A Generalization of Semi-Markov Processes

Iosifescu, Marius

doi:10.1007/978-1-4613-3288-6_2

Cited by 17 publications

(35 citation statements)

References 5 publications

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“…Qi et al included all their calculated diffusion rate constants into Mean First-Passage Time (MFPT) calculations based on the theory of absorbing Markov chains, − to obtain net interfacet diffusion times and their reciprocal interfacet diffusion rates R 100→111 and R 111→100 . In the theory of absorbing Markov chains, time evolution is based on the Master equation, which is given by normald P⃗ normald t = prefix− bold-italicA P⃗ where P⃗ = { P i } is the probability state i occurs at time t , and A is the transition-rate matrix, with A i j = { true ∑ k r i k , if i = j − r j i , if i ≠ j Here r ij is the rate to transit from state i to j .…”

Section: Kinetics Of Nanocrystal Structurementioning

confidence: 99%

Theory of Anisotropic Metal Nanostructures

Fichthorn

2023

Chem. Rev.

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A significant challenge in the development of functional materials is understanding the growth and transformations of anisotropic colloidal metal nanocrystals. Theory and simulations can aid in the development and understanding of anisotropic nanocrystal syntheses. The focus of this review is on how results from first-principles calculations and classical techniques, such as Monte Carlo and molecular dynamics simulations, have been integrated into multiscale theoretical predictions useful in understanding shape-selective nanocrystal syntheses. Also, examples are discussed in which machine learning has been useful in this field. There are many areas at the frontier in condensed matter theory and simulation that are or could be beneficial in this area and these prospects for future progress are discussed. CONTENTST 3.3. Kinetic Wulff Shapes V 4. Machine Learning AB 5. Conclusions and Outlook

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Section: Kinetics Of Nanocrystal Structurementioning

confidence: 99%

Theory of Anisotropic Metal Nanostructures

Fichthorn

2023

Chem. Rev.

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“…Iosifescu (1980, pp. 67−68, p. 129) considers a Markov chain with transition matrix given in Figure A1.…”

Section: Fig A1mentioning

confidence: 99%

“…The model is stochastic, using Markov chain theory, in contrast to most of those constructed to study the sex ratio, which are deterministic. It starts from a formulation set out by Iosifescu (1980), among others. It uses an idea introduced by Moran (1958) for potential change in a population when a single individual drops out.…”

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confidence: 99%

A Markov Chain Model for the Evolution of Sex Ratio

Stark

Seneta

2023

Twin Res Hum Genet

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“…The latter can be treated as the transpose of a Markov chain with transient states. [10] derived the variance of certain life history traits using limiting distribution results for passage times, as delineated by [11]. For example, if N = (I -U) −1 , the expected longevity E[L] is provided by the sum of the first column of the elements in the matrix N, and the variance of longevity is given by:…”

Section: Introductionmentioning

confidence: 99%

Exact confidence intervals for population growth rate, longevity and generation time

Hernandez-Suarez

Rabinovich

2023

Preprint

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By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into population dynamics. Although point estimates of demographic parameters have been employed since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces a novel method for accurately calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. These confidence intervals are determined by utilising the statistical properties of known life history trait estimates. The key finding is the accurate estimation of the confidence interval forr, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organised in extended life tables or as a matrix of vital rates.

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A Generalization of Semi-Markov Processes

Cited by 17 publications

References 5 publications

Theory of Anisotropic Metal Nanostructures

Theory of Anisotropic Metal Nanostructures

A Markov Chain Model for the Evolution of Sex Ratio

Exact confidence intervals for population growth rate, longevity and generation time

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