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  1. Free, publicly-accessible full text available September 1, 2024
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  5. Abstract

    In this paper, we study a new discrete tree and the resulting branching process, which we call the erlang weighted tree(EWT). The EWT appears as the local weak limit of a random graph model proposed in La and Kabkab, Internet Math. 11 (2015), no. 6, 528–554. In contrast to the local weak limit of well‐known random graph models, the EWT has an interdependent structure. In particular, its vertices encode a multi‐type branching process with uncountably many types. We derive the main properties of the EWT, such as the probability of extinction, growth rate, and so forth. We show that the probability of extinction is the smallest fixed point of an operator. We then take a point process perspective and analyze the growth rate operator. We derive the Krein–Rutman eigenvalue and the corresponding eigenfunctions of the growth operator, and show that the probability of extinction equals one if and only if .

     
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  6. Abstract

    Quantitative multi-image analysis (QMA) is the systematic extraction of new information and insight through the simultaneous analysis of multiple, related images. We present examples illustrating the potential for QMA to advance materials research in multi-image characterization, automatic feature identification, and discovery of novel processing-structure–property relationships. We conclude by discussing opportunities and challenges for continued advancement of QMA, including instrumentation development, uncertainty quantification, and automatic parsing of literature data.

    Graphical abstract

     
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  7. Abstract X-ray bursts are among the brightest stellar objects frequently observed in the sky by space-based telescopes. A type-I X-ray burst is understood as a violent thermonuclear explosion on the surface of a neutron star, accreting matter from a companion star in a binary system. The bursts are powered by a nuclear reaction sequence known as the rapid proton capture process (rp process), which involves hundreds of exotic neutron-deficient nuclides. At so-called waiting-point nuclides, the process stalls until a slower β + decay enables a bypass. One of the handful of rp process waiting-point nuclides is 64 Ge, which plays a decisive role in matter flow and therefore the produced X-ray flux. Here we report precision measurements of the masses of 63 Ge, 64,65 As and 66,67 Se—the relevant nuclear masses around the waiting-point 64 Ge—and use them as inputs for X-ray burst model calculations. We obtain the X-ray burst light curve to constrain the neutron-star compactness, and suggest that the distance to the X-ray burster GS 1826–24 needs to be increased by about 6.5% to match astronomical observations. The nucleosynthesis results affect the thermal structure of accreting neutron stars, which will subsequently modify the calculations of associated observables. 
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    Free, publicly-accessible full text available August 1, 2024