Transition probability estimates for non-Markov multi-state models

Molecular dynamics (MD) simulation software allows probing the equilibrium structural dynamics of a molecule of interest, revealing how a molecule navigates its structure space one structure at a time. To obtain a broader view of dynamics, typically one needs to launch many such simulations, obtaining many trajectories. A summarization of the equilibrium dynamics requires integrating the information in the various trajectories, and Markov State Models (MSM) are increasingly being used for this task. At its core, the task involves organizing the structures accessed in simulation into structural states, and then constructing a transition probability matrix revealing the transitions between states. While now considered a mature technology and widely used to summarize equilibrium dynamics, the underlying computational process in the construction of an MSM ignores energetics even though the transition of a molecule between two nearby structures in an MD trajectory is governed by the corresponding energies. In this paper, we connect theory with simulation and analysis of equilibrium dynamics. A molecule navigates the energy landscape underlying the structure space. The structural states that are identified via off-the-shelf clustering algorithms need to be connected to thermodynamically-stable and semi-stable (macro)states among which transitions can then be quantified. Leveraging recent developments in the analysis of energy landscapes that identify basins in the landscape, we evaluate the hypothesis that basins, directly tied to stable and semi-stable states, lead to better models of dynamics. Our analysis indicates that basins lead to MSMs of better quality and thus can be useful to further advance this widely-used technology for summarization of molecular equilibrium dynamics.

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The volume and time comparison principle and transition probability estimates for random walks

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3334 ◽

2003 ◽

Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽

Author(s):

András Telcs

Keyword(s):

Random Walks ◽

Transition Probability ◽

Exit Time ◽

Sufficient Conditions ◽

Probability Estimates ◽

Mean Exit Time ◽

International Audience ◽

The Mean ◽

Necessary And Sufficient ◽

Upper Estimate

International audience This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the mean exit time from a ball are independent of the center, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is given if the mean exit time is independent of the center but the volume is not.

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Incorporating rainy season and reproductive phenology into the survival and transition rates of the invasive species Sambucus nigra: An approximation with multi-state models

Invasive Plant Science and Management ◽

10.1017/inp.2021.37 ◽

2021 ◽

pp. 1-28

Author(s):

Leticia Bonilla-Valencia ◽

Mariana Hernández-Apolinar ◽

J. Jaime Zúñiga-Vega ◽

Francisco J Espinosa-García ◽

Yuriana Martínez-Orea ◽

...

Keyword(s):

Invasive Species ◽

Phenotypic Plasticity ◽

Rainy Season ◽

Environmental Changes ◽

Transition Probability ◽

Interactive Effects ◽

Reproductive Phenology ◽

Demographic Model ◽

Sambucus Nigra ◽

State Models

Abstract Although it has been demonstrated that environmental changes within a year can affect the reproduction, survival, and growth of invasive species, these factors have rarely been incorporated into the demographic analysis. Therefore, we applied multi-state demographic models (based on capture–recapture animal methods accounting for imperfect detectability of individuals in natural conditions) to evaluate the effects of reproductive phenology and rainy season on the survival and transition/retrogression rates among stage categories of Sambucus nigra (L)—an invasive tree species, widely distributed in temperate forests of Europe and America. In the Abies religiosa temperate forest, Mexico City, a multi-state demographic model of S. nigra was built using bi-monthly censuses during a year. We selected the best-fitting model according to Akaike’s information criterion (AICc). We determined the response of reproductive phenology of S. nigra to the rainy season for two years through repeatability and phenotypic plasticity indexes. Our results showed that the reproductive phenology of S. nigra has a low repeatability index and a high phenotypic plasticity index. We demonstrated that additive and interactive effects of reproductive phenology and rainy season promote changes in survival and transition/retrogression rates among stage categories. During the rainy season, the survival probability of seedlings and transition probability towards the adult category increased. Therefore, our study represents a significant contribution to the knowledge of the demographic dynamics of invasive species on an intra-annual scale.

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Comparison of Males' and Females' Estimates of Transition Probability in Speech

Perceptual and Motor Skills ◽

10.2466/pms.1974.38.3c.1121 ◽

1974 ◽

Vol 38 (3_suppl) ◽

pp. 1121-1122 ◽

Cited By ~ 2

Author(s):

Nicholas Schiavetti ◽

John P. Burke

Keyword(s):

Transition Probability ◽

Experimental Conditions ◽

Probability Estimates ◽

Males And Females ◽

Highly Correlated

Transition probability estimates yielded by male and by female guessers were highly correlated under various experimental conditions.

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Applied Methods for Estimating Transition Probabilities from Electronic Health Record Data

Medical Decision Making ◽

10.1177/0272989x20985752 ◽

2021 ◽

Vol 41 (2) ◽

pp. 143-152 ◽

Cited By ~ 2

Author(s):

Patricia J. Rodriguez ◽

Zachary J. Ward ◽

Michael W. Long ◽

S. Bryn Austin ◽

Davene R. Wright

Keyword(s):

Electronic Health Record ◽

Transition Probabilities ◽

Transition Probability ◽

Emergency Department Visits ◽

Survival Models ◽

Health Record ◽

Health State ◽

Electronic Health Record Data ◽

Probability Estimates ◽

Electronic Health

Background Electronic health record (EHR) data contain longitudinal patient information and standardized diagnostic codes. EHR data may be useful for estimating transition probabilities for state-transition models, but no guidelines exist on appropriate methods. We applied 3 potential methods to estimate transition probabilities from EHR data, using pediatric eating disorders (EDs) as a case study. Methods We obtained EHR data from PEDsnet, which includes 8 US children’s hospitals. Data included inpatient, outpatient, and emergency department visits for all patients with an ED. We mapped diagnoses to 3 ED health states: anorexia nervosa, bulimia nervosa, and other specified feeding or eating disorder. We estimated 1-y transition probabilities for males and females using 3 approaches: simple first-last proportions, a multistate Markov (MSM) model, and independent survival models. Results Transition probability estimates varied widely between approaches. The first-last proportion approach estimated higher probabilities of remaining in the same health state, while the MSM and independent survival approaches estimated higher probabilities of transitioning to a different health state. All estimates differed substantially from published literature. Limitations As a source of health state information, EHR data are incomplete and sometimes inaccurate. EHR data were especially challenging for EDs, limiting the estimation and interpretation of transition probabilities. Conclusions The 3 approaches produced very different transition probability estimates. Estimates varied considerably from published literature and were rescaled and calibrated for use in a microsimulation model. Estimation of transition probabilities from EHR data may be more promising for diseases that are well documented in the EHR. Furthermore, clinicians and health systems should work to improve documentation of ED in the EHR. Further research is needed on methods for using EHR data to inform transition probabilities.

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A Test of Discrete State Models of Recognition Memory: How Do Participants Use a Continuous Response Scale?

PsycEXTRA Dataset ◽

10.1037/e528942014-780 ◽

2014 ◽

Author(s):

Tina Chen ◽

Jeffrey Starns ◽

Caren Rotello ◽

Benjamin H. Zobel

Keyword(s):

Recognition Memory ◽

Response Scale ◽

Discrete State ◽

Continuous Response ◽

State Models

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Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

10.32792/utq/utjsci/vol7/2/32 ◽

2020 ◽

pp. 149-152

Keyword(s):

Experimental Data ◽

Transition Probability ◽

Energy Levels ◽

Dynamical Symmetry ◽

Interacting Boson Model ◽

Excitation Energies ◽

Electromagnetic Transition ◽

Boson Model ◽

Energy States ◽

Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

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