Transition Probability Parameters Research Articles

Latent Profile Transition Analysis with Random Intercepts (RI-LPTA)

The primary objective of this investigation is the formulation of random intercept latent profile transition analysis (RI-LPTA). Our simulation investigation suggests that the election between LPTA and RI-LPTA for examination has negligible impact on the estimation of transition probability parameters when the population parameters are generated based on the LPTA model. However, an estimation bias in the transition probabilities is observed in all simulated conditions when LPTA is used for analysis and the generated population parameters follow the RI-LPTA model. Researchers constructing empirical longitudinal models are advised to prioritize the use of RI-LPTA in model construction, regardless of whether LPTA exhibits random intercept effect. This measure helps to reduce the possible bias in the estimation parameters which may occur if the random intercept effect of LPTA is not taken into account during model specification.

Quantifying the primary and secondary effects of antimicrobial resistance on surgery patients: Methods and data sources for empirical estimation in England.

Antimicrobial resistance (AMR) may negatively impact surgery patients through reducing the efficacy of treatment of surgical site infections, also known as the “primary effects” of AMR. Previous estimates of the burden of AMR have largely ignored the potential “secondary effects,” such as changes in surgical care pathways due to AMR, such as different infection prevention procedures or reduced access to surgical procedures altogether, with literature providing limited quantifications of this potential burden. Former conceptual models and approaches for quantifying such impacts are available, though they are often high-level and difficult to utilize in practice. We therefore expand on this earlier work to incorporate heterogeneity in antimicrobial usage, AMR, and causative organisms, providing a detailed decision-tree-Markov-hybrid conceptual model to estimate the burden of AMR on surgery patients. We collate available data sources in England and describe how routinely collected data could be used to parameterise such a model, providing a useful repository of data systems for future health economic evaluations. The wealth of national-level data available for England provides a case study in describing how current surveillance and administrative data capture systems could be used in the estimation of transition probability and cost parameters. However, it is recommended that such data are utilized in combination with expert opinion (for scope and scenario definitions) to robustly estimate both the primary and secondary effects of AMR over time. Though we focus on England, this discussion is useful in other settings with established and/or developing infectious diseases surveillance systems that feed into AMR National Action Plans.

Density Functional Theory Analysis of Ground State and Evaluation of Transition Probability Parameters for Carbon Mono-Fluoride Molecule

Density Functional Theory Analysis of Ground State and Evaluation of Transition Probability Parameters for Carbon Mono-Fluoride Molecule

Empirical-Markovian approach for estimating the flexible pavement structural capacity: Caltrans method as a case study

An Empirical-Markovian approach is proposed to estimate the pavement structural capacity as a function of key stochastic and design parameters. The key stochastic parameters are the initial and terminal deterioration transition probabilities typically estimated from pavement distress records. These two transition probabilities have a major impact on the pavement performance trend predicted using Markovian processes. In addition, typical pavement design factors are included as related to traffic loadings, materials properties, and climate conditions. In particular, two distinct Empirical-Markovian models are developed to estimate the pavement structural capacity in terms of relative strength indicators such as the structural number (SN) and gravel equivalent (GE). The first model can estimate the structural capacity based on the initial transition probability and relevant design parameters, while the second one deploys the terminal transition probability along with other design parameters. The recommendation is to use the higher of the two structural capacity values estimated for a particular pavement project. The sample models presented based on the California Department of Transportation (Caltrans) design method have resulted in good model fittings as demonstrated by the various deployed statistics and error analysis, thus indicating the usefulness of the proposed Empirical-Markovian approach in estimating the pavement structural capacity for rehabilitation and design purposes. The model exponents can be obtained from solving a linear system of equations using data from a small project sample or solving a multi-variable linear regression model when a large road sample is available. The latter case provided sample generalized models with statistics indicating their high significance.

Decomposition methods for solving Markov decision processes with multiple models of the parameters

We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We study an approach in which the decision maker considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the performance with respect to each model, such as maximizing the expected performance or maximizing worst-case performance. Existing solution methods rely on mixed-integer program (MIP) formulations, but have previously been limited to small instances, due to the computational complexity. In this article, we present branch-and-cut and policy-based branch-and-bound (PB-B&B) solution methods that leverage the decomposable structure of the problem and allow for the solution of MDPs that consider many models of the parameters. Numerical experiments show that a customized implementation of PB-B&B significantly outperforms the MIP-based solution methods and that the variance among model parameters can be an important factor in the value of solving these problems.

Theoretical study of the low-lying doublet and quartet electronic states of 7Li16O molecule including spin-orbit coupling effect and a new limit to the adiabatic ionization energy

Abstract The potential energy curves of 7Li16O molecule for energies below 50,000 cm−1 have been investigated. All doublet and quartet electronic states considered here are studied at the CASSCF/icMRCI(Q) level of theory associated with the aug-cc-pV5Z basis set. Within this range of energies, analytical representations are proposed. To evaluate the accuracy of these functional forms, a novel set of spectroscopic parameters have been derived. Transition probability parameters as the Franck–Condon factors and Einstein A coefficients of certain vibronic emissions from the A 2 Σ + - X 2 Π , 2 2 Π - X 2 Π , and 2 2 Π - A 2 Σ + band systems are reported. It was found that rotationless radiative lifetimes of the order of milliseconds are determined for A-X and C-X bands. Overall, our results transition probabilities suggest that these vibronic emissions are weak and, therefore, difficult to measure in spectroscopy experiments. Additionally, we obtained an adiabatic ionization energy value of 68,002 cm−1.

A New Method for Predicting Crosstalk of Random Cable Bundle Based on BAS-BP Neural Network Algorithm

Accurate analytical solution for the crosstalk of random cable bundle is difficult to obtain, but the limit of the crosstalk can be predicted. This paper proposes a method to predict the crosstalk of random cable bundle. Based on the idea of cascade method, the model takes into account the random rotation of the cross-section and the random transposition of the core. A neural network algorithm based on back propagation optimized by the beetle antennae search method (BAS-BPNN) is introduced to mathematically describe the random rotation of the cross-section. The elementary row-to-column transformation of the unit length RLCG parameter matrix is used to deal with the random transposition of the core. The discontinuity between segments generated by transposition is solved by introducing transition probability parameters. Finally, combined with the finite-difference time-domain (FDTD) algorithm, the crosstalk of the random cable bundle is obtained. The numerical experimental results show that the new method can reduce a lot of experimental work in the crosstalk problem of random cable bundle, and has higher accuracy and a wider frequency range.

Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM

Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

Assessment of Demographic and Socio-Behavioral Factors on Adherence to HIV Pre-Exposure Prophylaxis Using a Markov Modeling Approach.

Purpose: Adherence is important for the effectiveness of human immunodeficiency virus (HIV) preexposure prophylaxis (PrEP). The objective of the current work is to assess the impact of multiple demographic and socio-behavioral factors on the adherence to tenofovir-based PrEP among HIV serodiscordant couples in East Africa using Markov mixed-effects modeling approach. Methods: The Partners Demonstration Project was a prospective, open-label, implementation science-driven study of HIV PrEP among heterosexual HIV serodiscordant couples in Kenya and Uganda. The uninfected partner received oral PrEP according to the “bridge to antiretroviral therapy [ART]” strategy (i.e., until the infected partner had been on ART for ≥6 months). Adherence was monitored electronically; demographic and socio-behavioral data were collected during study visits. Analyzed data reflect 12 months of follow-up per participant. A two-state, first-order, discrete time Markov model was developed with longitudinal adherence data characterized by “dose taking (1)” and “dose missing (0).” Covariate effects were linearly added in the logit domain of transition probability parameters (P01 and P10) in the model. The full covariate model was initially developed, followed by backward elimination process to reduce the model. All significant covariates reported by a prior primary statistical analysis of the same data were included in the full covariate model. Results: The model included data from 920 participants, who were predominantly male (65%). Significant covariates associated with higher adherence were 25 years or older [odds ratio (OR) for P10, 0.61], female sex (OR for P10, 0.67), participant wanting the relationship with the partner to succeed (OR for P10, 0.79; OR for P01, 1.45), and sex with partner either with 100% or <100% condom use compared to those reported no sex (OR for P10, 0.84; OR for P01, 1.21). Significant covariates associated with lower adherence were partner on ART >6 months (OR for P01, 0.86; OR for P10, 1.34), subject in the study for >6 months (OR for P01, 0.8; OR for P10, 1.25), and problematic alcohol use (OR for P01, 0.63; OR for P10, 1.16). Conclusion: The developed Markov model provides a mechanistic understanding of relationship between demographic, socio-behavioral covariates, and PrEP adherence, by indicating the pattern of adherence influenced by each factor over time. Such data can be used for further intervention development to promote PrEP adherence.

Radiative transition probabilities, lifetimes and the vibrational temperature for the astrophysical molecule CaF

With the purpose of providing the spectroscopic parameters that can contribute to future identification of calcium fluoride (CaF) molecule in sunspot, interstellar and circumstellar environments, the present work by focusing mainly on the astrophysically significant molecule CaF, provides the qualitative study of i) the transition probability parameters like Franck–Condon factors and r-centroids for the electronic transitions C–X, D–X, E–X, C–B, C–B’ and E’–A and ii) the transition moment, oscillator strength, Einstein coefficients, vibrational temperature and radiative lifetimes of the higher electronic state E, using the derived transition probability parameters for E–X transition. The evaluated transition probability parameters reveal the astrophysical importance of CaF molecular transitions and they are discussed elaborately using the spectroscopic technique. Based on the present calculations, radiative lifetimes for the vibrational levels from 1 to 5 for the state E are predicted to be 14.0, 21.9, 36.1, 82.8, 97.0 ns respectively and it is found that the calculated values are in excellent agreement with the experimental results reported earlier. The observed vibrational temperature of 1451 ± 134 K for the electronic transition E–X also favors the prediction of the existence of CaF molecule in cold sunspot.

Inference of the Transition Matrix in Convolved Hidden Markov Models and the Generalized Baum–Welch Algorithm

A convolved two-level hidden Markov model is defined, with convolved observations as the top layer, continuous responses as the hidden middle layer, and categorical variables following a Markov chain as the hidden bottom layer. The model parameters include the transition probabilities of the Markov chain, response means and variances, and the convolution kernel and error variance. The focus of this study is on categorical deconvolution of the observations into the hidden bottom categorical layer when the transition probability parameters defining the Markov chain transition matrix are unknown. The inversion is cast in a Bayesian setting where the solution is represented by an approximate posterior model. Three algorithms, all of them based on the approximate model, for inference on the unknown parameters are defined and discussed. The inference techniques are compared in two empirical studies and in a seismic case study from a petroleum reservoir offshore Norway. We conclude that an approximate expectation-maximization algorithm, appearing as a generalized Baum–Welch algorithm, is preferable if point parameter estimates and marginal maximum a posterior class predictions are required. If uncertainty quantifications are also required, a more computationally demanding Bayesian Markov chain Monte Carlo algorithm must be used.

Occupancy grid map of semi-static objects by mobile observer

In this research we propose a method for spatial representation of semi-static objects in dynamic environment. For this objective, we extend IMAC (Independent Markov Chain Occupancy) model, which is a map constructing method for dynamic environment. In the IMAC model, a mobile observer cannot estimate the grid map correctly if it does not stop enough time at the same location. To overcome this limitation, we propose a technique to estimate the IMAC grid map from an analytical discussion by simulating a grid-world model for a simple straight line path. The simulation result shows that if the number of observations for a given grid cell is sufficient, both parameters of the two transition probability parameters of IMAC model can be estimated correctly. We carried out a simple test in real-world environment using a vehicle. The experimental results show that we can create a map from GPS data recorded by a smartphone installed on a vehicle. The contributions of this paper are as follows: (1) propose a new technique for estimating Poisson parameters for IMAC grid map in dynamic environment; (2) prove the model can be used in real world.

Spectral Dataset for an Astrophysically Significant BaF Molecule

In view of the lack of precise transition probability parameters such as Franck–Condon factors (FCFs) and r-centroids for electronic transitions A, B, C, D, D′, E–X of a barium monofluoride (BaF) molecule, we have evaluated them by employing a reliable numerical integration procedure. The vibration-rotation interaction (VRI) effect on FCFs for the bands of above band systems of the BaF molecule was also studied, and the results indicate that VRI insignificantly influences FCFs. The physical and astrophysical significances of the computed FCFs and r-centroids are discussed for certain band systems of the BaF molecule whose presence is still questionable in many astrophysical sources.

Some useful data for the astrophysical molecules AlS and BS

The vibronic (vibration-electronic) transition probability parameters such as Franck-Condon (FC) factors and r-centroids of diatomic molecular species could be useful in the identification of molecular lines and in the estimation of relative abundance of the species in astrophysical sources. In this study, they have been evaluated for the electronic transitions A 2 Σ + → X 2 Σ + and A ′ 2 Σ + → X 2 Σ + of AlS and C 2 Π r → X 2 Σ + , E 2 Σ + → X 2 Σ + and B 2 Σ + → A 2 Π i of BS molecules, by a numerical integration procedure using a suitable potential. The physical and astrophysical significances of our evaluated FC factors and r-centroids have also been discussed, which would be helpful in the prediction of the presence of AlS and BS molecules in umbral sunspots and other celestial bodies.

Astrophysically Useful Parameters for Some Vibronic Transitions of AlH and BH

For molecular identification in astrophysical sources, an astrophysicist needs some spectroscopic parameters such as dissociation energy, vibrational or rotational temperature of the source, band or line wavelengths, transition probability parameters, etc. The Franck-Condon(FC) factors are proportional to the transition probabilities. In this study, the FC factors and r-centroids for the vibronic (vibration-electronic) transitions C1 Σ + → X1 Σ + of aluminium hydride (AlH), b3 Σ ( −) → a3 Π, C1 Σ + → A1 Π & C′1 Δ → Δ 1 Π of boron hydride (BH) have been evaluated and the results are presented in tables which include band origin/head wavelengths. The physical & astrophysical significances of our evaluated FC factors & r-centroids have been discussed and the possible presence of AlH in sunspot umbral spectra is also predicted.

Astrophysically useful parameters for certain band systems of BeH, BeD and BeT molecules

The vibronic (vibration-electronic) transition probability parameters such as Franck-Condon (FC) factors and r-centroids of diatomic molecular species could be useful in the identification of molecular bands and in the estimation of relative abundance of the emitted species in astrophysical sources. In this study, they have been evaluated for the electronic transitions A2?r-X2?+, B2?r-X2?+ and C2?+ - X2?+ systems of BeH, A2?r - X2? and C2?+ - X2?+ system of BeD and A2?r - X2?+ system of BeT molecules using a suitable potential.

Improving Profile HMM Discrimination by Adapting Transition Probabilities

Profile hidden Markov models (HMMs) are used to model protein families and for detecting evolutionary relationships between proteins. Such a profile HMM is typically constructed from a multiple alignment of a set of related sequences. Transition probability parameters in an HMM are used to model insertions and deletions in the alignment. We show here that taking into account unrelated sequences when estimating the transition probability parameters helps to construct more discriminative models for the global/local alignment mode. After normal HMM training, a simple heuristic is employed that adjusts the transition probabilities between match and delete states according to observed transitions in the training set relative to the unrelated (noise) set. The method is called adaptive transition probabilities (ATP) and is based on the HMMER package implementation. It was benchmarked in two remote homology tests based on the Pfam and the SCOP classifications. Compared to the HMMER default procedure, the rate of misclassification was reduced significantly in both tests and across all levels of error rate.

Transition probability parameters for the band systems G, H and I-B of astrophysical molecule PO

The transition probability parameters, Franck – Condon factors and r-centroids, have been evaluated by the more reliable numerical integration procedure for the bands of G, H and I-B systems of astrophysical molecule PO, using a suitable potential.

Transition probability parameters for certain band systems of astrophysical molecule GeO

The transition probability parameters, Franck–Condon factors and r-centroids, have been evaluated using the most reliable numerical integration procedure for the bands of E 1Σ +, F 1Σ +, GΣ, HΠ, JΣ–X 1Σ + systems of astrophysical molecule GeO, using a suitable potential.

The r-centroid concept revisited

The r-centroid concept, was proposed the in 1950s to permit factoring of the band strength integral Sυ',υ'' into the product of the Franck–Condon factor qυ',υ'', and of the square of the electronic transition moment Re (r), when taken at the r-centroid value of the internuclear separation, r = [Formula: see text]υ',υ'', which is the most likely value r at which the υ' « υ'' transition will occur. It has been much used since then in the interpretation of intensity measurements on many band systems of importance in astrophysics, atmospheric physics, space physics, and chemical physics to determine the variation of the electronic transition moment with internuclear separation, and thereby to derive band strengths, and other molecular transition probability parameters. It has been somewhat less used in recent years in the study of individual band systems, since the development of powerful computing facilities now allow for exact ab initio numerical studies to be made of individual molecules and their radiative transitions. Nevertheless the r-centroid concept, and some of its recent developments, provide much insight into the general systematics of diatomic molecular band systems and their spectra. This partly tutorial paper reviews the origins, properties, applications, and recent developments of the r-centroid concept. PACS No.: 33.70