Probability Distribution Of Number Research Articles

Probability Aspects of Entrance Exams at University

The entrance examinations tests were shorted from 50 questions to 40 questions at the Faculty of International Relations at University of Economics in Prague due to time reasons. These tests are the multiple choice question tests. The multiple choice question tests are suitable for entrance examinations at University of Economics in Prague - the tests are objective and results can be evaluated quite easily and quickly for large number of students. On the other hand, a student can obtain certain number of points in the test purely by guessing the right answers. This shortening of the tests from 50 questions to 40 questions has negative influence on the probability distributions of number of points in the tests (under assumption of the random choice of answers). Therefore, this paper is suggested a solution of this problem. The comparison of these three ways of acceptance of applicants to study the Faculty of International Relations at University of Economics from probability point of view is performed in present paper. The results of this paper show that there has been a significant improvement of the probability distributions of number of points in the tests. The obtained conclusions can be used for admission process at the Faculty of International Relations in coming years.

Higher order correlations in a levitated nanoparticle phonon laser.

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [R. M. Pettit et al., Nature Photonics 13, 402 (2019)]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle's position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

A Stochastic Queueing - Inventory System with Renewal Demands and Positive Lead Time

This article analyses a stochastic inventory system with a service facility. This is an extended work of Yadavalli et al. (2008) by including the positive lead time. The customer arrives according to a renewal process and demanded item is delivered to the customer after performing an exponentially distributed service time. An (s, S) type ordering policy is adopted with exponentially distributed lead times. The stationary probability distribution for number of customers in the system and inventory level at arrival epoch and at arbitrary time point are derived. Some system performance measures in the steady state are computed and using these system performance measures the long-run expected cost rate is calculated. Since the long run expected cost rate is highly complex, the mixed integer distributed ant colony optimisation is used to obtain the optimal values. A sensitivity analysis to illustrate the effects of parameters and cost on the optimal values is also carried out in this work. [Received: 13 December 2018; Accepted: 10 October 2019]

A stochastic queueing - inventory system with renewal demands and positive lead time

This article analyses a stochastic inventory system with a service facility. This is an extended work of Yadavalli et al. (2008) by including the positive lead time. The customer arrives according to a renewal process and demanded item is delivered to the customer after performing an exponentially distributed service time. An (s, S) type ordering policy is adopted with exponentially distributed lead times. The stationary probability distribution for number of customers in the system and inventory level at arrival epoch and at arbitrary time point are derived. Some system performance measures in the steady state are computed and using these system performance measures the long-run expected cost rate is calculated. Since the long run expected cost rate is highly complex, the mixed integer distributed ant colony optimisation is used to obtain the optimal values. A sensitivity analysis to illustrate the effects of parameters and cost on the optimal values is also carried out in this work. [Received: 13 December 2018; Accepted: 10 October 2019]

Experimental Investigation on the Impact Resistance of Carbon Fibers Reinforced Coral Concrete.

In this study, the impact resistance of coral concrete with different carbon fiber (CF) dosages subjected to drop-weight impact test was investigated. For this purpose, three concrete strength grades (C20, C30, C40) and six CF dosages (0.0%, 0.3%, 0.6%, 1.0%, 1.5%, and 2.0% by weight of the binder) were considered, and a total of 18 groups of carbon fibers reinforced coral concrete (CFRCC) were cast. For each group, eight specimens were tested following the drop-weight impact test suggested by CECS 13. Then, the two-parameter Weibull distribution theory was adopted to statistically analyze the variations in experimental results. The results indicated that the addition of CFs could transform the failure pattern from obvious brittleness to relatively good ductility and improve the impact resistance of coral concrete. Moreover, the impact resistance of CFRCC increases with the CF dosage increasing. The statistical analysis showed that the probability distribution of the blow numbers at the initial crack and final failure of CFRCC approximately follows the two-parameter Weibull distribution.

First-principles molecular dynamics simulations on the local structure and thermo-kinetic properties of molten magnesium chloride

MgCl2 is a salt of considerable interest for the concentrating solar thermal power (CSP) system with advantages of high operating temperature and low cost. While the value of first-principles molecular dynamics (FPMD) simulations in investigating molten salt has been illustrated in many studies, there have been very few studies on molten MgCl2 from a first-principles method. In this work, FPMD simulations are employed to investigate the local coordination structure, as well as its structural dynamics, and thermo-kinetic properties of molten MgCl2. The basic thermo-kinetic properties of density, diffusivity, and ion conductivity are calculated for pure MgCl2 at multiple temperatures. The partial radial distribution function, partial structure factor, probability distribution of coordination numbers, and bond angle distribution are also derived from FPMD simulations. FPMD simulations are found to give satisfactory structural and transport characteristics compared with experiments. This study shows that the four-fold coordinated Mg2+ cations exist in pure MgCl2 and the Mg2+ first coordination shell has more octahedral geometry with anion vacancies. In conclusion, this work shows that FPMD simulations provide an effective method for exploring molten salts, which can be used in future research on Mg-based salts.

Probability distributions of extinction times, species richness, and immigration and extinction rates in neutral ecological models

In community ecology, neutral models make the assumption that species are equivalent, such that species abundances differ only because of demographic stochasticity. Despite their ecological simplicity, neutral models have been found to give reasonable descriptions of expected patterns of biodiversity in communities with many species. Such patterns include the expected total number of species and species-abundance distributions describing the expected number of species in different abundance classes. However, the expected patterns represent only the central tendencies of the full distributions of possible outcomes. Thus, ecological inferences and conclusions based only on expected patterns are incomplete, and may be misleading. Here, we address this issue for the spatially implicit neutral model, by using classic results from birth–death processes to derive (1) the probability distribution of extinction time of a species with given abundance for the metacommunity; (2) the probability distributions of total species richness and number of species with given abundance for both the metacommunity and local community; and (3) the probability distributions of the average immigration and extinction rates in the local community, across different values of total species richness. We illustrate the utility of these probability distributions in providing greater ecological insight via statistical inference. Firstly, we show that under the neutral metacommunity model, there is only 2.65×10−9 probability that the age of a common tree species in the Amazon is ≤ 3 × 108 yr, which is approximately the oldest estimated age of the first angiosperm. Thus, species ages from the model are unrealistically high. Secondly, for a tree community in a 50 ha plot at Barro Colorado Island in Panama, we show that the spatially implicit model can be fitted to observed species richness and an independent estimate of the immigration parameter, with the fitted model predicting a species-abundance distribution close to the observed distribution. Our results complement those using sampling formulae that specify the multivariate probability distribution of species abundances from neutral models.

Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to a generalized Laguerre differential equation. The properties of the distribution, together with the effect of noise intensity, are analyzed. The distribution is demonstrated using parameter values relevant to the transmission dynamics of influenza in the United States.

Cell-to-cell variability in organelle abundance reveals mechanisms of organelle biogenesis.

How cells regulate the number of organelles is a fundamental question in cell biology. While decades of experimental work have uncovered four fundamental processes that regulate organelle biogenesis, namely, de novo synthesis, fission, fusion, and decay, a comprehensive understanding of how these processes together control organelle abundance remains elusive. Recent fluorescence microscopy experiments allow for the counting of organelles at the single-cell level. These measurements provide information about the cell-to-cell variability in organelle abundance in addition to the mean level. Motivated by such measurements, we build upon a recent study and analyze a general stochastic model of organelle biogenesis. We compute the exact analytical expressions for the probability distribution of organelle numbers, their mean, and variance across a population of single cells. It is shown that different mechanisms of organelle biogenesis lead to distinct signatures in the distribution of organelle numbers which allow us to discriminate between these various mechanisms. By comparing our theory against published data for peroxisome abundance measurements in yeast, we show that a widely believed model of peroxisome biogenesis that involves de novo synthesis, fission, and decay is inadequate in explaining the data. Also, our theory predicts bimodality in certain limits of the model. Overall, the framework developed here can be harnessed to gain mechanistic insights into the process of organelle biogenesis.

Nonhomogeneous Poisson Process and Compound Poisson Process in the Modelling of Random Processes Related to Road Accidents

Abstract The stochastic processes theory provides concepts and theorems that allow building probabilistic models concerning accidents. So called counting process can be applied for modelling the number of the road, sea and railway accidents in the given time intervals. A crucial role in construction of the models plays a Poisson process and its generalizations. The new theoretical results regarding compound Poisson process are presented in the paper. A nonhomogeneous Poisson process and the corresponding nonhomogeneous compound Poisson process are applied for modelling the road accidents number and number of injured and killed people in the Polish road. To estimate model parameters were used data coming from the annual reports of the Polish police [9, 10]. Constructed models allowed anticipating number of accidents at any time interval with a length of h and the accident consequences. We obtained the expected value of fatalities or injured and the corresponding standard deviation in the given time interval. The statistical distribution of fatalities number in a single accident and statistical distribution of injured people number and also probability distribution of fatalities or injured number in a single accident are computed. It seems that the presented examples explain basic concepts and results discussed in the paper.

A Making method of Time-series energy demand data of non-residential buildings for urban energy analysis

Urban energy supply systems are changing to distributed energy supply systems according to the spreading of renewable energy. In order to effectively arrange and operate distributed energy supply systems in the city, it is necessary to (1) predict energy demands for each use in each building, (2) consider operation technology such as interchange or storage, and (3) study on a city scale rather than a building scale. Therefore, we aim to construct a method to calculate the optimal energy supply system with renewable energy based on data from geographical information systems (GIS). This paper describes the development of an energy-demand prediction method for non-residential buildings and a demand analysis in Japanese business areas by using this method. For the demand analysis, we developed a method to predict the demand of electricity and heat (heating, cooling and hot water) of non-residential buildings for one year. This program fluctuations in demand by five-minute intervals depending on the type of buildings (office, hospital, hotel, store, restaurant and school), total floor area, outdoor air temperature and so on. The standard demand amount of each type of buildings is based on statistical data and measurement data about energy consumption of non-residential buildings in Japan. Furthermore the fluctuation method of the demand incorporates random number simulation and probability distribution to reproduce an actual fluctuation. We predicted and accumulated the demand for hundreds of buildings by three districts for the demand analysis in the whole district. One of these analyses showed that there are large fluctuations in the demand of each building, and these fluctuations decrease by grouping the buildings in the block. Moreover, we analyzed the gap of peak demand between aggregated individual buildings and districts. This analysis revealed that some of peak demand in districts are less than 40% of aggregated individual.

Non-Markovian full counting statistics of cotunneling assisted sequential tunneling in a side-coupled double quantum dot system

We study the influences of the quantum coherence and the cotunneling processes on the non-Markovian full counting statistics (FCS) of electron tunneling through a side-coupled double quantum-dot (SCDQD) system weakly coupled to two electron reservoirs. We demonstrate that, for the SCDQD system with strong coherence of the reduced density matrix, in the sequential tunneling regime, the competition or interplay between the quantum coherence and the cotunneling processes determines whether the super-Poissonian shot noise appears or not, and particularly the magnitudes and signs of the skewness and the kurtosis, which characterize the asymmetry of the transferred-electron number and the combined weight of the tails relative to the rest of the probability distribution of the transferred-electron number, respectively. Thus, they provide further information for the FCS beyond the shot noise, and present a deeper insight into understanding of electron tunneling through the SCDQD system.

Extreme values in SIR epidemic models with two strains and cross-immunity.

The paper explores the dynamics of extreme values in an SIR (susceptible → infectious → removed) epidemic model with two strains of a disease. The strains are assumed to be perfectly distinguishable, instantly diagnosed and each strain of the disease confers immunity against the second strain, thus showing total cross-immunity. The aim is to derive the joint probability distribution of the maximum number of individuals simultaneously infected during an outbreak and the time to reach such a maximum number for the first time. Specifically, this distribution is analyzed by distinguishing between a global outbreak and the local outbreaks, which are linked to the extinction of the disease and the extinction of particular strains of the disease, respectively. Based on the mass function of the maximum number of individuals simultaneously infected during the outbreak, we also present an iterative procedure for computing the final size of the epidemic. For illustrative purposes, the twostrain SIR-model with cross-immunity is applied to the study of the spread of antibiotic-sensitive and antibiotic-resistant bacterial strains within a hospital ward.

Variability of collective dynamics in random tree networks of strongly coupled stochastic excitable elements

We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.

Baryon number probability distribution at finite temperature

The probability distribution of the net baryon number is investigated within the functional renormalization group approach. We find that the Roberge-Weiss periodicity related to the Z(3) symmetry of the gluon fields results directly in that, states of the net baryon number $N_B=N\pm 1/3$ with $N\in\mathbb{Z}$ are prohibited, and only those of $N_B=N$ are possible. By employing the probability distribution of the net baryon number, we also compute the cumulants of the baryon number distribution, which are found to be well consistent with those obtained from the generalized susceptibilities. A question about the relation between the color confinement and the probability distribution of net baryon number is put forward.

The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network

The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model on a complex network, over which a conserved quantity is transported in a random fashion, we study the dynamics of many elementary packets transported through the network by means of a master equation approach and compare with the mean field approximation and stochastic simulations. By use of the mean field theory, it is possible to compute an approximation to the ensemble average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the master equation. However, the master equation gives a more complete description of the stochastic system and provides a probabilistic view of the occupation number at each node. Of particular relevance is the standard deviation of the occupation number at each node, which is not uniform for a complex network. We analyze and compare different network topologies (small world, scale free, Erdos-Renyi, among others). Given the computational complexity of directly evaluating the asymptotic, or equilibrium, occupation number probability distribution, we propose a scaling relation with the number of packets in the network, that allows to construct the asymptotic probability distributions from the network with one packet. The approximation, which relies on the same matrix found in the mean field approach, becomes increasingly more accurate for a large number of packets.

Analysis of loss systems with overlapping resource requirements

In this paper, a queueing system with multicast service, random resource requirements and general probability distributions of busy and idle periods is considered. Motivated by challenges from practical applications in the area of performance analysis of telecommunication systems, the model is built on the basis of well-known resource queueing systems theory. Two distinctive features of the model related to resource requirements are: the volume of a requirement, which is random with a given probability distribution function, and the resource requirements which overlap with each other. The first feature comes from the analysis of wireless networks, where the volume of resource depends on the location of the mobile equipment, type of telecommunication service, required data bitrate and radio signal path loss. The second feature relates to the multicast approach to data delivery in modern telecommunication networks. The stationary probability distribution of the number of customers in the system is derived. The main characteristics for the performance analysis of multicast telecommunication systems including the blocking probability, the mean number of customers in the system and the mean of the total amount of occupied resources are proposed. The analytical formulas for the performance calculations are obtained for the Frechet-type distribution of a requested resources volume.

Simulation and Analysis of List Mode Measurements on SILENE Reactor

ABSTRACTNeutron time correlation measurements are used to characterize fissile systems. For this purpose, detailed information are obtained using list mode measurements where the neutron detection times are recorded in a file called the time list file. In this article, we present the simulation and analysis of list mode measurements performed on SILENE reactor. Analogue Monte Carlo simulations are performed using MCNPX code and the synthetic time list file is obtained by processing the MCNPX-PTRAC coincidence capture file. Both measured and computed time list files are processed using the same postprocessor that we have developed. This software is used to calculate counting statistics data like counting number probability distribution, Rossi alpha and Feynman functions for time gates of increasing duration. The parameter uncertainties are evaluated using a block bootstrap method.

N -tag probability law of the symmetric exclusion process

The symmetric exclusion process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognized qualitatively for a long time, up to now there has been no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically its large-time limit for an arbitrary density of particles, and its full dynamics in the high-density limit. In this limit, we obtain the time-dependent large deviation function of the problem and unveil a universal scaling form shared by the cumulants.

Intertwined electron-nuclear motion in frustrated double ionization in driven heteronuclear molecules

We study frustrated double ionization (FDI) in a strongly-driven heteronuclear molecule HeH+ and compare with H2. We compute the probability distribution of the sum of the final kinetic energies of the nuclei for strongly-driven HeH+. We find that this distribution has more than one peak for strongly-driven HeH+, a feature we do not find to be present for strongly-driven H2. Moreover, we compute the probability distribution of the principal quantum number n of FDI. We find that this distribution has several peaks for strongly-driven HeH+, while the respective distribution has one main peak and a ‘shoulder’ at lower principal quantum numbers n for strongly-driven H2. Surprisingly, we find this feature to be a clear signature of the intertwined electron-nuclear motion.