Unmitigated spread in Brazil: Despite an extensive network of primary care availability, Brazil has suffered profoundly during the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Using daily data from state health offices, Castro et al. analyzed the pattern of spread of COVID-19 cases and deaths in the country from February to October 2020. Clusters of deaths before cases became apparent indicated unmitigated spread. SARS-CoV-2 circulated undetected in Brazil for more than a month as it spread north from Sã o Paulo. In Manaus, transmission reached unprecedented levels after a momentary respite in mid-2020. Faria et al. tracked the evolution of a new, more aggressive lineage called P.1, which has 17 mutations, including three (K417T, E484K, and N501Y) in the spike protein. After a period of accelerated evolution, this variant emerged in Brazil during November 2020. Coupled with the emergence of P.1, disease spread was accelerated by stark local inequalities and political upheaval, which compromised a prompt federal response. Science , abh1558 and abh2644, this issue p. 821 and p. 815

Attack rate in Manaus: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence peaked in Manaus, Brazil, in May 2020 with a devastating toll on the city's inhabitants, leaving its health services shattered and cemeteries overwhelmed. Buss et al. collected data from blood donors from Manaus and São Paulo, noted when transmission began to fall, and estimated the final attack rates in October 2020 (see the Perspective by Sridhar and Gurdasani). Heterogeneities in immune protection, population structure, poverty, modes of public transport, and uneven adoption of nonpharmaceutical interventions mean that despite a high attack rate, herd immunity may not have been achieved. This unfortunate city has become a sentinel for how natural population immunity could influence future transmission. Events in Manaus reveal what tragedy and harm to society can unfold if this virus is left to run its course. Science , this issue p. 288 ; see also p. 230

As is well known, Hessian-based adaptive filters (such as the recursive-least squares algorithm (RLS) for supervised adaptive filtering, or the Shalvi-Weinstein algorithm (SWA) for blind equalization) converge much faster than gradient-based algorithms [such as the least-mean-squares algorithm (LMS) or the constant-modulus algorithm (CMA)]. However, when the problem is tracking a time-variant filter, the issue is not so clear-cut: there are environments for which each family presents better performance. Given this, we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability. We show the potential of this combination and provide a unified theoretical model for the steady-state excess mean-square error for convex combinations of gradient- and Hessian-based algorithms, assuming a random-walk model for the parameter variations. The proposed model is valid for algorithms of the same or different families, and for supervised (LMS and RLS) or blind (CMA and SWA) algorithms.

Introduction: Little evidence exists on the differential health effects of COVID-19 on disadvantaged population groups. Here we characterise the differential risk of hospitalisation and death in São Paulo state, Brazil, and show how vulnerability to COVID-19 is shaped by socioeconomic inequalities. Methods: We conducted a cross-sectional study using hospitalised severe acute respiratory infections notified from March to August 2020 in the Sistema de Monitoramento Inteligente de São Paulo database. We examined the risk of hospitalisation and death by race and socioeconomic status using multiple data sets for individual-level and spatiotemporal analyses. We explained these inequalities according to differences in daily mobility from mobile phone data, teleworking behaviour and comorbidities. Results: Throughout the study period, patients living in the 40% poorest areas were more likely to die when compared with patients living in the 5% wealthiest areas (OR: 1.60, 95% CI 1.48 to 1.74) and were more likely to be hospitalised between April and July 2020 (OR: 1.08, 95% CI 1.04 to 1.12). Black and Pardo individuals were more likely to be hospitalised when compared with White individuals (OR: 1.41, 95% CI 1.37 to 1.46; OR: 1.26, 95% CI 1.23 to 1.28, respectively), and were more likely to die (OR: 1.13, 95% CI 1.07 to 1.19; 1.07, 95% CI 1.04 to 1.10, respectively) between April and July 2020. Once hospitalised, patients treated in public hospitals were more likely to die than patients in private hospitals (OR: 1.40%, 95% CI 1.34% to 1.46%). Black individuals and those with low education attainment were more likely to have one or more comorbidities, respectively (OR: 1.29, 95% CI 1.19 to 1.39; 1.36, 95% CI 1.27 to 1.45). Conclusions: Low-income and Black and Pardo communities are more likely to die with COVID-19. This is associated with differential access to quality healthcare, ability to self-isolate and the higher prevalence of comorbidities.

To ensure signal receiving quality, robust adaptive beamforming (RAB) is of vital importance in modern communications. In this letter, we propose a new low-complexity RAB approach based on interference-plus-noise covariance matrix (IPNC) reconstruction and steering vector (SV) estimation. In this method, the IPNC and desired signal covariance matrices are reconstructed by estimating all interference powers as well as the desired signal power using the principle of maximum entropy power spectrum (MEPS). Numerical simulations demonstrate that the proposed method can provide superior performance to several previously proposed beamformers.