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1. The temporal structure of parent talk to toddlers about objects

   https://doi.org/10.1016/j.cognition.2022.105266  

   Slone, Lauren K; Abney, Drew H; Smith, Linda B; Yu, Chen (January 2023, Cognition)

   Toddlers learn words in the context of speech from adult social partners. The present studies quantitatively describe the temporal context of parent speech to toddlers about objects in individual real-world interactions. We show that at the temporal scale of a single play episode, parent talk to toddlers about individual objects is predominantly, but not always, clustered. Clustered speech is characterized by repeated references to the same object close in time, interspersed with lulls in speech about the object. Clustered temporal speech patterns mirror temporal patterns observed at longer timescales, and persisted regardless of play context. Moreover, clustered speech about individual novel objects predicted toddlers’ learning of those objects’ novel names. Clustered talk may be optimal for toddlers’ word learning because it exploits domain-general principles of human memory and attention, principles that may have evolved precisely because of the clustered structure of natural events important to humans, including human behavior. 

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2. Bridging coherence optics and classical mechanics: A generic light polarization-entanglement complementary relation

   https://doi.org/10.1103/PhysRevResearch.5.033110  

   Qian, Xiao-Feng; Izadi, Misagh (August 2023, Physical Review Research)

   While optics and mechanics are two distinct branches of physics, they are connected. It is well known that the geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between coherence wave optics and classical mechanics are rarely reported. Here we report links of the two through a systematic quantitative analysis of polarization and entanglement, two optical coherence properties under the wave description of light pioneered by Huygens and Fresnel. A generic complementary identity relation is obtained for arbitrary light fields. More surprisingly, through the barycentric coordinate system, optical polarization, entanglement, and their identity relation are shown to be quantitatively associated with the mechanical concepts of center of mass and moment of inertia via the Huygens-Steiner theorem for rigid body rotation. The obtained result bridges coherence wave optics and classical mechanics through the two theories of Huygens. 

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3. Schneider, R.M., & Barner, D. (2020). Children use one-to-one correspondence to establish equality after learning to count. 42nd Annual Meeting of the Cognitive Science Society.

   Schneider, R.M. (January 2020, 42nd Annual Meeting of the Cognitive Science Society.)

   null (Ed.)

   Humans make frequent and powerful use of external symbols to express number exactly, leading some to question whether exact number concepts are only available through the acquisition of symbolic number systems. Although prior work has addressed this longstanding debate on the relationship between language and thought in innumerate populations and seminumerate children, it has frequently produced conflicting results, leaving the origin of exact number concepts unclear. Here, we return to this question by replicating methods previously used to assess exact number knowledge in innumerate groups, such as the Piraha, with a large sample of semi- numerate US toddlers. We replicate previous findings from both innumerate cultures and developmental studies showing that numeracy is linked to the concept of exact number. However, we also find evidence that this knowledge is surprisingly fragile even amongst numerate children, suggesting that numeracy alone does not guarantee a full understanding of exactness. 

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4. Sato-Tate distributions of y^2 = x^p − 1 and y^2 = x^{2p} − 1

   https://doi.org/10.1016/j.jalgebra.2022.01.002  

   Emory, Melissa; Goodson, Heidi (May 2022, Journal of Algebra)

   We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form y^2 = x^p−1 and y2 = x^{2p}−1, where p is an odd prime. Our results rely on the fact the Jacobians of these curves are nondegenerate, a fact that we prove in the paper. Furthermore, we compute moment statistics associated to the Sato-Tate groups. These moment statistics can be used to verify the equidistribution statement of the generalized Sato-Tate conjecture by comparing them to moment statistics obtained for the traces in the normalized L-polynomials of the curves. 

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5. Band-limited photodetection of temporal coherence

   https://doi.org/10.1364/OE.462445  

   Chen, Zijun; Fainman, Yeshaiahu (April 2023, Optics Express)

   The quantum theory of optical coherence plays a ubiquitous role in identifying optical emitters. An unequivocal identification, however, presumes that the photon number statistics is resolved from timing uncertainties. We demonstrate from first principle that the observed nth-order temporal coherence is a n-fold convolution of the instrument responses and the expected coherence. The consequence is detrimental in which the photon number statistics is masked from the unresolved coherence signatures. The experimental investigations are thus far consistent with the theory developed. We envision the present theory will mitigate the false identification of optical emitters and enlarge the coherence deconvolution to an arbitrary order. 

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