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1. Collective spontaneous emission and kinetic equations for one-photon light in random media

   https://doi.org/10.1063/5.0055171  

   Kraisler, Joseph; Schotland, John C. (March 2022, Journal of Mathematical Physics)

   We consider the theory of spontaneous emission for a random medium of stationary two-level atoms. We investigate the dynamics of the field and atomic probability amplitudes for a one-photon state of the system. At long times and large distances, we show that the corresponding average probability densities can be determined from the solutions to a pair of kinetic equations. 

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2. The Development of Nonsymbolic Probability Judgments in Children

   https://doi.org/10.1111/cdev.13222  

   O'Grady, Shaun; Xu, Fei (May 2020, Child Development)

   Abstract Two experiments were designed to investigate the developmental trajectory of children's probability approximation abilities. In Experiment 1, results revealed 6- and 7-year-old children's (N = 48) probability judgments improve with age and become more accurate as the distance between two ratios increases. Experiment 2 replicated these findings with 7- to 12-year-old children (N = 130) while also accounting for the effect of the size and the perceived numerosity of target objects. Older children's performance suggested the correct use of proportions for estimating probability; but in some cases, children relied on heuristic shortcuts. These results suggest that children's nonsymbolic probability judgments show a clear distance effect and that the acuity of probability estimations increases with age. 

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3. An Exploration of Parameter Duality in Statistical Inference

   https://doi.org/10.1017/psa.2023.174  

   Thornton, Suzanne; Xie, Minge (December 2023, Philosophy of Science)

   Abstract Well-known debates among statistical inferential paradigms emerge from conflicting views on the notion of probability. One dominant view understands probability as a representation of sampling variability; another prominent view understands probability as a measure of belief. The former generally describes model parameters as fixed values, in contrast to the latter. We propose that there are actually two versions of a parameter within both paradigms: a fixed unknown value that generated the data and a random version to describe the uncertainty in estimating the unknown value. An inferential approach based on CDs deciphers seemingly conflicting perspectives on parameters and probabilities. 

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4. The Moran Process on a Random Graph

   https://doi.org/10.1002/rsa.70003  

   Frieze, Alan; Pegden, Wesley (May 2025, Random Structures & Algorithms)

   ABSTRACT We study the fixation probability for two versions of the Moran process on the random graph at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughout the process, there are vertices of two types, mutants, and non‐mutants. Mutants have fitness and non‐mutants have fitness 1. The process starts with a unique individual mutant located at the vertex . In the Birth‐Death version of the process a random vertex is chosen proportionally to its fitness and then changes the type of a random neighbor to its own. The process continues until the set of mutants is empty or . In the Death‐Birth version, a uniform random vertex is chosen and then takes the type of a random neighbor, chosen according to fitness. The process again continues until the set of mutants is empty or . Thefixation probabilityis the probability that the process ends with . We show that asymptotically correct estimates of the fixation probability depend only on the degree of and its neighbors. In some cases we can provide values for these estimates and in other places we can only provide non‐linear recurrences that could be used to compute values. 

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5. Reduced strength and increased variability of extinction selectivity during mass extinctions

   https://doi.org/10.1098/rsos.230795  

   Monarrez, Pedro M; Heim, Noel A; Payne, Jonathan L (September 2023, Royal Society Open Science)

   Two of the traits most often observed to correlate with extinction risk in marine animals are geographical range and body size. However, the relative effects of these two traits on extinction risk have not been investigated systematically for either background times or during mass extinctions. To close this knowledge gap, we measure and compare extinction selectivity of geographical range and body size of genera within five classes of benthic marine animals across the Phanerozoic using capture–mark–recapture models. During background intervals, narrow geographical range is strongly associated with greater extinction probability, whereas smaller body size is more weakly associated with greater extinction probability. During mass extinctions, the association between geographical range and extinction probability is reduced in every class and fully eliminated in some, whereas the association between body size and extinction probability varies in strength and direction across classes. While geographical range is universally the stronger predictor of survival during background intervals, variation among classes during mass extinction suggests a fundamental shift in extinction processes during these global catastrophes. 

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