A steadystate, semianalytical model of energetic particle acceleration in radiojet shear flows due to cosmicray viscosity obtained by Webb et al. is generalized to take into account more general cosmicray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution function
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Abstract f _{0}(r ,p ) at cylindrical radiusr from the jet axis (assumed to lie along thez axis) is given by convolving the particle momentum spectrum with the Green’s function ${f}_{0}(\infty ,p\prime )$ , which describes the monoenergetic spectrum solution in which $G(r,p;p\prime )$ as ${f}_{0}\to \delta (pp\prime )$r → ∞ . Previous work by Webb et al. studied only the Green’s function solution for . In this paper, we explore for the first time, solutions for more general and realistic forms for $G(r,p;p\prime )$ . The flow velocity ${f}_{0}(\infty ,p\prime )$ =u u (r ) _{z}is along the axis of the jet (thee z axis). is independent ofu z , andu (r ) is a monotonic decreasing function ofr . The scattering time in the shear flow region 0 < $\tau {(r,p)={\tau}_{0}(p/{p}_{0})}^{\alpha}$r <r _{2}, and , where $\tau {(r,p)={\tau}_{0}(p/{p}_{0})}^{\alpha}{(r/{r}_{2})}^{s}$s > 0 in the regionr >r _{2}is 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 distribution that particles observed at ( ${\psi}_{p}(r,p;p\prime )$r ,p ) originated fromr → ∞ with momentum . The acceleration of ultrahighenergy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described. $p\prime $Free, publiclyaccessible full text available November 22, 2024 
In response to COVID19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARSCoV2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV2. 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 realworld data to show the efficacy of our methods.more » « less

Efficient contact tracing and isolation is an effective strategy to control epidemics, as seen in the Ebola epidemic and COVID19 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 NPHard. 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.more » « less

Abstract An Earthanalog 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 spinorbit 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 Earthanalog orbits. An Earthanalog 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 Earthanalogs within the habitable zone of α Centauri B can experience a much greater range of climate states, which is in contrast to Earthanalogs in the habitable zone of α Centauri A.more » « less

null (Ed.)DenseNets introduce concatenationtype skip connections that achieve stateoftheart accuracy in several computer vision tasks. In this paper, we reveal that the topology of the concatenationtype 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 NNMass to quantify how effectively information flows through DNNs. Moreover, we empirically show that NNMass also works for other types of skip connections, e.g., for ResNets, WideResNets (WRNs), and MobileNets, which contain additiontype skip connections (i.e., residuals or inverted residuals). As such, for both DenseNetlike CNNs and ResNets/WRNs/MobileNets, our theoretically grounded NNMass can identify models with similar accuracy, despite having significantly different size/compute requirements. Detailed experiments on both synthetic and real datasets (e.g., MNIST, CIFAR10, CIFAR100, ImageNet) provide extensive evidence for our insights. Finally, the closedform equation of our NNMass enables us to design significantly compressed DenseNets (for CIFAR10) and MobileNets (for ImageNet) directly at initialization without timeconsuming training and/or searching.more » « less