Delay Distribution Research Articles

A novel particle filtering for nonlinear systems with multi-step randomly delayed measurements

For nonlinear discrete-time systems where measurements can be randomly delayed by multiple sampling periods, measurements are dependent conditioned on the state trajectory, and the dependence becomes more complicated with the increase of step of random delay. A particle filtering for this system is developed, which is novel in that the likelihood is computed allowing multi step of delay and dependence of measurements. Multi step of delay is dealt with through utilizing the formula of total probability skillfully, and dependence is dealt with through estimating the filtering probability distribution of random delay. The novel particle filtering is applied to two examples to validate its effectiveness and superiority.

An approximate marginal spread computation approach for the budgeted influence maximization with delay

Given a social network of users with selection cost and a fixed budget, the problem of Budgeted Influence Maximization finds a subset of the nodes ( known as seed nodes) for initial activation to maximize the influence, such that the total selection cost is within the allocated budget. Existing solution methodologies for this problem make two assumptions, which are not applicable to real-life situations. First, an influenced node of the current time stamp can trigger only once in the next time stamp to its inactive neighbors and the other one is the diffusion process continues forever. To make the problem more practical, in this paper, we introduce the Budgeted Influence Maximization with Delay by relaxing the single time triggering constraint and imposing an additional constraint for maximum allowable diffusion time. For this purpose, we consider a delay distribution for each edge of the network, and consider a node is influenced, if it is so, within the allowable diffusion time. We first propose an incremental greedy strategy for solving this problem, which works based on the approximate computation of marginal gain in influence spread. Next, we make two subsequent improvements of this algorithm in terms of efficiency by exploiting the sub-modularity property of the time delayed influence function. We implement the proposed methodologies with three benchmark datasets. Reported results show that the seed set selected by the proposed methodologies can lead to more number of influenced nodes compared to that obtained by other baseline methods. We also observe that between the two improvised methodologies, the second one is more efficient for the larger datasets.

Stability and bifurcations in Wilson-Cowan systems with distributed delays, and an application to basal ganglia interactions

The traditional Wilson-Cowan model of excitatory and inhibitory meanfield interactions in neuronal populations considers a weak Gamma distribution of time delays when processing inputs, and is obtained via a time-coarse graining technique that averages the population response. Previous analyses of the stability of the Wilson-Cowan model focused on more simplified cases, where the delays were either not present, constant or were of a specific type. Since these simplifications may significantly alter the behavior of the model, we focus on understanding the behavior of the system before time-course graining, and for a wider range of delay distributions.For these generalized delay equations, we perform stability and bifurcation analyses with respect to parameters that capture both the coupling profile, and the time delay. The investigation is done through the examination of the system’s associated characteristic equation. Under mild assumptions, we give complete mathematical proofs of our theoretical results, for the model with general delay distributions and prove the transversality condition for the possible Hopf bifurcations, in a generalized context. The stability region in this parameter space is described theoretically for several types of delay kernels, and numerical simulations are presented to substantiate the theoretical results.We found that the stability regions and bifurcations differ significantly between different types of delay distributions: weak Gamma distributions promote stable firing rates, while strong Gamma distributions are associated with regular oscillations, and Dirac distributions appear to facilitate more complex aperiodic patterns. This supports the unexplored possibility of different delay distributions being used as the substrate for different functional behaviors, and emphasizes the importance of a careful choice of the delay kernel in the mathematical model.We illustrate these theoretical principles in an application to a basal ganglia circuit, in which β-band oscillations have been associated with Parkinson’s Disease.

Public Transport Network Vulnerability and Delay Distribution among Travelers

Methodologies and approaches for assessing the vulnerability of a public transport network are generally based on quantifying the average delay generated for passengers by some type of disruption. In this work, a novel methodology is proposed, which combines the traditional approach, based on the quantitative evaluation of averaged disruption effects, with the analysis of the asymmetry of effects among users, by means of Lorenz curves and Gini index. This allows evaluating whether the negative consequences of disruptions are equally spread among passengers or if differences exist. The results obtained show the potential of the proposed method to provide better knowledge about the effects of a disruption on a public transport network. Particularly, it emerged that disrupted scenarios that appear similar in terms of average impacts are actually very different in terms of the asymmetry of effects among users.

Subjective Quality Assessment for Cloud Gaming

Using subjective testing, we study the effect of the network parameters, delay and packet loss ratio, on the QoE of cloud gaming. We studied three different games, selected based on genre, popularity, content complexity and pace, and tested them in a controlled network environment, using a novel emulator to create realistic lognormal delay distributions instead of relying on a static mean delay, as used previously; we also used Parsec as a good representative of the state of the art. We captured user ratings on an ordinal Absolute Category Rating scale for three quality dimensions: Video QoE, Game-Playability QoE, and Overall QoE. We show that Mean Opinion Scores (MOS) for the game with the highest levels of content complexity and pace are most severely affected by network impairments. We also show that the QoE of interactive cloud applications rely more on the game playability than the video quality of the game. Unlike earlier studies, the differences in MOS are validated using the distributions of the underlying dimensions. A Wilcoxon Signed-Rank test showed that the distributions of Video QoE and Game Playability QoE are not significantly different.

Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method

Abstract This article first introduces neural networks and their characteristics. Based on a comparison of the structure and function of biological neurons and artificial neurons, it focuses on the structure, classification, activation rules, and learning rules of neural network models. Based on the existing literature, this article adds a distributed time lag term of the neural network system. In the actual problem, history has a very important influence on the current change situation, and it is not only at a specific time in the past. It has an impact on the current state change rate. Therefore, based on the existing literature that only has discrete time lags, this paper adds distributed time lags. Such neural network systems can better reflect real-world problems. In this paper, we use three different inequality scaling methods to study the existence, uniqueness, and global asymptotic stability of a class of neural network systems with mixed delays and uncertain parameters. First, using the principle of homeomorphism, a new upper-norm norm is introduced for the correlation matrix of the neural network, and enough conditions for the existence of unique equilibrium points in several neural network systems are given. Under these conditions, the appropriate Lyapunov is used. Krasovskii functional, we prove that the equilibrium point of the neural network system is globally robust and stable. Numerical experiments show that the stability conditions of the neural network system we obtained are feasible, and the conservativeness of the stability conditions of the neural network system is reduced. Finally, some applications and problems of neural network models in psychology are briefly discussed.

Delay Propagation in Large Railway Networks with Data-Driven Bayesian Modeling

Reliability and punctuality are the key evaluation criteria in railway service for both passengers and operators. Delays spanning over spatial and temporal dimensions significantly affect the reliability and punctuality level of train operation. The optimization of capacity utilization and timetable design requires the prediction of the reliability and punctuality level of train operations, which is determined by train delays and delay propagation. To predict the punctuality level of train operations, the distributions of arrival and departure delays must be estimated as realistically as possible by taking into account the complex railway network structure and different types of delays caused by route conflict and connected trips. This paper aims to predict the propagation of delays on the railway network in the Greater Sydney area by developing a conditional Bayesian model. In the model, the propagation satisfies the Markov property if one can predict future delay propagation in the network based solely on its present state just as well as one could knowing the process’s full history, so that it is independent of such historical procedures. Meanwhile, we consider the throughput estimation for the cases of delay caused by interchange line conflicts and train connection in this model. To the best of the authors’ knowledge, this is the first work of data-driven delay propagation modeling that examines both spatial and temporal dimensions under four different scenarios for railway networks. Implementation on real-world railway network operation data shows the feasibility and accuracy of the proposed model compared with traditional probability models.

Stochastic Network Calculus Model for Delay Distribution of Time Division Multiple Access and Carrier Sense Multiple Access in Underwater Acoustic Wireless Communication

Underwater Acoustic wireless communication becomes a popular research area for transmitting and receiving data between the communicators in the ocean environment. High accuracy in data communication can be succeeded by proficient modeling of carrier sense multiple access and time division access. For such innovations, the system has to proceed with an appropriate framework to make constant data traffic and limitations on start to finish data traffic delays. There are two major wireless communication multiple access methods that can be utilized in real-time underwater networks. One of the multiple access schemes is TDMA and another one is CSMA/CA. This paper concentrated on the modeling of TDMA and CSMA/CA also proposes the comparison of delay (end-end) of both multiple access protocols. The results using SNC to obtain delay bounds and are associated with simulation. The results show TDMA has a lesser efficiency than CSMA/CA in the acoustic environment.

Non-Statistical Method for Validation the Time Characteristics of Digital Control Systems with a Cyclic Processing Algorithm

The paper discusses the problem of performance and timing parameters with respect to the validation of digital instrumentation and control systems (I&C). Statistical methods often implicitly assume that the probability distribution law of the estimated parameters is close to normal. Thus, the confidence intervals for the parameter are determined on the grounds of this assumption. However, we encountered cases when the delay distribution law in I&C is not normal. In these cases, we used the non-statistical network calculus method for time parameters estimation. The network calculus method is well elaborated for lossless digital system models with seamless processing algorithm depending only on data volume. We consider the extension of the method to the case of I&C systems with considerable changes in the data flow and content-dependent processing disciplines. The model is restricted to systems with cyclic processing algorithms and fast network connections. Network calculus describes the data flow and system parameters in terms of flow envelopes and service curves that are generally unknown in advance. In this paper, we define equations that allow the calculation of these characteristics from experimental data. The correspondence of the Network Calculus and classical statistical estimation methods is discussed. Additionally, we give an example of model application to a real I&C system.

The impact of turbulent mixing on the galactic r-process enrichment by binary neutron star mergers

ABSTRACT We study the enrichment of the interstellar medium (ISM) with rapid neutron capture (r-process) elements produced in binary neutron star (BNS) mergers. We use a semi-analytic model to describe galactic evolution, with merger rates and time delay distributions of BNS mergers consistent with the latest population synthesis models. In order to study the dispersion of the relative abundances of r-process elements and iron, we applied a turbulent mixing scheme, where the freshly synthesized elements are gradually dispersed in the ISM. We show that within our model the abundances observed in Milky Way stars, in particular the scatter at low metallicities, can be entirely explained by BNS mergers. Our results suggest that BNS mergers could be the dominant source of r-process elements in the Galaxy.

Parameterization of channel characteristics based on statistical analysis at refuge chamber

In view of the wireless channel complexity in refuge chamber environments, we parameterize the channel characteristics for reliable signal propagation under line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. According to the Saleh-Valenzuela channel model, the multipath components (MPCs) arrive at the receiver in cluster form. Therefore, clustering algorithms are required to identify clusters. However, the drawback of conventional KMeans and KPowerMeans algorithms is their limitation to an a priori cluster number. In this paper, we propose a clustering algorithm that uses a fitted curve to intersect the slope curve of the normalized power delay profile (PDP). The effectiveness of the proposed algorithm is verified based on the statistical measurement data by comparison with the conventional KMeans and KPowerMeans algorithms. Based on the clustering results, we explore the distribution of the cluster arrival delay and cluster power. We then analyze the probability density function (PDF) of the first MPC arrival delay in each cluster by comparison with conventional models. Finally, we investigate the path loss exponent (PLE) and shadow fading factor of the large-scale path loss. The outcomes of this paper is in the provision of theoretical support for mobile communications in refuge chamber environments.

Bayesian back-calculation and nowcasting for line list data during the COVID-19 pandemic.

Surveillance is critical to mounting an appropriate and effective response to pandemics. However, aggregated case report data suffers from reporting delays and can lead to misleading inferences. Different from aggregated case report data, line list data is a table contains individual features such as dates of symptom onset and reporting for each reported case and a good source for modeling delays. Current methods for modeling reporting delays are not particularly appropriate for line list data, which typically has missing symptom onset dates that are non-ignorable for modeling reporting delays. In this paper, we develop a Bayesian approach that dynamically integrates imputation and estimation for line list data. Specifically, this Bayesian approach can accurately estimate the epidemic curve and instantaneous reproduction numbers, even with most symptom onset dates missing. The Bayesian approach is also robust to deviations from model assumptions, such as changes in the reporting delay distribution or incorrect specification of the maximum reporting delay. We apply the Bayesian approach to COVID-19 line list data in Massachusetts and find the reproduction number estimates correspond more closely to the control measures than the estimates based on the reported curve.

Reliable sampled‐data control for nonlinear switched systems with packet dropout and multiple sampling periods

This paper addresses the problems of exponential mean‐square stability and reliable sampling data control design for nonlinear switched systems. First, a common model of actuator fault is used to give a description of the nonlinear of controller. The packet loss is assumed to be affected by multiple sampling periods. By input delay method, probability distribution of stochastic delay which takes value in m (m ≥ 2) given intervals is obtained. Second, using average dwell time method, sufficient conditions in the form of linear matrix inequality (LMI) are obtained to ensure the stability of considered switched systems. Moreover, an illustration example is used to demonstrate the validity of the sampling controller designed.

Measurement and simulation of the neutron propagation time distribution inside a neutron monitor

Using a setup for testing a prototype for a satellite-borne cosmic-ray ion detector, we have operated a stack of scintillator and silicon detectors on top of the Princess Sirindhorn Neutron Monitor (PSNM), an NM64 detector at 2560-m altitude at Doi Inthanon, Thailand (18.59∘N, 98.49∘E). Monte Carlo simulations have indicated that about 15% of the neutron counts by PSNM are due to interactions (mostly in the lead producer) of GeV-range protons among the atmospheric secondary particles from cosmic ray showers, which can be detected by the scintillator and silicon detectors. Those detectors can provide a timing trigger for measurement of the propagation time distribution of such neutrons as they scatter and propagate through the NM64, processes that are similar whether the interaction was initiated by an energetic proton (for 15% of the count rate) or neutron (for 80% of the count rate). This propagation time distribution underlies the time delay distribution between successive neutron counts, from which we can determine the leader fraction (inverse multiplicity), which has been used to monitor Galactic cosmic ray spectral variations over ∼1-40 GV. Here we have measured and characterized the propagation time distribution from both the experimental setup and Monte Carlo simulations of atmospheric secondary particle detection. We confirm a known propagation time distribution with a peak (at ≈70 μs) and tail over a few ms, dominated by neutron counts. We fit this distribution using an analytic model of neutron diffusion and absorption, for both experimental and Monte Carlo results. In addition we identify a group of prompt neutron monitor pulses that arrive within 20 μs of the charged-particle trigger, of which a substantial fraction can be attributed to charged-particle ionization in a proportional counter, according to both experimental and Monte Carlo results. Prompt pulses, either due to neutrons or charged-particle ionization, are associated with much higher mean multiplicity than typical pulses. These results validate and point the way to some improvements in Monte Carlo simulations and the resulting yield functions used to interpret the neutron monitor count rate and leader fraction.

Delay distributions on encrypted real-time traffics

Real-time streams are common for nowadays communication for both data and video. Real-time data communication such as chat application and telemetry, as well as real-time video communication such as video call, video conference, or monitoring video are prone to the third party attacked. End to end encryption has been considered as the most realistic solution such as applied by WhatsApp so that the transmitted data is difficult to be revealed by the attacker. Since encryption and decryption processes injected additional delay, the algorithm should be fast enough to avoid inconvenience to users. This paper examines delay distribution for encrypted real-time traffics. The simulation shows that the decryption contributed the most to the end to end delay. Decryption delay is about 4.58 times higher than encryption and transmission delay. Although assessment involves only two links, the complex network has relatively lower than the obtained decryption delay. Meanwhile, encryption contributed only about 0.2% to the overall end to end delay.

Time-resolved analysis of negative pulsed discharges in water: streamer initiation and propagation modes

Analyses of the initiation and propagation-mode transitions of negative streamers are essential to develop a thorough understanding of underwater pulsed discharges. This paper presents experimental observations of negative streamers in deionized water performed using time-resolved visualization and electrical measurements. Based on the distributions of discharge inception delay and quantitative calculations of the ionization initiation fields, a streamer initiation model combining Zener ionization and field emission processes is proposed to account for discharges with short inception delays (<200 ns). Joule heating is the main mechanism responsible for discharges with an inception delay on the order of microseconds. The evolutions of bushy streamer morphology show that streamers exhibit more uniform structures under higher voltages, as most of the streamer branches grow simultaneously. A large-area discharge of bushy streamers is observed and is speculated to be closely related to the charge dynamics at the gas/liquid interface. The propagation of filamentary streamers and the transitions from filamentary to bushy streamers are presented. The redistribution of deposited charge and mitigation of the electric field during branching are the main causes for the mode transitions of streamers.

The Time Delay Distribution and Formation Metallicity of LIGO-Virgo’s Binary Black Holes

Abstract We derive the first constraints on the time delay distribution of binary black hole (BBH) mergers using the LIGO-Virgo Gravitational-Wave Transient Catalog. Assuming that the progenitor formation rate follows the star formation rate (SFR), the data favor that 43%–100% of mergers have delay times &lt;4.5 Gyr (90% credibility). Adopting a model for the metallicity evolution, we derive joint constraints for the metallicity-dependence of the BBH formation efficiency and the distribution of time delays between formation and merger. Short time delays are favored regardless of the assumed metallicity dependence, although the preference for short delays weakens as we consider stricter low-metallicity thresholds for BBH formation. For a p(τ) ∝ τ −1 time delay distribution and a progenitor formation rate that follows the SFR without metallicity dependence, we find that τ min &lt; 2.2 Gyr, whereas considering only the low-metallicity Z &lt; 0.3 Z ⊙ SFR, τ min &lt; 3.0 Gyr (90% credibility). Alternatively, if we assume long time delays, the progenitor formation rate must peak at higher redshifts than the SFR. For example, for a p(τ) ∝ τ −1 time delay distribution with τ min = 4 Gyr, the inferred progenitor rate peaks at z &gt; 3.9 (90% credibility). Finally, we explore whether the inferred formation rate and time delay distribution vary with BBH mass.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay.

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system’s linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Probabilistic Flight Delay Predictions Using Machine Learning and Applications to the Flight-to-Gate Assignment Problem

The problem of flight delay prediction is approached most often by predicting a delay class or value. However, the aviation industry can benefit greatly from probabilistic delay predictions on an individual flight basis, as these give insight into the uncertainty of the delay predictions. Therefore, in this study, two probabilistic forecasting algorithms, Mixture Density Networks and Random Forest regression, are applied to predict flight delays at a European airport. The algorithms estimate well the distribution of arrival and departure flight delays with a Mean Absolute Error of less than 15 min. To illustrate the utility of the estimated delay distributions, we integrate these probabilistic predictions into a probabilistic flight-to-gate assignment problem. The objective of this problem is to increase the robustness of flight-to-gate assignments. Considering probabilistic delay predictions, our proposed flight-to-gate assignment model reduces the number of conflicted aircraft by up to 74% when compared to a deterministic flight-to-gate assignment model. In general, the results illustrate the utility of considering probabilistic forecasting for robust airport operations’ optimization.

Wastewater monitoring outperforms case numbers as a tool to track COVID-19 incidence dynamics when test positivity rates are high

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2–4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.