability supernovae (PISN) mass-scale MPISN(Z*) at a stellar metallicity Z*. For a fiducial value of the stellar metallicity Z* = 10−4, we find the $\rm M_{\rm PISN}(Z_*)=44.4^{+7.9}_{-6.3}$$\rm M_\odot$. This is in accordance with the theoretical prediction of the lower edge of the PISN mass-scale and differs from previous analyses. Although we find a strong dependence of the PISN value on metallicity, the model that we explored is not strongly favoured over those that do not account for metallicity as the Bayes factors are inconclusive. In the future with more data, evidence towards metallicity dependence of the PISN will have a significant impact on our understanding of stellar physics.

Forecasting COVID-19 activity in Australia to support pandemic response: May to October 2020

As of January 2021, Australia had effectively controlled local transmission of COVID-19 despite a steady influx of imported cases and several local, but contained, outbreaks in 2020. Throughout 2020, state and territory public health responses were informed by weekly situational reports that included an ensemble forecast of daily COVID-19 cases for each jurisdiction. We present here an analysis of one forecasting model included in this ensemble across the variety of scenarios experienced by each jurisdiction from May to October 2020. We examine how successfully the forecasts characterised future case incidence, subject to variations in data timeliness and completeness, showcase how we adapted these forecasts to support decisions of public health priority in rapidly-evolving situations, evaluate the impact of key model features on forecast skill, and demonstrate how to assess forecast skill in real-time before the ground truth is known. Conditioning the model on the most recent, but incomplete, data improved the forecast skill, emphasising the importance of developing strong quantitative models of surveillance system characteristics, such as ascertainment delay distributions. Forecast skill was highest when there were at least 10 reported cases per day, the circumstances in which authorities were most in need of forecasts to aid in planning and response.

Exploring Microscopic Characteristics of Bicycle Riders’ following Behaviors in a Single-File Movement

Cycling can bring a wide range of social, economic, and health benefits to individuals and communities. The safety and efficiency of bicycle facilities can be significantly impacted by the interactions among riders. This study aims to examine the microscopic characteristics of how cyclists interact with each other when they are in a single file movement based on the trajectory data collected from an experiment. Reaction delay was obtained by optimizing the correlation between relative speed and acceleration curves for individual cyclists and it was found that even for a given cyclist, this characteristic time delay could vary considerably, and be situation-dependent. Furthermore, it was found that the distribution of reaction delay, which has an average (±SD) of 0.66 s (±0.33 s), followed a log-normal distribution. The strong correlation observed between relative speed and time-delayed acceleration resembles the behavior observed in car-following situations, highlighting that relative speed is an essential factor influencing the acceleration behavior of cyclists. Multiple linear regression models were used to understand the association between acceleration and other key microscopic variables, e.g., spacing and relative speed, which are commonly used in microscopic behavior models. While the spacing between cyclists was found to have a significant impact on acceleration behavior, its effect was not as significant as that of relative speed. The outcomes of this study provide valuable insights into the cyclists’ behavior and can aid in the development of microscopic simulation models.

Stability and bifurcations in scalar differential equations with a general distributed delay

For a differential equation involving a general distributed time delay, a local stability and bifurcation analysis is performed, relying on fundamental properties of the characteristic function of the random variable whose probability density function is the delay distribution. Based on the root locus method, the bifurcation curves are determined in the considered parameter plane, also providing the number of unstable roots of the analyzed characteristic equation in each of the open connected regions delimited by these curves. This leads to a characterisation of the stability region of the considered equilibrium in the corresponding parameter plane. A Hopf bifurcation analysis is also completed in the general setting, and the criticality is analyzed by employing the method of multiple times scales. In contrast with some previously reported results from the literature, our analysis is accomplished in a general context and only then exemplified for particular types of delay distributions (e.g. Dirac, Gamma, uniform and triangular). The theoretical results are showcased in the framework of a simple neural model.

Improvement of cell internal weak defects detection under process variation by optimizing test path and test pattern

Advances in integrated circuit process technology have led to new defect mechanisms, and weak resistive defects in standard cells have received attention in addition to traditional defect types. Such defects are categorized as small delay defects that affect the reliability of a circuit. The delay introduced by such defects overlaps with the delay distribution resulting from the random process variation. Combining the results of the theoretical analysis, we propose a test method to improve the probability of detecting cell internal weak defects in the presence of process variation. The path with the minimum logic depth is selected as the test path, and the test pattern that enhanced the small delay of weak defects is paired with the test path. The improvements in defect detection probability over traditional tests are demonstrated on the ISCAS89 benchmark circuits. The results show that the proposed method provides an order of magnitude improvement in the probability of detecting cell internal weak defects.

A Bayesian Multi-Armed Bandit Algorithm for Dynamic End-to-End Routing in SDN-Based Networks with Piecewise-Stationary Rewards

To handle the exponential growth of data-intensive network edge services and automatically solve new challenges in routing management, machine learning is steadily being incorporated into software-defined networking solutions. In this line, the article presents the design of a piecewise-stationary Bayesian multi-armed bandit approach for the online optimum end-to-end dynamic routing of data flows in the context of programmable networking systems. This learning-based approach has been analyzed with simulated and emulated data, showing the proposal’s ability to sequentially and proactively self-discover the end-to-end routing path with minimal delay among a considerable number of alternatives, even when facing abrupt changes in transmission delay distributions due to both variable congestion levels on path network devices and dynamic delays to transmission links.

Insect visuomotor delay adjustments in group flight support swarm cohesion

Flying insects routinely demonstrate coordinated flight in crowded assemblies despite strict communication and processing constraints. This study experimentally records multiple flying insects tracking a moving visual stimulus. System identification techniques are used to robustly identify the tracking dynamics, including a visuomotor delay. The population delay distributions are quantified for solo and group behaviors. An interconnected visual swarm model incorporating heterogeneous delays is developed, and bifurcation analysis and swarm simulation are applied to assess swarm stability under the delays. The experiment recorded 450 insect trajectories and quantified visual tracking delay variation. Solitary tasks showed a 30ms average delay and standard deviation of 50ms, while group behaviors show a 15ms average and 8ms standard deviation. Analysis and simulation indicate that the delay adjustments during group flight support swarm formation and center stability, and are robust to measurement noise. These results quantify the role of visuomotor delay heterogeneity in flying insects and their role in supporting swarm cohesion through implicit communication.

Delay Analysis of IEEE 802.11be Multi-Link Operation Under Finite Load

Multi-link Operation (MLO), arguably the most disruptive feature introduced in IEEE 802.11be, will cater for delay-sensitive applications by using multiple radio interfaces concurrently. In this paper, we analyze the delay distribution of MLO under non-saturated traffic. Our results show that upgrading from legacy single-link to MLO successfully contains the $95$th percentile delay as the traffic load increases, but also that adding extra interfaces yields rapidly diminishing gains. Further experiments we conduct on Google Stadia traces, accounting for realistic traffic with batch arrivals, confirm the insights stemming from our theoretical analysis, vouching for MLO to support high-resolution real-time video with a controlled delay.

Allocating edge service resources to the up-offloaded vehicle tasks in ICV environment

Inspired by the rapid proliferation of intelligent transportation and smart city, ICV (Intelligent and Connected Vehicle) has drawn much attention, which not only brings great opportunities but also poses new challenges to the dynamic vehicle task serving mode. In this paper, we focus on the edge resource allocation process of the overloaded vehicle tasks that offloaded to edge servers in ICV environment. First of all, we introduce MEC and SDN technology into the traditional IoV (Internet of Vehicle) architecture to construct an SDN-assisted ICV network model. Next, a BiGRU+Attention edge service resource demands predicting model is designed, and based on the above model, we are able to further assess the future edge service resources availability and perceive the future vehicle mobility. Then, we build a task serving delay minimization problem for the edge service resource allocation process, where the impact of resource allocation decision-makings on the global network performance is also considered in the form of soft constraints. Furthermore, we put forward a timeslot-based edge service resource allocation algorithm with three phases. Finally, we simulate our scheme and another three schemes on NS3 platform, the results show that our algorithm outperforms in terms of average task serving delay, success ratio and load distribution.

Multi-objective vaccine delivery problem considering low carbon and customer loss aversion

The high energy consumption and on-time delivery requirements of vaccine last-mile delivery require us to rethink deeply about the vaccine delivery problem. First, using a fuel consumption model, we examine the main factors affecting vaccine distribution vehicles' fuel consumption and carbon emission. And then, we construct a delivery delay penalty function based on the characteristics of customer behavior for loss aversion. Second, we develop a dual-objective vaccine distribution model that includes minimizing the total logistics cost and minimizing the total distribution delay. Lastly, we design a new crossover mechanism of multi-population evolution and embed the simulated annealing criteria into the multi-objective algorithm. In numerical experiments, we demonstrate the effectiveness of our multi-objective algorithm in solving vaccine distribution problems of this type. Besides, the results show that we can scientifically configure the logistics route by reducing the usage of delivery vehicles without increasing fuel consumption while achieve to balance both logistics cost and delivery efficiency.

A vehicle cloud control system considering communication quantization and stochastic delay

AbstractA novel kind of networked feedback controller is designed for the vehicle cloud control system in the presence of both sensor‐controller/controller‐actuator delay and communication quantization. Firstly, the vehicle cloud control system with delayed and quantized communication is modeled using the lateral/longitudinal vehicle dynamic and Markovian jump linear system (MJLS) theory. Then, some efficient stabilization conditions in matrix inequalities forms are derived for the considered cloud‐controlled vehicles. Furthermore, a cone complementary linearization method is utilized to solve the nonlinear matrix inequalities involved in the stabilization conditions. Simulation tests on connected vehicle lateral and longitudinal control are conducted to verify the effectiveness of the analytical results. Compared with the commonly used constant‐parameter controllers, the proposed method is practical to design vehicle cloud controllers under stochastic delay and communication quantization scenarios, with known delay distribution. Lastly, the stability of the vehicle cloud control system is guaranteed under the infection of unreliable communication factors with the proposed control method.

Extreme Path Delay Estimation of Critical Paths in Within-Die Process Fluctuations Using Multi-Parameter Distributions

Two multi-parameter distributions, namely the Pearson type IV and metalog distributions, are discussed and suggested as alternatives to the normal distribution for modelling path delay data that determines the maximum clock frequency (FMAX) of a microprocessor or other digital circuit. These distributions outperform the normal distribution in goodness-of-fit statistics for simulated path delay data derived from a fabricated microcontroller, with the six-term metalog distribution offering the best fit. Furthermore, 99.7% confidence intervals are calculated for some extreme quantiles on each dataset using the previous distributions. Considering the six-term metalog distribution estimates as the golden standard, the relative errors in single paths vary between 4 and 14% for the normal distribution. Finally, the within-die (WID) variation maximum critical path delay distribution for multiple critical paths is derived under the assumption of independence between the paths. Its density function is then used to compute different maximum delays for varying numbers of critical paths, assuming each path has one of the previous distributions with the metalog estimates as the golden standard. For 100 paths, the relative errors are at most 14% for the normal distribution. With 1000 and 10,000 paths, the corresponding errors extend up to 16 and 19%, respectively.

Analytical Delay Modeling for a Sub-Threshold Cell Circuit with the Inverse Gaussian Distribution Function

Considering that power consumption (PC) is an extremely important indicator in digital circuit design, lower PC has always been our pursuit. PC and power supply voltage are positively correlated, and in this case, we must reduce the operating voltage of the circuit. However, as the voltage continues to decrease, various secondary effects and process variations become increasingly influential, making the delay distribution and its statistical characteristics more difficult to predict. In this paper, an inverse Gaussian distribution is used to model the propagation delay. Taking into account the local process variation, the multi-input delay analytical expression is derived according to the sub-threshold current formula to accurately predict the distribution and statistical characteristics of the delay, and the delay is obtained by calculation instead of Monte Carlo simulation, which greatly reduces the simulation time. The accuracy of the delay expression and delay distribution have been tested under 22 nm FDSOI technology and good results were obtained with operating voltages from 0.20 V to 0.30 V, in which the mean error of the delay is approx. 1.5%, the variance error is approx. 4.3%, and the error of the cumulative distribution function is approx. 2%.

The resonance fluorescence cascade of a laser-excited two-level atom

The cascade of fluorescence photons by a two-level atom excited by coherent laser light is reviewed. The discussion emphasizes the random nature of resonance fluorescence and uses the distribution of delays between two successively emitted photons as the primary characterization of the process. Other characterizations such as photon counting and photon correlation are deduced.

Vaccination games and imitation dynamics with memory

In this paper, we model dynamics of pediatric vaccination as an imitation game, in which the rate of switching of vaccination strategies is proportional to perceived payoff gain that consists of the difference between perceived risk of infection and perceived risk of vaccine side effects. To account for the fact that vaccine side effects may affect people's perceptions of vaccine safety for some period of time, we use a delay distribution to represent how memory of past side effects influences current perception of risk. We find disease-free, pure vaccinator, and endemic equilibria and obtain conditions for their stability in terms of system parameters and characteristics of a delay distribution. Numerical bifurcation analysis illustrates how stability of the endemic steady state varies with the imitation rate and the mean time delay, and this shows that it is not just the mean duration of memory of past side effects, but also the actual distribution that determines whether disease will be maintained in the population at some steady level, or if sustained periodic oscillations around this steady state will be observed. Numerical simulations illustrate a comparison of the dynamics for different mean delays and different distributions, and they show that even when periodic solutions are observed, there are differences in their amplitude and period for different distributions. We also investigate the effect of constant public health information campaigns on vaccination dynamics. The analysis suggests that the introduction of such campaigns acts as a stabilizing factor for endemic equilibrium, allowing it to remain stable for larger values of mean time delays.

Synchronization of Delayed Fuzzy Neural Networks with Probabilistic Communication Delay and Its Application to Image Encryption

This article studies the design of fuzzy synchronization controller of Takagi—Sugeno (T-S) fuzzy neural networks with distributed time-varying delay and probabilistic network communication delay. Compared with the existing model of neural networks with distributed time-varying delay without kernel, a more general model containing a distributed delay kernel is considered. By utilizing the probability distribution of random communication delays, a distributed but deterministic delay model is established. In this model, the delay probability density function is treated as the distributed delay kernel. By developing a new Lyapunov-Krasovskii functional (LKF) related to the distributed delay kernels and using an integral inequality, new sufficient conditions for the existence of a synchronization controller are presented. Finally, a numerical simulation and an application of encrypting the image are carried out to illustrate the effectiveness of the developed strategy.

Treasure Maps for Detections of Extreme Energy Cosmic Rays

The origin of ultra-high-energy cosmic rays is a 60 yr old mystery. We show that with more events at the highest energies (above 150 EeV) it may be possible to limit the character of the sources and learn about the intervening magnetic fields. Individual sources become more prominent, relative to the background, as the horizon diminishes. An event-by-event, composition-dependent observatory would allow a “tomography” of the sources as different mass and energy groups probe different GZK horizons. A major goal here is to provide a methodology to distinguish between steady and transient or highly variable sources. Using recent Galactic magnetic field models, we calculate “treasure” sky maps to identify the most promising directions for detecting Extreme Energy Cosmic Rays doublets, events that are close in arrival time and direction. On this basis, we predict the incidence of doublets as a function of the nature of the source host galaxy. Based on the asymmetry in the distribution of time delays, we show that observation of doublets might distinguish source models. In particular, the Telescope Array hotspot could exhibit temporal variability as it is in a “magnetic window” of small time delays. These considerations could improve the use of data with existing facilities and the planning of future ones such as Global Cosmic Ray Observatory (GCOS).

Timestamp-Free Synchronization Under Delays With Arbitrary Distribution in Wireless Sensor Networks

Clock synchronization is a key technology in wireless sensor networks (WSNs). It is significant and challenging to track clock parameters under arbitrary delay distributions. This letter proposes an Adaptive Gaussian mixture extended Kalman particle filter (AGMEKPF), which is robust to arbitrarily distributed delays in practical WSNs and can jointly track clock skew and offset. It is combined with the timestamp-free synchronization, which is a clock synchronization protocol that can effectively reduce energy consumption without exchanging timestamps. Simulation results show that the proposed method outperforms similar methods in terms of accuracy and complexity.

Forecasting Waste Mobile Phone (WMP) Quantity and Evaluating the Potential Contribution to the Circular Economy: A Case Study of Turkey

Information and communication technology (ICT)-based products have a significant effect on increasing levels of waste electrical and electronic equipment (WEEE) or electronic waste (e-waste) due to their shorter lifespan as a result of rapid technological changes. Mobile phones are the most popular ICT products, and their market share is increasing gradually. Therefore, effective management of waste mobile phones (WMP) is sought as their recovery brings enormous economic and regulatory benefits. Forecasting the quantities of WMP and their recoverable material content generates valuable data for the related stakeholders in the circular economy (CE) in the design and management of their supply chain networks. This paper presents an approach to determining the WMP quantity for Turkey considering the system from sales to end-of-life (EOL) stages and the years between 2001 and 2035. The proposed model includes two main parts: estimation and forecasting. Firstly, the generated WMP quantity is estimated based on dynamic lifespan and sales using the Distribution Delay (DD) Method considering the years from 2001 to 2020. To select the most suitable model for future projection, seven different time series methods (e.g., Simple Exponential Smoothing, Holt’s, Logistics, Gompertz, Logarithmic, Bass, and ARIMA models) are considered to estimate the generated WMP. For the given data, the Holt’s Method is determined to be the best method to forecast the WMP quantities for the years from 2021 to 2035. In addition, waste materials amount and revenue potentials are estimated for the years from 2001 to 2035. The WMP for Turkey is expected to be approximately 11.5 million units and has a 52 million US$ revenue potential in 2035. The present study contributes to the literature, as it is the first holistic forecasting study on the quantification of WMPs in Turkey. Moreover, since WMPs include remarkable recovery potential in terms of CE, the data and findings of this study may help policymakers, governments, producers, consumers, and all stakeholders to establish effective e-waste management approaches.

Simulating neutrino echoes induced by secret neutrino interactions

New neutrino interactions beyond the Standard Model (BSM) have been of much interest in not only particle physics but also cosmology and astroparticle physics. We numerically investigate the time delay distribution of astrophysical neutrinos that interact with the cosmic neutrino background. Using the Monte Carlo method, we develop a framework that enables us to simulate the time-dependent energy spectra of high-energy neutrinos that experience even multiple scatterings en route and to handle the sharp increase in the cross section at the resonance energy. As an example, we focus on the case of secret neutrino interactions with a scalar mediator. While we find the excellent agreement between analytical and simulation results for small optical depths, our simulations enable us to study optically thick cases that are not described by the simplest analytic estimates. Our simulations are used to understand effects of cosmological redshifts, neutrino spectra and flavors. The developments will be useful for probing BSM neutrino interactions with not only current neutrino detectors such as IceCube and Super-Kamiokande but also future neutrino detectors such as IceCube-Gen2 and Hyper-Kamiokande.