Probability Distribution Of Time Research Articles

Personalized medicine comes to a blood center near you

Personalized medicine comes to a blood center near you

A Non-Extensive Statistical Physics View of the Temporal Properties of the Recent Aftershock Sequences of Strong Earthquakes in Greece

Greece is one of Europe’s most seismically active areas. Seismic activity in Greece has been characterized by a series of strong earthquakes with magnitudes up to Mw = 7.0 over the last five years. In this article we focus on these strong events, namely the Mw6.0 Arkalochori (27 September 2021), the Mw6.3 Elassona (3 March 2021), the Mw7.0 Samos (30 October 2020), the Mw5.1 Parnitha (19 July 2019), the Mw6.6 Zakynthos (25 October 2018), the Mw6.5 Kos (20 July 2017) and the Mw6.1 Mytilene (12 June 2017) earthquakes. Based on the probability distributions of interevent times between the successive aftershock events, we investigate the temporal evolution of their aftershock sequences. We use a statistical mechanics model developed in the framework of Non-Extensive Statistical Physics (NESP) to approach the observed distributions. NESP provides a strictly necessary generalization of Boltzmann–Gibbs statistical mechanics for complex systems with memory effects, (multi)fractal geometries, and long-range interactions. We show how the NESP applicable to the temporal evolution of recent aftershock sequences in Greece, as well as the existence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for longer interevent times. The observed behavior is further discussed in terms of superstatistics. In this way a stochastic mechanism with memory effects that can produce the observed scaling behavior is demonstrated. To conclude, seismic activity in Greece presents a series of significant earthquakes over the last five years. We focus on strong earthquakes, and we study the temporal evolution of aftershock sequences of them using a statistical mechanics model. The non-extensive parameter q related with the interevent times distribution varies between 1.62 and 1.71, which suggests a system with about one degree of freedom.

Throughput Analysis on Slotted Underwater Acoustic Sensor Networks With Guard Time

A guard time is a short time interval that is added between packet transmissions, and has been applied in time- slotted underwater acoustic sensor networks (UASNs) to balance the transmission rate and the inter-slot interference. In this article, we take a physical-layer approach and investigate the throughput performance in time-slotted UASN with guard time. Based on the geographical node distribution, we first derive the probability distribution of the arrival time of an interfering packet and further the distribution of the packet overlap duration. We then derive the expression of the probability density functions (pdfs) of the signal-to-interference-plus-noise ratio (SINR). Expressions for the outage probability and the normalized throughput of a typical link between two nodes are also obtained. We show that when the length of guard time is properly selected, time-slotted network with guard time has higher throughput than those without guard time. Simulation results validate the theoretical results and illustrate typical features of the interference in an underwater network.

A stochastic Petri Net‐based approach for operational performance estimation of quay cranes

AbstractReliability, availability, and maintainability (RAM) of quay cranes (QCs) are essential for an effective port operation. This study estimates operational RAM of QCs using the Stochastic Petri Net (SPN) modelling. Asset Performance Assessment (APA) was performed to conduct the study by a SPN model. Based on the operation and maintenance data, probability distributions of Mean Time Between Failure (MTBF) and Mean Time to Repair (MTTR) is determined by Goodness of Fit Test of Anderson Darling. Subsequently, these distributions are applied in APA to determine the frequencies of failure/breakdowns, duration of downtimes, availability, and reliability with the assistance of the SPN model and Monte Carlo Simulation. The availability of the analysed QC is 0.97 or 97%. The results of this work are verified by the comparison with historical data. The outcomes of this paper contribute to reliability, availability, maintainability, and risk management of QCs.

A Pareto–Poisson process model for intermittent debris flow surges developing from slope failures

Many debris flows originate from shallow slope failures over the source area of valley and move in form of successive surges. In order to understand the behavior of such failures, we conducted seven sets of experiments of rainfall-induced soil failures in a 4 × 8 m spot on a slope under different rainfall intensities ranging from 12 to 60 mm/h, according to the local rainfall conditions in the valley of Jiangjia Gully, and this work is based on the experimental data. It is found that the failures are realization of a Poisson process with failure volume satisfying the Pareto distribution, thus the failure process can be simulated using a combinative Pareto-Poisson process (PPP) model. The PPP model incorporates a Poisson process determining the failure time, and a Pareto distribution characterizing the fluctuation of failure volume. The developing course of a debris flow surge is reduced to the hierarchic evolution of the failures from their source to the mainstream, which amounts to a cascade thinning process of the Poisson sequence in the PPP model framework. Given the controlling parameters (i.e., the Poisson intensity, Pareto distribution parameters, and thinning ratio), the model is capable of predicting surge sequences that agree well with the monitored surges in terms of time interval, magnitude fluctuation, and probability distribution. This study represents the first attempt to formulate a stochastic framework for debris flows developing from source to mainstream, which applies to debris flows fed by discontinuous material supplies from shallow slope failures.

Optimal Observational Scheduling Framework for Binary and Multiple Stellar Systems* *Based in part on observations obtained at the international Gemini Observatory, a program of NSF's NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United

The optimal instant of observation of astrophysical phenomena for objects that vary on human timescales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper, we address this problem in the case of tight visual binary systems through a Bayesian framework based on the maximum entropy sampling principle. Our proposed information-driven methodology exploits the periodic structure of binary systems to provide a computationally efficient estimation of the probability distribution of the optimal observation time. We show the optimality of the proposed sampling methodology in the Bayes sense and its effectiveness through direct numerical experiments. We successfully apply our scheme to the study of two visual-spectroscopic binaries and one purely astrometric triple hierarchical system. We note that our methodology can be applied to any time-evolving phenomena, a particularly interesting application in the era of dedicated surveys, where a definition of the cadence of observations can have a crucial impact on achieving the science goals.

Strategies and first-absorption times in the random walk game

Purpose of this work is to determine the average time to reach the boundaries, as well as to identify the strategy in the game between two players, controlling point movements on the finite square lattice using an independent choice of strategies. One player wants to survive, i. e., to stay within the interior of the square, as long as possible, while his opponent wants to reach the absorbing boundary. A game starts from the center of the square and every next movement of the point is determined by independent strategy choices made by the players. The value of the game is the survival time that is the number of steps before the absorption happens. In addition we present series of experiments involving both human players and an autonomous agent (bot) and analysis of the survival time probability distributions. Methods. In this work, methods of the theory of absorbing Markov chains were used to analyze strategies and absorption times, as well as the Monte Carlo method to simulate trajectories. Additionally, a large-scale field experiment was conducted using the developed mobile application. Results. The players’ strategies are experimentally obtained for the cases of playing against an autonomous agent (bot), as well as human players against each other. A comparison with optimal strategies and a random walk is made: the difference between the experimental strategies and the optimal ones is shown, however, the resulting strategies show a much better result of games than a simple random walk. In addition, especially long-running games do not show the Markovian property in case of the simulation corresponding strategies. Conclusion. The sampled histograms indicate that the game-driven walks are more complex than a random walk on a finite lattice but it can be reproduced with a Markov Chain model.

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences.

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences.

Variability of the times remaining in surgical cases and the importance of knowing when closure has started

BackgroundWhen a patient enters the operating room, the projected time to room exit is the time of room entry plus the estimated case duration. Subsequent estimates are provided based on a probability distribution for time remaining in the case, conditional on the interval from room entry. There have been several recent studies investigating and showing good accuracy of different suitable methods. However, it is unknown whether and why these methods are useful compared with the historical data and original surgeon/ scheduler estimate known before the case started. We hypothesized that knowing when closure has started, patient has been extubated, etc., gives substantive incremental information. MethodsOur retrospective cohort study included all 23,343 surgical cases at a large hospital over 4.2 years wherein each case's surgeon scheduled the procedure ≥29 times. The sample size was n = 244 combinations of scheduled Current Procedural Terminology code and surgeon. ResultsVariability in the logarithmic scale (i.e., proportional variability in the time scale) increased progressively as cases advanced. Specifically, the 90th percentiles of times to operating room exit were ≈40% longer than 50th percentiles (medians) at the start of cases versus 142% longer at the time of the start of closure. These ratios were less at starts of cases than at closures for 99.2% of n = 244 combinations (P <0.0001). The 5th percentiles were ≈32% briefer than 50th percentiles at the start of cases versus 85% briefer at the time of the start of closure. These ratios were less at starts of cases than at closures for 100% of combinations (P <0.0001). ConclusionsThere is considerable information value in knowing when key milestones have occurred near the end of cases that managers can use for quality decision-making (e.g., when closure has started). Organizations should document these milestones in real-time.

Flight reliability during periods of high uncertainty

In times of great uncertainty for the airline industry, travelers are in search of reliable itineraries now more than ever. With condensed airline schedules and less options, air travelers must rely on making flight connections and manage layover times to arrive at their final destination on time. In an era with readily available information, passengers expect accurate and transparent reliability information to help improve decision making for multi-leg itineraries. However, often for reliability in air travel, this information is incomplete or not useful. In this paper we utilize historical probability distributions of flight arrival and departure times using publicly available data to give an intuitive and predictive flight itinerary reliability metric. The COVID-19 pandemic significantly affected air-travel in the US and this uncertainty is still being felt with cancellations and delays due to staff shortages and reduced demand. Therefore, we extend the stochastic network model from our previous research to air travel during COVID-19 to see the effects on flight reliability. Using this model, we conduct computational experiments to evaluate air travel through multiple reliability metrics. We show that during periods of high uncertainty, predictive historical distributions of flight data considering recency and seasonal effects are less accurate given many cancellations and a reduced flight schedule.

Safety Stock Optimization under Lead Time Ambiguity

Purpose: The purpose of this study is to investigate how ambiguity faced by the risk-neutral manager affects the firm’s optimal level of safety stock.&#x0D; Design/methodology/approach: This study adopts the traditional model of Arrow et al. (1951) and employ a manager who has multiple prior beliefs about the probability distribution of the lead time.&#x0D; Findings: This study finds that facing lead time ambiguity, the manager becomes more conservative when choosing the optimal stock level to hold and the amount of safety stock.&#x0D; Research limitations/implications: The future research would consider a risk-averse manager who could be compensated or punished as a result of stock management. Then the future research would examine the interactive effects of the manager’s risk aversion and lead time ambiguity on the optimal safety stock level.&#x0D; Originality/value: This would be the first study that investigates the effects of ambiguity on the level of safety stock.

Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects

This paper investigates the multi-type traffic sensor location problem for simultaneous estimation of origin-destination (OD) demands and link travel times while also considering the two sources of spatial covariance effects on a road network with uncertainties. The first source is the statistical correlation of the vehicular traffic demands for different OD pairs in a typical hourly period (e.g., morning peak hour) on a daily scale, as the travel demand patterns vary daily, weekly, and seasonally over the year. The second source is the stochastic nature of the link travel times on different road links during the peak hour period and their correlation with adjacent links in congested conditions. By considering these aspects, a novel model is formulated to optimize the number and locations of multi-type traffic sensors for simultaneous estimation of stochastic OD demands and link travel times during the same peak-hour period over a year. This estimation is supported by the data recorded by multi-type traffic sensors such as point sensors and automatic vehicle identification sensors, which yield the link speed/flow and path travel time information, respectively. Based on the integrated observations from multi-type traffic sensors, a novel Kullback–Leibler divergence-based model is developed to accommodate different probability distributions of OD demands and link travel times in different traffic conditions. Moreover, an improved firefly algorithm is developed to solve the multi-type sensor location problem. Specifically, the search strategy of this algorithm is enhanced by considering the mean and covariance of the OD demands and link travel times. Numerical examples of synthetic and real-world road networks are used to illustrate the applications and merits of the developed multi-type sensor location model for simultaneously estimating the OD demands and link travel times while also considering covariance effects.

Near-instantaneous battery End-of-Discharge prognosis via uncertain event likelihood functions

The prediction of the time of occurrence of future events has been studied for decades in various scientific disciplines. Such events have historically been defined as moments where variables of interest (or indicators) hit pre-determined thresholds (i.e. the first-hitting time). Recently, semi-closed mathematical expressions were reported in the literature to analytically characterize the probability distribution of the occurrence time of future events, extending the event triggering criteria based on thresholds to a more general and intuitive threshold-less approach, where the occurrence of events is declared through the use of uncertain event likelihood functions. The End-of-Discharge time prognosis problem is formalized in this article via the definition of uncertain event likelihood functions. Moreover, a novel numerical method is proposed to compute the probability distribution of its future time of occurrence based on this conceptualization and exploiting the capability of uncertain event likelihood functions to assimilate uncertainty in analytic expressions. A case study related to energy autonomy in electromobility applications is considered; specifically an electric bicycle. Obtained results show that the proposed method achieves an extraordinary level of convergence in less than a tenth of a second, while the same level of convergence using Monte Carlo simulations under the traditional threshold crossing approach takes hours to be achieved.

Cardinality of Joint and Disjoint Sets and a Related Discrete Distribution

The number of elements belonging to the intersection of some overlapped sets and that belonging precisely to the junction of some overlapped sets are related. We have demonstrated a more straightforward presentation with some examples for a broad spectrum of students and instructors. It shows an apparent relationship between the cardinality of joint and disjoint sets. There is a probability distribution associated with it, and it is unexplored. We have provided some examples to illustrate it. We have derived the factorial moment structure of the probability distribution for the first time, and they found it to be elegant. We have also derived raw and corrected moments of the distribution.

FACTORS ASSOCIATED WITH SURVIVAL TIME FOR PATIENTS WITH HIV/AIDS IN THE STATE OF MATO GROSSO DO SUL: PARAMETRIC APPROACH

The goal of this study was to use frequentist and Bayesian methodologiesto adjust some probability distributions for survival time in HIV/AIDS patients in Mato Grosso do Sul, Brazil, followeds from 2009 to 2018. The influence of explanatory variables on the response variable can be calculated using regression models. The Log-Normal distribution was shown to be the most parsimonious for the data using the Akaike information criterion (AIC) values and the maximum likelihood logarithm.Two regression models were built based on the described methodologies, converging to the same interpretation of the explanatory variables: sex, race, education, and injecting drug use. The median time to death from HIV/AIDS is approximately: 2.1 higher for females, 1.8 higher for white people, 5.4 higher for individuals with more than 8 years of education, 5.5 higher for individuals who do not use injecting drugs, according to the study. Based on the interpretations of the coefficients of the model parameters, the need for prevention and early diagnosis policies focused on groups that have a shorter median survival time after notification of HIV infection can be discussed.

Alternating rotation of coordinated and anti-coordinated action due to environmental feedback and noise

The alternating rotation of coordinated and anti-coordinated behaviors is a common phenomenon in real life, for example, consistent and polarizing behaviors in opinion dynamics, innovation and imitation behaviors in the dynamics of product or technology spread. In this paper, we use environmental feedback dynamics to correlate coordination games and anti-coordination games to describe this phenomenon. Interestingly, the dynamic phenomenon of alternating rotation of coordination and anti-coordination is successfully observed in our model, namely the existence of neutral stability centers. We derive theoretically and numerically the conditions for the arising and stability of these stable states. Remarkably, we find that the two regions that do not overlap or intersect and are not affected by the relative feedback parameter. The demarcation of the two regions is determined by the payoff matrix parameter. However, stochastic noise plays a crucial role, and the introduction of a tiny stochastic noise can have a significant effect that the left and right regions can cross each other. The rotation of the emergence and demise of hippies (new products, technology or opinions), and the emergence and dominance of hippies can form a closed trajectory, which can be transformed by each other. The probability distribution of the sojourn time between the system staying in the previous region before entering the next region is well approximated by a power law with an exponential cutoff. Our results have the potential to maintain alternating rotation of coordinated and anti-coordinated behaviors.

Quantitative microbial risk assessment indicates very low risk for Vibrio parahaemolyticus foodborne illness from Jeotgal in South Korea

In this study, a microbial risk assessment was performed for the bacteria Vibrio parahaemolyticus, which causes a foodborne illness following the consumption of Jeotgal, a fermented seafood in South Korea. The assessment comprised of six stages: product, market, home, consumption, dose-response, and risk. The initial contamination level (IC) was calculated based on the prevalence of V. parahaemolyticus in 90 Jeotgal samples. The kinetic behavior of V. parahaemolyticus was described using predictive models. The data on transportation conditions from manufacturer to market and home were collected through personal communication and from previous studies. Data for the Jeotgal consumption status were obtained, and an appropriate probability distribution was established. The simulation models responding to the scenario were analyzed using the @RISK program. The IC of V. parahaemolyticus was estimated using beta distribution [Beta (1, 91)]. The cell counts during transportation were estimated using Weibull and polynomial models [δ = 1 / (0.0718 – 0.0097 × T + 0.0005 × T2)], while the probability distributions for time and temperature were estimated using Pert, Weibull, Uniform, and LogLogistic distributions. Daily average consumption amounts were assessed using the Pareto distribution [0.60284,1.32,Risk Truncate(0,155)]. The results indicated that the risk of V. parahaemolyticus infection through Jeotgal consumption is low in South Korea.

Extracting nucleation rates from ramped temperature measurements of gas hydrate formation

The formation of solids in the energy industry poses a threat to safety and reliability of operational facilities across numerous process stages. Experimental studies of gas hydrate formation probability are conducted under both fixed-temperature and ramped-temperature conditions. Although a method to extract nucleation rates from constant temperature measurements of induction time probability distributions is well established, extracting such rates from constant cooling data is complicated by the time-dependent driving force for hydrate formation. Here, we present and use a method for extracting the stationary nucleation rate as a function of temperature from constant cooling experiments based on the hazard function, which accounts for the system’s history and the instantaneous formation probability. This method yields nucleation rates consistent with those measured using more time-consuming constant temperature experiments, while providing far more information about the underlying nucleation phenomena by sampling a wider range of temperatures. Measurements of methane hydrate formation probability obtained in well-mixed systems at 12 MPa with temperature ramp rates (1–3) K·min−1 were analysed using a framework based on Classical Nucleation Theory. The results suggest that the heterogeneous nucleation sites primarily responsible for the observed nucleation rate become more numerous and have higher average energy barriers as subcooling increases. This hypothesis is also consistent with recent experimental studies of systems containing kinetic hydrate inhibitors and provides a pathway to more reliable predictions of hydrate formation probability in production systems that experience a wide range of subcoolings.

When to swing into high gear? A time-limit approach to problem escalation

In manufacturing and services, random problems arise that disrupt normal operations. Organizations must resolve these problems in a timely and cost-efficient manner—which can be a daunting task. A typical management response is assigning escalation routes whereby the lowest tier initially owns a problem that may later be escalated to higher tiers. To minimize the costs associated with these problems, we consider a management policy that specifies a time limit beyond which problems must move up a tier; the setting is formulated as a stochastic dynamic program. For scenarios involving a single problem type, we find that optimal time limits can exist when the problem service times are generally distributed or correlated and when the marginal delay cost increases with time; we also characterize the single–problem type, multi-tier optimal solution when the marginal delay cost is constant. When multiple types of problems are pooled together, we show that a time-limit–based approach is robust to various probability distributions of service times and performs reasonably well even when the problem type is unidentified ex ante. Finally, we derive comparative statics on how parameter values, problem characteristics, and the composition of problems each affect the optimal time limit.

Conditional multivariate distributions of phase-type for a finite mixture of Markov jump processes given observations of sample path

This paper presents conditional joint probability distributions of first-exit times to absorbing sets of a finite mixture of right-continuous Markov jump processes given observations of its sample path. Each underlying Markov jump process comprising the mixture has its own intensity matrix and is defined on the same finite state space with overlapping absorbing sets. The main distinctive aspect of the mixture is that despite the underlying processes have the Markov property, the mixture itself in general does not. Conditional transition matrix and the joint probability distribution of the first-exit times form non-stationary functions of time with ability to capture path dependence when conditioning on available information (either full or partial) of the sample path. In particular, initial profile of the joint distribution forms a generalized mixture of the multivariate phase-type distributions of Assaf et al. (1984). When the underlying Markov processes have the same intensity matrix, in which case the mixture becomes a simple Markov jump process, the path dependence and non-stationary properties are removed from the transition matrix and the joint distribution, while the initial profile distribution reduces to Assaf et al. (1984). Some explicit and numerical examples are discussed to illustrate the results.