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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. 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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3. 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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4. Size of nodal domains of the eigenvectors of a graph

   https://doi.org/10.1002/rsa.20925  

   Huang, Han; Rudelson, Mark (April 2020, Random Structures & Algorithms)

   Consider an eigenvector of the adjacency matrix of aG(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other. 

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5. BRIDGING FREQUENTIST AND CLASSICAL PROBABILITY THROUGH DESIGN

   Provost, A. Lim (January 2022, Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N..; Strayer, J.; Drown, S. (Ed.)

   The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always clear in our life experiences, we aimed to examine how an instructional design that begins with a scientific scenario that does not naturally connect to theoretical probability, such as the weather, may support students’ bridging of these two models. In this paper, we present data from a design experiment in a sixth-grade classroom to discuss how students’ shifts of reasoning as they engaged with such a design supported their construction of bridges between the two probability models. 

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