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The design of data-driven dashboards that inform municipalities on ongoing changes in infections within their community is addressed in this research. Daily reports of Covid-19 infections published by the state of Wisconsin as the initial surge in the pandemic ensued during the October 2020 to September 2021 time frame is considered as a case study. Of particular interest is the identification of regions and population groups distinguished by race and ethnicity that may be experiencing a disproportional rate of infections over time. This study integrates the municipality-level daily positive cases that are disaggregated by race and ethnicity and population size data derived from the US Census Bureau. The goal is to present timely data-driven information in a manner that is accessible to the general population, is relatable to the constituents and promotes community engagement in managing and mitigating the infections. A statistical metric referred to as the rank difference and its persistence over time is used to capture the disproportional incidence of Covid-19 positive cases on particular race and ethnic groups in relation to their population size. A persistence index is derived to identify regions that continually exhibit positive rank differences on a daily time scale and indicate disparity in disease incidence. The analysis leads to the identification that several municipalities in Wisconsin that are located in regions of low population and away from the denser urban centers are those that continue to exhibit disparity in the infection rates for Black/African American and Hispanic/Latino population groups. Examples of a dashboard that can be utilized to capture both aggregate level and temporal patterns of Covid-19 infections are presented., Comment: 10 pages, 6 figures

We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation, which is achieved by introducing a generalized Fourier transform covariant with respect to the nonrelativistic background spacetime. As a first test, we apply this method to compute the anisotropic Weyl anomaly for a (2+1)-dimensional scalar field theory around a z=2 Lifshitz point and corroborate the previously found result. We then proceed to general scalar operators and evaluate their one-loop effective action. The covariant heat kernel method that we develop also directly applies to operators with spin structures in arbitrary dimensions., Comment: 47 pages, 1 figure; v2: appendix C updated, minor typos corrected, references added; v3: typos fixed

Boundary, defect, and interface RG flows, as exemplified by the famous Kondo model, play a significant role in the theory of quantum fields. We study in detail the holographic dual of a non-conformal supersymmetric impurity in the D1/D5 CFT. Its RG flow bears similarities to the Kondo model, although unlike the Kondo model the CFT is strongly coupled in the holographic regime. The interface we study preserves $d = 1$ $\mathcal{N} = 4$ supersymmetry and flows to conformal fixed points in both the UV and IR. The interface's UV fixed point is described by $d = 1$ fermionic degrees of freedom, coupled to a gauge connection on the CFT target space that is induced by the ADHM construction. We briefly discuss its field-theoretic properties before shifting our focus to its holographic dual. We analyze the supergravity dual of this interface RG flow, first in the probe limit and then including gravitational backreaction. In the probe limit, the flow is realized by the puffing up of probe branes on an internal $\mathsf{S}^3$ via the Myers effect. We further identify the backreacted supergravity configurations dual to the interface fixed points. These supergravity solutions provide a geometric realization of critical screening of the defect degrees of freedom. This critical screening arises in a way similar to the original Kondo model. We compute the $g$-factor both in the probe brane approximation and using backreacted supergravity solutions, and show that it decreases from the UV to the IR as required by the $g$-theorem., Comment: 61 pages, 7 figures, Minor clarifications, Final version