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  1. Abstract

    A steady-state, semi-analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity obtained by Webb et al. is generalized to take into account more general cosmic-ray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution functionf0(r,p) at cylindrical radiusrfrom the jet axis (assumed to lie along thez-axis) is given by convolving the particle momentum spectrumf0(,p)with the Green’s functionG(r,p;p), which describes the monoenergetic spectrum solution in whichf0δ(pp)asr→ ∞ . Previous work by Webb et al. studied only the Green’s function solution forG(r,p;p). In this paper, we explore for the first time, solutions for more general and realistic forms forf0(,p). The flow velocityu=u(r)ezis along the axis of the jet (thez-axis).uis independent ofz, andu(r) is a monotonic decreasing function ofr. The scattering timeτ(r,p)=τ0(p/p0)αin the shear flow region 0 <r<r2, andτ(r,p)=τ0(p/p0)α(r/r2)s, wheres> 0 in the regionr>r2is outside the jet. Other original aspects of the analysis are (i) the use of cosmic ray flow lines in (r,p) space to clarify the particle spatial transport and momentum changes and (ii) the determination of the probability distributionψp(r,p;p)that particles observed at (r,p) originated fromr→ ∞ with momentump. The acceleration of ultrahigh-energy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described.

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    Free, publicly-accessible full text available November 22, 2024
  2. In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods. 
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  3. Efficient contact tracing and isolation is an effective strategy to control epidemics, as seen in the Ebola epidemic and COVID-19 pandemic. An important consideration in contact tracing is the budget on the number of individuals asked to quarantine—the budget is limited for socioeconomic reasons (e.g., having a limited number of contact tracers). Here, we present a Markov Decision Process (MDP) framework to formulate the problem of using contact tracing to reduce the size of an outbreak while limiting the number of people quarantined. We formulate each step of the MDP as a combinatorial problem, MinExposed, which we demonstrate is NP-Hard. Next, we develop two approximation algorithms, one based on rounding the solutions of a linear program and another (greedy algorithm) based on choosing nodes with a high (weighted) degree. A key feature of the greedy algorithm is that it does not need complete information of the underlying social contact network, making it implementable in practice. Using simulations over realistic networks, we show how the algorithms can help in bending the epidemic curve with a limited number of isolated individuals. 
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  4. Abstract An Earth-analog orbiting within the habitable zone of α Centauri B was shown to undergo large variations in its obliquity, or axial tilt, which affects the planetary climate by altering the radiative flux for a given latitude. We examine the potential implications of these obliquity variations for climate through Milankovitch cycles using an energy balance model with ice growth and retreat. Similar to previous studies, the largest amplitude obliquity variations from spin-orbit resonances induce snowball states within the habitable zone, while moderate variations can allow for persistent ice caps or an ice belt. Particular outcomes for the global ice distribution can depend on the planetary orbit, obliquity, spin precession, binary orbit, and which star the Earth-analog orbits. An Earth-analog with an inclined orbit relative to the binary orbital plane can periodically transition through several global ice distribution states and risk runaway glaciation when ice appears at both poles and the equator. When determining the potential habitability for planets in general stellar binaries, more care must be taken due to the orbital and spin dynamics. For Earth-analogs within the habitable zone of α Centauri B can experience a much greater range of climate states, which is in contrast to Earth-analogs in the habitable zone of α Centauri A. 
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  5. null (Ed.)
    DenseNets introduce concatenation-type skip connections that achieve state-of-the-art accuracy in several computer vision tasks. In this paper, we reveal that the topology of the concatenation-type skip connections is closely related to the gradient propagation which, in turn, enables a predictable behavior of DNNs’ test performance. To this end, we introduce a new metric called NN-Mass to quantify how effectively information flows through DNNs. Moreover, we empirically show that NN-Mass also works for other types of skip connections, e.g., for ResNets, Wide-ResNets (WRNs), and MobileNets, which contain addition-type skip connections (i.e., residuals or inverted residuals). As such, for both DenseNet-like CNNs and ResNets/WRNs/MobileNets, our theoretically grounded NN-Mass can identify models with similar accuracy, despite having significantly different size/compute requirements. Detailed experiments on both synthetic and real datasets (e.g., MNIST, CIFAR-10, CIFAR-100, ImageNet) provide extensive evidence for our insights. Finally, the closed-form equation of our NN-Mass enables us to design significantly compressed DenseNets (for CIFAR-10) and MobileNets (for ImageNet) directly at initialization without time-consuming training and/or searching. 
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