Initial-State Temperature of Light Meson Emission Source From Squared Momentum Transfer Spectra in High-Energy Collisions

The squared momentum transfer spectra of light mesons, π0, π+, η, and ρ0, produced in high-energy virtual photon-proton (γ*p) → meson + nucleon process in electron-proton (ep) collisions measured by the CLAS Collaboration are analyzed by the Monte Carlo calculations, where the transfer undergoes from the incident γ* to emitted meson or equivalently from the target proton to emitted nucleon. In the calculations, the Erlang distribution from a multi-source thermal model is used to describe the transverse momentum spectra of emitted particles. Our results show that the average transverse momentum (⟨pT⟩) and the initial-state temperature (Ti) increase from lower squared photon virtuality (Q2) and Bjorken variable (xB) to higher one. This renders that the excitation degree of emission source, which is described by ⟨pT⟩ and Ti, increases with increasing of Q2 and xB.

A Multi-Stage Model of Cell Proliferation and Death: Tracking Cell Divisions with Erlang Distributions

Lymphocyte populations, stimulated in vitro or in vivo , grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, each can be imagined as sampling from a probability density of times to division. The most convenient choice of density in mathematical and computational work, the exponential density, overestimates the probability of short division times. We consider a multi-stage model that produces an Erlang distribution of times to division, and an exponential distribution of times to die. The resulting dynamics of competing fates is a type of cyton model. Using Approximate Bayesian Computation, we compare our model to published cell counts, obtained after CFSE-labelled OT-I and F5 T cells were transferred to lymphopenic mice. The death rate is assumed to scale linearly to the generation (number of divisions) and the number of stages of undivided cells (generation 0) is allowed to differ from that of cells that have divided at least once (generation greater than zero). Multiple stages are preferred in posterior distributions, and the mean time to first division is longer than the mean time to subsequent divisions.

Inventory Management at the Enterprise in the Field of Probability Models

The inventory management system is designed to continuously ensure the production activities of the enterprise with all necessary resources. The purpose of this study is to build a probabilistic model that can be proposed as a new inventory model, which establishes the relationship of period factors between the purchase of parts and the duration of their suitability, which affect inventory management. The research methods are based on a probabilistic approach using continuous distributions. Using the statistical method, point estimates were found for the studied parameters: mean and standard deviation. The histograms of relative frequencies between dates of two next purchases, volume of purchases of details and days of replacement of the fulfilled details are constructed. The critical areas for the studied parameters are illustrated. The values of the difference in days between the purchases of parts and the values of purchases of parts that meet the normal distribution of random variables with the appropriate parameters, as well as the critical values of the need for parts in the production process. The size of the part reserve, which corresponds to Erlang distribution, was found, depending on the established risk factor. For different values of this factor, the value of the difference in days between the purchases of parts, the size of purchases and the reserve of parts that correspond to the distributions of random variables, as well as the critical value of the need for parts in the production process to avoid downtime. Using the central limit theorem, it is shown that the purchase volume of parts and the volume of used parts are distributed according to the normal law. The study concludes that the probabilistic approach is the basis for forecasting inventory management in the enterprise, taking into account the risks associated with determining the optimal demand for raw materials in the enterprise

Improving scheduling performance in congested networks

With continuously rising trends in applications of information and communication technologies in diverse sectors of life, the networks are challenged to meet the stringent performance requirements. Increasing the bandwidth is one of the most common solutions to ensure that suitable resources are available to meet performance objectives such as sustained high data rates, minimal delays, and restricted delay variations. Guaranteed throughput, minimal latency, and the lowest probability of loss of the packets can ensure the quality of services over the networks. However, the traffic volumes that networks need to handle are not fixed and it changes with time, origin, and other factors. The traffic distributions generally follow some peak intervals and most of the time traffic remains on moderate levels. The network capacity determined by peak interval demands often requires higher capacities in comparison to the capacities required during the moderate intervals. Such an approach increases the cost of the network infrastructure and results in underutilized networks in moderate intervals. Suitable methods that can increase the network utilization in peak and moderate intervals can help the operators to contain the cost of network intrastate. This article proposes a novel technique to improve the network utilization and quality of services over networks by exploiting the packet scheduling-based erlang distribution of different serving areas. The experimental results show that significant improvement can be achieved in congested networks during the peak intervals with the proposed approach both in terms of utilization and quality of service in comparison to the traditional approaches of packet scheduling in the networks. Extensive experiments have been conducted to study the effects of the erlang-based packet scheduling in terms of packet-loss, end-to-end latency, delay variance and network utilization.

Population Pharmacokinetics And Bayesian Estimation of Mycophenolate Mofetil In Patients With Autoimmune Hepatitis

Background: Mycophenolate mofetil (MMF) is the most widely used second-line agent in auto-immune hepatitis (AIH). It is generally titrated up to patient response and continued for at least two years following complete liver enzyme normalization. However, in this maintenance phase individual dose adjustment to reach mycophenolic acid (MPA) exposure with the best benefit-risk probability may avoid adverse outcomes. The aim of the present study was to develop population pharmacokinetic (popPK) models and Maximum A-Posteriori Bayesian estimators (MAP-BEs) to estimate MPA inter-dose area under the curve (AUC0-12h) in AIH patients administered MMF using nonlinear mixed effect modelling. Methods: We analysed 50 MPA PK profiles from 34 different patients, together with some demographic, clinical, and laboratory test data. The median number of samples per profile, immediately preceding and following the morning MMF dose, was 7 [4 – 10]. PopPK modeling was performed using parametric, top-down, nonlinear mixed effect modelling with NONMEM 7.3. MAP-BEs were developed based on the the best popPK model and the best limited sampling strategy (LSS) selected among several. Results: The pharmacokinetic data were best described by a 2-compartment model, Erlang distribution to describe the absorption phase, and a proportional error. The best MAP-BE relied on the LSS at 0.33, 1 and 3 hours after mycophenolate mofetil dose administration and was very accurate (bias=5.6%) and precise (RMSE<20%). Conclusion: The precise and accurate Bayesian estimator developed in this study for AIH patients on MMF can be used to improve the therapeutic management of these patients.

Spectral expansion method for analysis of a system with shifted Erlang and hyper-Erlang distributions

In this paper, we obtained a spectral expansion of the solution to the Lindley integral equation for a queuing system with a shifted Erlang input flow of customers and a hyper-Erlang distribution of the service time. On its basis, a calculation formula is derived for the average waiting time in the queue for this system in a closed form. As you know, all other characteristics of the queuing system are derivatives of the average waiting time. The resulting calculation formula complements and expands the well-known unfinished formula for the average waiting time in queue in queuing theory for G/G/1 systems. In the theory of queuing, studies of private systems of the G/G/1 type are relevant due to the fact that they are actively used in the modern theory of teletraffic, as well as in the design and modeling of various data transmission systems.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events. Methods Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence. Results We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age. Conclusions This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

Initial- and Final-State Temperatures of Emission Source from Differential Cross-Section in Squared Momentum Transfer in High-Energy Collisions

The differential cross-section in squared momentum transfer of ρ , ρ 0 , ω , ϕ , f 0 980 , f 1 1285 , f 0 1370 , f 1 1420 , f 0 1500 , and J / ψ produced in high-energy virtual photon-proton ( γ ∗ p ), photon-proton ( γ p ), and proton-proton ( p p ) collisions measured by the H1, ZEUS, and WA102 Collaborations is analyzed by the Monte Carlo calculations. In the calculations, the Erlang distribution, Tsallis distribution, and Hagedorn function are separately used to describe the transverse momentum spectra of the emitted particles. Our results show that the initial- and final-state temperatures increase from lower squared photon virtuality to a higher one and decrease with the increase of center-of-mass energy.

Statistical Behavior of Lepton Pair Spectrum in the Drell-Yan Process and Signal from Quark-Gluon Plasma in High-Energy Collisions

We analyze the transverse momentum ( p T ) spectra of lepton pairs ( ℓ ℓ ¯ ) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy s N N or s if in a simplified form) range from ~ 20 GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the p T spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of s and invariant mass Q . In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark ( q ) or anti-quark ( q ¯ ). The Drell-Yan process is then described by the statistical method.