As deep learning architectures are a technique to write a learning system where gradients are the only necessary requirements. FNet uses the Fourier transform to replace the Self-Attention of BERT [3]. The Fourier transform is a technique to embedding an existing function by one using the sinusoidal functions as a basis which originally was though to take O(n²) time complexity where n exists as the size of the input. The Cooley-Tukey Paper from Scripps described a method which takes O(n log n) in 1965 [1]. The Fast Fourier Transform was found because of performing the calculations by hand, a possible reason why people use pen and paper.

SMT solvers generally tackle quantifiers by instantiating their variables with tuples of terms from the ground part of the formula. Recent enumerative approaches for quantifier instantiation consider tuples of terms in some heuristic order. This paper studies different strategies to order such tuples and their impact on performance. We decouple the ordering problem into two parts. First is the order of the sequence of terms to consider for each quantified variable, and second is the order of the instantiation tuples themselves. While the most and least preferred tuples, i.e. those with all variables assigned to the most or least preferred terms, are clear, the combinations in between allow flexibility in an implementation. We look at principled strategies of complete enumeration, where some strategies are more fair, meaning they treat all the variables the same but some strategies may be more adventurous, meaning that they may venture further down the preference list. We further describe new techniques for discarding irrelevant instantiations which are crucial for the performance of these strategies in practice. These strategies are implemented in the SMT solver cvc5, where they contribute to the diversification of the solver's configuration space, as shown by our experimental results.

Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices and has found its applications in characterizing semantics for various classes of logic programs and nonmonotonic languages. In this paper, we show one more application of this kind: the alternating fixpoint operator by Knorr et al. for the study of the well-founded semantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in disguise, which, thanks to the power of abstraction of AFT, characterizes not only the well-founded semantics but also two-valued as well as three-valued semantics for hybrid MKNF knowledge bases. Furthermore, we show an improved approximator for these knowledge bases, of which the least stable fixpoint is information richer than the one formulated from Knorr et al.'s construction. This leads to an improved computation for the well-founded semantics. This work is built on an extension of AFT that supports consistent as well as inconsistent pairs in the induced product bilattice, to deal with inconsistencies that arise in the context of hybrid MKNF knowledge bases. This part of the work can be considered generalizing the original AFT from symmetric approximators to arbitrary approximators.

Sampling is an established technique to scale graph neural networks to large graphs. Current approaches however assume the graphs to be homogeneous in terms of relations and ignore relation types, critically important in biomedical graphs. Multi-relational graphs contain various types of relations that usually come with variable frequency and have different importance for the problem at hand. We propose an approach to modeling the importance of relation types for neighborhood sampling in graph neural networks and show that we can learn the right balance: relation-type probabilities that reflect both frequency and importance. Our experiments on drug-drug interaction prediction show that state-of-the-art graph neural networks profit from relation-dependent sampling in terms of both accuracy and efficiency.

Santiago, Chile, is a highly segregated city with distinct zones of affluence and deprivation. This setting offers a window on how social factors propel the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic in an economically vulnerable society with high levels of income inequality. Mena et al. analyzed incidence and mortality attributed to SARS-CoV-2 to understand spatial variations in disease burden. Infection fatality rates were higher in lower-income municipalities because of comorbidities and lack of access to health care. Disparities between municipalities in the quality of their health care delivery system became apparent in testing delays and capacity. These indicators explain a large part of the variation in COVID-19 underreporting and deaths and show that these inequalities disproportionately affected younger people. Science , abg5298, this issue p. [eabg5298][1] ### INTRODUCTION The COVID-19 crisis has exposed major inequalities between communities. Understanding the societal risk factors that make some groups particularly vulnerable is essential to ensure more effective interventions for this and future pandemics. Here, we focus on socioeconomic status as a risk factor. Although it is broadly understood that social and economic inequality has a negative impact on health outcomes, the mechanisms by which socioeconomic status affects disease outcomes remain unclear. These mechanisms can be mediated by a range of systemic structural factors, such as access to health care and economic safety nets. We address this gap by providing an in-depth characterization of disease incidence and mortality and their dependence on demographic and socioeconomic strata in Santiago, a highly segregated city and the capital of Chile. ### RATIONALE Combining publicly available data sources, we conducted a comprehensive analysis of case incidence and mortality during the first wave of the pandemic. We correlated COVID-19 outcomes with behavioral and health care system factors while studying their interaction with age and socioeconomic status. To overcome the intrinsic biases of incomplete case count data, we used detailed mortality data. We developed a parsimonious Gaussian process model to study excess deaths and their uncertainty and reconstructed true incidence from the time series of deaths with a new regularized maximum likelihood deconvolution method. To estimate infection fatality rates by age and socioeconomic status, we implemented a hierarchical Bayesian model that adjusts for reporting biases while accounting for incompleteness in case information. ### RESULTS We find robust associations between COVID-19 outcomes and socioeconomic status, based on health and behavioral indicators. Specifically, we show in lower–socioeconomic status municipalities that testing was almost absent early in the pandemic and that human mobility was not reduced by lockdowns as much as it was in more affluent locations. Test positivity and testing delays were much higher in these locations, indicating an impaired capacity of the health care system to contain the spread of the epidemic. We also find that 73% more deaths than in a normal year were observed between May and July 2020, and municipalities at the lower end of the socioeconomic spectrum were hit the hardest, both in relation to COVID-19–attributed deaths and excess deaths. Finally, the socioeconomic gradient of the infection fatality rate appeared particularly steep for younger age groups, reflecting worse baseline health status and limited access to health care in municipalities with low socioeconomic status. ### CONCLUSION Together, these findings highlight the substantial consequences of socioeconomic and health care disparities in a highly segregated city and provide practical methodological approaches useful for characterizing the COVID-19 burden and mortality in other urban centers based on public data, even if reports are incomplete and biased. ![Figure][2] Effect of socioeconomic inequalities on COVID-19 outcomes. The map on the left shows the municipalities that were included in this study, colored by their socioeconomic status score. For the comparison between COVID-19 deaths and excess deaths (top right), COVID-19–confirmed deaths are shown in light green and COVID-19–attributed deaths in dark green. Excess deaths, shown in gray, correspond to the difference between observed and predicted deaths. Predicted deaths were estimated using a Gaussian process model. The shading indicates 95% credible intervals for the excess deaths. The infection fatality rates (bottom right) were inferred by implementing a hierarchical Bayesian model, with vertical lines representing credible intervals by age and socioeconomic status. The COVID-19 pandemic has affected cities particularly hard. Here, we provide an in-depth characterization of disease incidence and mortality and their dependence on demographic and socioeconomic strata in Santiago, a highly segregated city and the capital of Chile. Our analyses show a strong association between socioeconomic status and both COVID-19 outcomes and public health capacity. People living in municipalities with low socioeconomic status did not reduce their mobility during lockdowns as much as those in more affluent municipalities. Testing volumes may have been insufficient early in the pandemic in those places, and both test positivity rates and testing delays were much higher. We find a strong association between socioeconomic status and mortality, measured by either COVID-19–attributed deaths or excess deaths. Finally, we show that infection fatality rates in young people are higher in low-income municipalities. Together, these results highlight the critical consequences of socioeconomic inequalities on health outcomes. [1]: /lookup/doi/10.1126/science.abg5298 [2]: pending:yes

The largest ever map showing where dark matter can be found throughout the universe has been created by astronomers using the light from 100 million galaxies. Using artificial intelligence to analyse images of the shape and light from galaxies, astronomers from University College London and the École Normale Supérieure in Paris created a map of the invisible matter throughout the universe. Dark matter makes up about 80 per cent of all matter in the universe, but isn't directly visible, spotted instead through its interaction with other objects. Working as part of the international Dark Energy Survey (DES), they looked for light travelling to Earth from distant galaxies being distorted by the dark matter. The team says an accurate map showing the spread of dark matter can one day help answer questions including what the universe is made of and how it has evolved. Co-lead author Dr Niall Jeffrey from École Normale Supérieure, Paris, and UCL told MailOnline that they've mapped about a quarter of the southern hemisphere sky so far, finding dark matter covering seven billion light years.

Despite the a wave of national strategies on artificial intelligence that has washed over the world, none have yet proposed or published specific ethical or legal frameworks for artificial intelligence. Over the past several years, a wave of national strategies on artificial intelligence (AI) has washed over the world, with many jurisdictions introducing policies for its regulation. With the exception of the European Union (EU), none have yet proposed or published specific ethical or legal frameworks for AI. Canada led the way, announcing national AI policies in 2017, and has since been followed by many other jurisdictions. The Organization for Economic Co-operation and Development (OECD) AI Policy Observatory early last year released a continuously updated database of over 600 AI policy initiatives from 60 countries, territories, and the EU. Of course, not all are the same, but some are noteworthy.

The insurance industry was at a standstill before the development of insurtech – now the field has been revolutionised, with old insurance companies having to digitise or fear being left behind. Founded: New York, NY – 2015. Lemonade is a provider of a peer-to-peer insurance platform designed for renters and homeowners. It is powered by artificial intelligence and behavioral economics and utilizes bots and machine learning to create an insurance experience. However, as of April 2021, Lemonade has announced its plans to branch out into other insurance lanes as it aims to be a one-stop-shop.

On a warm day in 2008, Silicon Valley's titans-in-the-making found themselves packed around a bulky, blond-wood conference room table. Although they are big names today, the success of their businesses was hardly assured at the time. Jeff Bezos's Amazon operated on extremely tight margins and was not profitable. They had just launched the cloud computing side business that would become Amazon's cash cow, but they didn't know it yet. Sean Parker had been forced out of Facebook, retreating to a role as managing partner of Peter Thiel's Founders Fund.

Researchers on the OcéanIA project are developing new artificial intelligence and mathematical modelling tools to contribute to the understanding of the oceans and their role in regulating and sustaining the biosphere, and tackling climate change. You may have seen our recent interview with the director of the project, and of Inria Chile, Nayat Sánchez-Pi. She explained the challenges of research in the field, what they are working on as part of the project, and the role that AI methods play. A key part of the project is data, and much of this is being collected by the Tara Microbiome-CEODOS expedition. The objective of this expedition is to study the marine microorganisms which play a fundamental role in ocean ecosystems.