Waiting Time Distribution Research Articles

Giant Micropulse Emission in the Vela Pulsar at the C Band

Abstract We present here the analysis of giant micropulses from the Vela pulsar. A total of 4187 giant micropulses with peak flux density >2.5 Jy were detected during almost 4 hr of observations carried out with the Yunnan 40 m radio telescope at 6800 MHz. Nine of the giant micropulses arrived approximately 3–4 ms earlier than the peak of average pulse profile, longer than that at lower frequencies. The remaining giant micropulses were clustered into three distributions that correspond to three main emission regions, including four giant micropulses occurring on the trailing edge of the averaged profile. We find that the peak flux density distribution follows a power law with index α ≈ −4. Furthermore, a certain amount of memory is present from the giant micropulse waiting time distribution. Possible emission mechanisms are discussed.

Memory-Induced Bifurcation and Oscillations in the Chemical Brusselator Model

Previous studies assumed that the reaction processes in the chemical Brusselator model are memoryless or Markovian. However, as long as a reactant interacts with its environment, the reaction kinetics cannot be described as a memoryless process. This raises a question: how do we predict the behavior of the chemical Brusselator system with molecular memory characterized by nonexponential waiting-time distributions? Here, a novel technique is developed to address this question. This technique converts a non-Markovian question to a Markovian one by introducing effective transition rates that explicitly decode the memory effect. Based on this conversion, it is analytically shown that molecular memory can induce bifurcations and oscillations. Moreover, a set of sufficient conditions are derived, which can guarantee that the system of the rate equations for the Markovian reaction system generates oscillations via memory index-induced bifurcation. In turn, these conditions can guarantee that the original non-Markovian reaction system generates stochastic oscillations. Numerical simulation verifies the theoretical prediction. The overall analysis indicates that molecular memory is not a negligible factor affecting a chemical system’s behavior.

Full counting statistics of spin-flip and spin-conserving charge transitions in Pauli-spin blockade

We investigate the full counting statistics (FCS) of spin-conserving and spin-flip charge transitions in Pauli-spin blockade regime of a GaAs double quantum dot. A theoretical model is proposed to evaluate all spin-conserving and spin-flip tunnel rates, and to demonstrate the fundamental relation between FCS and waiting time distribution. We observe the remarkable features of parity effect and a tail structure in the constructed FCS, which do not appear in the Poisson distribution, and are originated from spin degeneracy and coexistence of slow and fast transitions, respectively. This study is potentially useful for elucidating the spin-related and other complex transition dynamics in quantum systems.

Modelling within-day ridehailing service provision with limited data

This paper proposes a holistic, within-day ridehailing service provision modelling approach, focusing on large-scale services with human-driven fleets. The model is powered by a full, two-year record of ridehailing trips in Toronto. Canada. Despite the abundant data, operations and fleet-related data still lacks, and uncertainty still exists concerning actual service provision deployment. Hence, a novel approach dealing with limited data availability is developed, which extracts implicit supply levels from trip-based demand data. The model is time-step driven, agent-based, and uses list-based data structures. It focuses on three key components: matching mechanisms, time intervals, and (several features of) driver activity. After testing various component combinations, a Hungarian matching algorithm, a normal distribution of driver work hours, and 5-minute time intervals allow close replication of observed wait time distributions and unique drivers per hour. Emergent model outputs also include VKT by vehicle states (idling, en-route, in-service), vehicle shifts and trip chains.

Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications

In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of occupancy models. Finally, we treat several examples in order to demonstrate how our theoretical results are employed for the investigation of the random occupancy models along with numerical results.

Generalized uncertainty relations for semi-Markov processes

The thermodynamic and kinetic uncertainty relations provide finite-time bounds on the observable fluctuation in Markov processes. Herein, we generalize these bounds for semi-Markov processes. Specifically, we prove that, unlike in the Markovian case, the fluctuation of time-antisymmetric observables is bounded not only by entropy production but also by a memory term. For generic observables, we analogously show that the fluctuation is bounded by both dynamical activity and a memory term. Our results indicate that memory plays an important role in the bounds. Interestingly, with a proper form of the waiting-time distribution, the memory can decrease the observable fluctuation. When the waiting-time distribution is Poissonian (i.e., the process becomes Markov), the memory terms vanish, and the derived bounds reduce to the conventional bounds.

Vapor-Deposited Glasses Highlight the Role of Density in Photostability.

Photoresponsive molecules can be integrated into glassy materials to probe the local environment and invoke responsive changes in polymer behavior. For example, recent experiments and simulations have studied increased stability in vapor-deposited glasses by examining the photoisomerization rate of a probe molecule. At the theoretical level, past work relied on coarse-grained simulations to explain the role of photoisomerization on glass behavior. In order to effectively exploit these molecular probes, an ability to quantify how the local environment influences the photoisomerization rate is needed. In this work, we present all-atom molecular-dynamics (MD) simulations of molecular glasses of photoresponsive azobenzene (AB) molecules. The stability of these in-silico samples is probed using photoisomerization, where AB molecules can undergo trans → cis transition upon light exposure. Vapor-deposited and bulk-cooled glasses of AB are simulated using a classical dihedral-switching potential developed by Böckmann et al. (J. Phys. Chem. A 2010, 114, 745-754) to model the photoisomerization process. The MD simulations include thousands of molecules and run for tens of nanoseconds. These size and time scales allow us to explore the broad distribution of photoisomerization wait times, which yields two results. First, the wait-time distributions for both physical vapor deposition and bulk-cooled glasses depend strongly on sample and local density, showing that density or local packing is a primary factor in glass stability against photoisomerization and the experimentally measured photoresponse. Second, the distribution follows a power-law with exponent b ≈ 1.25-1.3 that extends to longer times with increasing density. The power-law distribution suggests a connection with previous experiments that related barriers to photoisomerization with an effective photoisomerization temperature.

Stationary Analysis of an Infinite-Buffer D-MAP/D-MSP/1 Queueing System

This paper deals with the analysis of an infinite-buffer single-server D-MAP/D-MSP/1 queueing system. This queueing system can be analyzed by representing level-independent quasi-birth-and-death process in tridiagonal structure. The proposed analysis is based on the use of matrix-geometric method in conjunction with the spectral method to obtain the system-length distribution at outside observer’s epoch. We derive the stationary system-length distributions at random, prearrival, intermediate and post-departure epochs using the system-length distribution at outside observer’s epoch. The waiting-time distribution in the queue measured in slots of an arriving customer is also carried out. Computational procedures along with numerical results are provided to confirm the correctness of our analytical results.

Waiting-time statistics in magnetic systems

Many complex systems, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials, respond with a noise consisting of discrete avalanche-like events with broad range of sizes and durations, separated by waiting times. Here we focus on the waiting-time statistics in magnetic systems. By investigating the Barkhausen noise in amorphous and polycrystalline ferromagnetic films having different thicknesses, we uncover the form of the waiting-time distribution in time series recorded from the irregular and irreversible motion of magnetic domain walls. Further, we address the question of if the waiting-time distribution evolves with the threshold level, as well as with the film thickness and structural character of the materials. Our results, besides informing on the temporal avalanche correlations, disclose the waiting-time statistics in magnetic systems also bring fingerprints of the universality classes of Barkhausen avalanches and a dimensional crossover in the domain wall dynamics.

Short-term market efficiency indicator based on the waiting-time distribution

This paper presents a quantitative approach to measure market efficiency based on the waiting-time distribution. We use the spread between two classes of ordinary shares of Royal Dutch Shell Plc, and two listings of Australia and New Zealand Banking Group Limited to observe market inefficient states. We find that the parameter of the waiting-time distribution provides a quantitative measure of the market inefficiency and can be used as a short-term market efficiency indicator. This approach can be applied to liquid financial markets and has clear implications for the investors, hedgers, regulators and policymakers.

Markovian modeling for dependent interrecurrence times in bladder cancer

A methodology to model a process in which repeated events occur is presented. The context is the evolution of non‐muscle‐invasive bladder carcinoma (NMIBC), characterized by recurrent relapses. It is based on the statistical flowgraph approach, a technique specifically suited for semi‐Markov processes. A very useful feature of the flowgraph framework is that it naturally incorporates the management of censored data. However, this approach presents two difficulties with the process to be modeled. On one hand, the management of covariates is not straightforward. However, it is of great interest to know how the characteristics of a certain patient influence the evolution of the disease. On the other hand, repeated events on the same subject are generally not independent, in which case the semi‐Markov framework is not sufficient because the semi‐Markov assumption implies independence among waiting time distributions. We solve this issue by extending the flowgraph methodology using the Markovian arrival process (MAP), which does successfully model the dependence between events. Along the way, we provide a procedure to consider covariates and censored times in MAPs, a pending task needed in this field. In short, we have managed to extend the flowgraph methodology beyond the semi‐Markovian framework, simplifying the incorporation of covariates and keeping the management of censored times. All of which has allowed us to build a multistate model of the evolution of NMIBC. The developed model allows us to compute the Survival function for any evolution of a patient with specific clinic‐pathological characteristics in this primary tumor.

Field observation and analysis of waiting passengers at subway platform — A case study of Beijing subway stations

As a common human activity in the subway platform, waiting occupies a large amount of passengers’ time and plays an important role in the aggregation, circulation, and segregation of passenger flows. The initial spatial distribution of waiting passengers at the subway platform may contribute significantly to the operational efficiency of the subway station. In this paper, we explore the behaviors of waiting passengers by field observations and video recordings at two of Beijing’s subway stations under normal conditions and intervention of guide. The data, including distribution of waiting pedestrians on waiting zones, percentages of waiting modes under different density levels, as well as distributions of distance headway, movement speed, and mean waiting time are collected and analyzed in two cases. Quantitative analyses of the collected data of waiting passengers under normal and intervention conditions are conducted to assess the impact of the guide on the behavior of waiting passengers by comparing the indicators of the number of passengers in each waiting zone, percentages of waiting modes, distance headway, as well as mean waiting time. Through analyses of the collected data, the behavioral characteristics of waiting passengers under the tactical and operational levels are revealed. The findings of this paper are beneficial to the organization of waiting passengers and the improvement of operational efficiency of subway stations.

Self-excitation in the solar flare waiting time distribution

Solar flares release high amounts of energy into the solar system and can negatively impact earth based systems through their effects on satellites and power systems. It is hence important to understand and forecast their occurrence. The solar flare waiting time distribution (WTD) defines the amount of time which elapses between the occurrence of successive flares and hence provides a starting point for forecasts and risk assessment. Previous research has hypothesized that the observed WTD can be derived from a simple model which posits that flares follow a nonstationary Poisson process. This Poissonian assumption has implications for fundamental physical theories about the origin of flares, since it is a direct consequence of the widely studied avalanche model. However in this paper we call the Poissonian assumption into question, by showing that the occurrence of solar flares seems to have a substantial amount of burstiness and self-excitation that continues to exist even when controlling for the solar cycle. This leads to a strong non-Poissonian dependence between the occurrence time of successive flares.

Observation and Modeling of High-temperature Solar Active Region Emission during the High-resolution Coronal Imager Flight of 2018 May 29

Abstract Excellent coordinated observations of NOAA active region 12712 were obtained during the flight of the High-resolution Coronal Imager (Hi-C) sounding rocket on 2018 May 29. This region displayed a typical active region core structure with relatively short, high-temperature loops crossing the polarity inversion line and bright “moss” located at the footpoints of these loops. The differential emission measure (DEM) in the active region core is very sharply peaked at about 4 MK. Further, there is little evidence for impulsive heating events in the moss, even at the high spatial resolution and cadence of Hi-C. This suggests that active region core heating is occurring at a high frequency and keeping the loops close to equilibrium. To create a time-dependent simulation of the active region core, we combine nonlinear force-free extrapolations of the measured magnetic field with a heating rate that is dependent on the field strength and loop length and has a Poisson waiting time distribution. We use the approximate solutions to the hydrodynamic loop equations to simulate the full ensemble of active region core loops for a range of heating parameters. In all cases, we find that high-frequency heating provides the best match to the observed DEM. For selected field lines, we solve the full hydrodynamic loop equations, including radiative transfer in the chromosphere, to simulate transition region and chromospheric emission. We find that for heating scenarios consistent with the DEM, classical signatures of energy release, such as transition region brightenings and chromospheric evaporation, are weak, suggesting that they would be difficult to detect.

Analytical results for non-Markovian models of bursty gene expression.

Modeling stochastic gene expression has long relied on Markovian hypothesis. In recent years, however, this hypothesis is challenged by the increasing availability of time-resolved data. Correspondingly, there is considerable interest in understanding how non-Markovian reaction kinetics of gene expression impact protein variations across a population of genetically identical cells. Here, we analyze a stochastic model of gene expression with arbitrary waiting-time distributions, which includes existing gene models as its special cases. We find that stationary probabilistic behavior of this non-Markovian system is exactly the same as that of an equivalent Markovian system with the same substrates. Based on this fact, we derive analytical results, which provide insight into the roles of feedback regulation and molecular memory in controlling the protein noise and properties of the steady states, which are inaccessible via existing methodology. Our results also provide quantitative insight into diverse cellular processes involving stochastic sources of gene expression and molecular memory.

Using the waiting time distribution with random index dates to estimate prescription durations in the presence of seasonal stockpiling.

A pervasive problem in registry-based pharmacoepidemiological studies is what exposure duration to assign to individual prescriptions. The parametric waiting time distribution (WTD) has been proposed as a method to estimate such durations. However, when prescription durations vary due to seasonal stockpiling, WTD estimates will vary with choice of index date. To counter this, we propose using random index dates. Within a calendar period of a given length, δ, we randomly sample individual index dates. We include the last prescription redemption prior to the index date in the analysis. Only redemptions within distance δ of the index date are included. In a simulation study with varying types and degrees of stockpiling at the end of the year, we investigated bias and precision of the reverse WTD with fixed and random index dates, respectively. In addition, we applied the new method to estimate durations of Norwegian warfarin prescriptions in 2014. In simulation settings with stockpiling, the reverse WTD with random index dates had low relative biases (-0.65% to 6.64%) and high coverage probabilities (92.0% to 95.3%), although when stockpiling was pronounced, coverage probabilities decreased (2.7% to 85.8%). Using a fixed index date was inferior. The estimated duration of warfarin prescriptions in Norway using random index dates was 131 (130; 132) days. In the presence of seasonal stockpiling, the WTD with random index dates provides estimates of prescription durations, which are more stable, less biased and with better coverage when compared to using a fixed index date.

Statistical Analysis of Acoustic Emission in Uniaxial Compression of Tectonic and Non-Tectonic Coal

Tectonic coal has become an important research topic for preventing coal mine disasters and for exploring and developing coal-bed methane resources. To investigate the mechanical and acoustic properties of tectonic coal, we conducted a uniaxial compression test for tectonic and non-tectonic coal, and acoustic emission (AE) signals have been simultaneous captured in the compression process. The AE energy and waiting time of events have been studied statistically. The results show that the probability density function of AE energy follows the power law distribution well, and indicates that the AE of non-tectonic coal is mainly generated from the fracture source, while the probability density function distribution of tectonic coal is the mixing result of fracture and friction effects. Only the waiting time distribution of non-tectonic coal follows the typical brittle fracture’s double power law behavior. The waiting time distribution of tectonic coal shows the single power law with a smaller exponent value, which is associated with the granular microstructure of tectonic coal. The distribution of aftershock and Båth’s law are not sensitive to microstructure, and are identical for non-tectonic and tectonic coal. At last, the correlation dimension results for the spatial distribution of AE hypocenters indicated that the rough continuous decrease in multifractal dimension might be a precursor to devastating destruction.

Fluidization of spherical versus elongated particles - experimental investigation using X-ray tomography

In many industrial applications, particles used in fluidized bed clearly deviate from ideal spheres. This leads to an increasing need for better understanding and developing better simulation models for fluidization of non-spherical particles. So far, the literature is quite scarce when it comes to experimental results which can be used for validation of numerical models. Also, the exact difference in fluidization behavior between spherical and elongated particles in dense fluidizing conditions is not well understood. In this work, we apply X-ray tomography to compare the fluidization behavior of a bed of a Geldart D-type spherical particles of aspect ratio 4 to that of volume equivalent spherocylindrical particles for different gas velocities. Even though the beds of both spherical and elongated particles are operating in the slugging regime, due their size and high bed height to width ratio, we see clear differences in their fluidization behavior. Our results indicate that the bed of elongated particles is slugging less than the one with spherical particles. This is indicated by a lower average bubble size in the case of elongated particles, together with a higher bubble rise velocity. The bed of elongated particles has a considerably higher distribution of small and medium bubbles. The slug waiting time distribution and slug frequency distribution indicate that a bed of elongated particles periodically switches between slugging and turbulent fluidization, unlike the bed of spherical particles which remains in the constant slugging regime.

Numerical Scheme for the Fokker–Planck Equations Describing Anomalous Diffusions with Two Internal States

Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the distribution of positions of the particles [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)]. In this paper, we first develop the Sobolev regularity of the FFPEs with two internal states, including the homogeneous problem with smooth and nonsmooth initial values and the inhomogeneous problem with vanishing initial value, and then we design the numerical scheme for the system of fractional partial differential equations based on the finite element method for the space derivatives and convolution quadrature for the time fractional derivatives. The optimal error estimates of the scheme under the above three different conditions are provided for both space semidiscrete and fully discrete schemes. Finally, one- and two-dimensional numerical experiments are performed to confirm our theoretical analysis and the predicted convergence order.