Calculation Of Transition Probabilities Research Articles

Recursive estimation of multivariate hidden Markov model parameters

This article addresses a recursive parameter estimation algorithm for a hidden Markov model (HMM). The work focuses on an HMM with multiple states that are assumed to follow from a multivariate Gaussian distribution. The novelty of this study lies in a state transition probability calculation technique that simplifies the application of the backward stage of the forward–backward algorithm. For sequential observation analysis, the complexity of the created recursive algorithm for learning the HMM parameters is merely linear. Meanwhile, the classical Baum–Welch algorithm has second order complexity; therefore, it cannot be applied in online analysis situations. The properties of the proposed recursive expectation–maximization (EM) algorithm were explored by a computer simulation solving test examples and demonstrate that this algorithm can be efficiently applied to solve online tasks related to HMM parameter estimation.

Atomic structure and excitation cross section by electron impact of tungsten ions, W38+

Excitation energies, radiative rates, and cross sections of tungsten ions (W38+) by electron impact have been calculated using the multiconfiguration Dirac–Fock and R-matrix methods for a configuration state list, which consists of , and and f. A set of configuration state functions with double excitations up to 5l orbitals have been included within the calculations of energy levels and transition probabilities. R-matrix calculations of collision strength and cross section have been executed for the intercombination transitions between 4d, and 4p54f. Resonance collision strengths have been observed at low energies of incident electrons in the range of ∼5−40 Ryd; however, the strong lines limited between 12−25 Ryd. To estimate the accuracy of the calculated energy levels and transition probabilities, comparisons with experimental observations and theoretical calculations are presented, and between different methods for collision strengths and cross sections, as well.

Theoretical Study of Transition Probabilities and Stark Broadening Parameters and of Several Spectral Lines with Astrophysical Interest of Double-ionized Thallium

Abstract Leckrone et al. reported the presence of double-ionized thallium (Tl iii) in the stellar atmosphere of the chemically peculiar star, χ Lupi, in 1999. Two spectral lines at 1332.3 and 1558.6 Å were detected in its stellar spectrum. Here, we claim that there are ions and lines that need further study to make possible the LTE abundance analysis once improved atomic data is available. In this sense, Tl iii is included in the ions list that requires improved atomic data. To contribute to the solution of this problem, an analysis of the atomic parameters of the double-ionized thallium is presented here. In this work, calculations of transition probabilities were made to obtain values of the theoretical radiative lifetimes and theoretical Stark parameters for widths and shifts of 22 spectral lines of Tl iii. Relativistic Hartree–Fock calculations using Cowan’s code allowed us to obtain the required transition probabilities. In our calculations, the core polarization effects were included. Later, the Griem semiempirical approach was used to obtain the Stark parameters. Our lifetimes values for 10 levels were compared with the experimental ones. In this paper, we discuss the behavior of the Stark parameters versus the temperature of three relevant spectral lines. Stark width values of the isoelectronic sequence Tl iii–Pb iv are also displayed.

SYSTEM DYNAMICS MODEL OF TAX BEHAVIOR TAKING INTO ACCOUNT INCOME DISTRIBUTION

The problem of investigating the impact of taxation on the behavior of economic agents remains relevant within a long period of time. This is due, on the one hand, to the multiplicity of channels of this influence, which cover different aspects of people's activity (consumption, investment, employment etc.), and on the other – due to the importance of this issue for the economic government policy. One of the powerful channels of the influence of taxation on the economic agents’ activity of is opportunism as a behavioral property. The effect of this channel is tax evasion – one of the most pressing issues within this range of problems. The article proposes a system-dynamic model that takes into account traditional factors that influence tax evasion (tax control parameters), as well as the assumption that people's tax behavior can be determined by their financial status. The model allows to adjust the parameters of taxation and tax control, as well as the elasticity of reaction of economic agents as for tax evasion, depending on their level of income. Three groups of agents by income criterion are considered, the transitions between groups is modeled as a non-stationary Markov random process with the calculation of conditional transition probabilities at each time step, depending on the indicators of tax control effectiveness. Further directions of the study foresee detailed substantiation of the parameters of the model operators on the basis of the research of real regularities, that determine the intergroup dynamics and mechanisms of evasion, characteristic for different income groups. The model can be used as a virtual training ground, providing extensive experimentation options to test various theoretical assumptions and to study the influence of exogenous factors on the dynamics of endogenous variables, as well as building regression meta-models that will reflect the dependence of the selected response functions of the a number of exogenous factors, taking into account their combined effect.

Electron impact excitation and ionization cross section of tungsten ions, W[formula omitted

Atomic structure data, electron impact excitations and ionization cross sections of tungsten ions, W44+, have been calculated using the multi-configuration Dirac–Fock and R-matrix methods for a set of configurations consists of 3d104s2, 3d104s4l, and 3d104p4l. A set of configuration state functions (CSFs) with doubly excitations up to 5l orbitals have been included within the calculations of energy levels and transition probabilities. As well as, 4-electron excitation to 4l-levels and 3-electron to 5l-levels have been involved in the computation process. R-matrix calculations of collision strength and cross section have been executed for the intercombination transitions between 3d104s2, 3d104s4p, 3d104s4d, and 3d104s4f at different angular momenta using DARC code. Resonance collision strengths have been observed at low energy of incident electron in the range of ∼ 6 – 40 Ryd, however, the strong lines are limited to 6–25 Ryd. For cross section of various transitions, resonances arising from these transitions are observed at low-electron energies in the range of 6–25 Ryd. To estimate the accuracies of calculated energy levels and transition probabilities, comparisons between experimental observations and theoretical calculations are presented. The convergence between different methods for collision strengths and cross sections are observed. Different calculations of electron impact ionization cross section of the present ion in the collision energy range of 100–1000 Ryd are evaluated.

Single- and multiple-electron processes in water molecules colliding with proton beams

Single- and multiple-electron removal processes (ionization, capture and transfer-ionization) from water molecules by the impact of protons have been studied. A prior version of the three-body continuum distorted wave-eikonal initial state (3B-CDW-EIS) approximation within the independent electron approximation is used to calculate transition probabilities as a function of the impact parameter and consequently pure and net absolute cross sections for the collisions under consideration. A unitarization procedure is employed to avoid possible overestimation of the 3B-CDW-EIS single-particle impact parameter probabilities at intermediate collision energies. Multiple-electron transitions are determined using a statistical multinomial distribution. A critical analysis of the validity of this type of distribution for describing pure single-electron processes is presented. The results are compared with other theoretical calculations and available experimental data at impact energies from 50 keV to 5 MeV. New physical insights into the reactions studied are introduced.

Hidden Markov model and driver path preference for floating car trajectory map matching

Here, a hidden Markov model (HMM) and driver path preference (DPP)-based algorithm was proposed for floating car trajectory map matching. The algorithm focused on two improvements over existing HMM-based map matching algorithm: (i) the use of distance difference feature and average speed difference feature for transition probability calculation, which reasonably describe the context information between the two adjacent sampling points. It results in a more accurate matching capability; (ii) the DPP overcomes the shortcoming of feature attenuation in calculating the transition probability at low floating car sampling rates. It assures the matching accuracy of the algorithm at low sampling rates. The algorithm was evaluated using ground truth data and the results of the experiment show that the new transition probability significantly improves the matching capability. The proposed DPP can significantly help to maintain the matching accuracy under the condition of low sampling rates.

Luminescence Intensity Ratio thermometry and Judd-Ofelt analysis of TiO2:Eu3+

Luminescence thermometry on europium doped TiO2 films, prepared by the plasma electrolytic oxidation, was investigated by the Luminescence Intensity Ratio method. The performance of the material for temperature sensing was tested from room temperature to 260 °C. The theoretical fit of the emission intensity ratio of Eu3+5D1→7F1 and 5D0→7F2 transitions revealed the energy difference between 5D1 and 5D0 levels of 1777 cm−1. Temperature sensitivity was calculated on the entire temperature range, with maximum value of 3.43 %K−1 at 293 K. The relationship between Judd-Ofelt and thermometric parameters was demonstrated, and further utilized for the calculation of the radiative transition probability, dipole strength and radiative lifetime of the 5D1→7F1 transition.

High accuracy theoretical calculation of wavelengths and transition probabilities in Se- through Ga-like ions of tungsten

The Ab initio multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations of atomic parameters have been carried out with high accuracy for four highly charged tungsten ions from Se-like W40+ to Ga-like W43+. The second-order relativistic many-body perturbation theory (MBPT) was used to confirm the accuracy of the MCDHF calculations. Excitation energies, wavelengths and transition rates of E1, M1, E2, M2, E3 and lifetimes are presented. The core-valence electron correlation effects arising from deep subshells 3d and 3p, have been taken into account along with relativistic effects. The calculated wavelengths are in good agreement with available experimental results.

Calculation of Transition Probabilities of SDEs Only from the Knowledge of Marginal Probabilities Using the CDF-Equivalent Brownian Motion Method

In this article, we show how to calculate the conditional and transition probabilities of any SDE between two different points across time only from the knowledge of their marginal probabilities on these two time grids. Briefly, we construct CDF-Equivalent standard Brownian motion grids from the knowledge of marginal probabilities of the SDE. The solution of conditional and transition probability of the SDE is the found from the solution of transition probabilities between the corresponding nodes of the CDF-Equivalent standard Brownian motion grids which can be easily calculated. What is the most interesting is that we do not need to know the SDE dynamics for calculation of conditional probabilities and the method requires only the knowledge of marginal probabilities. We can, in fact, use this method to determine the SDE that is best suited as a data generating process.

Photoabsorption spectra of small mercury clusters: a computational study.

Photoabsorption spectra of small HgN clusters (N = 2-5) have been calculated using a diatomics-in-molecules interaction model and an atoms-in-molecules approach for transition probability calculations. Absorption cross-sections are provided over a broad range of photon energies, Ephot = 4.0-7.5 eV, as calculated for various cluster temperatures ranging between T = 0 K and T = 40 K. Quantum as well as temperature-induced delocalization of nuclear positions has been taken into account at various levels using classical and quantum (path-integral) Monte Carlo methods as well as sampling from the square of cluster vibrational ground-state wavefunctions. A thorough comparison of the calculated data with available experimental records is also provided.

Analysis of the spectrum of the (5d[formula omitted]+5d[formula omitted]6s)[formula omitted](5d[formula omitted]6p+5d[formula omitted]6s6p) transitions of two times ionized osmium (Os III)

The spectrum of osmium was observed in the (225–2100) Å wavelength region. The (5d6+ 5d56s)− (5d56p + 5d46s6p) transition array of two times ionized osmium, Os III, has been investigated and 1039 spectral lines have been classified in the region. The analysis has led to the determination of the 5d6, 5d56s, 5d56p and 5d46s6p configurations. Fifty-eight levels of the 5d6 and 5d56s configurations in the even system and 142 levels of the 5d56p and 5d46s6p configurations in the odd system have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Spectrum of Sn5+ in the Region 500–1300 Å

The spectrum of tin, excited in a vacuum spark, was recorded in the region 500–1131 Å on a 6.65-m normal incidence spectrograph. The transitions between 4d85s, 4d86s, 4d85p and 4d85d excited configurations in Sn VI were studied. More than 500 lines of the 4d85p–4d85d and 4d85p–4d86s were identified with the aid of the Cowan code calculations. 67 energy levels (out of 70 possible levels of the 4d85d configuration) and all but two 4d86s levels were found. The wavelength of the 4d85s–4d85p transitions in the region 839–1131 Å were re-measured and supplemented by Sn VI lines in the region 1131–1300 Å measured previously by Srivastava et al. (1977) for optimisation of the energy level values. The SnVI line list in the region 500–1300 Å contains now 741 lines with calculated transition probabilities.

Method of Momentum Representation in the Relativistic Jan–Teller Effect G g [3/2] × (t2g + e g )

The relativistic multimode Jahn-Teller effect G g [3/2] × (t2g + e g ), which takes place in cubic and octahedral molecular systems containing heavy atoms, is considered. The changeover from to the momentum representation in the vibronic Schrodinger equation, equivalent to the five-dimensional Fourier transform, makes it possible to lower the order of the differential operators, thereby achieving significant simplifications. The main result of this work is a quantum-mechanical calculation of the nonadiabatic transition probability in a system that does not admit a complete separation of the variables in the vibronic Schrodinger equation.

A high-performance cellular automata model for urban simulation based on vectorization and parallel computing technology

ABSTRACTCellular automata (CA) models can simulate complex urban systems through simple rules and have become important tools for studying the spatio-temporal evolution of urban land use. However, the multiple and large-volume data layers, massive geospatial processing and complicated algorithms for automatic calibration in the urban CA models require a high level of computational capability. Unfortunately, the limited performance of sequential computation on a single computing unit (i.e. a central processing unit (CPU) or a graphics processing unit (GPU)) and the high cost of parallel design and programming make it difficult to establish a high-performance urban CA model. As a result of its powerful computational ability and scalability, the vectorization paradigm is becoming increasingly important and has received wide attention with regard to this kind of computational problem. This paper presents a high-performance CA model using vectorization and parallel computing technology for the computation-intensive and data-intensive geospatial processing in urban simulation. To transfer the original algorithm to a vectorized algorithm, we define the neighborhood set of the cell space and improve the operation paradigm of neighborhood computation, transition probability calculation, and cell state transition. The experiments undertaken in this study demonstrate that the vectorized algorithm can greatly reduce the computation time, especially in the environment of a vector programming language, and it is possible to parallelize the algorithm as the data volume increases. The execution time for the simulation of 5-m resolution and 3 × 3 neighborhood decreased from 38,220.43 s to 803.36 s with the vectorized algorithm and was further shortened to 476.54 s by dividing the domain into four computing units. The experiments also indicated that the computational efficiency of the vectorized algorithm is closely related to the neighborhood size and configuration, as well as the shape of the research domain. We can conclude that the combination of vectorization and parallel computing technology can provide scalable solutions to significantly improve the applicability of urban CA.

Social Positioning of Older Persons in Rural South Africa: Change or Stability?

The South African context challenges the conventional categorisation of older persons as dependent after a certain age. The concurrence of old-age pensions, high unemployment, high HIV prevalence, and frailty related to ageing necessitate a more dynamic approach to understanding older persons’ social positioning. We examine the extent of change in older persons’ social positioning within their households and the correlates of change in a rural community in South Africa. Using data from the Agincourt Health and socio-Demographic Surveillance System and a new typology of older persons’ social positioning based on living arrangements, we (1) describe older persons’ living arrangements in two time periods; (2) calculate transition probabilities of older persons’ changing living arrangements over time; (3) identify possible drivers of change. Results show that while older persons experience stability in living arrangements over time, this stability is more prevalent among those who start in productive roles. Moreover, those who change arrangements are likely to move into productive roles. Taken together, these findings suggest that older South Africans fulfil productive roles in households while simultaneously experiencing ageing-related frailty and diminished labour capacity. These findings underscore the importance of considering ageing as both an individual and a relational process, with implications for older persons and their families.

The third spectrum of rhenium (Re III): Analysis of the (5d5 + 5d46s)–(5d46p + 5d36s6p) transition array

The spectrum of rhenium was observed in the (1017–2074) Å wavelength region. The (5d5 + 5d46s)–(5d46p + 5d36s6p) transition array of two times ionized rhenium, Re III, has been investigated and 1305 spectral lines have been classified in the region. The analysis has led to the determination of the 5d5, 5d46s, 5d46p and 5d36s6p configurations. Seventy levels of the 5d5 and 5d46s configurations in the even system and 161 levels of the 5d46p and 5d36s6p configurations in the odd system have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences.

Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.

Current recommendations on the estimation of transition probabilities in Markov cohort models for use in health care decision-making: a targeted literature review.

ObjectiveAlthough Markov cohort models represent one of the most common forms of decision-analytic models used in health care decision-making, correct implementation of such models requires reliable estimation of transition probabilities. This study sought to identify consensus statements or guidelines that detail how such transition probability matrices should be estimated.MethodsA literature review was performed to identify relevant publications in the following databases: Medline, Embase, the Cochrane Library, and PubMed. Electronic searches were supplemented by manual-searches of health technology assessment (HTA) websites in Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and the UK. One reviewer assessed studies for eligibility.ResultsOf the 1,931 citations identified in the electronic searches, no studies met the inclusion criteria for full-text review, and no guidelines on transition probabilities in Markov models were identified. Manual-searching of the websites of HTA agencies identified ten guidelines on economic evaluations (Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and UK). All identified guidelines provided general guidance on how to develop economic models, but none provided guidance on the calculation of transition probabilities. One relevant publication was identified following review of the reference lists of HTA agency guidelines: the International Society for Pharmacoeconomics and Outcomes Research taskforce guidance. This provided limited guidance on the use of rates and probabilities.ConclusionsThere is limited formal guidance available on the estimation of transition probabilities for use in decision-analytic models. Given the increasing importance of cost-effectiveness analysis in the decision-making processes of HTA bodies and other medical decision-makers, there is a need for additional guidance to inform a more consistent approach to decision-analytic modeling. Further research should be done to develop more detailed guidelines on the estimation of transition probabilities.

New scheme for calculating the kinetic coefficients in CdTe based on first-principle wave function

The main innovative issue of this paper is the calculation of kinetic coefficients using ab initio DFT wave functions. In the framework of short-range scattering models the calculations of transition probabilities presented without fitting parameters for electron interaction with polar and nonpolar optical phonons, piezoelectric, acoustic phonons and ionized impurities. Transition matrix elements have been evaluated by the numerical eigenfunctions obtained within the ab initio density functional theory (DFT). It is used here in the generalized gradient approximation (GGA) suggested by Perdew, Burke and Ernzerhof. For the first time temperature dependences of calculated CdTe electron mobility and Hall factor in the range of 10–1210K are well compared with experiment. For the first time seven scattering mechanisms are treated without fitting parameters. It is shown that short-range scattering models describe qualitatively and quantitatively the experiment in comparison with long-range scattering models.