Estimating age conditional probability of developing disease from surveillance data
Fay Michael P
2004-07-01
Full Text Available Abstract Fay, Pfeiffer, Cronin, Le, and Feuer (Statistics in Medicine 2003; 22; 1837–1848 developed a formula to calculate the age-conditional probability of developing a disease for the first time (ACPDvD for a hypothetical cohort. The novelty of the formula of Fay et al (2003 is that one need not know the rates of first incidence of disease per person-years alive and disease-free, but may input the rates of first incidence per person-years alive only. Similarly the formula uses rates of death from disease and death from other causes per person-years alive. The rates per person-years alive are much easier to estimate than per person-years alive and disease-free. Fay et al (2003 used simple piecewise constant models for all three rate functions which have constant rates within each age group. In this paper, we detail a method for estimating rate functions which does not have jumps at the beginning of age groupings, and need not be constant within age groupings. We call this method the mid-age group joinpoint (MAJ model for the rates. The drawback of the MAJ model is that numerical integration must be used to estimate the resulting ACPDvD. To increase computational speed, we offer a piecewise approximation to the MAJ model, which we call the piecewise mid-age group joinpoint (PMAJ model. The PMAJ model for the rates input into the formula for ACPDvD described in Fay et al (2003 is the current method used in the freely available DevCan software made available by the National Cancer Institute.
47 CFR 1.1623 - Probability calculation.
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall...
Validation of fluorescence transition probability calculations
M. G. PiaINFN, Sezione di Genova; P. Saracco(INFN, Sezione di Genova); Manju Sudhaka(INFN, Sezione di Genova)
2015-01-01
A systematic and quantitative validation of the K and L shell X-ray transition probability calculations according to different theoretical methods has been performed against experimental data. This study is relevant to the optimization of data libraries used by software systems, namely Monte Carlo codes, dealing with X-ray fluorescence. The results support the adoption of transition probabilities calculated according to the Hartree-Fock approach, which manifest better agreement with experimen...
Necessity of Exact Calculation for Transition Probability
LIU Fu-Sui; CHEN Wan-Fang
2003-01-01
This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedby phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explainthe experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are veryimportant for the phonon-induced hopping rate enhancement in Pd-D system.
Calculation of radiative transition probabilities and lifetimes
Zemke, W. T.; Verma, K. K.; Stwalley, W. C.
1982-01-01
Procedures for calculating bound-bound and bound-continuum (free) radiative transition probabilities and radiative lifetimes are summarized. Calculations include rotational dependence and R-dependent electronic transition moments (no Franck-Condon or R-centroid approximation). Detailed comparisons of theoretical results with experimental measurements are made for bound-bound transitions in the A-X systems of LiH and Na2. New bound-free results are presented for LiH. New bound-free results and comparisons with very recent fluorescence experiments are presented for Na2.
Pade approximant calculations for neutron escape probability
The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)
Calculating nuclear accident probabilities from empirical frequencies
Ha-Duong, Minh; Journé, V.
2014-01-01
International audience Since there is no authoritative, comprehensive and public historical record of nuclear power plant accidents, we reconstructed a nuclear accident data set from peer-reviewed and other literature. We found that, in a sample of five random years, the worldwide historical frequency of a nuclear major accident, defined as an INES level 7 event, is 14 %. The probability of at least one nuclear accident rated at level ≥4 on the INES scale is 67 %. These numbers are subject...
Computational methods for probability of instability calculations
Wu, Y.-T.; Burnside, O. H.
1990-01-01
This paper summarizes the development of the methods and a computer program to compute the probability of instability of a dynamic system than can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the roots of the characteristics equation or Routh-Hurwitz test functions are investigated. Computational methods based on system reliability analysis methods and importance sampling concepts are proposed to perform efficient probabilistic analysis. Numerical examples are provided to demonstrate the methods.
Cross section probability tables in multi-group transport calculations
The use of cross section probability tables in multigroup transport calculations is presented. Emphasis is placed on how probability table parameters are generated in a multigroup cross section processor and how existing transport codes must be modifed to use them. In order to illustrate the accuracy obtained by using probability tables, results are presented for a variety of neutron and photon transport problems
Calculating state-to-state transition probabilities within TDDFT
Rohringer, Nina; Peter, Simone; Burgdörfer, Joachim
2005-01-01
The determination of the elements of the S-matrix within the framework of time-dependent density-functional theory (TDDFT) has remained a widely open question. We explore two different methods to calculate state-to-state transition probabilities. The first method closely follows the extraction of the S-matrix from the time-dependent Hartree-Fock approximation. This method suffers from cross-channel correlations resulting in oscillating transition probabilities in the asymptotic channels. An a...
Calculating the probability of detecting radio signals from alien civilizations
Horvat, Marko
2006-01-01
Although it might not be self-evident, it is in fact entirely possible to calculate the probability of detecting alien radio signals by understanding what types of extraterrestrial radio emissions can be expected and what properties these emissions can have. Using the Drake equation as the obvious starting point, and logically identifying and enumerating constraints of interstellar radio communications can yield the probability of detecting a genuine alien radio signal.
Calculating the probability of detecting radio signals from alien civilizations
Horvat, Marko
2007-01-01
Although it might not be self-evident, it is in fact entirely possible to calculate the probability of detecting alien radio signals by understanding what types of extraterrestrial radio emissions can be expected and what properties these emissions can have. Using the Drake equation as the obvious starting point, and logically identifying and enumerating constraints of interstellar radio communications can yield the probability of detecting a genuine alien radio signal.
Calculating the Probability of Returning a Loan with Binary Probability Models
Julian Vasilev
2014-12-01
Full Text Available The purpose of this article is to give a new approach in calculating the probability of returning a loan. A lot of factors affect the value of the probability. In this article by using statistical and econometric models some influencing factors are proved. The main approach is concerned with applying probit and logit models in loan management institutions. A new aspect of the credit risk analysis is given. Calculating the probability of returning a loan is a difficult task. We assume that specific data fields concerning the contract (month of signing, year of signing, given sum and data fields concerning the borrower of the loan (month of birth, year of birth (age, gender, region, where he/she lives may be independent variables in a binary logistics model with a dependent variable “the probability of returning a loan”. It is proved that the month of signing a contract, the year of signing a contract, the gender and the age of the loan owner do not affect the probability of returning a loan. It is proved that the probability of returning a loan depends on the sum of contract, the remoteness of the loan owner and the month of birth. The probability of returning a loan increases with the increase of the given sum, decreases with the proximity of the customer, increases for people born in the beginning of the year and decreases for people born at the end of the year.
Fostering Positive Attitude in Probability Learning Using Graphing Calculator
Tan, Choo-Kim; Harji, Madhubala Bava; Lau, Siong-Hoe
2011-01-01
Although a plethora of research evidence highlights positive and significant outcomes of the incorporation of the Graphing Calculator (GC) in mathematics education, its use in the teaching and learning process appears to be limited. The obvious need to revisit the teaching and learning of Probability has resulted in this study, i.e. to incorporate…
Calculation of the isotope cluster for polypeptides by probability grouping.
Olson, Matthew T; Yergey, Alfred L
2009-02-01
This paper presents a novel theoretical basis for accurately calculating the isotope cluster of polypeptides. In contrast to previous approaches to this problem, which consider exhaustive or near exhaustive combinations of isotopic species, the program, Neutron Cluster, groups probabilities to yield highly accurate information without elucidating any fine structure within a nominal mass unit. This is a fundamental difference from any previously described algorithm for calculating the isotope cluster. As a result of this difference, the accurate isotope clusters for high molecular weight polypeptides can be calculated rapidly without any pruning. When applied to isotope enriched polypeptides, the algorithm introduces "grouping error", which is described, quantified, and avoided by using probability partitioning. PMID:19026561
Selection of minimum earthquake intensity in calculating pipe failure probabilities
In a piping reliability analysis, it is sometimes necessary to specify a minimum ground motion intensity, usually the peak acceleration, below which the ground motions are not considered as earthquakes and, hence, are neglected. The calculated probability of failure of a piping system is dependent on this selected minimum earthquake intensity chosen for the analysis. A study was conducted to determine the effects of the minimum earthquake intensity on the probability of pipe failure. The results indicated that the probability of failure of the piping system is not very sensitive to the variations of the selected minimum peak ground acceleration. However, it does have significant effects on various scenarios that make up the system failure
Selection of minimum earthquake intensity in calculating pipe failure probabilities
Lo, T.Y.
1985-01-01
In a piping reliability analysis, it is sometimes necessary to specify a minimum ground motion intensity, usually the peak acceleration, below which the ground motions are not considered as earthquakes and, hence, are neglected. The calculated probability of failure of a piping system is dependent on this selected minimum earthquake intensity chosen for the analysis. A study was conducted to determine the effects of the minimum earthquake intensity on the probability of pipe failure. The results indicated that the probability of failure of the piping system is not very sensitive to the variations of the selected minimum peak ground acceleration. However, it does have significant effects on various scenarios that make up the system failure.
Calculating the probability of injected carbon dioxide plumes encountering faults
Jordan, P.D.
2011-04-01
One of the main concerns of storage in saline aquifers is leakage via faults. In the early stages of site selection, site-specific fault coverages are often not available for these aquifers. This necessitates a method using available fault data to estimate the probability of injected carbon dioxide encountering and migrating up a fault. The probability of encounter can be calculated from areal fault density statistics from available data, and carbon dioxide plume dimensions from numerical simulation. Given a number of assumptions, the dimension of the plume perpendicular to a fault times the areal density of faults with offsets greater than some threshold of interest provides probability of the plume encountering such a fault. Application of this result to a previously planned large-scale pilot injection in the southern portion of the San Joaquin Basin yielded a 3% and 7% chance of the plume encountering a fully and half seal offsetting fault, respectively. Subsequently available data indicated a half seal-offsetting fault at a distance from the injection well that implied a 20% probability of encounter for a plume sufficiently large to reach it.
On calculating the probability of a set of orthologous sequences
Junfeng Liu
2009-02-01
Full Text Available Junfeng Liu1,2, Liang Chen3, Hongyu Zhao4, Dirk F Moore1,2, Yong Lin1,2, Weichung Joe Shih1,21Biometrics Division, The Cancer, Institute of New Jersey, New Brunswick, NJ, USA; 2Department of Biostatistics, School of Public Health, University of Medicine and Dentistry of New Jersey, Piscataway, NJ, USA; 3Department of Biological Sciences, University of Southern California, Los Angeles, CA, USA; 4Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT, USAAbstract: Probabilistic DNA sequence models have been intensively applied to genome research. Within the evolutionary biology framework, this article investigates the feasibility for rigorously estimating the probability of a set of orthologous DNA sequences which evolve from a common progenitor. We propose Monte Carlo integration algorithms to sample the unknown ancestral and/or root sequences a posteriori conditional on a reference sequence and apply pairwise Needleman–Wunsch alignment between the sampled and nonreference species sequences to estimate the probability. We test our algorithms on both simulated and real sequences and compare calculated probabilities from Monte Carlo integration to those induced by single multiple alignment.Keywords: evolution, Jukes–Cantor model, Monte Carlo integration, Needleman–Wunsch alignment, orthologous
Calculation of cranial nerve complication probability for acoustic neuroma radiosurgery
Purpose: Estimations of complications from stereotactic radiosurgery usually rely simply on dose-volume or dose-diameter isoeffect curves. Due to the sparse clinical data available, these curves have typically not considered the target location in the brain, target histology, or treatment plan conformality as parameters in the calculation. In this study, a predictive model was generated to estimate the probability of cranial neuropathies as a result of acoustic schwannoma radiosurgery. Methods and Materials: The dose-volume histogram reduction scheme was used to calculate the normal tissue complication probability (NTCP) from brainstem dose-volume histograms. The model's fitting parameters were optimized to provide the best fit to the observed complication data for acoustic neuroma patients treated with stereotactic radiosurgery at the University of Florida. The calculation was then applied to the remainder of the patients in the database. Results: The best fit to our clinical data was obtained using n = 0.04, m = 0.15, and no. alphano. /no. betano. = 2.1 Gy-1. Although the fitting parameter m is relatively consistent with ranges found in the literature, both the volume parameter, n, and no. alphano. /no. betano. are much smaller than the values quoted in the literature. The fit to our clinical data indicates that brainstem, or possibly a specific portion of the brainstem, is more radiosensitive than the parameters in the literature indicate, and that there is very little volume effect; in other words, irradiation of a small fraction of the brainstem yields NTCPs that are nearly as high as those calculated for entire volume irradiation. These new fitting parameters are specific to acoustic neuroma radiosurgery, and the small volume effect that we observe may be an artifact of the fixed relationship of acoustic tumors to specific regions of the brainstem. Applying the model to our patient database, we calculate an average NTCP of 7.2% for patients who had no cranial
Revised transition probabilities for Fe XXV: Relativistic CI calculations
Revised data are provided for transition probabilities between fine-structure components of levels with n ≤ 6 in Fe XXV. Earlier published data for transitions between fine-structure levels in Fe XXV are found to be in error, especially for certain classes of transitions. The purpose of the present note is to provide a corrected database for transitions in Fe XXV. Wavefunctions and energies for states with n ≤ 6 and J = 0, 1, 2, 3 are determined using a relativistic configuration interaction (CI) expansion that includes the Breit interaction. To measure and control the numerical accuracy of the calculations, we compare our CI energies and matrix elements with values calculated using relativistic second-order many-body perturbation theory (MBPT), also including the Breit interaction. We obtain good agreement between our CI and MBPT calculations but disagree with earlier calculations for transitions with ΔL = 2 and for intercombination transitions (ΔS = 1). We provide wavelengths, line strengths, and transitions rates for fine-structure transition between levels with n ≤ 6 in Fe XXV
CALCULATION OF PER PARCEL PROBABILITY FOR DUD BOMBS IN GERMANY
S. M. Tavakkoli Sabour
2014-10-01
Full Text Available Unexploded aerial Bombs, also known as duds or unfused bombs, of the bombardments in the past wars remain explosive for decades after the war under the earth’s surface threatening the civil activities especially if dredging works are involved. Interpretation of the aerial photos taken shortly after bombardments has been proven to be useful for finding the duds. Unfortunately, the reliability of this method is limited by some factors. The chance of finding a dud on an aerial photo depends strongly on the photography system, the size of the bomb and the landcover. On the other hand, exploded bombs are considerably better detectable on aerial photos and confidently represent the extent and density of a bombardment. Considering an empirical quota of unfused bombs, the expected number of duds can be calculated by the number of exploded bombs. This can help to have a better calculation of cost-risk ratio and to classify the areas for clearance. This article is about a method for calculation of a per parcel probability of dud bombs according to the distribution and density of exploded bombs. No similar work has been reported in this field by other authors.
Jet identification based on probability calculations using Bayes' theorem
The problem of identifying jets at LEP and HERA has been studied. Identification using jet energies and fragmentation properties was treated separately in order to investigate the degree of quark-gluon separation that can be achieved by either of these approaches. In the case of the fragmentation-based identification, a neural network was used, and a test of the dependence on the jet production process and the fragmentation model was done. Instead of working with the separation variables directly, these have been used to calculate probabilities of having a specific type of jet, according to Bayes' theorem. This offers a direct interpretation of the performance of the jet identification and provides a simple means of combining the results of the energy- and fragmentation-based identifications. (orig.)
Calculation of transition probabilities using the multiconfiguration Dirac-Fock method
The performance of the multiconfiguration Dirac-Fock (MCDF) method in calculating transition probabilities of atoms is reviewed. In general, the MCDF wave functions will lead to transition probabilities accurate to ∼ 10% or better for strong, electric-dipole allowed transitions for small atoms. However, it is more difficult to get reliable transition probabilities for weak transitions. Also, some MCDF wave functions for a specific J quantum number may not reduce to the appropriate L and S quantum numbers in the nonrelativistic limit. Transition probabilities calculated from such MCDF wave functions for nonrelativistically forbidden transitions are unreliable. Remedies for such cases are discussed
Calculation of transition probabilities using the multiconfiguration Dirac-Fock method
The performance of the multiconfiguration Dirac-Fock (MCDF) method in calculating transition probabilities of atoms is reviewed. In general, the MCDF wave functions will lead to transition probabilities accurate to ∼10% or better for strong, electric-dipole allowed transitions for small atoms. However, it is more difficult to get reliable transition probabilities for weak transitions. Also, some MCDF wave functions for specific J quantum number may not reduce to the appropriate L and S quantum numbers in the nonrelativistic limit. Transition probabilities calculation from such MCDF wave functions for nonrelativistically forbidden transitions are unreliable. Remedies for such cases are discussed.
In order to calculate the more accurate top event probability from cutsets or minimal cut sets (MCSs) than the conventional method that adopts the rare event approximation (REA) or min cut upper bound (MCUB) calculation, advanced cutset upper bound estimator (ACUBE) software had been developed several years ago and shortly became a vital tool for calculating the accurate core damage frequency of nuclear power plants in probabilistic safety assessment (PSA). Usually, the whole cutsets in the industry PSA models cannot be converted into a Binary decision diagram (BDD) due to the limited computational memory. So, the ACUBE selects the major cutsets whose probabilities are larger than the others, and then converts the major cutsets into a BDD in order to calculate more accurate top event probability from cutsets. This study (1) suggests when and where the ACUBE should be employed by predicting the amount of overestimation of the top event probability depending on the cutset structure, (2) explains the details of the ACUBE algorithm, and (3) demonstrates the efficiency of the ACUBE by calculating the top event probability of some PSA cutsets. - Highlights: • EPRI report [32] introduces many successful events in the seismic PSA cutsets. • This results in drastically overestimated top event probability. • In order to overcome this problem, the author developed ACUBE software. • ACUBE calculation can be determined according to the cutset structure (Section 4). • ACUBE calculation removes unnecessary conservatism in the top event probability
Duality-based calculations for transition probabilities in birth-death processes
Ohkubo, Jun
2015-01-01
Transition probabilities in birth-death processes are fomulated via the corresponding dual birth-death processes. In order to obtain the corresponding dual processes, the Doi-Peliti formalism is employed. Conventional numerical evaluation enables us to obtain the transition probabilities from a fixed initial state; on the other hand, the duality relation gives us a useful method to calculate the transition probabilities to a fixed final state. Furthermore, it is clarified that the transition ...
Inclusive probability calculations for the K-vacancy transfer in collisions of S{^15+} on Ar
Kürpick, Peter; Sepp, Wolf-Dieter; Fricke, Burkhard
1992-01-01
Using the single-particle amplitudes from a 20-level coupled-channel calculation with ab initio relativistic self consistent LCAO-MO Dirac-Fock-Slater energy eigenvalues and matrix elements we calculate within the frame of the inclusive probability formalism impact-parameter-dependent K-hole transfer probabilities. As an example we show results for the heavy asymmetric collision system S{^15+} on Ar for impact energies from 4.7 to 16 MeV. The inclusive probability formalism whi...
Quantum dynamics calculation of reaction probability for H+Cl2→HCl+Cl
无
2001-01-01
We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + Cl2 based on the GHNS potential energy surface with total angular momentum J = 0. The effects of the translational, vibrational and rotational excitation of Cl2 on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.
Quantum dynamics calculation of reaction probability for H+Cl2→HC1+Cl
王胜龙; 赵新生
2001-01-01
We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + CI2 based on the GHNS potential energy surface with total angular momentum J= 0. The effects of the translational, vibrational and rotational excitation of CI2 on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.
The risk of major nuclear accident: calculation and perception of probabilities
Whereas before the Fukushima accident, already eight major accidents occurred in nuclear power plants, a number which is higher than that expected by experts and rather close to that corresponding of people perception of risk, the author discusses how to understand these differences and reconcile observations, objective probability of accidents and subjective assessment of risks, why experts have been over-optimistic, whether public opinion is irrational regarding nuclear risk, and how to measure risk and its perception. Thus, he addresses and discusses the following issues: risk calculation (cost, calculated frequency of major accident, bias between the number of observed accidents and model predictions), perceived probabilities and aversion for disasters (perception biases of probability, perception biases unfavourable to nuclear), the Bayes contribution and its application (Bayes-Laplace law, statistics, choice of an a priori probability, prediction of the next event, probability of a core fusion tomorrow)
Calculating Probability Tables for the Unresolved-Resonance Region Using Monte Carlo Methods
A new module, Probability tables for the Unresolved Region using Monte Carlo (PURM), has been developed for the AMPX-2000 cross-section-processing system. PURM uses a Monte Carlo approach to calculate probability tables on an evaluator-defined energy grid in the unresolved-resonance region. For each probability table, PURM samples a Wigner spacing distribution for pairs of resonances surrounding the reference energy (i.e., energy specified in the cross-section evaluation). The resonance distribution is sampled for each spin sequence (i.e., l-J pair), and PURM uses the δ3-statistics test to determine the number of resonances to sample for each spin sequence. For each resonance, PURM samples the resonance widths from a chi-square distribution for a specified number of degrees of freedom. Once the resonance parameters are sampled, PURM calculates the total, capture, fission, and scatter cross sections at the reference energy using the single-level Breit-Wigner formalism with appropriate treatment for temperature effects. Probability tables have been calculated and compared with NJOY. The probability tables and cross-section values that are calculated by PURM and NJOY are in agreement, and the verification studies with NJOY establish the computational capability for generating probability tables using the new AMPX module PURM
Hyun-Kyung Chung; Per Jönsson; Alexander Kramida
2013-01-01
Atomic structure and transition probabilities are fundamental physical data required in many fields of science and technology. Atomic physics codes are freely available to other community users to generate atomic data for their interest, but the quality of these data is rarely verified. This special issue addresses estimation of uncertainties in atomic structure and transition probability calculations, and discusses methods and strategies to assess and ensure the quality of theoretical atomic...
'PRIZE': A program for calculating collision probabilities in R-Z geometry
PRIZE is an IBM7090 program which computes collision probabilities for systems with axial symmetry and outputs them on cards in suitable format for the PIP1 program. Its method of working, data requirements, output, running time and accuracy are described. The program has been used to compute non-escape (self-collision) probabilities of finite circular cylinders, and a table is given by which non-escape probabilities of slabs, finite and infinite circular cylinders, infinite square cylinders, cubes, spheres and hemispheres may quickly be calculated to 1/2% or better. (author)
Torpedo's Search Trajectory Design Based on Acquisition and Hit Probability Calculation
LI Wen-zhe; ZHANG Yu-wen; FAN Hui; WANG Yong-hu
2008-01-01
Taking aim at light torpedo search trajectory characteristic of warship, by analyzing common used torpedo search trajectory, a better torpedo search trajectory is designed, a mathematic model is built up, and the simulation calculation taking MK46 torpedo for example is carried out. The calculation results testify that this method can increase acquisition probability and hit probability by about 10%-30% at some situations and becomes feasible for the torpedo trajectory design. The research is of great reference value for the acoustic homing torpedo trajectory design and the torpedo combat efficiency research.
The paper illustrates an application of new mathematical formulae to calculate the failure probability of a system when the time for repair is limited to a maximum value. Failure of all redundant sub-systems does not cause instant damage; the system must remain in the failed state for a given finite time T for damage to occur. If repair to any sub-system is completed within T the damage will be averted; otherwise the system will suffer irrepairable damage. The example chosen does not refer to any particular system although the data used are taken from real components. It consists of a vessel accommodating a constant heat source for a period of 6 months. The system failure considered is damage caused by excessive temperature. The probability of exceeding this temperature for the system is calculated and the results are compared with simple unreliability calculations. The effect of different repair conditions on the calculations is also considered. (author)
A semi-mechanistic approach to calculate the probability of fuel defects
In this paper the authors describe the status of a semi-mechanistic approach to the calculation of the probability of fuel defects. This approach expresses the defect probability in terms of fundamental parameters such as local stresses, local strains, and fission product concentration. The calculations of defect probability continue to reflect the influences of the conventional parameters like power ramp, burnup and CANLUB. In addition, the new approach provides a mechanism to account for the impacts of additional factors involving detailed fuel design and reactor operation, for example pellet density, pellet shape and size, sheath diameter and thickness, pellet/sheath clearance, and coolant temperature and pressure. The approach has been validated against a previous empirical correlation. AN illustrative example shows how the defect thresholds are influenced by changes in the internal design of the element and in the coolant pressure. (Author) (7 figs., tab., 12 refs.)
Calculation of ruin probabilities for a dense class of heavy tailed distributions
Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady
2015-01-01
any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest such as the...... renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation of...... distributions with a slowly varying tail. An example from risk theory, comparing ruin probabilities for a classical risk process with Pareto distributed claim sizes, is presented and exact known ruin probabilities for the Pareto case are compared to the ones obtained by approximating by an infinite...
PABS: A Computer Program to Normalize Emission Probabilities and Calculate Realistic Uncertainties
The program PABS normalizes relative particle emission probabilities to an absolute scale and calculates the relevant uncertainties on this scale. The program is written in Java using the JDK 1.6 library. For additional information about system requirements, the code itself, and compiling from source, see the README file distributed with this program. The mathematical procedures used are given.
Calculation of Quantum Probability in O(2,2) String Cosmology with a Dilaton Potential
YAN Jun
2006-01-01
The quantum properties of O(2,2) string cosmology with a dilaton potential are studied in this paper. The cosmological solutions are obtained on three-dimensional space-time. Moreover, the quantum probability of transition between two duality universe is calculated through a Wheeler-De Witt approach.
We investigated how the pulse parameters of optical frequency combs affect the rotational excitation probability of the lithium chloride (7Li37Cl) molecule. Time evolution of the rotational population distribution was calculated by the close-coupling method. It was confirmed that the rotational excitation is restricted owing to the centrifugal distortion of the rotating molecule. (author)
Calculation of the Multivariate Probability Distribution Function Values and their Gradient Vectors
Szantai, T.
1987-01-01
The described collection of subroutines developed for calculation of values of multivariate normal, Dirichlet and gamma distribution functions and their gradient vectors is an unique tool that can be used e.g. to compute the Loss-of-Load Probability of electric networks and to solve optimization problems with a reliability constraint.
PABS: A Computer Program to Normalize Emission Probabilities and Calculate Realistic Uncertainties
Caron, D. S.; Browne, E.; Norman, E. B.
2009-08-21
The program PABS normalizes relative particle emission probabilities to an absolute scale and calculates the relevant uncertainties on this scale. The program is written in Java using the JDK 1.6 library. For additional information about system requirements, the code itself, and compiling from source, see the README file distributed with this program. The mathematical procedures used are given below.
Calculation of the escape probabilities of Fe ⅹⅦ resonance lines for the Voigt profile
Jian HE; Qing-guo ZHANG
2008-01-01
Using the Voigt profile we obtained, we cal-culate the escape probabilities of Fe ⅹⅦ resonance lines at 15.02, 13.28, 12.12, 11.13, 11.02 and 10.12 A for op-tically thick plasma, both for slab and cylindrical ge-ometry. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed in this calculation. Results show that the escape probabilities for the slab geometry are larger than that for the cylindrical geom-etry. This calculation is useful for the study of the Fe ⅹⅦ resonance lines.
An algorithm for calculating steady state probabilities of $M|E_r|c|K$ queueing systems
Hochrainer, Stefan; Hochreiter, Ronald; Pflug, Georg
2014-01-01
This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this matrix can be written down immediately for many other $M|PH|c|K$ queueing systems with phase-type service times (e.g. Coxian, Hypoexponential, \\ldots), it requires a more careful analysis for systems with Erlangian service times. The constructed matrix may t...
Results from multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) calculations are presented for the n=3 to n′=3 transitions in the Mg isoelectronic sequence. The calculated values for the lowest 35 levels including core–valence correlation are found to be similar and to compare very well with other theoretical and experimental values. The Breit interaction and leading quantum electrodynamic effects are included as perturbations. The calculations can provide useful data for the experimental study of determining the fine structure levels in future work. - Highlights: • Multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction calculations were used. • The valence–valence and core–valence correlations are considered. • Energy levels and transitions probabilities are calculated for 35 levels of magnesium-like ions. • Detail QED and total energy for four configurations were presented
The calculations given in the paper are intended to explain the delayed neutron emission (energy spectra and emission probabilities Pn) which follows the β- disintegration of the precursors produced by fission. The probability of β- transition, the level density ω (E, J) of the emitter and the competition (β-, γ) and (β-, n) de-energizations are analysed for each precursor studied. All the possible channels open to the process of neutron emission on grounds of energy considerations (Qβ-, Bn) are taken into account through the introduction of the spin and parity selection rules at each stage of the sequence: precursor, emitter, final nucleus. The results of the calculations are compared with the known experimental measurements of the neutron energy spectra and probabilities Pn. The precursors 87Br, 88Br, 137I and 93-97Rb were selected for this examination. This comparison shows in particular that the structure of experimental energy spectra can be well reproduced by the calculations given in the paper. Moreover, it emerges that the spectra calculated are very sensitive to the choice of the spins of the precursor and the final nucleus. (author)
Corrections to vibrational transition probabilities calculated from a three-dimensional model.
Stallcop, J. R.
1972-01-01
Corrections to the collision-induced vibration transition probability calculated by Hansen and Pearson from a three-dimensional semiclassical model are examined. These corrections come from the retention of higher order terms in the expansion of the interaction potential and the use of the actual value of the deflection angle in the calculation of the transition probability. It is found that the contribution to the transition cross section from previously neglected potential terms can be significant for short range potentials and for the large relative collision velocities encountered at high temperatures. The correction to the transition cross section obtained from the use of actual deflection angles will not be appreciable unless the change in the rotational quantum number is large.
Comparison of three methods for calculation of electron transfer probability in H+ + Ne
We have developed a theoretical model of ion-atom collisions where we described electron dynamics by the time-dependent density-functional theory (TDDFT) and the ion dynamics by classical mechanics through the Ehrenfest method. We have compared three methods to calculate the probability of electron transfer during H+ + Ne collision. By discussing these issues we shall be able to understand how these methods work, what their limitations are and whether they admit of any improvements. -- Highlights: ► We have developed a theoretical model of ion-atom collisions based on TDDFT. ► We have compared three methods to calculate the probability of electron transfer in H+ + Ne. ► Electron transfer cross sections showed a good agreement with available experimental data.
The Calculations of Oscillator Strengths and Transition Probabilities for Atomic Fluorine
ÇELİK, Gültekin; KILIÇ, H. Şükür; Akin, Erhan
2006-01-01
Oscillator strengths for transitions between individual lines belonging to some doublet and quartet terms, and multiplet transition probabilities of atomic fluorine have been calculated using weakest bound electron potential model theory (WBEPMT). In the determination of relevant parameters, we employed numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii and the necessary energy values have been taken from experimental energy data in the liter...
The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2 x 2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. We also discuss the application of this method to multi-level systems
Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ebeida, Mohamed Salah [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Romero, Vicente J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Swiler, Laura Painton [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rushdi, Ahmad A. [Univ. of Texas, Austin, TX (United States); Abdelkader, Ahmad [Univ. of Maryland, College Park, MD (United States)
2015-09-01
This SAND report summarizes our work on the Sandia National Laboratory LDRD project titled "Efficient Probability of Failure Calculations for QMU using Computational Geometry" which was project #165617 and proposal #13-0144. This report merely summarizes our work. Those interested in the technical details are encouraged to read the full published results, and contact the report authors for the status of the software and follow-on projects.
Skripnichenko, P.; Galushina, T.; Loginova, M.
2015-08-01
This work is devoted to the description of the software EROS (Ephemeris Research and Observation Services), which is being developed both by the astronomy department of Ural Federal University and Tomsk State University. This software provides the ephemeris support for the positional observations. The most interesting feature of the software is an automatization of all the processes preparation for observations from the determination of the night duration to the ephemeris calculation and forming of a program observation schedule. The accuracy of ephemeris calculation mostly depends on initial data precision that defined from errors of observations which used to determination of orbital elements. In the case if object has a small number of observations which spread at short arc of orbit there is a real necessity to calculate not only at nominal orbit but probability domain both. In this paper under review ephemeris we will be understand a field on the celestial sphere which calculated based on the probability domain. Our software EROS has a relevant functional for estimation of review ephemeris. This work contains description of software system and results of the program using.
Validation of the ROVER-F code for ROP trip probability calculations
An important task in the operation of CANDU reactors is the prevention of fuel damage as a result of fuel dryout that can occur when the fuel sheath temperature exceeds the temperature at which the coolant can efficiently remove heat. The power at which fuel dryout is expected to occur is called the critical channel power and is a function of flux shape and the fuel channel thermalhydraulics. In CANDU reactors, protection against overpowers large enough to cause dryout is provided by two regional overpower protection (ROP) systems of in-core flux detectors, arrayed through the core, each organized into three safety (or logic) channels. Each of the two independent ROP systems is associated with one of the two independent shutdown systems (SDS-1 and SDS-2). The detectors in one ROP system (associated with SDS-1) are placed in vertical penetrations, whereas the other system (associated with SDS-2) uses detectors in horizontal penetrations in the core. Each ROP system is capable of initiating the shutdown of the reactor by actuating the corresponding shutdown system. Each ROP system must be so designed that in each safety channel at l east one detector will reach its setpoint before there is damaging overpower in any fuel channel. The trip of a single detector in a safety channel will trip that channel, and the trip of two of the three safety channels in an ROP system will trip that ROP system. ROVER-F is a FORTRAN program which calculates the trip probability and the setpoint adjustment required to attain the target trip probability, for a given set of flux shapes. This calculation is performed with the assumption that the most effective safety channel is unavailable and therefore the remaining two safety channels must both trip. The calculation of trip probability itself is non-iterative, but once the trip probability of the specified system has been calculated, a convergence iteration using a binomial search is used to determine the adjustment to the trip setpoints
Calculation of Auger-neutralization probabilities for He{sup +}-ions in LEIS
Goebl, D., E-mail: dominik.goebl@jku.at [Institut Fuer Experimentalphysik, Abt. Atom- und Oberflaechenphysik, Johannes Kepler Universitaet, A-4040 Linz (Austria); Monreal, R.C.; Valdes, D.; Primetzhofer, D. [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid (Spain); Bauer, P. [Institut Fuer Experimentalphysik, Abt. Atom- und Oberflaechenphysik, Johannes Kepler Universitaet, A-4040 Linz (Austria)
2011-06-01
In Low Energy Ion Scattering (LEIS), Auger-neutralization is an omnipresent charge exchange mechanism, especially when noble gas ions are used as projectiles, with a primary energy below the threshold energy, E{sub th}, for collision induced charge exchange processes (neutralization and reionization). Recent experiments revealed a significant dependence of the ion survival probability, P{sup +}, on the crystal plane, when He{sup +} ions are scattered from a metal surface. This is in contrast to the fact, that the neutralization probability in LEIS is usually assumed to be independent of the chemical environment of the collision partner (absence of matrix effects). In order to investigate this crystal effect, an existent theory on Auger-neutralization (based on a Linear Combination of Atomic Orbitals) is adapted to the LEIS geometry. With this model, Auger-neutralization rates are calculated for a Ag(1 1 0) surface. Trajectories for He particles scattered from this surface into different azimuth directions are obtained by means of Molecular Dynamics simulations. Subsequently, the ion survival probability is calculated and compared to measurements. Good agreement is obtained which gives confidence in the applicability of this model in the LEIS regime. Moreover, it was possible to obtain detailed information on the properties of the neutralization process.
Computing Moment-Based Probability Tables for Self-Shielding Calculations in Lattice Codes
As part of the self-shielding model used in the APOLLO2 lattice code, probability tables are required to compute self-shielded cross sections for coarse energy groups (typically with 99 or 172 groups). This paper describes the replacement of the multiband tables (typically with 51 subgroups) with moment-based tables in release 2.5 of APOLLO2. An improved Ribon method is proposed to compute moment-based probability tables, allowing important savings in CPU resources while maintaining the accuracy of the self-shielding algorithm. Finally, a validation is presented where the absorption rates obtained with each of these techniques are compared with exact values obtained using a fine-group elastic slowing-down calculation in the resolved energy domain. Other results, relative to the Rowland's benchmark and to three assembly production cases, are also presented
An improved collision probability method for thermal-neutron-flux calculation in a cylindrical reactor cell has been developed. Expanding the neutron flux and source into a series of even powers of the radius, one' gets a convenient method for integration of the one-energy group integral transport equation. It is shown that it is possible to perform an analytical integration in the x-y plane in one variable and to use the effective Gaussian integration over another one. Choosing a convenient distribution of space points in fuel and moderator the transport matrix calculation and cell reaction rate integration were condensed. On the basis of the proposed method, the computer program DISKRET for the ZUSE-Z 23 K computer has been written. The suitability of the proposed method for the calculation of the thermal-neutron-flux distribution in a reactor cell can be seen from the test results obtained. Compared with the other collision probability methods, the proposed treatment excels with a mathematical simplicity and a faster convergence. (author)
Analyses of the resonant multiphoton ionization of atoms require knowledge of ac Stark energy shifts and of multiphoton, bound-to-bound state, transition amplitudes. In this paper, we consider the three-photon photoionization of hydrogen atoms at frequencies that are at and surrounding the two-photon 1s to 2s resonance. AC energy shift sums of both the 1s and 2s states are calculated as a function of the laser frequency along with two-photon 1s → 2s resonant transition amplitude sums. These quantities are calculated using an extended version of a method, which has often been employed in a variety of ways, of calculating these sums by expressing them in terms of solutions to a variety of differential equations that are derived from the different sums being evaluated. We demonstrate how exact solutions are obtained to these differential equations, which lead to exact evaluations of the corresponding sums. A variety of different cases are analysed, some involving analytic continuation, some involving real number analysis and some involving complex number analysis. A dc Stark sum calculation of the 2s state is carried out to illustrate the case where analytic continuation, pole isolation and pole subtraction are required and where the calculation can be carried out analytically; the 2s state, ac Stark shift sum calculations involve a case where no analytic continuation is required, but where the solution to the differential equation produces complex numbers owing to the finite photoionization lifetime of the 2s state. Results from these calculations are then used to calculate three-photon ionization probabilities of relevance to an analysis of the multiphoton ionization data published by Kyrala and Nichols (1991 Phys. Rev. A 44, R1450)
Calculation of oscillation probabilities of atmospheric neutrinos using nuCraft
Wallraff, Marius
2014-01-01
NuCraft (nucraft.hepforge.org) is an open-source Python project that calculates neutrino oscillation probabilities for neutrinos from cosmic-ray interactions in the atmosphere for their propagation through Earth. The solution is obtained by numerically solving the Schr\\"odinger equation. The code supports arbitrary numbers of neutrino flavors including additional sterile neutrinos, CP violation, arbitrary mass hierarchies, matter effects with a configurable Earth model, and takes into account the production height distribution of neutrinos in the Earth's atmosphere.
Failures probability calculation of the energy supply of the Angra-1 reactor rods assembly
This work analyses the electric power system of the Angra I PWR plant. It is demonstrated that this system is closely coupled with the safety engineering features, which are the equipments provided to prevent, limit, or mitigate the release of radioactive material and to permit the safe reactor shutdown. Event trees are used to analyse the operation of those systems which can lead to the release of radioactivity following a specified initial event. The fault trees technique is used to calculate the failure probability of the on-site electric power system
Theoretical Calculations of Transition Probabilities and Oscillator Strengths for Sc(Ⅲ) and Y(Ⅲ)
Tian-yi Zhang; Neng-wu Zheng
2009-01-01
The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc(Ⅲ) and Y(Ⅲ). In this method, by solving the SchrSdinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The ob-tained results of Sc(Ⅲ) from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy (NIST) data base, most deviations are within the accepted level. For Y(Ⅲ) there are no accepted values reported by the NIST data base. So we compared our results of Y(Ⅲ) with other theoretical results, good agreement is also obtained.
Research on calculation modes of tumor control probability following internal radionuclide therapy
Objective: To construct a calculation model of tumor control probability (TCP) with consideration of the effect of dose and biological factors. It is expected that the result calculated by the model following internal radionuclide therapy would be appropriate to the actual value. Methods: Referring to the TCP models of radiotherapy and the models of cell survival rate reported by other authors, a TCP model (model 3) following internal radionuclide therapy, which considered the effect factors of dose, repair of DNA single-strand damage, radiosensitivity has been set up. Then using nuclide 32P as an example, model 3 will be compared with the other two models (model 1 and 2) by calculation the TCP value under the same treatment conditions. Results: Compared with model 1 and 2, the result calculated by model 3 shows that: 1. With a certain treatment activity (3.7 x 107 Bq), the radius of tumor which can be cured is closer to the experiment result. 2. If the given activity is infinitely great, the largest tumor radius which can be cured is smaller and coincide with the largest range of nuclide 32P. So the result calculated by model 3 is fitter with the actual value than that calculated by the other two models. Conclusion: The model 3 has considered more factors than others, so if the biological parameters are known, it could be used to calculate the TCP value under a certain kind of treatment condition to predict the internal radionuclide therapy result and estimate whether the treatment plan is reasonable
Direct calculation of the probability of pionium ionization in the target
The goal of the DIRAC experiment at CERN is the lifetime measurement of pionium (π+π- atom). Its lifetime is mainly defined by the charge-exchange process π+π-→ π0π0. The value of the lifetime in the ground state is predicted in the framework of chiral perturbation theory with high precision: τ1S = (2.9 ± 0.1) x 10-15 s. The method used by DIRAC is based on analysis of π+π--pair spectra with small relative momenta in their center-of-mass system in order to find out the signal from pionium ionization (breakup) in the target. Pioniums are produced in proton-nucleus collisions and have relativistic velocities (γ > 10). For fixed values of the pionium momentum and the target thickness, the probability of pionium ionization in the target depends on its lifetime in a unique way; thus, the pionium lifetime can be deduced from the experimentally defined probability of pionium ionization. On the basis of ionization cross sections of pionium with target atoms, we perform the first direct calculation of the pionium ionization probability in the target.
New energy levels, calculated lifetimes and transition probabilities in Xe IX
Gallardo, M; Raineri, M; Reyna Almandos, J [Centro de Investigaciones Opticas (CIOp), CC 3 (1897) Gonnet, La Plata (Argentina); Biemont, E [IPNAS, Universite de Liege, B15 Sart Tilman, B-4000 Liege (Belgium)
2011-02-28
Twenty-one new experimental energy levels belonging to the 4d{sup 9}6p, 4d{sup 9}4f and 4d{sup 9}5f configurations of Xe IX are presented. They have been deduced from 75 newly classified lines involving the configurations 4d{sup 9}5p, 4d{sup 9}6p, 4d{sup 9}4f, 4d{sup 9}5f and 4d{sup 9}5d, 4d{sup 9}5s, 4d{sup 9}6s for the odd and even parities, respectively. The radiative lifetimes of these levels as well as the weighted oscillator strengths and transition probabilities for all the observed spectral lines have been calculated with optimized parameters deduced from a least-squares fitting procedure applied in the framework of a relativistic Hartree-Fock method including core-polarization effects. The scale of transition probabilities has also been assessed through comparisons with lifetimes calculated using a relativistic multiconfigurational Dirac-Fock approach.
Barengoltz, Jack
2016-07-01
Monte Carlo (MC) is a common method to estimate probability, effectively by a simulation. For planetary protection, it may be used to estimate the probability of impact P{}_{I} by a launch vehicle (upper stage) of a protected planet. The object of the analysis is to provide a value for P{}_{I} with a given level of confidence (LOC) that the true value does not exceed the maximum allowed value of P{}_{I}. In order to determine the number of MC histories required, one must also guess the maximum number of hits that will occur in the analysis. This extra parameter is needed because a LOC is desired. If more hits occur, the MC analysis would indicate that the true value may exceed the specification value with a higher probability than the LOC. (In the worst case, even the mean value of the estimated P{}_{I} might exceed the specification value.) After the analysis is conducted, the actual number of hits is, of course, the mean. The number of hits arises from a small probability per history and a large number of histories; these are the classic requirements for a Poisson distribution. For a known Poisson distribution (the mean is the only parameter), the probability for some interval in the number of hits is calculable. Before the analysis, this is not possible. Fortunately, there are methods that can bound the unknown mean for a Poisson distribution. F. Garwoodfootnote{ F. Garwood (1936), ``Fiduciary limits for the Poisson distribution.'' Biometrika 28, 437-442.} published an appropriate method that uses the Chi-squared function, actually its inversefootnote{ The integral chi-squared function would yield probability α as a function of the mean µ and an actual value n.} (despite the notation used): This formula for the upper and lower limits of the mean μ with the two-tailed probability 1-α depends on the LOC α and an estimated value of the number of "successes" n. In a MC analysis for planetary protection, only the upper limit is of interest, i.e., the single
Calculating inspector probability of detection using performance demonstration program pass rates
Cumblidge, Stephen; D'Agostino, Amy
2016-02-01
The United States Nuclear Regulatory Commission (NRC) staff has been working since the 1970's to ensure that nondestructive testing performed on nuclear power plants in the United States will provide reasonable assurance of structural integrity of the nuclear power plant components. One tool used by the NRC has been the development and implementation of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Section XI Appendix VIII[1] (Appendix VIII) blind testing requirements for ultrasonic procedures, equipment, and personnel. Some concerns have been raised, over the years, by the relatively low pass rates for the Appendix VIII qualification testing. The NRC staff has applied statistical tools and simulations to determine the expected probability of detection (POD) for ultrasonic examinations under ideal conditions based on the pass rates for the Appendix VIII qualification tests for the ultrasonic testing personnel. This work was primarily performed to answer three questions. First, given a test design and pass rate, what is the expected overall POD for inspectors? Second, can we calculate the probability of detection for flaws of different sizes using this information? Finally, if a previously qualified inspector fails a requalification test, does this call their earlier inspections into question? The calculations have shown that one can expect good performance from inspectors who have passed appendix VIII testing in a laboratory-like environment, and the requalification pass rates show that the inspectors have maintained their skills between tests. While these calculations showed that the PODs for the ultrasonic inspections are very good under laboratory conditions, the field inspections are conducted in a very different environment. The NRC staff has initiated a project to systematically analyze the human factors differences between qualification testing and field examinations. This work will be used to evaluate and prioritize
Delarue, B. J.; Pope, S. B.
1998-02-01
A particle method applying the probability density function (PDF) approach to turbulent compressible reacting flows is presented. The method is applied to low and high Mach number reacting plane mixing layers. Good agreement is obtained between the model calculations and the available experimental data. The PDF equation is solved using a Lagrangian Monte Carlo method. To represent the effects of compressibility on the flow, the velocity PDF formulation is extended to include thermodynamic variables such as the pressure and the internal energy. Full closure of the joint PDF transport equation is made possible in this way without coupling to a finite-difference-type solver. The stochastic differential equations (SDE) that model the evolution of Lagrangian particle properties are based on existing models for the effects of compressibility on turbulence. The chemistry studied is the fast hydrogen-fluorine reaction. For the low Mach number runs, low heat release calculations are performed with equivalence ratios different from one. Heat release is then increased to study the effect of chemical reaction on the mixing layer growth rate. The subsonic results are compared with experimental data, and good overall agreement is obtained. The calculations are then performed at a higher Mach number, and the results are compared with the subsonic results. Our purpose in this paper is not to assess the performances of existing models for compressible or reacting flows. It is rather to present a new approach extending the domain of applicability of PDF methods to high-speed combustion.
Full text: he IPCC Fourth Assessment Report (Meehl ef al. 2007) presents multi-model means of the CMIP3 simulations as projections of the global climate change over the 21st century under several SRES emission scenarios. To assess the possible range of change for Australia based on the CMIP3 ensemble, we can follow Whetton etal. (2005) and use the 'pattern scaling' approach, which separates the uncertainty in the global mean warming from that in the local change per degree of warming. This study presents several ways of representing these two factors as probability density functions (PDFs). The beta distribution, a smooth, bounded, function allowing skewness, is found to provide a useful representation of the range of CMIP3 results. A weighting of models based on their skill in simulating seasonal means in the present climate over Australia is included. Dessai ef al. (2005) and others have used Monte-Carlo sampling to recombine such global warming and scaled change factors into values of net change. Here, we use a direct integration of the product across the joint probability space defined by the two PDFs. The result is a cumulative distribution function (CDF) for change, for each variable, location, and season. The median of this distribution provides a best estimate of change, while the 10th and 90th percentiles represent a likely range. The probability of exceeding a specified threshold can also be extracted from the CDF. The presentation focuses on changes in Australian temperature and precipitation at 2070 under the A1B scenario. However, the assumption of linearity behind pattern scaling allows results for different scenarios and times to be simply obtained. In the case of precipitation, which must remain non-negative, a simple modification of the calculations (based on decreases being exponential with warming) is used to avoid unrealistic results. These approaches are currently being used for the new CSIRO/ Bureau of Meteorology climate projections
Chatzinotas, Symeon
2010-01-01
During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements. However, the majority of studies in this area were carried out ignoring cochannel interference. Only a small number of investigations have considered cochannel interference, but even therein simple channel models were employed, assuming identically distributed fading coefficients. In this paper, a generic model for a multi-antenna channel is presented incorporating four impairments, namely additive white Gaussian noise, flat fading, path loss and cochannel interference. Both point-to-point and multiple-access MIMO channels are considered, including the case of cooperating Base Station clusters. The asymptotic capacity limit of this channel is calculated based on an asymptotic free probability approach which exploits the additive and multiplicative free convolution in the R- and S-transform domain respectively, as ...
In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional “abnormal” intensities are found at n = 14 and 23. Criteria for the appearance of such “anomalies” are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases
Medvedev, Emile S.; Meshkov, Vladimir V.; Stolyarov, Andrey V.; Gordon, Iouli E.
2015-10-01
In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional "abnormal" intensities are found at n = 14 and 23. Criteria for the appearance of such "anomalies" are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases.
Medvedev, Emile S., E-mail: esmedved@orc.ru [The Institute of Problems of Chemical Physics, Russian Academy of Sciences, Prospect Akademika Semenova 1, 142432 Chernogolovka (Russian Federation); Meshkov, Vladimir V.; Stolyarov, Andrey V. [Department of Chemistry, Lomonosov Moscow State University, Leninskie gory 1/3, 119991 Moscow (Russian Federation); Gordon, Iouli E. [Atomic and Molecular Physics Division, Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, Massachusetts 02138 (United States)
2015-10-21
In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional “abnormal” intensities are found at n = 14 and 23. Criteria for the appearance of such “anomalies” are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases.
MA Dong-Ping; LIU Yan-Yun; CHEN Ju-Rong
2001-01-01
On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R,The theoretically predicted transition probabilities are in good agreement with the experimental ones.PACS numbers: 71.70.Ch, 78.20.Nv, 63.20.Mt, 63.20.Kr
Since volumetric dose distributions are available with 3-dimensional radiotherapy treatment planning they can be used in statistical evaluation of response to radiation. This report presents a method to calculate the influence of dose inhomogeneity and fractionation in normal tissue complication probability evaluation. The mathematical expression for the calculation of normal tissue complication probability has been derived combining the Lyman model with the histogram reduction method of Kutcher et al. and using the normalized total dose (NTD) instead of the total dose. The fitting of published tolerance data, in case of homogeneous or partial brain irradiation, has been considered. For the same total or partial volume homogeneous irradiation of the brain, curves of normal tissue complication probability have been calculated with fraction size of 1.5 Gy and of 3 Gy instead of 2 Gy, to show the influence of fraction size. The influence of dose distribution inhomogeneity and α/β value has also been simulated: Considering α/β=1.6 Gy or α/β=4.1 Gy for kidney clinical nephritis, the calculated curves of normal tissue complication probability are shown. Combining NTD calculations and histogram reduction techniques, normal tissue complication probability can be estimated taking into account the most relevant contributing factors, including the volume effect. (orig.)
Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability P(d,N)m,n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality d. In the limit d → ∞, the distances between pair of points become independent (random link model) and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbour or not
van Vugt, Heidi A.; Kranse, Ries; Steyerberg, Ewout W.; van der Poel, Henk G.; Busstra, Martijn; Kil, Paul; Oomens, Eric H.; de Jong, Igle J.; Bangma, Chris H.; Roobol, Monique J.
2012-01-01
Background: Prediction models need validation to assess their value outside the development setting. Objective: To assess the external validity of the European Randomised study of Screening for Prostate Cancer (ERSPC) Risk Calculator (RC) in a contemporary clinical cohort. Methods: The RC calculates
Stadler, Tanja; Degnan, James H
2012-01-01
Background The ancestries of genes form gene trees which do not necessarily have the same topology as the species tree due to incomplete lineage sorting. Available algorithms determining the probability of a gene tree given a species tree require exponential computational runtime. Results In this paper, we provide a polynomial time algorithm to calculate the probability of a ranked gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal v...
The risk of a major nuclear accident: calculation and perception of probabilities
The accident at Fukushima Daiichi, Japan, occurred on 11 March 2011. This nuclear disaster, the third on such a scale, left a lasting mark in the minds of hundreds of millions of people. Much as Three Mile Island or Chernobyl, yet another place will be permanently associated with a nuclear power plant which went out of control. Fukushima Daiichi revived the issue of the hazards of civil nuclear power, stirring up all the associated passion and emotion. The whole of this paper is devoted to the risk of a major nuclear accident. By this we mean a failure initiating core meltdown, a situation in which the fuel rods melt and mix with the metal in their cladding. Such accidents are classified as at least level 5 on the International Nuclear Event Scale. The Three Mile Island accident, which occurred in 1979 in the United States, reached this level of severity. The explosion of reactor 4 at the Chernobyl plant in Ukraine in 1986 and the recent accident in Japan were classified as class 7, the highest grade on this logarithmic scale. The main difference between the top two levels and level 5 relates to a significant or major release of radioactive material to the environment. In the event of a level-5 accident, damage is restricted to the inside of the plant, whereas, in the case of level-7 accidents, huge areas of land, above or below the surface, and/or sea may be contaminated. Before the meltdown of reactors 1, 2 and 3 at Fukushima Daiichi, eight major accidents affecting nuclear power plants had occurred worldwide. This is a high figure compared with the one calculated by the experts. Observations in the field do not appear to fit the results of the probabilistic models of nuclear accidents produced since the 1970's. Oddly enough the number of major accidents is closer to the risk as perceived by the general public. In general we tend to overestimate any risk relating to rare, fearsome accidents. What are we to make of this divergence? How are we to reconcile
In this paper we propose the use of angular-momentum-projected generator coordinator method (GCM) wave functions for the evaluation of transition probabilities in heavy nuclei. We derive the relevant equations and discuss ways to cope with the technical difficulties which appear in the application of the theory. We show the feasibility of the method by applying it to the calculation of B(E3) transition probabilities in light nuclei within the GCM, in the gaussian overlap approximation (GOA). In the calculations we use the density-dependent Gogny force. The theoretical projected results are in much better agreement with experiment than the unprojected ones. (orig.)
Mielke, Steven L.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.
ELIPGRID-PC: A PC program for calculating hot spot probabilities
ELIPGRID-PC, a new personal computer program has been developed to provide easy access to Singer's 1972 ELIPGRID algorithm for hot-spot detection probabilities. Three features of the program are the ability to determine: (1) the grid size required for specified conditions, (2) the smallest hot spot that can be sampled with a given probability, and (3) the approximate grid size resulting from specified conditions and sampling cost. ELIPGRID-PC also provides probability of hit versus cost data for graphing with spread-sheets or graphics software. The program has been successfully tested using Singer's published ELIPGRID results. An apparent error in the original ELIPGRID code has been uncovered and an appropriate modification incorporated into the new program
Nathenson, Manuel; Donnelly-Nolan, Julie M.; Champion, Duane E.; Lowenstern, Jacob B.
2007-01-01
Medicine Lake volcano has had 4 eruptive episodes in its postglacial history (since 13,000 years ago) comprising 16 eruptions. Time intervals between events within the episodes are relatively short, whereas time intervals between the episodes are much longer. An updated radiocarbon chronology for these eruptions is presented that uses paleomagnetic data to constrain the choice of calibrated ages. This chronology is used with exponential, Weibull, and mixed-exponential probability distributions to model the data for time intervals between eruptions. The mixed exponential distribution is the best match to the data and provides estimates for the conditional probability of a future eruption given the time since the last eruption. The probability of an eruption at Medicine Lake volcano in the next year from today is 0.00028.
Calculation of rotational transition probabilities in molecular collisions - Application to N2 + N2
Itikawa, Y.
1975-01-01
A computational method is proposed to obtain rotational transition probabilities in collisions between two diatomic molecules. The potential method of Rabitz and an exponential approximation are used to solve the semiclassical coupled equations without invoking any perturbational technique. The collision trajectory is determined in the classical modified-wave-number approximation. The method can treat systems involving strong interactions and provide probabilities for transitions even with a multiquantum jump. A simultaneous transition in the rotational states of both molecules, i.e., the rotational-rotational energy transfer, is taken into account. An application to the system N2 + N2 is presented.
On a best-estimate approach to the calculation of dryout probability during BWR transients
A method is proposed whereby uncertainty of any dryout margin measure (figure of merit) may be quantified when the only experimental information available for validation is whether dryout has occurred or not. The method does not involve the heater temperature, except as a discrete dryout indicator. This is an advantage when analysing anticipated operational occurrences for which the acceptance criterion refers exclusively to the probability of dryout occurrence. The derived uncertainty provides a direct relation between the simulated dryout margin and the aforementioned probability. Furthermore, the method, which is based on logistic regression, has been designed to be consistent with more common parametric methods of uncertainty analysis that are likely to be used for other parts of a thermal hydraulic model. One example is provided where the method is utilized to assess statistical properties, which would have been difficult to quantify by other means. (author)
Monte Carlo calculation of the total probability for gamma-Ray interaction in toluene
Interaction and absorption probabilities for gamma-rays with energies between 1 and 1000 KeV have been computed and tabulated. Toluene based scintillator solution has been assumed in the computation. Both, point sources and homogeneously dispersed radioactive material have been assumed. These tables may be applied to cylinders with radii between 1.25 cm and 0.25 cm and heights between 4.07 cm and 0.20 cm. (Author) 26 refs
Per Jönsson; Hyun-Kyung Chung
2013-01-01
There exist several codes in the atomic physics community to generate atomic structure and transition probabilities freely and readily distributed to researchers outside atomic physics community, in plasma, astrophysical or nuclear physics communities. Users take these atomic physics codes to generate the necessary atomic data or modify the codes for their own applications. However, there has been very little effort to validate and verify the data sets generated by non-expert users. [...
Optimization of next-event estimation probability in Monte Carlo shielding calculations
In Monte Carlo radiation transport calculations with point detectors, the next-event estimation is employed to estimate the response to each detector from all collision sites. The computation time required for this estimation process is substantial and often exceeds the time required to generate and process particle histories in a calculation. This estimation from all collision sites is, therefore, very wasteful in Monte Carlo shielding calculations. For example, in the source region and in regions far away from the detectors, the next-event contribution of a particle is often very small and insignificant. A method for reducing this inefficiency is described
An integral transport method of calculating the geometrical shadowing factor in multiregion annular cells for infinite closely packed lattices in cylindrical geometry is developed. This analytical method has been programmed in the TPGS code. This method is based upon a consideration of the properties of the integral transport method for a nonuniform body, which together with Bonalumi's approximations allows the determination of the approximate multiregion collision probability matrix for infinite closely packed lattices with sufficient accuracy. The multiregion geometrical shadowing factors have been calculated for variations in fuel pin annular segment rings in a geometry of annular cells. These shadowing factors can then be used in the calculation of neutron transport from one annulus to another in an infinite lattice. The result of this new geometrical shadowing and collision probability matrix are compared with the Dancoff-Ginsburg correction and the probability matrix using constant shadowing on Yankee fuel elements in an infinite lattice. In these cases the Dancoff-Ginsburg correction factor and collision probability matrix using constant shadowing are in difference by at most 6.2% and 6%, respectively
Large-scale Breit-Pauli R-matrix calculations for transition probabilities of Fe V
Nahar, Sultana N.; Pradhan, Anil K.
2000-01-01
Ab initio theoretical calculations are reported for the electric (E1) dipole allowed and intercombination fine structure transitions in Fe V using the Breit-Pauli R-matrix (BPRM) method. We obtain 3865 bound fine structure levels of Fe V and $1.46 x 10^6$ oscillator strengths, Einstein A-coefficients and line strengths. In addition to the relativistic effects, the intermediate coupling calculations include extensive electron correlation effects that represent the complex configuration interac...
Costa, A M; Santos, J P; Indelicato, P J; Parente, F; Indelicato, Paul
2006-01-01
Energies and transition probabilities of K$\\beta$ hypersatellite lines are computed using the Dirac-Fock model for several values of $Z$ throughout the periodic table. The influence of the Breit interaction on the energy shifts from the corresponding diagram lines and on the K$\\beta\\_{1}^{\\rm h}$/K$\\beta\\_{3}^{\\rm h}$ intensity ratio is evaluated. The widths of the double-K hole levels are calculated for Al and Sc. The results are compared to experiment and to other theoretical calculations.
Gedeborg, R.; Warner, M.; Chen, L. H.;
2014-01-01
BACKGROUND: The International Statistical Classification of Diseases, 10th Revision (ICD-10) -based Injury Severity Score (ICISS) performs well but requires diagnosis-specific survival probabilities (DSPs), which are empirically derived, for its calculation. The objective was to examine if DSPs...... country's own DSPs for ICISS calculation, the pooled DSPs resulted in somewhat reduced discrimination in predicting mortality (difference in c statistic varied from 0.006 to 0.04). Calibration was generally good when the predicted mortality risk was less than 20%. When Danish and Swedish data were used...
Calculated level energies, transition probabilities, and lifetimes of silicon-like ions
The authors present theoretical excitation energies and lifetimes for the 27 low-lying levels of silicon-like ions of S, Ar, Ca, Ti, Fe, Zn, and Kr (16 ≤ Z ≤ 36). Special attention has been paid to provide a complete tabulation of all electric-dipole (E1) allowed transitions from levels of the 3s3p3 and 3s23p3d excited configurations to those of the 3s23p2 ground-state configuration, including all weak and intercombination transitions. Large-scale multiconfiguration Dirac-Fock wave functions are applied to compute transition energies and probabilities. They further investigate the decay of the 3s23p3dJ = 4 level which is connected to the ground-state configuration only via forbidden M2 transitions but otherwise mainly decays via M1 to lower-lying levels of the same parity. For a few selected data, they compare the results with experiment and with previous computations
The vibrational transition probability expressions for the forced Morse oscillator have been derived using the commutation relations of the anharmonic Boson operators. The formulation is based on the collinear collision model with the exponential repulsive potential in the framework of semiclassical collision dynamics. The sample calculation results for H2 + He collision system, where the anharmonicity is large, are in excellent agreement with those from an exact, numerical quantum mechanical study by Clark and Dickinson, using the reactance matrix. Our results,however, are markedly different from those of Ree, Kim, and Shin's in which they approximate the commutation operator Io as unity, the harmonic oscillator limit. We have concluded that the quantum number dependence in Io must be retained to get accurate vibrational transition probabilities for the Morse oscillator
The collision probability method in neutron transport, as applied to 2D geometries, consume a great amount of computer time, for a typical 2D assembly calculation about 90% of the computing time is consumed in the collision probability evaluations. Consequently RZ or 3D calculations became prohibitive. In this paper the author presents a simple but efficient parallel algorithm based on the message passing host/node programmation model. Parallelization was applied to the energy group treatment. Such approach permits parallelization of the existing code, requiring only limited modifications. Sequential/parallel computer portability is preserved, which is a necessary condition for a industrial code. Sequential performances are also preserved. The algorithm is implemented on a CRAY 90 coupled to a 128 processor T3D computer, a 16 processor IBM SPI and a network of workstations, using the Public Domain PVM library. The tests were executed for a 2D geometry with the standard 99-group library. All results were very satisfactory, the best ones with IBM SPI. Because of heterogeneity of the workstation network, the author did not ask high performances for this architecture. The same source code was used for all computers. A more impressive advantage of this algorithm will appear in the calculations of the SAPHYR project (with the future fine multigroup library of about 8000 groups) with a massively parallel computer, using several hundreds of processors
HORI, MASAKI; Korobov, Vladimir I.
2010-01-01
Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is in principle possible by exciting transitions of the type (n,L)->(n-2,L-2) between antiprotonic states of principal and angular momentum quantum numbers n~L-1~35, first by using highly monochromatic, nanosecond laser beams of intensities 10^4...
Energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to configurations of sulfur-like iron, Fe XI, have been calculated. These states are represented by configuration interaction wavefunctions and have configurations 3s23p4, 3s3p5, 3s23p33d, 3s23p34s, 3s23p34p, and 3s23p34d, which give rise to 123 fine-structure energy levels. Extensive configuration interaction calculations using the CIV3 code have been performed. To assess the importance of relativistic effects, the intermediate coupling scheme by means of the Breit–Pauli Hamiltonian terms, such as the one-body mass correction and Darwin term, and spin–orbit, spin–other-orbit, and spin–spin corrections, are incorporated within the code. These incorporations adjusted the energy levels, therefore the calculated values are close to the available experimental data. Comparisons between the present calculated energy levels as well as oscillator strengths and both experimental and theoretical data have been performed. Our results show good agreement with earlier works, and they might be useful in thermonuclear fusion research and astrophysical applications. -- Highlights: •Accurate atomic data of iron ions are needed for identification of solar corona. •Extensive configuration interaction wavefunctions including 123 fine-structure levels have been calculated. •The relativistic effects by means of the Breit–Pauli Hamiltonian terms are incorporated. •This incorporation adjusts the energy levels, therefore the calculated values are close to experimental values
Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is, in principle, possible by exciting transitions of the type (n,L)→(n-2,L-2) between antiprotonic states of principal and angular momentum quantum numbers n∼L-1∼35, first by using highly monochromatic, nanosecond laser beams of intensities 104-105 W/cm2, and then by tuning the virtual intermediate state close (e.g., within 10-20 GHz) to the real state (n-1,L-1) to enhance the nonlinear transition probability. We expect that ac Stark shifts of a few MHz or more will become an important source of systematic error at fractional precisions of better than a few parts in 109. These shifts can, in principle, be minimized and even canceled by selecting an optimum combination of laser intensities and frequencies. We simulated the resonance profiles of some two-photon transitions in the regions n=30-40 of the p4He+ and p3He+ isotopes to find the best conditions that would allow this.
Paradisopoulou, P. M.; Papadimitriou, E. E.; Karakostas, V. G.; Taymaz, T.; Kilias, A.; Yolsal, S.
2010-08-01
hazards is given by translating the calculated stress changes into earthquake probability using an earthquake nucleation constitutive relation, which includes permanent and transient effects of the sudden stress changes.
Nuclear reactor design and analysis of next-generation reactors require a comprehensive computing which is better to be executed in a high performance computing. Flat flux (FF) approach is a common approach in solving an integral transport equation with collision probability (CP) method. In fact, the neutron flux distribution is not flat, even though the neutron cross section is assumed to be equal in all regions and the neutron source is uniform throughout the nuclear fuel cell. In non-flat flux (NFF) approach, the distribution of neutrons in each region will be different depending on the desired interpolation model selection. In this study, the linear interpolation using Finite Element Method (FEM) has been carried out to be treated the neutron distribution. The CP method is compatible to solve the neutron transport equation for cylindrical geometry, because the angle integration can be done analytically. Distribution of neutrons in each region of can be explained by the NFF approach with FEM and the calculation results are in a good agreement with the result from the SRAC code. In this study, the effects of the mesh on the keff and other parameters are investigated.
Savukov, I. M.
2016-02-01
The precision of the mixed configuration-interaction plus many-body-perturbation-theory (CI+MBPT) method is limited in multivalence atoms by the large size of valence CI space. Previously, to study this problem, the CI+MBPT method was applied to calculations of energies in a four-valence electron atom, Si i. It was found that by using a relatively small cavity of 30 a.u. and by choosing carefully the configuration space, quite accurate agreement between theory and experiment at the level of 100 cm-1 can be obtained, especially after subtraction of systematic shifts for groups of states of the same J and parity. However, other properties are also important to investigate. In this work, the CI+MBPT method is applied to studies of transition probabilities, oscillator strengths, and lifetimes. A close agreement with accurate experimental measurements and other elaborate theories is obtained. The long-term goal is to extend the CI+MBPT approach to applications in more complex atoms, such as lantanides and actinides.
Vilkas, M J; Ishikawa, Y; Trabert, E
2007-03-27
Relativistic multireference many-body perturbation theory calculations have been performed on Xe{sup 43+}-Xe{sup 39+} ions, resulting in energy levels, electric dipole transition probabilities, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, frequency-dependent Breit correction and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.
Theoretical calculation for forbidden transition probability of ΔL=±2, ΔS=±1 lines in N II
The forbidden transition probabilities have been calculated for the 2p3d-2p2 and 2p3d-2p3p (ΔL = +-2, ΔS = +-1) spectra of N II by using a large-scale multiconfiguration Dirac-Fock (MCDF) method. The most important effects of relativity, correlation, and relaxation are considered in the calculation Comparing with other calculations, a remarkable improvement is achieved
Radiation induced normal tissue complication probability is calculated for three different organs: brain, liver and kidney. The model applied is a reliability model where the volume effect of the tissue is described by the structural parameter, k, which reflects the architecture of the functional subunits of the organ. The complication probability depends on k, the inactivation probability of the functional subunits (p) and the irradiated volume fraction (n). For partial, homogeneous irradiation of the brain, a k-value close to unity was found, and the respective values for liver and kidney were 0.92 and 0.77. An extension of the reliability model to account for individual inactivation probability of the subunits allows calculation of complication probability for inhomogeneous dose distributions. For the brain, intercomparisons of a three-field and a two-field technique demonstrated a small reduction in complication probability for the former at low total doses. At high total doses a minimum complication probability was achieved applying a three-field technique, being three times less than that associated with the two-field technique. (author)
The Waste Isolation Pilot Plant (WIPP), in southeastern New Mexico, is a research and development facility to demonstrate safe disposal of defense-generated transuranic waste. The US Department of Energy will designate WIPP as a disposal facility if it meets the US Environmental Protection Agency's standard for disposal of such waste; the standard includes a requirement that estimates of cumulative releases of radioactivity to the accessible environment be incorporated in an overall probability distribution. The WIPP Project has chosen an approach to calculation of an overall probability distribution that employs the concept of scenarios for release and transport of radioactivity to the accessible environment. This report reviews the use of Monte Carlo methods in the calculation of an overall probability distribution and presents a logical and mathematical foundation for use of the scenario concept in such calculations. The report also draws preliminary conclusions regarding the shape of the probability distribution for the WIPP system; preliminary conclusions are based on the possible occurrence of three events and the presence of one feature: namely, the events ''attempted boreholes over rooms and drifts,'' ''mining alters ground-water regime,'' ''water-withdrawal wells provide alternate pathways,'' and the feature ''brine pocket below room or drift.'' Calculation of the WIPP systems's overall probability distributions for only five of sixteen possible scenario classes that can be obtained by combining the four postulated events or features
The Fortran IV code PAPIN has been developed to calculate cross section probability tables, Bondarenko self-shielding factors and average self-indication ratios for non-fissile isotopes, below the inelastic threshold, on the basis of the ENDF/B prescriptions for the unresolved resonance region. Monte-Carlo methods are utilized to generate ladders of resonance parameters in the unresolved resonance region, from average resonance parameters and their appropriate distribution functions. The neutron cross-sections are calculated by the single level Breit-Wigner (SLBW) formalism, with s, p and d-wave contributions. The cross section probability tables are constructed by sampling the Doppler-broadened cross sections. The various self-shielded factors are computed numerically as Lebesgue integrals over the cross section probability tables. The program PAPIN has been validated through extensive comparisons with several deterministic codes
Munoz-Cobos, J. G.
1981-08-01
A FORTRAN 4 code was developed to calculate cross section probability tables, Bondarenko self-shielding factors, and average self-indication ratios for non-fissile isotopes, below the inelastic threshold, on the basis of prescriptions for the unresolved resonance region. Monte-Carlo methods are utilized to generate ladders of resonance parameters in he unresolved resonance region, from average resonance parameters and their appropriate distribution functions. The neutron cross sections are calculated by the single level Breit-Wigner formalism, with s, p and d-wave contributions. The cross section probability tables are constructed by sampling the Doppler-broadened cross sections. The various self-shielded factors are computed numerically as Lebesgue integrals over the cross section probability tables. The program was validated through extensive comparisons with several deterministic codes.
The program makes it possible to calculate the E1, E2 and M1 reduced transition probabilities in odd-odd deformed nuclei. The mixed wave functions used result from a least-squares fit of energy levels (taking the Coriolis effect into account) to the experimental ones, performed with the modified ODDODDCORI subprogram. (orig./HSI)
S Nasirimoghadam
2011-09-01
Full Text Available The ultracold atoms fermion gas such as 6Li undergo superfluidity state. The transport quantities of these fluids have a direct dependence on the transition probabilities. Here, by obtaining possible processes in p-wave superfluid, we have shown that only binary processes are dominate at low temperatures.
Six indices are presented for linear compartment systems that quantify the probable pathways of matter or energy transfer, the likelihood of recurrence if the model contains feedback loops, and the number of steps (transfers) through the system. General examples are used to illustrate how these indices can simplify the comparison of complex systems or organisms in unrelated systems
Carney, J.H.; DeAngelis, D.L.; Gardner, R.H.; Mankin, J.B.; Post, W.M.
1981-02-01
Six indices are presented for linear compartment systems that quantify the probable pathways of matter or energy transfer, the likelihood of recurrence if the model contains feedback loops, and the number of steps (transfers) through the system. General examples are used to illustrate how these indices can simplify the comparison of complex systems or organisms in unrelated systems.
Frictional heating of high-melting-point grit particles during oblique impacts of consolidated explosives is considered to be the major source of ignition in accidents involving dropped explosives. It has been shown in other work that the lower temperature melting point of two frictionally interacting surfaces will cap the maximum temperature reached, which provides a simple way to mitigate the danger in facilities by implementing surfaces with melting points below the ignition temperature of the explosive. However, a recent series of skid testing experiments has shown that ignition can occur on low-melting-point surfaces with a high concentration of grit particles, most likely due to a grit–grit collision mechanism. For risk-based safety engineering purposes, the authors present a method to estimate the probability of grit contact and/or grit–grit collision during an oblique impact. These expressions are applied to potentially high-consequence oblique impact scenarios in order to give the probability of striking one or more grit particles (for high-melting-point surfaces), or the probability of one or more grit–grit collisions occurring (for low-melting-point surfaces). The probability is dependent on a variety of factors, many of which can be controlled for mitigation to achieve acceptable risk levels for safe explosives handling operations. - Highlights: • Unexpectedly, grit-mediated ignition of a PBX occurred on low-melting point surfaces. • On high-melting surfaces frictional heating is due to a grit–surface interaction. • For low-melting point surfaces the heating mechanism is grit–grit collisions. • A method for estimating the probability of ignition is presented for both surfaces
Inman, Keith; Rudin, Norah; Cheng, Ken; Robinson, Chris; Kirschner, Adam; Inman-Semerau, Luke; Lohmueller, Kirk E.
2015-01-01
Background Technological advances have enabled the analysis of very small amounts of DNA in forensic cases. However, the DNA profiles from such evidence are frequently incomplete and can contain contributions from multiple individuals. The complexity of such samples confounds the assessment of the statistical weight of such evidence. One approach to account for this uncertainty is to use a likelihood ratio framework to compare the probability of the evidence profile under different scenarios....
It is indispensable to know the fluence on the nuclear reactor pressure vessel. The cross sections and their treatment have an important rule to this problem. In this study, two ''benchmarks'' have been interpreted by the Monte Carlo transport program TRIPOLI to qualify the calculational method and the cross sections used in the calculations. For the treatment of the cross sections, the multigroup method is usually used but it exists some problems such as the difficulty to choose the weighting function and the necessity of a great number of energy to represent well the cross section's fluctuation. In this thesis, we propose a new method called ''Probability Table Method'' to treat the neutron cross sections. For the qualification, a program of the simulation of neutron transport by the Monte Carlo method in one dimension has been written; the comparison of multigroup's results and probability table's results shows the advantages of this new method. The probability table has also been introduced in the TRIPOLI program; the calculational results of the iron deep penetration benchmark has been improved by comparing with the experimental results. So it is interest to use this new method in the shielding and neutronic calculation. (author). 42 refs., 109 figs., 36 tabs
The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise
We present converged quantum dynamics for the H + D2 reaction at a total energy high enough to produce HD in the v' = 3, j' = 7 vibrational-rotational state and for total angular momenta J = 0, 1, and 2. We compare state-to-state partial cross sections for H + D2 (v = 0-2, j = 0, J = 0-2) → HD (v' = 0-2, j') + H and H + D2 (v = 1, j = 6, J = 0-2) → HD (v' = 0-2, j') + H as calculated from classical trajectory calculations with quantized initial conditions, i.e., a quasiclassical trajectory (QCT) simulation, to the results of converged quantum dynamics calculations involving up to 654 coupled channels. Final states in the QCT calculations are assigned by the quadratic smooth sampling (QSS) method. Since the quasiclassical and quantal calculations are carried out with the same potential energy surface, the comparison provides a direct test of the accuracy of the quasiclassical simulations as a function of the initial vibrational-rotational state and the final vibrational-rotational state
Energy levels, line strengths, oscillator strengths, and transition rates are calculated for electric dipole nl1nl2[LSJ]-nl3nl4[L'S'J'] transition in Be- (n=2), Mg- (n=3), Zn- (n=4) and Sm- (n=5) like ions with nuclear charges ranging from Z=N to 100 where N is number of electron in system. (author)
Glushkov, Alexander [Odessa University (Ukraine); Russian Academy of Sciences, Troitsk (Russian Federation); Khetselius, Olga; Dubrovskaya, Yuliya [Odessa University (Ukraine); Lovett, Ludmila [UK National Academy of Sciences and Bookdata Co., London (United Kingdom)
2009-07-01
New theoretical scheme for calculating the beta decay characteristics and an account for chemical environment effect on the beta decay ones is developed. As method of calculation of the relativistic fields and electron wave functions, the gauge invariant Dirac-Fock and Dirac-Kohn-Sham approaches are used. The results of calculating the decay probabilities for the beta decays: {sup 33}P-{sup 33}S, {sup 35}S-{sup 35}Cl, {sup 63}Ni-{sup 63}Cu, {sup 241}Pu-{sup 241}Am are presented. Comparison of the Fermi function values is carried out for different approximations of an exchange effect account, calculation with using wave functions on the boundary of the charged spherical nucleus and with using squires of the amplitudes of expansion of these functions near zero.
Safronova, U.I.; Johnson, W.R. [Dept. of Physics, Univ. of Notre Dame, IN (United States)
2000-01-01
Energy levels, line strengths, oscillator strengths, and transition rates are calculated for electric dipole nl{sub 1}nl{sub 2}[LSJ]-nl{sub 3}nl{sub 4}[L'S'J'] transition in Be- (n=2), Mg- (n=3), Zn- (n=4) and Sm- (n=5) like ions with nuclear charges ranging from Z=N to 100 where N is number of electron in system. (author)
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.; Malvagi, F.
2014-06-01
Pile-oscillation experiments are performed in the MINERVE reactor at the CEA Cadarache to improve nuclear data accuracy. In order to precisely calculate small reactivity variations (TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. Other applications of this perturbation method are presented and tested like the calculation of exact kinetic parameters (βeff, Λeff) or sensitivity parameters.
Mateja, Piotr; Wojcik, Mariusz
2016-07-01
A computer simulation method is applied to study electron-ion recombination in tracks of low-energy nuclear recoils in nonpolar liquids in which the electron transport can be described as ideal diffusion. The electron escape probability is calculated as a function of applied electric field, both for the field parallel to the track and for the field perpendicular to the track. The dependence of escape probability on the field direction is the stronger, the longer the ionization track, with a significant effect being found already for tracks of ~100 nm length. The results are discussed in the context of possible applications of nonpolar molecular liquids as target media in directional dark matter detectors.
Impact of aging conditions on mechanical properties of thermoplastic polyurethane
In this study, impact of environmental aging conditions on the mechanical properties of thermoplastic polyurethane (TPU) was investigated. Especially, effect of temperature on water diffusion has been studied. Water-sorption experiments, tensile test and dynamic mechanical thermal analysis (DMTA) were performed after immersion in distilled water at different temperatures (25, 70 and 90 oC). The sorption process was analyzed by gravimetric measurements at different temperatures. Also, diffusion coefficients of solvent molecules in the TPU samples were identified. Therefore the activation energy and the mixing enthalpy were deduced. The aging impact on some mechanical properties of this material has been investigated after various aging cycles. Degradation of mechanical properties was observed. In fact, elastic modulus and stress at 200% of strain were decreased. It was also shown that such degradation largely depends on both aging temperature and aging immersion duration. The storage modulus (E') was also affected by the hygrothermal (HT) environment. The modification of mechanical properties seems to be well correlated to structural observations obtained from scanning electron microscopy (SEM) photographs. Finally, through thermal aging experiments, it was deduced that the combination of temperature with water seems to be a major factor of TPU degradation.
Korb, Andrew R.; Grossman, Stanley I.
2015-05-01
A model was developed to understand the effects of spatial resolution and Signal to Noise ratio on the detection and tracking performance of wide-field, diffraction-limited electro-optic and infrared motion imagery systems. False positive detection probability and false positive rate per frame were calculated as a function of target-to-background contrast and object size. Results showed that moving objects are fundamentally more difficult to detect than stationary objects because SNR for fixed objects increases and false positive probability detection rates diminish rapidly with successive frames whereas for moving objects the false detection rate remains constant or increases with successive frames. The model specifies that the desired performance of a detection system, measured by the false positive detection rate, can be achieved by image system designs with different combinations of SNR and spatial resolution, usually requiring several pixels resolving the object; this capability to tradeoff resolution and SNR enables system design trades and cost optimization. For operational use, detection thresholds required to achieve a particular false detection rate can be calculated. Interestingly, for moderate size images the model converges to the Johnson Criteria. Johnson found that an imaging system with an SNR >3.5 has a probability of detection >50% when the resolution on the object is 4 pixels or more. Under these conditions our model finds the false positive rate is less than one per hundred image frames, and the ratio of the probability of object detection to false positive detection is much greater than one. The model was programmed into Matlab to generate simulated images frames for visualization.
Valdes, Gilmer, E-mail: gilmer.valdes@uphs.upenn.edu [Department of Radiation Oncology, Perelman Center for Advanced Medicine, University of Pennsylvania, Philadelphia, PA (United States); Robinson, Clifford [Department of Radiation Oncology, Siteman Cancer Center, Washington University in St. Louis, St. Louis, MO (United States); Lee, Percy [Department of Radiation Oncology, David Geffen School of Medicine, UCLA, Los Angeles, CA (United States); Morel, Delphine [Department of Biomedical Engineering, AIX Marseille 2 University, Marseille (France); Department of Medical Physics, Joseph Fourier University, Grenoble (France); Low, Daniel; Iwamoto, Keisuke S.; Lamb, James M. [Department of Radiation Oncology, David Geffen School of Medicine, UCLA, Los Angeles, CA (United States)
2015-04-01
Four-dimensional (4D) dose calculations for lung cancer radiotherapy have been technically feasible for a number of years but have not become standard clinical practice. The purpose of this study was to determine if clinically significant differences in tumor control probability (TCP) exist between 3D and 4D dose calculations so as to inform the decision whether 4D dose calculations should be used routinely for treatment planning. Radiotherapy plans for Stage I-II lung cancer were created for 8 patients. Clinically acceptable treatment plans were created with dose calculated on the end-exhale 4D computed tomography (CT) phase using a Monte Carlo algorithm. Dose was then projected onto the remaining 9 phases of 4D-CT using the Monte Carlo algorithm and accumulated onto the end-exhale phase using commercially available deformable registration software. The resulting dose-volume histograms (DVH) of the gross tumor volume (GTV), planning tumor volume (PTV), and PTV{sub setup} were compared according to target coverage and dose. The PTV{sub setup} was defined as a volume including the GTV and a margin for setup uncertainties but not for respiratory motion. TCPs resulting from these DVHs were estimated using a wide range of alphas, betas, and tumor cell densities. Differences of up to 5 Gy were observed between 3D and 4D calculations for a PTV with highly irregular shape. When the TCP was calculated using the resulting DVHs for fractionation schedules typically used in stereotactic body radiation therapy (SBRT), the TCP differed at most by 5% between 4D and 3D cases, and in most cases, it was by less than 1%. We conclude that 4D dose calculations are not necessary for most cases treated with SBRT, but they might be valuable for irregularly shaped target volumes. If 4D calculations are used, 4D DVHs should be evaluated on volumes that include margin for setup uncertainty but not respiratory motion.
Four-dimensional (4D) dose calculations for lung cancer radiotherapy have been technically feasible for a number of years but have not become standard clinical practice. The purpose of this study was to determine if clinically significant differences in tumor control probability (TCP) exist between 3D and 4D dose calculations so as to inform the decision whether 4D dose calculations should be used routinely for treatment planning. Radiotherapy plans for Stage I-II lung cancer were created for 8 patients. Clinically acceptable treatment plans were created with dose calculated on the end-exhale 4D computed tomography (CT) phase using a Monte Carlo algorithm. Dose was then projected onto the remaining 9 phases of 4D-CT using the Monte Carlo algorithm and accumulated onto the end-exhale phase using commercially available deformable registration software. The resulting dose-volume histograms (DVH) of the gross tumor volume (GTV), planning tumor volume (PTV), and PTVsetup were compared according to target coverage and dose. The PTVsetup was defined as a volume including the GTV and a margin for setup uncertainties but not for respiratory motion. TCPs resulting from these DVHs were estimated using a wide range of alphas, betas, and tumor cell densities. Differences of up to 5 Gy were observed between 3D and 4D calculations for a PTV with highly irregular shape. When the TCP was calculated using the resulting DVHs for fractionation schedules typically used in stereotactic body radiation therapy (SBRT), the TCP differed at most by 5% between 4D and 3D cases, and in most cases, it was by less than 1%. We conclude that 4D dose calculations are not necessary for most cases treated with SBRT, but they might be valuable for irregularly shaped target volumes. If 4D calculations are used, 4D DVHs should be evaluated on volumes that include margin for setup uncertainty but not respiratory motion
The growth and the cracks propagation by fatigue are a typical degradation mechanism that is presented in the nuclear industry as in the conventional industry; the unstable propagation of a crack can cause the catastrophic failure of a metallic component even with high ductility; for this reason, activities of programmed maintenance have been established in the industry using inspection and visual techniques and/or ultrasound with an established periodicity allowing to follow up to these growths, controlling the undesirable effects; however, these activities increase the operation costs; and in the peculiar case of the nuclear industry, they increase the radiation exposure to the participant personnel. The use of mathematical processes that integrate concepts of uncertainty, material properties and the probability associated to the inspection results, has been constituted as a powerful tool of evaluation of the component reliability, reducing costs and exposure levels. In this work the evaluation of the failure probability by cracks growth preexisting by fatigue is presented, in pipes of a Reactor Core Isolation Cooling system (Rcic) in a nuclear power station. The software WinPRAISE 07 (Piping Reliability Analysis Including Seismic Events) was used supported in the probabilistic fracture mechanics principles. The obtained values of failure probability evidenced a good behavior of the analyzed pipes with a maximum order of 1.0 E-6, therefore is concluded that the performance of the lines of these pipes is reliable even extrapolating the calculations at 10, 20, 30 and 40 years of service. (Author)
Purpose: The commercial release of volumetric modulated arc therapy techniques using a conventional linear accelerator and the growing number of helical tomotherapy users have triggered renewed interest in dose verification methods, and also in tools for exploring the impact of machine tolerance and patient motion on dose distributions without the need to approximate time-varying parameters such as gantry position, MLC leaf motion, or patient motion. To this end we have developed a Monte Carlo-based calculation method capable of simulating a wide variety of treatment techniques without the need to resort to discretization approximations. Methods: The ability to perform complete position-probability-sampled Monte Carlo dose calculations was implemented in the BEAMnrc/DOSXZYnrc user codes of EGSnrc. The method includes full accelerator head simulations of our tomotherapy and Elekta linacs, and a realistic representation of continous motion via the sampling of a time variable. The functionality of this algorithm was tested via comparisons with both measurements and treatment planning dose distributions for four types of treatment techniques: 3D conformal, step-shoot intensity modulated radiation therapy, helical tomotherapy, and volumetric modulated arc therapy. Results: For static fields, the absolute dose agreement between the EGSnrc Monte Carlo calculations and measurements is within 2%/1 mm. Absolute dose agreement between Monte Carlo calculations and treatment planning system for the four different treatment techniques is within 3%/3 mm. Discrepancies with the tomotherapy TPS on the order of 10%/5 mm were observed for the extreme example of a small target located 15 cm off-axis and planned with a low modulation factor. The increase in simulation time associated with using position-probability sampling, as opposed to the discretization approach, was less than 2% in most cases. Conclusions: A single Monte Carlo simulation method can be used to calculate patient
Probability and paternity testing.
Elston, R C
1986-01-01
A probability can be viewed as an estimate of a variable that is sometimes 1 and sometimes 0. To have validity, the probability must equal the expected value of that variable. To have utility, the average squared deviation of the probability from the value of that variable should be small. It is shown that probabilities of paternity calculated by the use of Bayes' theorem under appropriate assumptions are valid, but they can vary in utility. In particular, a recently proposed probability of p...
In this paper, the interacting boson model (IBM-1) is discussed and employed for calculating the energy level and the electromagnetic transition probabilities B(E2) of the even - even 174-180Hf isotopes. These isotopes have been investigated based on two different arrangements; i.e., the dynamical symmetry of 176-180Mf isotopes, SU (3) (deformed nuclei) and the dynamical symmetry of 174Hf isotopein transition region SU(30-O(6). The determined values using the IBM-1 Hamiltonian showed significant agreement with the experimentally reported energy level and B(E2) values. The model provides a fast and accurate predication method of energy level B(E2)values. (authors).
Shimada, Mitsuhiro; Watanabe, Shin; Tagami, Shingo; Matsumoto, Takuma; Shimizu, Yoshifumi R.; Yahiro, Masanobu
2016-06-01
We perform simultaneous analysis of (1) matter radii, (2) B (E 2 ;0+→2+) transition probabilities, and (3) excitation energies, E (2+) and E (4+) , for Mg-4024 by using the beyond-mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric β2 deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for rm,B (E 2 ) , and E (2+) and E (4+) , indicating that it is quite useful for data analysis; particularly for low-lying states. We also discuss the absolute value of the deformation parameter β2 deduced from measured values of B (E 2 ) and rm. This framework makes it possible to investigate the effects of β2 deformation, the change in β2 due to restoration of rotational symmetry, β2 configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.
Lexicographic probability, conditional probability, and nonstandard probability
Halpern, Joseph Y.
2003-01-01
The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS's), and nonstandard probability spaces (NPS's) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS's are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS's are equivalent to NPS's. However, if the state space is infinite, NPS's are ...
Maiheu, Bino; Nele, Veldeman; Janssen, Stijn; Fierens, Frans; Trimpeneers, Elke
2010-05-01
RIO is an operational air quality interpolation model developed by VITO and IRCEL-CELINE and produces hourly maps for different pollutant concentrations such as O3, PM10 and NO2 measured in Belgium [1]. The RIO methodology consists of residual interpolation by Ordinary Kriging of the residuals of the measured concentrations and pre-determined trend functions which express the relation between land cover information derived from the CORINE dataset and measured time-averaged concentrations [2]. RIO is an important tool for the Flemish administration and is among others used to report, as is required by each member state, on the air quality status in Flanders to the European Union. We feel that a good estimate of the uncertainty of the yearly average concentration maps and the probability of norm-exceedance are both as important as the values themselves. In this contribution we will discuss the uncertainties specific to the RIO methodology, where we have both contributions from the Ordinary Kriging technique as well as the trend functions. Especially the parameterisation of the uncertainty w.r.t. the trend functions will be the key indicator for the degree of confidence the model puts into using land cover information for spatial interpolation of pollutant concentrations. Next, we will propose a method which enables us to calculate the uncertainty on the yearly average concentrations as well as the number of exceedance days, taking into account the temporal auto-correlation of the concentration fields. It is clear that the autocorrelation will have a strong impact on the uncertainty estimation [3] of yearly averages. The method we propose is based on a Monte Carlo technique that generates an ensemble of interpolation maps with the correct temporal auto-correlation structure. From a generated ensemble, the calculation of norm-exceedance probability at each interpolation location becomes quite straightforward. A comparison with the ad-hoc method proposed in [3], where
The URR computer code has been developed to calculate cross-section probability tables, Bondarenko self-shielding factors, and self-indication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the single-level Breit-Wigner formalism with s-, p-, and d-wave contributions. The cross-section probability tables are constructed by sampling by Doppler broadened cross-sections. The various self-shielding factors are computer numerically as Lebesgue integrals over the cross-section probability tables
Shimada, Mitsuhiro; Tagami, Shingo; Matsumoto, Takuma; Shimizu, Yoshifumi R; Yahiro, Masanobu
2016-01-01
We perform simultaneous analysis of (1) matter radii, (2) $B(E2; 0^+ \\rightarrow 2^+ )$ transition probabilities, and (3) excitation energies, $E(2^+)$ and $E(4^+)$, for $^{24-40}$Mg by using the beyond mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric $\\beta_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{\\rm m}$, $B(E2)$, and $E(2^+)$ and $E(4^+)$, indicating that it is quite useful for data analysis, particularly for low-lying states. We also discuss the absolute value of the deformation parameter $\\beta_2$ deduced from measured values of $B(E2)$ and $r_{\\rm m}$. This framework makes it possible to investigate the effects of $\\beta_2$ deformation, the change in $\\beta_2$ due to restoration of rotational symmetry, $\\beta_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation,...
Verma, Sanjeet K.; Oliveira, Elson P.
2013-08-01
In present work, we applied two sets of new multi-dimensional geochemical diagrams (Verma et al., 2013) obtained from linear discriminant analysis (LDA) of natural logarithm-transformed ratios of major elements and immobile major and trace elements in acid magmas to decipher plate tectonic settings and corresponding probability estimates for Paleoproterozoic rocks from Amazonian craton, São Francisco craton, São Luís craton, and Borborema province of Brazil. The robustness of LDA minimizes the effects of petrogenetic processes and maximizes the separation among the different tectonic groups. The probability based boundaries further provide a better objective statistical method in comparison to the commonly used subjective method of determining the boundaries by eye judgment. The use of readjusted major element data to 100% on an anhydrous basis from SINCLAS computer program, also helps to minimize the effects of post-emplacement compositional changes and analytical errors on these tectonic discrimination diagrams. Fifteen case studies of acid suites highlighted the application of these diagrams and probability calculations. The first case study on Jamon and Musa granites, Carajás area (Central Amazonian Province, Amazonian craton) shows a collision setting (previously thought anorogenic). A collision setting was clearly inferred for Bom Jardim granite, Xingú area (Central Amazonian Province, Amazonian craton) The third case study on Older São Jorge, Younger São Jorge and Maloquinha granites Tapajós area (Ventuari-Tapajós Province, Amazonian craton) indicated a within-plate setting (previously transitional between volcanic arc and within-plate). We also recognized a within-plate setting for the next three case studies on Aripuanã and Teles Pires granites (SW Amazonian craton), and Pitinga area granites (Mapuera Suite, NW Amazonian craton), which were all previously suggested to have been emplaced in post-collision to within-plate settings. The seventh case
刘健; 杨仲江; 卢慧慧
2016-01-01
Fire accidents caused by lightning strike on large external floating roof ( EFR) oil tanks have occurred for many times, so it is practically significant to evaluate the safety objectively and calculate the probability of fire caused by lightning. The harm modes of lightning on oil tanks were presented.The annual incidence of lightning strike for external floating roof oil tanks were calculated by means of Monte Carlo method combined with electro-geometric model ( EGM ) .The difference in protection effects of conventional electrostatic conductors and retractable grounding assemblies ( RGA) were analyzed.The annual accident rates of spark discharge by lightning on oil tanks installing RGAs were discussed.The results showed that the annual incidence of lightning strike increase with the increasing diameters and heights of oil tanks.The protection effect by u-sing RGA is better than that of conventional electrostatic conductors.The probability and annual accident rates of spark dis-charge can be significantly decreased when multiple RGAs are installed.The annual accident rates of spark discharge by lightning on oil tanks can be reduced to 10 -5 when only two RGAs are installed.%大型外浮顶储罐多次发生雷击起火事故，因此对其安全性做出客观评价，计算雷击起火概率现实意义重大。通过分析雷电对外浮顶油罐的危害方式，利用蒙特卡洛方法结合电气几何模型计算外浮顶油罐年雷击率。分析采用导静电线和可伸缩接地装置（ RGA）的防护效果差别。最后计算安装可伸缩接地装置后油罐遭受雷击产生火花放电的年事故率。计算结果表明：年雷击率随着油罐直径和罐壁高度的增大而增加；采用可伸缩接地装置的防护效果明显优于传统导静电线；安装多个可伸缩接地装置可以明显降低产生火花的概率和年事故率。两个RGA就可以将油罐遭受雷击产生火花放电的年事故率降至10－5以下。
The aim of this work is to investigate the influence of the statistical fluctuations of Monte Carlo (MC) dose distributions on the dose volume histograms (DVHs) and radiobiological models, in particular the Poisson model for tumour control probability (tcp). The MC matrix is characterized by a mean dose in each scoring voxel, d, and a statistical error on the mean dose, σd; whilst the quantities d and σd depend on many statistical and physical parameters, here we consider only their dependence on the phantom voxel size and the number of histories from the radiation source. Dose distributions from high-energy photon beams have been analysed. It has been found that the DVH broadens when increasing the statistical noise of the dose distribution, and the tcp calculation systematically underestimates the real tumour control value, defined here as the value of tumour control when the statistical error of the dose distribution tends to zero. When increasing the number of energy deposition events, either by increasing the voxel dimensions or increasing the number of histories from the source, the DVH broadening decreases and tcp converges to the 'correct' value. It is shown that the underestimation of the tcp due to the noise in the dose distribution depends on the degree of heterogeneity of the radiobiological parameters over the population; in particular this error decreases with increasing the biological heterogeneity, whereas it becomes significant in the hypothesis of a radiosensitivity assay for single patients, or for subgroups of patients. It has been found, for example, that when the voxel dimension is changed from a cube with sides of 0.5 cm to a cube with sides of 0.25 cm (with a fixed number of histories of 108 from the source), the systematic error in the tcp calculation is about 75% in the homogeneous hypothesis, and it decreases to a minimum value of about 15% in a case of high radiobiological heterogeneity. The possibility of using the error on the tcp to
This work gives a description of the adjustment process of NUCIRC code to the actual aging conditions of Embalse nuclear power plant. For this adjustment the flow of the fuel channels of the primary heat transport system (PHTS) is calculated using the channel heat balance flow (CHBF) methodology. Then roughness and the localized loss of charge are modified in NUCIRC code for different groups of channels. These adjustments are done in way to fit by regions the channels flows calculated with NUCIRC to the CHBF flows. The fitting results in a discrepancy by regions of less than 0,1% and an average quadratic error of 5% approximately. These values indicate that the code NUCIRC is right adjusted for critical channel power calculations and aging tracking of PHTS. (author)
Gudder, Stanley P
2014-01-01
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the ne
Asmussen, Søren; Albrecher, Hansjörg
, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially......The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....
Shiryaev, Albert N
2016-01-01
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study. To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.
The URR computer code has been developed to calculate cross-section probability tables, Bondarenko self-shielding factors, and self- indication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the single-level Breit-Wigner formalism with s-, p-, and d-wave contributions. The cross-section probability tables are constructed by sampling the Doppler broadened cross-section. The various shelf-shielded factors are computed numerically as Lebesgue integrals over the cross-section probability tables. 6 refs
Waste Package Misload Probability
J.K. Knudsen
2001-11-20
The objective of this calculation is to calculate the probability of occurrence for fuel assembly (FA) misloads (i.e., Fa placed in the wrong location) and FA damage during FA movements. The scope of this calculation is provided by the information obtained from the Framatome ANP 2001a report. The first step in this calculation is to categorize each fuel-handling events that occurred at nuclear power plants. The different categories are based on FAs being damaged or misloaded. The next step is to determine the total number of FAs involved in the event. Using the information, a probability of occurrence will be calculated for FA misload and FA damage events. This calculation is an expansion of preliminary work performed by Framatome ANP 2001a.
Waste Package Misload Probability
The objective of this calculation is to calculate the probability of occurrence for fuel assembly (FA) misloads (i.e., Fa placed in the wrong location) and FA damage during FA movements. The scope of this calculation is provided by the information obtained from the Framatome ANP 2001a report. The first step in this calculation is to categorize each fuel-handling events that occurred at nuclear power plants. The different categories are based on FAs being damaged or misloaded. The next step is to determine the total number of FAs involved in the event. Using the information, a probability of occurrence will be calculated for FA misload and FA damage events. This calculation is an expansion of preliminary work performed by Framatome ANP 2001a
Monte Carlo transition probabilities
Lucy, L. B.
2001-01-01
Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Numerical experiments with one-point statistical equilibrium problems for Fe II and Hydrogen confirm this asymptotic behaviour. In addition, the re...
Benzarti, Karim; QUIERTANT, Marc; Chataigner, Sylvain; Aubagnac, Christophe; Nishizaki, Itaru; Kato, Y.
2008-01-01
The durability of concrete slabs strengthened by bonded composite materials has been investigated in the framework of an international cooperation between two French and Japanese research institutes. Time evolution of the concrete/composite adhesive bond strength was studied under both controlled and environmental ageing conditions, by using different mechanical characterization methods. The first results of this ongoing experimental campaign are presented.
Effect of physicochemical aging conditions on the composite-composite repair bond strength
Brendeke, Johannes; Ozcan, Mutlu
2007-01-01
Purpose: This study evaluated the effect of different physicochemical aging methods and surface conditioning techniques on the repair bond strength of composite. It was hypothesized that the aging conditions would decrease the repair bond strength and surface conditioning methods would perform simil
To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p < 0.05) for VMAT AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy −1.5 Gy; p < 0.05). An apparent difference in TCP of between 1.2% and 3.1% was found depending on the choice of TCP model. OAR mean dose was lower in the AXB recalculated plan than the AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans
The first subject was the development of future ion beam driver with medium-mass ion specie. This may enable us to develop a compromised driver from the point of view of the micro-divergence angle and the cost. We produced nitrogen ion beams, and measured the micro-divergence angle on the anode surface. The measured value was 5-6mrad for the above beam with 300-400keV energy, 300A peak current and 50ns duration. This value was enough small and tolerable for the future energy driver. The corresponding value for the proton beam with higher peak current was 20-30mrad, which was too large. So that, the scale-up experiment with the above kind of medium-mass ion beam must be realized urgently to clarify the beam characteristics in more details. The reactor wall ablation with the implosion X-ray was also calculated as the second subject in this paper. (author)
Collision Probability Analysis
Hansen, Peter Friis; Pedersen, Preben Terndrup
1998-01-01
It is the purpose of this report to apply a rational model for prediction of ship-ship collision probabilities as function of the ship and the crew characteristics and the navigational environment for MS Dextra sailing on a route between Cadiz and the Canary Islands.The most important ship and crew...... characteristics are: ship speed, ship manoeuvrability, the layout of the navigational bridge, the radar system, the number and the training of navigators, the presence of a look out etc. The main parameters affecting the navigational environment are ship traffic density, probability distributions of wind speeds...... probability, i.e. a study of the navigator's role in resolving critical situations, a causation factor is derived as a second step.The report documents the first step in a probabilistic collision damage analysis. Future work will inlcude calculation of energy released for crushing of structures giving a...
This work validates the use of integrated polyvinylidene fluoride (PVDF) film sensors for dynamic testing, even after being subjected to UV-thermo-hygro-mechanical accelerated ageing conditions. The verification of PVDF sensors’ survivability in these environmental conditions, typically confronted by civil and military aircraft, is the main concern of the study. The evaluation of survivability is made by a comparison of dynamic testing results provided by the PVDF patch sensors subjected to an accelerated ageing protocol, and those provided by neutral non-aged sensors (accelerometers). The available measurements are the time-domain response signals issued from a modal analysis procedure, and the corresponding frequency response functions (FRF). These are in turn used to identify the constitutive properties of the samples by extraction of the modal parameters, in particular the natural frequencies. The composite specimens in this study undergo different accelerated ageing processes. After several weeks of experimentation, the samples exhibit a loss of stiffness, represented by a decrease in the elastic moduli down to 10%. Despite the ageing, the integrated PVDF sensors, subjected to the same ageing conditions, are still capable of providing reliable data to carry out a close followup of these changes. This survivability is a determinant asset in order to use integrated PVDF sensors to perform structural health monitoring (SHM) in the future of full-scale composite aeronautical structures. (paper)
苏伯尼; 黄弘; 李云涛
2013-01-01
In order to perform quantitative risk assessment of fire caused by lightning in oil tank areas,probabilities of lightning-induced floating roof tank fire and explosion are estimated.According to domestic and international standards,models of lightning and floating roof tanks were established.The risk probability of lightning hitting oil tanks was calculated using these models.After that,the risk probability of fire and explosion when lightning hit oil tanks was estimated according to some existing experimental results.The results show that probability of rim seal spark causing fire is greater than that of lightning burning through oil tank shell under normal circumstances.And probability of lightning-induced fire and explosion on tanks using mechanical primary seal is higher than that on tanks using soft primary seal.%为了对储油罐区雷击火灾进行定量的风险评估,估算雷电引发浮顶罐火灾爆炸事件的概率.根据国内外相关标准,建立闪电和浮顶罐的模型,并计算闪电击中不同尺寸油罐的概率.然后,根据已有的试验结果,估算闪电在击中不同尺寸油罐的情况下,通过烧穿油罐外壳以及引起密封圈火花2种途径导致火灾爆炸的概率,开展雷电引发油罐火灾爆炸的风险评估.计算结果表明:一般情况下,密封圈火花导致火灾的概率大于闪电烧穿油罐外壳导致火灾的概率；采用机械密封的浮顶罐雷击火灾事故概率比采用软密封的高.
Effect of age condition on fatigue properties of 2E12 aluminum alloy
YAN Liang; DU Feng-shan; DAI Sheng-long; YANG Shou-jie
2010-01-01
The fatigue behaviors of 2E12 aluminum alloy in T3 and T6 conditions at room temperature in air were investigated.The microstructures and fatigue fracture surfaces of the alloy were examined by transmission electron microscopy(TEM)and scanning electron microscopy(SEM).The results show that the alloy exhibits higher fatigue crack propagation(FCP)resistance in T3condition than in T6 condition,the fatigue life is increased by 54% and the fatigue crack growth rate(FCGR)decreases significantly.The fatigue fractures of the alloy in T3 and T6 conditions are transgranular.But in T3 condition,secondary cracks occur and fatigue striations are not clear.In T6 condition,ductile fatigue striations are observed.The effect of aging conditions on fatigue behaviors is explained in terms of the slip planarity of dislocations and the cyclic slip reversibility.
郑欣; 李全明; 许开立; 耿丽艳
2015-01-01
对国内外尾矿坝溃坝事故进行整理分析，得出坝坡失稳是导致溃坝的一个主要原因，利用突变理论对坝坡失稳进行分析，从突变学角度证明内摩擦角和粘聚力是尾矿坝坡失稳溃坝的主要影响因素。摒弃传统的尾矿坝抗滑稳定性安全系数定值计算方法，选取综合考虑诸因素的不确定性的概率方法来计算尾矿坝坡失稳溃坝概率，确定内摩擦角和粘聚力作为随机参数，建立尾矿坝坡失稳破坏的功能函数，确定模拟次数；采用考虑随机变量相关性的蒙特卡罗进行尾矿坝坡失稳溃坝概率计算。该方法成功克服了matlab传统子集模拟方法只能解决随机变量为正态分布且变量之间相互独立的不足，并以某尾矿坝为例对其因坝坡失稳导致的溃坝概率进行了计算。%The accidents of tailings dam failure at home and abroad were analyzed, and it showed that the dam slope instability was a major reason causing dam failure.The dam slope instability was analyzed by the catastrophe theory, and it proved from the perspective of catastrophe that the internal friction angle and cohesion strength were the main influence factors of dam slope instability and failure.Abandoning the traditional calculation method on an-ti-slide stability safety coefficient of tailings dam, the probability method comprehensively considering the uncertain-ty of each factor was selected to calculate the probability of dam failure.The internal friction angle and cohesion strength were taken as random parameters, the function of dam slope instability and failure was established, and the number of simulation was determined.The Monte Carlo considering the correlation between random variables was applied to calculate the probability of dam failure.This method overcomes the shortcomings that the traditional Mat-lab subset simulation method can only solve the problems that random variables are normal distribution and the
Interpretations of Negative Probabilities
Burgin, Mark
2010-01-01
In this paper, we give a frequency interpretation of negative probability, as well as of extended probability, demonstrating that to a great extent, these new types of probabilities, behave as conventional probabilities. Extended probability comprises both conventional probability and negative probability. The frequency interpretation of negative probabilities gives supportive evidence to the axiomatic system built in (Burgin, 2009; arXiv:0912.4767) for extended probability as it is demonstra...
Probability Aggregates in Probability Answer Set Programming
Saad, Emad
2013-01-01
Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of p...
Measurement uncertainty and probability
Willink, Robin
2013-01-01
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
The Probability Distribution for a Biased Spinner
Foster, Colin
2012-01-01
This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Gaussian Probabilities and Expectation Propagation
Cunningham, John P.; Hennig, Philipp; Lacoste-Julien, Simon
2011-01-01
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approximation is highly accurate. We also extend the derivations to the more general case of polyhedral integration regions. However, we find that in this polyhedral case, EP's answer...
Briggs, William M
2012-01-01
The probability leakage of model M with respect to evidence E is defined. Probability leakage is a kind of model error. It occurs when M implies that events $y$, which are impossible given E, have positive probability. Leakage does not imply model falsification. Models with probability leakage cannot be calibrated empirically. Regression models, which are ubiquitous in statistical practice, often evince probability leakage.
Lin, Jin-Ding; Lin, Lan-Ping; Hsu, Shang-Wei; Chen, Wen-Xiu; Lin, Fu-Gong; Wu, Jia-Ling; Chu, Cordia
2014-11-13
This study aims to answer the research question of "Are early onset aging conditions correlated to daily activity functions in youth and adults with Down syndrome (DS)?" A cross-sectional survey was employed to recruit 216 individuals with DS over 15 years of age in the analyses. A structured questionnaire included demographic data, brief self-reported aging conditions, Dementia Screening Questionnaire for Individuals with Intellectual Disabilities (DSQIID) and activity of daily living (ADL) scales were completed by the primary caregivers who were well-suited for providing information on the functioning conditions of the DS individuals. Results showed that the most five frequent aging conditions (sometimes, usually and always) included frailty (20.2%), vision problem (15.8%), loss of language ability (15.3%), sleep problem (14.9%) and memory impairment (14.5%). Other onset aging conditions included more chronic diseases (13.9%), hearing loss (13%), chewing ability and tooth loss (12.5%), incontinence (11.1%), depressive syndrome (7.7%), falls and gait disorder (7.2%), loss of taste and smell (7.2%). The data also showed scores of DSQIID, onset aging conditions and ADL has significant relationships each other in Pearson's correlation tests. Finally, multiple linear regression analyses indicated onset aging conditions (β=-0.735, p<0.001) can significantly predicted the variation in ADL scores after adjusting other factors (R(2)=0.381). This study suggests that the authority should initiate early intervention programs aim to improve healthy aging and ADL functions for people with DS. PMID:25462513
Koo, Reginald; Jones, Martin L.
2011-01-01
Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.
Goldberg, Samuel
2013-01-01
Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.
Fusion Probability in Dinuclear System
Hong, Juhee
2015-01-01
Fusion can be described by the time evolution of a dinuclear system with two degrees of freedom, the relative motion and transfer of nucleons. In the presence of the coupling between two collective modes, we solve the Fokker-Planck equation in a locally harmonic approximation. The potential of a dinuclear system has the quasifission barrier and the inner fusion barrier, and the escape rates can be calculated by the Kramers' model. To estimate the fusion probability, we calculate the quasifission rate and the fusion rate. We investigate the coupling effects on the fusion probability and the cross section of evaporation residue.
Emptiness Formation Probability
Crawford, Nicholas; Ng, Stephen; Starr, Shannon
2016-08-01
We present rigorous upper and lower bounds on the emptiness formation probability for the ground state of a spin-1/2 Heisenberg XXZ quantum spin system. For a d-dimensional system we find a rate of decay of the order {exp(-c L^{d+1})} where L is the sidelength of the box in which we ask for the emptiness formation event to occur. In the {d=1} case this confirms previous predictions made in the integrable systems community, though our bounds do not achieve the precision predicted by Bethe ansatz calculations. On the other hand, our bounds in the case {d ≥ 2} are new. The main tools we use are reflection positivity and a rigorous path integral expansion, which is a variation on those previously introduced by Toth, Aizenman-Nachtergaele and Ueltschi.
Ozcan, Mutlu; Barbosa, Silvia Helena; Melo, Renata Marques; Galhano, Graziela Avila Prado; Bottino, Marco Antonio
2007-01-01
Objectives. This study evaluated the effect of two different surface conditioning methods on the repair bond strength of a bis-GMA-adduct/bis-EMA/TEGDMA based resin composite after three aging conditions. Methods. Thirty-six composite resin blocks (Esthet X, Dentsply) were prepared (5 mm x 6 mm x 6
董海波; 顾学康
2013-01-01
基于模糊理论，提出了一种定量风险评估方法——模糊故障树方法。查阅历史数据库或者借助专家判断，给出故障树模型中各基本事件发生可能性的模糊数表示。考虑到不同专家意见之间可能存在的差异，给出了处理专家意见的运算法则及确定专家权重的理论方法。以半潜式钻井平台发生井喷为顶事件，构建了故障树模型，依据给出的模糊故障树理论模型，计算得到半潜式平台在钻进或固井过程中发生井喷的概率。%Based on fuzzy theory, a quantitative risk assessment method called fuzzy fault tree analysis is presented. By referring to risk database or by dint of expert judgements, this paper presents occurrence possibility of each basic event in the fault tree model which is expressed in the form of fuzzy numbers. Since each expert may have a different opinion, this paper developes an algorithm to aggregate expert opinion and a method to determine the importance weight of expert opinion. This paper constructs fault tree model on blowout of semi-submersible drilling platform. According to fuzzy fault tree analysis method, the probability of blowout is calculated during drilling or cementing on a semi-submersible drilling platform.
王程龙; 谢禹钧; 韦权权; 于小泽
2016-01-01
运用有限元软件 Ansys 对螺栓法兰接头进行模拟，得到了在预紧和操作工况下垫片的应力分布，计算出不同内压工况下垫片的应力。采用 Monte Carlo 法在管道工作压力不断波动时进行可靠性分析，创建极限方程并根据极限方程应用大型软件 Matlab 以变量的分布类型对变量进行反复随机抽样，计算出不同工作压力下螺栓法兰泄漏的概率。分析结果表明，工作压力的波动产生的附加载荷对螺栓法兰泄漏会产生很大的影响，必须加以足够的重视。%Bolted flange joints were simulated with the finite element software Ansys,getting the gasket stress distribution under the condition of the preload and operation,and calculating the gasket stress under different working condition of internal pressure.Due to constant fluctuations in pipeline pressure and the pipe stress complex,the working pressure,temperature, uncertain factors such as their own constraints on its tightness should be fully considered.The Monte Carlo method is used to have reliability analysis in pipeline working pressure fluctuating.Limit equation is created and according to the distribution of the variable type and limit equation using large-scale software Matlab is used to repeat random sampling to calculate the probability of bolt flange leakages under different working pressures.The results show that,the additional load produced by working pressure fluctuation will have a very big effect on the bolt flange leak,that must be got seriously enough attention.
Average Transmission Probability of a Random Stack
Lu, Yin; Miniatura, Christian; Englert, Berthold-Georg
2010-01-01
The transmission through a stack of identical slabs that are separated by gaps with random widths is usually treated by calculating the average of the logarithm of the transmission probability. We show how to calculate the average of the transmission probability itself with the aid of a recurrence relation and derive analytical upper and lower…
Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia
2011-01-01
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and zero- and unit-probability events pose no particular epistemological problems. We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov's axiomatization o...
Logical Probability Preferences
Saad, Emad
2013-01-01
We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming, called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem, c...
Probable Inference and Quantum Mechanics
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
Agreeing Probability Measures for Comparative Probability Structures
Wakker, Peter
1981-01-01
It is proved that fine and tight comparative probability structures (where the set of events is assumed to be an algebra, not necessarily a $\\sigma$-algebra) have agreeing probability measures. Although this was often claimed in the literature, all proofs the author encountered are not valid for the general case, but only for $\\sigma$-algebras. Here the proof of Niiniluoto (1972) is supplemented. Furthermore an example is presented that reveals many misunderstandings in the literature. At the...
Benci, Vieri; Wenmackers, Sylvia
2011-01-01
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and zero- and unit-probability events pose no particular epistemological problems. We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov's axiomatization of probability is replaced by a different type of infinite additivity.
Elements of probability theory
Rumshiskii, L Z
1965-01-01
Elements of Probability Theory presents the methods of the theory of probability. This book is divided into seven chapters that discuss the general rule for the multiplication of probabilities, the fundamental properties of the subject matter, and the classical definition of probability. The introductory chapters deal with the functions of random variables; continuous random variables; numerical characteristics of probability distributions; center of the probability distribution of a random variable; definition of the law of large numbers; stability of the sample mean and the method of moments
Evaluating probability forecasts
Lai, Tze Leung; Shen, David Bo; 10.1214/11-AOS902
2012-01-01
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence, or nonoccurrence, of the predicted events. We develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation of probability forecasts. This approach uses loss functions relating the predicted to the actual probabilities of the events and applies martingale theory to exploit the temporal structure between the forecast and the subsequent occurrence or nonoccurrence of the event.
Lane, S.M.
1979-08-01
An experimental investigation of the level structure of /sup 133/Te was performed by spectroscopy of gamma-rays following the beta-decay of 2.7 min /sup 133/Sb. Multiscaled gamma-ray singles spectra and 2.5 x 10/sup 7/ gamma-gamma coincidence events were used in the assignment of 105 of the approximately 400 observed gamma-rays to /sup 133/Sb decay and in the construction of the /sup 133/Te level scheme with 29 excited levels. One hundred twenty-two gamma-rays were identified as originating in the decay of other isotopes of Sb or their daughter products. The remaining gamma-rays were associated with the decay of impurity atoms or have as yet not been identified. A new computer program based on the Lanczos tridiagonalization algorithm using an uncoupled m-scheme basis and vector manipulations was written. It was used to calculate energy levels, parities, spins, model wavefunctions, neutron and proton separation energies, and some electromagnetic transition probabilities for the following nuclei in the /sup 132/Sn region: /sup 128/Sn, /sup 129/Sn, /sup 130/Sn, /sup 131/Sn, /sup 130/Sb, /sup 131/Sb, /sup 132/Sb, /sup 133/Sb, /sup 132/Te, /sup 133/Te, /sup 134/Te, /sup 134/I, /sup 135/I, /sup 135/Xe, and /sup 136/Xe. The results are compared with experiment and the agreement is generally good. For non-magic nuclei: the lg/sub 7/2/, 2d/sub 5/2/, 2d/sub 3/2/, 1h/sub 11/2/, and 3s/sub 1/2/ orbitals are available to valence protons and the 2d/sub 5/2/, 2d/sub 3/2/, 1h/sub 11/2/, and 3s/sub 1/2/ orbitals are available to valence neutron holes. The present CDC7600 computer code can accommodate 59 single particle states and vectors comprised of 30,000 Slater determinants. The effective interaction used was that of Petrovich, McManus, and Madsen, a modification of the Kallio-Kolltveit realistic force. Single particle energies, effective charges and effective g-factors were determined from experimental data for nuclei in the /sup 132/Sn region. 116 references.
Estimating extreme flood probabilities
Estimates of the exceedance probabilities of extreme floods are needed for the assessment of flood hazard at Department of Energy facilities. A new approach using a joint probability distribution of extreme rainfalls and antecedent soil moisture conditions, along with a rainfall runoff model, provides estimates of probabilities for floods approaching the probable maximum flood. This approach is illustrated for a 570 km2 catchment in Wisconsin and a 260 km2 catchment in Tennessee
Roussas, George G
2006-01-01
Roussas's Introduction to Probability features exceptionally clear explanations of the mathematics of probability theory and explores its diverse applications through numerous interesting and motivational examples. It provides a thorough introduction to the subject for professionals and advanced students taking their first course in probability. The content is based on the introductory chapters of Roussas's book, An Intoduction to Probability and Statistical Inference, with additional chapters and revisions. Written by a well-respected author known for great exposition an
Edwards, William F.; Shiflett, Ray C.; Shultz, Harris
2008-01-01
The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…
Interpretations of probability
Khrennikov, Andrei
2009-01-01
This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.
Childers, Timothy
2013-01-01
Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject. He explains the main interpretations of probability-frequentist, propensity, classical, Bayesian, and objective Bayesian-and uses stimulatingexamples to bring the subject to life. All students of philosophy will benefit from an understanding of probability,
Introduction to probability models
Ross, Sheldon M
2006-01-01
Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text. The book begins by introducing basic concepts of probability theory, such as the random v
Choice Probability Generating Functions
Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications....
Florescu, Ionut
2013-01-01
THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introductio
Choice probability generating functions
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2013-01-01
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to...
Ash, Robert B; Lukacs, E
1972-01-01
Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory.Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of var
In this work, I formulate the persistence probability for a qubit device as the probability of measuring its computational degrees of freedom in the unperturbed state without the decoherence arising from environmental interactions. A decoherence time can be obtained from the persistence probability. Drawing on recent work of Garg, and also Palma, Suomine, and Ekert, I apply the persistence probability formalism to a generic single-qubit device coupled to a thermal environment, and also apply it to a trapped-ion quantum register coupled to the ion vibrational modes. (author)
Simulations of Probabilities for Quantum Computing
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Probability Issues in without Replacement Sampling
Joarder, A. H.; Al-Sabah, W. S.
2007-01-01
Sampling without replacement is an important aspect in teaching conditional probabilities in elementary statistics courses. Different methods proposed in different texts for calculating probabilities of events in this context are reviewed and their relative merits and limitations in applications are pinpointed. An alternative representation of…
Freund, John E
1993-01-01
Thorough, lucid coverage of permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, binomial distribution, geometric distribution, standard deviation, law of large numbers, and much more. Exercises with some solutions. Summary. Bibliography. Includes 42 black-and-white illustrations. 1973 edition.
On Quantum Conditional Probability
Isabel Guerra Bobo
2013-02-01
Full Text Available We argue that quantum theory does not allow for a generalization of the notion of classical conditional probability by showing that the probability defined by the Lüders rule, standardly interpreted in the literature as the quantum-mechanical conditionalization rule, cannot be interpreted as such.
Prabhu, Narahari
2011-01-01
Recent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.
Probability, Nondeterminism and Concurrency
Varacca, Daniele
Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particula...
Elena Druica
2007-05-01
Full Text Available The science of probabilities has earned a special place because it tried through its concepts to build a bridge between theory and experimenting.As a formal notion which by definition does not lead to polemic, probability, nevertheless, meets a series of difficulties of interpretation whenever the probability must be applied to certain particular situations.Usually, the economic literature brings into discussion two interpretations of the concept of probability:the objective interpretation often found under the name of frequency or statistical interpretation and the subjective or personal interpretation. Surprisingly, the third appproach is excluded:the logical interpretation.The purpose of the present paper is to study some aspects of the subjective and logical interpretation of the probability, aswell as the implications in the economics.
Heterogeneous Calculation of ε
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of ε. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer
A case concerning the improved transition probability
Tang, Jian; Wang, An Min
2006-01-01
As is well known, the existed perturbation theory can be applied to calculations of energy, state and transition probability in many quantum systems. However, there are different paths and methods to improve its calculation precision and efficiency in our view. According to an improved scheme of perturbation theory proposed by [An Min Wang, quant-ph/0611217], we reconsider the transition probability and perturbed energy for a Hydrogen atom in a constant magnetic field. We find the results obt...
陈胜军; 贾方
2013-01-01
A general model of slider-crank mechanism precision analysis is established based on matrix analysis theory;probability analysis model of slider-crank mechanism movement precision is obtained based on state functions; the movement output accuracy model and probability analysis model of slider-crank mechanism are established based on centring slidercrank mechanism.The case study indicated that centring slider-crank mechanism has different kinematic error and different reliability under given design accuracy.The effectiveness probability of slider-crank mechanism can be given out under different motion stage by the models,and it is important for design and manufacture of slider-crank mechanism.%利用矩阵分析理论建立了曲柄滑块机构精度分析的一般模型,利用状态函数建立了曲柄滑块机构运动精度的概率分析模型,以对心曲柄滑块机构为具体对象,建立了曲柄滑块机构运动输出精度模型及其概率分析计算模型.算例分析表明:在给定的设计精度下,对心曲柄滑块机构在不同的运动状态有着不同的运动误差和不同的运动可靠度.模型可以定量地给出曲柄滑块机构在不同运动状态下的失效概率,对曲柄滑块机构的设计与制造具有应用价值.
A Novel Approach to Probability
Kafri, Oded
2016-01-01
When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system in which P much greater than L, our natural intuition tells us that the box with the average number of balls has the highest probability and that none of boxes are empty; however in reality, the probability of the empty box is always the highest. This fact is with contradistinction to sparse system in which the number of balls is smaller than the number of boxes (i.e. energy distribution in gas) in which the average value has the highest probability. Here we show that when we postulate the requirement that all possible configurations of balls in the boxes have equal probabilities, a realistic "long tail" distribution is obtained. This formalism when applied for sparse systems converges to distributions in which the average is preferred. We calculate some of the distributions resulted from this postulate and obtain most of the known distributions in nature, namely, Zipf law, Benford law, part...
The concept of probability is now, and always has been, central to the debate on the interpretation of quantum mechanics. Furthermore, probability permeates all of science, as well as our every day life. The papers included in this volume, written by leading proponents of the ideas expressed, embrace a broad spectrum of thought and results: mathematical, physical epistemological, and experimental, both specific and general. The contributions are arranged in parts under the following headings: Following Schroedinger's thoughts; Probability and quantum mechanics; Aspects of the arguments on nonlocality; Bell's theorem and EPR correlations; Real or Gedanken experiments and their interpretation; Questions about irreversibility and stochasticity; and Epistemology, interpretation and culture. (author). refs.; figs.; tabs
Billingsley, Patrick
2012-01-01
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this
Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 2s-2p electric dipole transitions in berylliumlike ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for the 16 possible E1 transitions. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order MBPT. The importance of virtual electron-positron pair (negative energy) contributions to the transition amplitudes is discussed. (orig.)
Using the multi-configuration Dirac—Fock self-consistent field method and the relativistic configuration-interaction method, calculations of transition energies, oscillator strengths and rates are performed for the 3s21S0-3s3p 1P1 spin-allowed transition, 3s21S0-3s3p 3P1,2 intercombination and magnetic quadrupole transition in the Mg isoelectronic sequence (Mg I, Al II, Si III, P IV and S V). Electron correlations are treated adequately, including intravalence electron correlations. The influence of the Breit interaction on oscillator strengths and transition energies are investigated. Quantum electrodynamics corrections are added as corrections. The calculation results are found to be in good agreement with the experimental data and other theoretical calculations. (atomic and molecular physics)
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
Hartmann, Stephan
2011-01-01
Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the first to provide a philosophical appraisal of probabilities in all of physics. Its main aim is to make sense of probabilistic statements as they occur in the various physical theories and models and to provide a plausible epistemology and metaphysics of probabilities. The essays collected here consider statistical physics, probabilistic modelling, and quantum mechanics, and critically assess the merits and disadvantages of objectivist and subjectivist views of probabilities in these fie...
Stochastic Programming with Probability
Andrieu, Laetitia; Vázquez-Abad, Felisa
2007-01-01
In this work we study optimization problems subject to a failure constraint. This constraint is expressed in terms of a condition that causes failure, representing a physical or technical breakdown. We formulate the problem in terms of a probability constraint, where the level of "confidence" is a modelling parameter and has the interpretation that the probability of failure should not exceed that level. Application of the stochastic Arrow-Hurwicz algorithm poses two difficulties: one is structural and arises from the lack of convexity of the probability constraint, and the other is the estimation of the gradient of the probability constraint. We develop two gradient estimators with decreasing bias via a convolution method and a finite difference technique, respectively, and we provide a full analysis of convergence of the algorithms. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of ...
Grimmett, Geoffrey
2014-01-01
Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...
Hemmo, Meir
2012-01-01
What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
Estimating Subjective Probabilities
Andersen, Steffen; Fountain, John; Harrison, Glenn W.;
2014-01-01
either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake 'calibrating adjustments' to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments that...
Estimating Subjective Probabilities
Andersen, Steffen; Fountain, John; Harrison, Glenn W.;
either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake “calibrating adjustments” to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments that...
Probability and Statistical Inference
Prosper, Harrison B.
2006-01-01
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
Marshall, Jennings B.
2007-01-01
This article describes how roulette can be used to teach basic concepts of probability. Various bets are used to illustrate the computation of expected value. A betting system shows variations in patterns that often appear in random events.
Probability in quantum mechanics
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Bayesian default probability models
Andrlíková, Petra
2014-01-01
This paper proposes a methodology for default probability estimation for low default portfolios, where the statistical inference may become troublesome. The author suggests using logistic regression models with the Bayesian estimation of parameters. The piecewise logistic regression model and Box-Cox transformation of credit risk score is used to derive the estimates of probability of default, which extends the work by Neagu et al. (2009). The paper shows that the Bayesian models are more acc...
Probability densities in strong turbulence
Yakhot, Victor
2006-03-01
In this work we, using Mellin’s transform combined with the Gaussian large-scale boundary condition, calculate probability densities (PDFs) of velocity increments P(δu,r), velocity derivatives P(u,r) and the PDF of the fluctuating dissipation scales Q(η,Re), where Re is the large-scale Reynolds number. The resulting expressions strongly deviate from the Log-normal PDF P(δu,r) often quoted in the literature. It is shown that the probability density of the small-scale velocity fluctuations includes information about the large (integral) scale dynamics which is responsible for the deviation of P(δu,r) from P(δu,r). An expression for the function D(h) of the multifractal theory, free from spurious logarithms recently discussed in [U. Frisch, M. Martins Afonso, A. Mazzino, V. Yakhot, J. Fluid Mech. 542 (2005) 97] is also obtained.
Experimental Probability in Elementary School
Andrew, Lane
2009-01-01
Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.
Isaac, Richard
1995-01-01
The ideas of probability are all around us. Lotteries, casino gambling, the al most non-stop polling which seems to mold public policy more and more these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairl...
Improving Ranking Using Quantum Probability
Melucci, Massimo
2011-01-01
The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of ...
New Zealand population and cancer statistics have been used to derive the probability that an existing cancer in an individual was the result of a known exposure to radiation. Hypothetical case histories illustrate how sex, race, age at exposure, age at presentation with disease, and the type of cancer affect this probability. The method can be used now to identify claims in which a link between exposure and disease is very strong or very weak, and the types of cancer and population sub-groups for which radiation is most likely to be the causative agent. Advantages and difficulties in using a probability of causation approach in legal or compensation hearings are outlined. The approach is feasible for any carcinogen for which reasonable risk estimates can be made
Minimum Probability Flow Learning
Sohl-Dickstein, Jascha; DeWeese, Michael R
2009-01-01
Learning in probabilistic models is often severely hampered by the general intractability of the normalization factor and its derivatives. Here we propose a new learning technique that obviates the need to compute an intractable normalization factor or sample from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the initial flow of probability away from the data distribution. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate the application of minimum probability flow learning to parameter estimation in Ising models, deep belief networks, multivariate Gaussian distributions and a continuous model with a highly general energy function defined as a power series. In the Ising model case, minimum probability flow learning outperforms cur...
Introduction to imprecise probabilities
Augustin, Thomas; de Cooman, Gert; Troffaes, Matthias C M
2014-01-01
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, includin
Choice probability generating functions
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2010-01-01
This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications...
Negative Probabilities and Contextuality
de Barros, J Acacio; Oas, Gary
2015-01-01
There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is contextuality-by-default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with contextuality-by-default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology.
Classic Problems of Probability
Gorroochurn, Prakash
2012-01-01
"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin
Probably Almost Bayes Decisions
Anoulova, S.; Fischer, Paul; Poelt, S.; Simon, H.- U.
1996-01-01
In this paper, we investigate the problem of classifying objects which are given by feature vectors with Boolean entries. Our aim is to "(efficiently) learn probably almost optimal classifications" from examples. A classical approach in pattern recognition uses empirical estimations of the Bayesian...
Plotnitsky, Arkady
2010-01-01
Offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schrodinger; in quantum mechanics; and in modern physics. This book considers the implications of these relationships and of quantum theory for our understanding of the nature of thinking and knowledge in general
Quznetsov, Gunn
1998-01-01
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function, which has all properties of the classical probability function. The logical analog of the Large Number Law is deduced from properties of this function.
Quznetsov, G. A.
2003-01-01
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function, which has all properties of the classical probability function. The logical analog of the Large Number Law is deduced from properties of this function.
Transition probabilities for atoms
Current status of advanced theoretical methods for transition probabilities for atoms and ions is discussed. An experiment on the f values of the resonance transitions of the Kr and Xe isoelectronic sequences is suggested as a test for the theoretical methods
Counterexamples in probability
Stoyanov, Jordan M
2013-01-01
While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix.
Negative probability in the framework of combined probability
Burgin, Mark
2013-01-01
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...
Semiclassical transition probabilities for interacting oscillators
Khlebnikov, S. Yu.
1994-01-01
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities. Solutions are found numerically for a system of two interacting quartic oscillators. In the double-well case, we find numerical evidence that certain regular {\\em minkowskian} trajectories have approximate stopping points or, equivalently, are approximately pe...
Failure probability of ceramic coil springs
Nohut, Serkan; Schneider, Gerold A.
2009-01-01
Ceramic springs are commercially available and a detailed reliability analysis of these components would be useful for their introduction in new applications. In this paper an analytical and a numerical analyses of the failure probability for coil springs under compression is presented. Based on analytically derived relationships and numerically calculated results, fitting functions for volume and surface flaws will be introduced which provide the prediction of the failure probability of cera...
This paper summarizes the results of aging, condition monitoring, and accident testing of various nuclear power plant cable products. Four sets of cables were aged under simultaneous thermal (≅95C) and radiation (≅0.10 kGy/hr) conditions. One set of cables was aged for 3 months, a second set was aged for 6 months, a third set was aged for 9 months, and a fourth set was not aged. A sequential accident consisting of high dose rate irradiation (≅6 kGy/hr) and high temperature steam was then performed on each set of cables. The results of the tests indicate that the feasibility of life extension of some popular cable products is promising. Mechanical measurements, primarily elongation, modulus, and density, were more effective than electrical measurements for monitoring age-related degradation. The broad objectives of this experimental program were twofold: (a) to determine the life extension potential of popular cable products used in nuclear power plants and (b) to determine the potential of condition monitoring for residual life assessment
This paper summarizes the results of aging, condition monitoring, and accident testing of Class 1E cables used in nuclear power generating stations. Three sets of cables were aged for up to 9 months under simultaneous thermal (≅ 100 degrees C) and radiation (≅0.10 kGy/hr) conditions. After the aging, the cables were exposed to a simulated accident consisting of high dose rate irradiation (≅6 kGy/hr) followed by a high temperature steam exposure. A fourth set of cables, which were unaged, were also exposed to the accident conditions. The cables that were aged for 3 months and then accident tested were subsequently exposed to a high temperature steam fragility test (up to 400 degrees C), while the cables that were aged for 6 months and then accident tested were subsequently exposed to a 1000-hour submergence test in a chemical solution. The results of the tests indicate that the feasibility of life extension of many popular nuclear power plant cable products is promising and that mechanical measurements (primarily elongation, modulus, and density) were more effective than electrical measurements for monitoring age-related degradation. In the high temperature steam test, ethylene propylene rubber (EPR) cable materials generally survived to higher temperatures than crosslinked polyolefin (XLPO) cable materials. In dielectric testing after the submergence testing, the XLPO materials performed better than the EPR materials. This paper presents some recent experimental data that are not yet available elsewhere and a summary of findings from the entire experimental program
This paper summarizes the results of aging, condition monitoring, and accident testing of Class 1E cables used in nuclear power generating stations. Three sets of cables were aged for up to 9 months under simultaneous thermal (≅ 100C) and radiation (≅ 0.10 kGy/hr) conditions. After the aging, the cables were exposed to a simulated accident consisting of high dose rate irradiation (≅ 6 kGy/hr) followed by a high temperature steam exposure. A fourth set of cables, which were unaged, were also exposed to the accident conditions. The cables that were aged for 3 months and then accident tested were subsequently exposed to a high temperature steam fragility test (up to 400C), while the cables that were aged for 6 months and then accident tested were subsequently exposed to a 1,000-hour submergence test in a chemical solution. The results of the tests indicate that the feasibility of life extension of many popular nuclear power plant cable products is promising and that mechanical measurements (primarily elongation, modulus, and density) were more effective than electrical measurements for monitoring age-related degradation. In the high temperature steam test, ethylene propylene rubber (EPR) cable materials generally survived to higher temperatures than crosslinked polyolefin (XLPO) cable materials. In dielectric testing after the submergence testing, the XLPO materials performed better than the EPR materials. This paper presents some recent experimental data that are not yet available elsewhere and a summary of findings from the entire experimental program
Aging, condition monitoring, and loss-of-coolant accident (LOCA) tests of class 1E electrical cables
This report describes the results of aging, condition monitoring, and accident testing of ethylene propylene rubber (EPR) cables. Three sets of cables were aged for up to 9 months under simultaneous thermal (≅100 degrees C) and radiation (≅0.10 kGy/hr) conditions. A sequential accident consisting of high dose rate irradiation (≅6 kGy/hr) and high temperature steam followed the aging. Also exposed to the accident conditions was a fourth set of cables, which were unaged. The test results indicate that most properly installed EPR cables should be able to survive an accident after 60 years for total aging doses of at least 150--200 kGy and for moderate ambient temperatures on the order of 45--55 degrees C (potentially higher or lower, depending on material specific activation energies and total radiation doses). Mechanical measurements (primarily elongation, modulus, and density) were more effective than electrical measurements for monitoring age-related degradation
Contributions to quantum probability
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a finite set can occur as the outcome
Contributions to quantum probability
Fritz, Tobias
2010-06-25
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a
Paradoxes in probability theory
Eckhardt, William
2013-01-01
Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Transition probabilities for argon I
Transition probabilities for ArI lines have been calculated on the basis of the (j,k)-coupling scheme for more than 16000 spectral lines belonging to the transition arrays 4s-np (n=4 to n=9), 5s-np (n=5 to n=9), 6s-np (n=6 to n=9), 7s-np (n=8 to n=9), 4p-ns (n=5 to n=10), 5p-ns (n=6 to n=9), 6p-ns (n=7 to n=8), 4p-nd (n=3 to n=9), 5p-nd (n=4 to n=9), 3d-np (n=5 to n=9), 4d-np (n=6 to n=9), 5d-np (n=7 to n=9), 3d-nf (n=4 to n=9), 4d-nf (n=4 to n=9), 5d-nf (n=5 to n=9), 4f-nd (n=5 to n=9) 5f-nd (n=6 to n=9), 4f-ng (n=5 to n=9), 5f-ng (n=6 to n=9). Inso far as values by other authors exist, comparison is made with these values. It turns out that the results obtained in (j,k)-coupling are close to those obtained in intermediate coupling except for intercombination lines. For high principal and/or orbital quantum numbers the transition probabilities for a multiplet approach those of the corresponding transitions in atomic hydrogen. The calculated values are applied to construct a simplified argon-atom model, which reflects the real transition properties and which allows simplified but realistic non-equilibrium calculations for argon plasmas which deviate from local thermodynamic equilibrium (LTE)
Objectifying Subjective Probabilities
Childers, Timothy
Dordrecht: Springer, 2012 - ( Weber , M.; Dieks, D.; Gonzalez, W.; Hartman, S.; Stadler, F.; Stöltzner, M.), s. 19-28. (The Philosophy of Science in a European Perspective. 3). ISBN 978-94-007-3029-8. [Pluralism in the Foundations of Statistics. Canterbury (GB), 09.09.2010-10.09.2010] R&D Projects: GA ČR(CZ) GAP401/10/1504 Institutional support: RVO:67985955 Keywords : probabilities * direct Inference Subject RIV: AA - Philosophy ; Religion
Whittle, Peter
1992-01-01
This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text...
Probability mapping of contaminants
Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds)
Sirca, Simon
2016-01-01
This book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy, Markov processes, and fundamentals of random number generation and Monte-Carlo methods.
Measurement Uncertainty and Probability
Willink, Robin
2013-02-01
Part I. Principles: 1. Introduction; 2. Foundational ideas in measurement; 3. Components of error or uncertainty; 4. Foundational ideas in probability and statistics; 5. The randomization of systematic errors; 6. Beyond the standard confidence interval; Part II. Evaluation of Uncertainty: 7. Final preparation; 8. Evaluation using the linear approximation; 9. Evaluation without the linear approximations; 10. Uncertainty information fit for purpose; Part III. Related Topics: 11. Measurement of vectors and functions; 12. Why take part in a measurement comparison?; 13. Other philosophies; 14. An assessment of objective Bayesian methods; 15. A guide to the expression of uncertainty in measurement; 16. Measurement near a limit - an insoluble problem?; References; Index.
Integration, measure and probability
Pitt, H R
2012-01-01
This text provides undergraduate mathematics students with an introduction to the modern theory of probability as well as the roots of the theory's mathematical ideas and techniques. Centered around the concept of measure and integration, the treatment is applicable to other branches of analysis and explores more specialized topics, including convergence theorems and random sequences and functions.The initial part is devoted to an exploration of measure and integration from first principles, including sets and set functions, general theory, and integrals of functions of real variables. These t
Harcourt Robert G
2006-02-01
Full Text Available Abstract Background Chemical immobilization of Weddell seals (Leptonychotes weddellii has previously been, for the most part, problematic and this has been mainly attributed to the type of immobilizing agent used. In addition to individual sensitivity, physiological status may play an important role. We investigated the use of the intravenous administration of a 1:1 mixture of tiletamine and zolazepam (Telazol® to immobilize adult females at different points during a physiologically demanding 5–6 week lactation period. We also compared performance between IV and IM injection of the same mixture. Results The tiletamine:zolazepam mixture administered intravenously was an effective method for immobilization with no fatalities or pronounced apnoeas in 106 procedures; however, there was a 25 % (one animal in four mortality rate with intramuscular administration. Induction time was slightly longer for females at the end of lactation (54.9 ± 2.3 seconds than at post-parturition (48.2 ± 2.9 seconds. In addition, the number of previous captures had a positive effect on induction time. There was no evidence for effects due to age, condition (total body lipid, stage of lactation or number of captures on recovery time. Conclusion We suggest that intravenous administration of tiletamine and zolazepam is an effective and safe immobilizing agent for female Weddell seals. Although individual traits could not explain variation in recovery time, we suggest careful monitoring of recovery times during longitudinal studies (> 2 captures. We show that physiological pressures do not substantially affect response to chemical immobilization with this mixture; however, consideration must be taken for differences that may exist for immobilization of adult males and juveniles. Nevertheless, we recommend a mass-specific dose of 0.50 – 0.65 mg/kg for future procedures with adult female Weddell seals and a starting dose of 0.50 mg/kg for other age classes and other
Lectures on probability and statistics
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. We begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probability of any specified outcome. We finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another
Lectures on probability and statistics
Yost, G.P.
1984-09-01
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. We begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probability of any specified outcome. We finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another.