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In this paper, we show that the finite subalgebra A R ( 1 ) \mathcal {A}^\mathbb {R}(1) , generated by S q 1 \mathrm {Sq}^1 and S q 2 \mathrm {Sq}^2 , of the R \mathbb {R} -motivic Steenrod algebra A R \mathcal {A}^\mathbb {R} can be given 128 different A R \mathcal {A}^\mathbb {R} -module structures. We also show that all of these A \mathcal {A} -modules can be realized as the cohomology of a 2 2 -local finite R \mathbb {R} -motivic spectrum. The realization results are obtained using an R \mathbb {R} -motivic analogue of the Toda realization theorem. We notice that each realization of A R ( 1 ) \mathcal {A}^\mathbb {R}(1) can be expressed as a cofiber of an R \mathbb {R} -motivic v 1 v_1 -self-map. The C 2 {\mathrm {C}_2} -equivariant analogue of the above results then follows because of the Betti realization functor. We identify a relationship between the R O ( C 2 ) \mathrm {RO}({\mathrm {C}_2}) -graded Steenrod operations on a C 2 {\mathrm {C}_2} -equivariant space and the classical Steenrod operations on both its underlying space and its fixed-points. This technique is then used to identify the geometric fixed-point spectra of the C 2 {\mathrm {C}_2} -equivariant realizations of A C 2 ( 1 ) \mathcal {A}^{\mathrm {C}_2}(1) . We find another application of the R \mathbb {R} -motivic Toda realization theorem: we produce an R \mathbb {R} -motivic, and consequently a C 2 {\mathrm {C}_2} -equivariant, analogue of the Bhattacharya-Egger spectrum Z \mathcal {Z} , which could be of independent interest. 

The COVID-19 pandemic brought to the forefront an unprecedented need for experts, as well as citizens, to visualize spatio-temporal disease surveillance data. Web application dashboards were quickly developed to fill this gap, including those built by JHU, WHO, and CDC, but all of these dashboards supported a particular niche view of the pandemic (ie, current status or specific regions). In this paper1, we describe our work developing our own COVID-19 Surveillance Dashboard, available at https://nssac.bii.virginia.edu/covid19/dashboard/, which offers a universal view of the pandemic while also allowing users to focus on the details that interest them. From the beginning, our goal was to provide a simple visual way to compare, organize, and track near-real-time surveillance data as the pandemic progresses. Our dashboard includes a number of advanced features for zooming, filtering, categorizing and visualizing multiple time series on a single canvas. In developing this dashboard, we have also identified 6 key metrics we call the 6Cs standard which we propose as a standard for the design and evaluation of real-time epidemic science dashboards. Our dashboard was one of the first released to the public, and remains one of the most visited and highly used. Our group uses it to support federal, state and local public health authorities, and it is used by people worldwide to track the pandemic evolution, build their own dashboards, and support their organizations as they plan their responses to the pandemic. We illustrate the utility of our dashboard by describing how it can be used to support data story-telling – an important emerging area in data science. 

We study allocation of COVID-19 vaccines to individuals based on the structural properties of their underlying social contact network. Even optimistic estimates suggest that most countries will likely take 6 to 24 months to vaccinate their citizens. These time estimates and the emergence of new viral strains urge us to find quick and effective ways to allocate the vaccines and contain the pandemic. While current approaches use combinations of age-based and occupation-based prioritizations, our strategy marks a departure from such largely aggregate vaccine allocation strategies. We propose a novel agent-based modeling approach motivated by recent advances in (i) science of real-world networks that point to efficacy of certain vaccination strategies and (ii) digital technologies that improve our ability to estimate some of these structural properties. Using a realistic representation of a social contact network for the Commonwealth of Virginia, combined with accurate surveillance data on spatio-temporal cases and currently accepted models of within- and between-host disease dynamics, we study how a limited number of vaccine doses can be strategically distributed to individuals to reduce the overall burden of the pandemic. We show that allocation of vaccines based on individuals' degree (number of social contacts) and total social proximity time is significantly more effective than the currently used age-based allocation strategy in terms of number of infections, hospitalizations and deaths. Our results suggest that in just two months, by March 31, 2021, compared to age-based allocation, the proposed degree-based strategy can result in reducing an additional 56{110k infections, 3.2{5.4k hospitalizations, and 700{900 deaths just in the Commonwealth of Virginia. Extrapolating these results for the entire US, this strategy can lead to 3{6 million fewer infections, 181{306k fewer hospitalizations, and 51{62k fewer deaths compared to age-based allocation. The overall strategy is robust even: (i) if the social contacts are not estimated correctly; (ii) if the vaccine efficacy is lower than expected or only a single dose is given; (iii) if there is a delay in vaccine production and deployment; and (iv) whether or not non-pharmaceutical interventions continue as vaccines are deployed. For reasons of implementability, we have used degree, which is a simple structural measure and can be easily estimated using several methods, including the digital technology available today. These results are significant, especially for resource-poor countries, where vaccines are less available, have lower efficacy, and are more slowly distributed. 

Abstract This article reports on the inclusive production cross section of several quarkonium states, $$\textrm{J}/\psi $$ J / ψ , $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) , $$\Upsilon \mathrm (1S)$$ Υ ( 1 S ) , $$\Upsilon \mathrm{(2S)}$$ Υ ( 2 S ) , and $$\Upsilon \mathrm{(3S)}$$ Υ ( 3 S ) , measured with the ALICE detector at the LHC, in pp collisions at $$\sqrt{s} = 5.02$$ s = 5.02  TeV. The analysis is performed in the dimuon decay channel at forward rapidity ( $$2.5< y < 4$$ 2.5 < y < 4 ). The integrated cross sections and transverse-momentum ( $$p_{\textrm{T}}$$ p T ) and rapidity ( $$y$$ y ) differential cross sections for $$\textrm{J}/\psi $$ J / ψ , $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) , $$\Upsilon \mathrm (1S)$$ Υ ( 1 S ) , and the $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) -to- $$\textrm{J}/\psi $$ J / ψ cross section ratios are presented. The integrated cross sections, assuming unpolarized quarkonia, are: $$\sigma _{\textrm{J}/\psi }$$ σ J / ψ  ( $$p_{\textrm{T}} <20$$ p T < 20  GeV/c) = 5.88 ± 0.03 ± 0.34 $$ ~\mu $$ μ b, $$\sigma _{\psi \mathrm{(2S)}}$$ σ ψ ( 2 S )  ( $$p_{\textrm{T}} <12$$ p T < 12  GeV/c) = 0.87 ± 0.06 ± 0.10 $$~\mu $$ μ b, $$\sigma _{\Upsilon \mathrm (1S)}$$ σ Υ ( 1 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 45.5 ± 3.9 ± 3.5 nb, $$\sigma _{\Upsilon \mathrm{(2S)}}$$ σ Υ ( 2 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 22.4 ± 3.2 ± 2.7 nb, and $$\sigma _{\Upsilon \mathrm{(3S)}}$$ σ Υ ( 3 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 4.9 ± 2.2 ± 1.0 nb, where the first (second) uncertainty is the statistical (systematic) one. For the first time, the cross sections of the three $$\Upsilon $$ Υ states, as well as the $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) one as a function of $$p_{\textrm{T}}$$ p T and $$y$$ y , are measured at $$\sqrt{s} = 5.02$$ s = 5.02  TeV at forward rapidity. These measurements also significantly extend the $$\textrm{J}/\psi $$ J / ψ $$p_{\textrm{T}}$$ p T reach and supersede previously published results. A comparison with ALICE measurements in pp collisions at $$\sqrt{s} = 2.76$$ s = 2.76 , 7, 8, and 13 TeV is presented and the energy dependence of quarkonium production cross sections is discussed. Finally, the results are compared with the predictions from several production models.