Mean Sojourn Times Research Articles

Cryopumping of hydrogen on stainless steel in the temperature range between 7 and 18 K

In cryogenic vacuum accelerator systems operated at temperatures below 20 K, hydrogen is typically the predominant residual gas component. The understanding of the cryopump mechanism of hydrogen on cryogenically refrigerated surfaces is thus a crucial prerequisite for a reliable design of such vacuum systems. Adsorption isotherms represent an experimental approach to understand the cryopump effect as a physisorption process of gases on cryogenic surfaces. Using a specially designed pumping system, the adsorption of hydrogen on an electropolished stainless steel surface was experimentally investigated in the temperature range between 7 and 18 K. The analysis of the measured H2 adsorption isotherms showed that the Dubinin-Radushkevich-Kaganer (DRK) isotherm, which is commonly used to theoretically describe the cryosorption process in the submonolayer coverage range, can be applied in the entire temperature range studied. The adsorption isotherms agree sufficiently well with the prediction of the DRK theory. Additionally, results on measurements of the sticking probability of H2 on stainless steel are presented for the above mentioned temperature range. Using the measured isotherms and sticking probabilities, the harmonic mean sojourn times of H2 molecules cryosorbed on a stainless steel surface were calculated as a function of temperature and surface coverage.In cryogenic vacuum accelerator systems operated at temperatures below 20 K, hydrogen is typically the predominant residual gas component. The understanding of the cryopump mechanism of hydrogen on cryogenically refrigerated surfaces is thus a crucial prerequisite for a reliable design of such vacuum systems. Adsorption isotherms represent an experimental approach to understand the cryopump effect as a physisorption process of gases on cryogenic surfaces. Using a specially designed pumping system, the adsorption of hydrogen on an electropolished stainless steel surface was experimentally investigated in the temperature range between 7 and 18 K. The analysis of the measured H2 adsorption isotherms showed that the Dubinin-Radushkevich-Kaganer (DRK) isotherm, which is commonly used to theoretically describe the cryosorption process in the submonolayer coverage range, can be applied in the entire temperature range studied. The adsorption isotherms agree sufficiently well with the prediction of the DRK theory....

On the estimation of misclassification probabilities of chronic kidney disease using continuous time hidden Markov models

Introduction: The severity of chronic kidney disease (CKD) is reflected in the form of stages of CKD and can be decided on the basis of estimated glomerular filtration rate (eGFR). The computation of eFGR may have computational and measurement errors which may lead to misclassification of stages. Objectives: Estimation of transition rates, mean sojourn times, probabilities of misclassification of stages and odds ratios for misclassification probabilities. Patients and Methods: The retrospective data of 117 patients suffering from CKD during the period March 2006 to October 2016 is used. Hidden Markov model (HMM) with continuous time has been developed to present the course of progression of CKD into various stages. Results: Under the HMM, the estimated transition intensity corresponding to transition from stage 1 to stage 2 is 0.0405 and reverse transition intensities are zero. The estimated mean sojourn time corresponding to stage 1, stage 2, stage 3 and stage 4 are 15.923 years, 11.976 years, 7.936 years and 2.890 years respectively. The probability of a CKD patient with stage 1 of disease will be misclassified as a patient of stage 2 is 0.211. The odds ratios for misclassification probabilities in the presence of prognostic factors are computed. The probability of misclassification corresponding to the observed stage 2 given the true stage 1 for females is approximately 3.8 times more than that of males. Conclusion: For CKD having progression in stages, the HMM is an appropriate model to draw the course of progression of the disease.

A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]/C-MSP/1 Queueing System

This paper deals with a batch arrival infinite-buffer single server queue. The interbatch arrival times are generally distributed and arrivals are occurring in batches of random size. The service process is correlated and its structure is presented through a continuous-time Markovian service process (C-MSP). We obtain the probability density function (p.d.f.) of actual waiting time for the first and an arbitrary customer of an arrival batch. The proposed analysis is based on the roots of the characteristic equations involved in the Laplace-Stieltjes transform (LST) of waiting times in the system for the first, an arbitrary, and the last customer of an arrival batch. The corresponding mean sojourn times in the system may be obtained using these probability density functions or the above LSTs. Numerical results for some variants of the interbatch arrival distribution (Pareto and phase-type) have been presented to show the influence of model parameters on the waiting-time distribution. Finally, a simple computational procedure (through solving a set of simultaneous linear equations) is proposed to obtain the “R” matrix of the corresponding GI/M/1-type Markov chain embedded at a prearrival epoch of a batch.

Construction of a semi-Markov model for the performance of a football team in the presence of missing data

ABSTRACTUsing play-by-play data from the very beginning of the professional football league in Turkey, a semi-Markov model is presented for describing the performance of football teams. The official match results of the selected teams during 55 football seasons are used and winning, drawing and losing are considered as Markov states. The semi-Markov model is constructed with transition rates inferred from the official match results. The duration between the last match of a season and the very first match of the following season is much longer than any other duration during the season. Therefore these values are considered as missing values and estimated by using expectation–maximization algorithm. The effect of the sojourn time in a state to the performance of a team is discussed as well as mean sojourn times after losing/winning are estimated. The limiting probabilities of winning, drawing and losing are calculated. Some insights about the performance of the selected teams are presented.

Stochastic analysis of a 2-out-of-2: G system with single cold standby and replacement using weibull distribution

A 2-out-of-2: G system has been analyzed stochastically in detail by taking one more unit in cold standby. The units are identical in nature each having two modes-operative and failure. There is a single server who attends the system immediately to carry out the repair activities whenever needed. The failed unit undergoes for replacement by new one in case its repair is not possible by the server in a pre-specific time. The failure, repair and replacement times of the unit follow Weibull distribution. The unit works as new after repair and its actual life time is same as original. The expressions for some important reliability measures such as mean sojourn times, mean time to system failure (MTSF), availability and profit function are derived in steady state using semi-Markov process and regenerative point technique. The behavior of these measures has been critically examined for arbitrary values of the parameters. The results are also obtained considering particular cases of Weibull distribution.

Clustered multistate models with observation level random effects, mover-stayer effects and dynamic covariates: modelling transition intensities and sojourn times in a study of psoriatic arthritis.

Summary In psoriatic arthritis, it is important to understand the joint activity (represented by swelling and pain) and damage processes because both are related to severe physical disability. The paper aims to provide a comprehensive investigation into both processes occurring over time, in particular their relationship, by specifying a joint multistate model at the individual hand joint level, which also accounts for many of their important features. As there are multiple hand joints, such an analysis will be based on the use of clustered multistate models. Here we consider an observation level random‐effects structure with dynamic covariates and allow for the possibility that a subpopulation of patients is at minimal risk of damage. Such an analysis is found to provide further understanding of the activity–damage relationship beyond that provided by previous analyses. Consideration is also given to the modelling of mean sojourn times and jump probabilities. In particular, a novel model parameterization which allows easily interpretable covariate effects to act on these quantities is proposed.

Clinical and demographic factors associated with change and maintenance of disease severity in a large registry of patients with rheumatoid arthritis

BackgroundWe examined models to predict disease activity transitions from moderate to low or severe and associated factors in patients with rheumatoid arthritis (RA).MethodsData from RA patients enrolled in the Corrona registry (October 2001 to August 2014) were analyzed. Clinical Disease Activity Index (CDAI) definitions were used for low (≤10), moderate (>10 and ≤22), and severe (>22) disease activity states. A Markov model for repeated measures allowing for covariate dependence was used to model transitions between three (low, moderate, severe) states and estimate population transition probabilities. Mean sojourn times were calculated to compare length of time in particular states. Logistic regression models were used to examine impacts of covariates (time between visits, chronological year, disease duration, age) on disease states.ResultsData from 29,853 patients (251,375 visits) and a sub-cohort of 9812 patients (46,534 visits) with regular visits (every 3–9 months) were analyzed. The probability of moving from moderate to low or severe disease by next visit was 47% and 18%, respectively. Patients stayed in moderate disease for mean 4.25 months (95% confidence interval: 4.18–4.32). Transition probabilities showed 20% of patients with low disease activity moved to moderate or severe disease within 6 months; >35% of patients with moderate disease remained in moderate disease after 6 months. Results were similar for the regular-visit sub-cohort. Significant interactions with prior disease state were seen with chronological year and disease duration.ConclusionA substantial proportion of patients remain in moderate disease, emphasizing the need for treat-to-target strategies for RA patients.

Using Simulation to Model and Validate Invasive Breast Cancer Progression in Women in the Study and Control Groups of the Canadian National Breast Screening Studies I and II.

Modeling breast cancer progression and the effect of various risk is helpful in deciding when a woman should start and end screening, and how often the screening should be undertaken. We modeled the natural progression of breast cancer using a hidden Markov process, and incorporated the effects of covariates. Patients are women aged 50-59 (older) and 40-49 (younger) years from the Canadian National Breast Screening Studies. We included prevalent cancers, estimated the screening sensitivities and rates of over-diagnosis, and validated the models using simulation. We found that older women have a higher rate of transition from a healthy to preclinical state and other causes of death but a lower rate of transition from preclinical to clinical state. Reciprocally, younger women have a lower rate of transition from a healthy to preclinical state and other causes of death but a higher rate of transition from a preclinical to clinical state. Different risk factors were significant for the age groups. The mean sojourn times for older and younger women were 2.53 and 2.96 years, respectively. In the study group, the sensitivities of the initial physical examination and mammography for older and younger women were 0.87 and 0.81, respectively, and the sensitivity of the subsequent screens were 0.78 and 0.53, respectively. In the control groups, the sensitivities of the initial physical examination for older and younger women were 0.769 and 0.671, respectively, and the sensitivity of the subsequent physical examinations for the control group aged 50-59 years was 0.37. The upper-bounds for over-diagnosis in older and younger women were 25% and 27%, respectively. The present work offers a basis for the better modeling of cancer incidence for a population with the inclusion of prevalent cancers.

Measuring concurrency using a joint multistate and point process model for retrospective sexual history data.

Understanding the impact of concurrency, defined as overlapping sexual partnerships, on the spread of HIV within various communities has been complicated by difficulties in measuring concurrency. Retrospective sexual history data consisting of first and last dates of sexual intercourse for each previous and ongoing partnership is often obtained through use of cross-sectional surveys. Previous attempts to empirically estimate the magnitude and extent of concurrency among these surveyed populations have inadequately accounted for the dependence between partnerships and used only a snapshot of the available data. We introduce a joint multistate and point process model in which states are defined as the number of ongoing partnerships an individual is engaged in at a given time. Sexual partnerships starting and ending on the same date are referred to as one-offs and modeled as discrete events. The proposed method treats each individual's continuation in and transition through various numbers of ongoing partnerships as a separate stochastic process and allows the occurrence of one-offs to impact subsequent rates of partnership formation and dissolution. Estimators for the concurrent partnership distribution and mean sojourn times during which a person has k ongoing partnerships are presented. We demonstrate this modeling approach using epidemiological data collected from a sample of men having sex with men and seeking HIV testing at a Los Angeles clinic. Among this sample, the estimated point prevalence of concurrency was higher among men later diagnosed HIV positive. One-offs were associated with increased rates of subsequent partnership dissolution. Copyright © 2016 John Wiley & Sons, Ltd.

On Round-Robin routing with FCFS and LCFS scheduling

We study the Round-Robin (RR) routing to a system of parallel queues, which serve jobs according to FCFS or preemptive LCFS scheduling disciplines. The cost structure comprises two components: a service fee and a queueing delay related component. With Poisson arrivals, the inter-arrival time to each queue obeys the Erlang distribution. This allows us to study the mean and transient behavior of the queues separately. The service fee is independent of the scheduling and queueing, and we obtain the corresponding mean cost rate and value function in closed forms. With respect to queueing delay, we first derive integral expressions enabling efficient computation of the corresponding size-aware value functions. By decomposition, these yield also the value function for the whole system of m parallel queues fed by RR. Given the value function, one can carry out the first policy iteration step with arbitrary holding cost rates (e.g., delay, slowdown, etc.) yielding efficient size-, cost- and state-aware policies. Moreover, the mean waiting and sojourn times in the corresponding systems get resolved at the same time. The results are demonstrated in the numerical examples, where we compute near optimal job routing policies for sample systems.

A quantitative insight into metastatic relapse of breast cancer

BackgroundMetastatic relapse is the principal source of breast cancer mortality. This work seeks to uncover unobservable, yet clinically important, aspects of post-surgery metastatic relapse of breast cancer and to quantify effects of surgery on metastatic progression. MethodsWe classified metastases into three categories: (1) solitary cancer cells that were formed before or during surgery and either circulate in blood or are lodged at various secondary sites; (2) dormant or slowly growing avascular metastases; and (3) vascular secondary tumors. We developed a general mathematical model aimed at describing post-surgery dynamics of these three metastatic states. One parametric version of the model assumed that sojourn times of metastases in the three states are exponentially distributed while another was based on Erlang distribution. Model parameters were estimated from a sample of metastatic relapse or censoring times for 673 breast cancer patients treated with surgery. ResultsWe estimated the expected number of metastases at surgery and mean sojourn times for the three states and found that both are decreasing with state number. We also computed the probability that metastatic relapse resulted from a metastasis in a given state at surgery. The values of these attribution probabilities suggest that under the Erlang model all three states have a considerable effect on metastatic relapse while in the case of exponential model this is true for states 1 and 2 only. Conclusions(1) In some patients metastasis occurred before surgery; (2) our results confirm significance of metastatic dormancy; (3) according to the model surgery stimulates escape from dormancy, promotes angiogenesis and accelerates metastatic growth in a fraction of breast cancer patients. Taken summarily, these findings call into question the benefits of primary tumor resection for certain categories of breast cancer patients.

On the three-queue priority polling system with threshold service policy

In this paper, a priority polling system consisting of three M / M / 1 queues, served by a single server is investigated. Queue 1 has the Head-of-Line (HoL) priority and Queue 2 has a higher priority over Queue 3 with threshold N. All the switches are instantaneous and preempting. Using the Kernel method we derive the probability of generating functions of the stationary joint queue-length distributions, which yields the mean queue lengths and the mean sojourn times. Furthermore, we consider the limit behaviors in the light-traffic and heavy-traffic scenarios. And an interpolation approximation for the sojourn times utilizing the light and heavy traffic limits are illustrated. To test the validity, we also undertake some simulation works.

Stochastic Model of a Cold-Stand by System with Waiting for Arrival & Treatment of Server

The service facility or server is the key constituent to keep a system operational for desired period of time. As any eventuality with the system necessitates immediate presence of it (server) so the time point of arrival and treatment of server significantly affects the system performance. This paper works out the steady state behavior of a cold standby system equipped with two similar units and a server with elapsed arrival and treatment times following general probability distributions. It practices the theory of semi-Markov processes, regenerative point technique and Laplace transforms to derive the expressions for state transition probabilities, mean sojourn times, mean time to system failure, system availability, server busy period and expected frequencies of repairs and treatments. The profit function is also developed taking different costs and revenue in to account. For tracing wider applicability of the model for different reliability and cost-effective systems, a particular case study is also presented as an illustration.

Investigating the factors affecting the transition rates between states of neonatal hypothermia using markov model

Background: At birth, the wet neonate is suddenly confronted with a cold and dry weather and reacts to this new situation by increasing heat production. Hypothermia is an important determinant of the survival of newborns, especially among low-birth-weight babies. Prolonged hypothermia leads to edema, general hemorrhage, jaundice and death.Aims and Objectives: the aim of this observational longitudinal study is to examine effective factors on passing the hypothermia state.Materials and Methods: In this study rectal temperature was measured immediately after birth and every half hour after that for 439 neonates, until they passed hypothermia stage. The rate of transition between states of neonatal hypothermia and effect of covariates, newborn baby birth weight, Apgar score and environmental temperature on it is estimated by multi state Markov model.Results: Newborn baby weight and environmental temperature were significant effect on transition rate from mild to normal hypothermia, too, but the Apgar score effect was not significant. Mean sojourn times in mild hypothermia state for three birth weight levels, very light, light and normal are 38, 29 and 22 min respectively. In addition, in the environmental temperature over 28 ºC, the average time in which the neonate remained in mild hypothermia state was shorter than that in the environmental temperature below 28 ºC (29 vs. 38 min).Conclusions: Since the birth weight is not under the control of the health personnel, keeping a suitable thermal environment for the newborns results in a faster change from hypothermia to a normal state. Therefore, training in this area is of enormous importance.Asian Journal of Medical Sciences Vol.7(2) 2015 34-38

An invariance principle for a class of non-ballistic random walks in random environment

We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed coordinate direction, and invariant under reflection in the coordinate hyperplanes. The invariance condition was used in Baur and Bolthausen (2014) as a weaker replacement of isotropy to study exit distributions. We obtain precise results on mean sojourn times in large balls and prove a quenched invariance principle, showing that for almost all environments, the random walk converges under diffusive rescaling to a Brownian motion with a deterministic (diagonal) diffusion matrix. We also give a concrete description of the diffusion matrix. Our work extends the results of Lawler (1982), where it is assumed that the environment is balanced in all coordinate directions.

Minimum divergence estimators for the Radon–Nikodym derivatives of the semi-Markov kernel

In this paper we face the problem of estimating the elements that define a homogeneous semi-Markov process. Given an observed sample path of the process in a finite interval , non-parametric estimators of the entries of the semi-Markov kernel and its derivatives can be constructed. These estimators exhibit good properties as consistency and asymptotic normality. On the other hand, in our approach we consider that we have some prior information about the underlying process. This information concerns the mean sojourn times in the different states of the process and has to be taken into account in the estimation procedure. So we start from the smoothed estimators and construct minimum divergence estimators (maximum entropy) under some constraints for the associated sojourn moments.

Using Markov Chains to predict the natural progression of diabetic retinopathy.

To study the natural progression of diabetic retinopathy in patients with type 2 diabetes. This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy (NPDR) were treated. Markov Chains and Chi-square test were used for statistical analysis. We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference (P=0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07y in moderate NPDR, be in the severe NPDR state for 1.33y before moving into PDR for roughly 8y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29y. Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR. However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy (PDR) and stay in that state for long periods before transitioning into blindness.

Simulation Study for the Sensitivity and Mean Sojourn Time Spec ific Lead Time in Cancer Screening When Human Lifetime is a Competin g Risk

Purpose: The purpose of this paper is to examine the sensitivity and mean sojourn time specific lead time distribution in cancer screening trials when lifetime is a random variable in order to explore possible optimal initial age at screening and screening frequency. Methods: Summarized methods from Wu et al. (2012). Simulation was used in order to estimate the distribution of the lead time for a hypothetical individual with a future screening schedule. The lifetime distribution used comes from the Social Security Administration’s actuarial life tables. The lead time distribution was then calculated based on a loglogistic sojourn time distribution with two mean sojourn times (2, and 10 years), using three different initial screening ages, t0=40, 50, 60, different screening sensitivities (0.3 and 0.5 for men; 0.8 and 0.9 for women), and two different screening frequencies, one and two years for both men and women. Results: Smaller time intervals between screenings yield a smaller probability of no early detection and a greater expected lead time.

Dynamical localization and eigenstate localization in trap models

The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same site, as given by the participation ratio, stays constant and high in a broad domain of intermediate times. This phenomenon is absent in dimensions two and higher. In finite lattices of all dimensions the participation ratio finally equilibrates to a different final value. We numerically investigate two-particle properties in a random trap model in one and in three dimensions, using a method based on spectral decomposition of the transition rate matrix. The method delivers a very effective computational scheme producing numerically exact results for the averages over thermal histories and initial conditions in a given landscape realization. Only a single averaging procedure over disorder realizations is necessary. The behavior of the participation ratio is compared to other measures of localization, as for example to the states' gyration radius, according to which the dynamically localized states are extended. This means that although the particles are found at the same site with a high probability, the typical distance between them grows. Moreover the final equilibrium state is extended both with respect to its gyration radius and to its Lyapunov exponent. In addition, we show that the phenomenon of dynamical localization is only marginally connected with the spectrum of the transition rate matrix, and is dominated by the properties of its eigenfunctions which differ significantly in dimensions one and three.

Combined performance and availability analysis of distributed resources in grid computing

This paper presents a mathematical model to evaluate the performance of grid resources when availability of the resources is taken into account. The proposed model uses continuous time Markov chains (CTMCs) to model the failure-repair behavior of a grid resource. In grid computing environment, a resource not only may fail during task execution, but also it can cancel its membership at any time. Hence, the proposed CTMC considers the availability of a grid resource to a grid user in both failure and membership refusal situations. After modeling the availability of the resource, the mean sojourn time of grid tasks in each of the availability states is estimated. Assigning the mean sojourn times of the tasks as performance levels to each of the CTMC's states, a Markov reward model (MRM) representing the combined performance and availability measures is obtained. Computing the cumulative state probability of the CTMC and multiplying reward rates of the MRM's states to each of the corresponding state probabilities, the expected accumulated sojourn time of grid tasks in each of the grid resources is achieved. An illustrative example is presented and the results obtained from the proposed model are reported in cases where various scheduling disciplines are considered inside the grid resource to simultaneously service grid and local tasks.