Satellite imagery has had limited application in the analysis of pre-colonial settlement archaeology in the Caribbean; visible evidence of wooden structures perishes quickly in tropical climates. Only slight topographic modifications remain, typically associated with middens. Nonetheless, surface scatters, as well as the soil characteristics they produce, can serve as quantifiable indicators of an archaeological site, detectable by analyzing remote sensing imagery. A variety of pre-processed, very diverse data sets went through a process of image registration, with the intention to combine multispectral bands to feed two different semi-automatic direct detection algorithms: a posterior probability, and a frequentist approach. Two 5 × 5 km 2 areas in the northwestern Dominican Republic with diverse environments, having sufficient imagery coverage, and a representative number of known indigenous site locations, served each for one approach. Buffers around the locations of known sites, as well as areas with no likely archaeological evidence were used as samples. The resulting maps offer quantifiable statistical outcomes of locations with similar pixel value combinations as the identified sites, indicating higher probability of archaeological evidence. These still very experimental and rather unvalidated trials, as they have not been subsequently groundtruthed, show variable potential of this method in diverse environments.
Decision forests (DF), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, DFs dominate other methods in tabular data, that is, when the feature space is unstructured, so that the signal is invariant to permuting feature indices. However, in structured data lying on a manifold-such as images, text, and speech-neural nets (NN) tend to outperform DFs. We conjecture that at least part of the reason for this is that the input to NN is not simply the feature magnitudes, but also their indices (for example, the convolution operation uses "feature locality"). In contrast, naïve DF implementations fail to explicitly consider feature indices. A recently proposed DF approach demonstrates that DFs, for each node, implicitly sample a random matrix from some specific distribution. Here, we build on that to show that one can choose distributions in a manifold aware fashion. For example, for image classification, rather than randomly selecting pixels, one can randomly select contiguous patches. We demonstrate the empirical performance of data living on three different manifolds: images, time-series, and a torus. In all three cases, our Manifold Forest (Morf) algorithm empirically dominates other state-of-the-art approaches that ignore feature space structure, achieving a lower classification error on all sample sizes. This dominance extends to the MNIST data set as well. Moreover, both training and test time is significantly faster for manifold forests as compared to deep nets. This approach, therefore, has promise to enable DFs and other machine learning methods to close the gap with deep nets on manifold-valued data.
Understanding how underlying health conditions and social determinants of health affect the severity of COVID-19 is critical for community response planning. Literature reports that groups at higher risk from COVID-19 include those 65 and older, living in nursing homes and long-term care facilities, and with severe obesity, diabetes, chronic lung disease, or asthma. In addition, other studies has shown that the disease disproportionately affects individuals with lower socio-economic status. Our research seeks to validate these findings and observe the effects of health measures and social determinants of health on COVID-19 mortality at the county-level. In addition to COVID-19 research from hospital population samples, public health officials can leverage county-level factors for novel disease mitigation. We use the Johns Hopkins University COVID-19 reports of confirmed cases and deaths to measure disease mortality for each county in the United States. Then, we compare mortality to multiple county social determinants of health such as age, obesity, diabetes, and smoking in hypothesis testing. We fit multivariate linear models as well as non-linear models to predict mortality as a function of these county measures. The analysis shows that there is little evidence of a relationship between the county health measures of obesity, diabetes, or smoking and COVID-19 mortality as of the date of this publication. However, the analysis does reveal a positive relationship between the percent of a county population that is 65 or older and COVID-19 mortality. Other factors such as overcrowding, the percent uninsured, and the length of time since the virus has been detected in the county are also correlated with county COVID-19 mortality. Potential reasons for these findings, including data quality, are discussed. We also emphasize the advantage of collecting high quality, detailed health data at the county-level and explain how such data could be used to understand factors affecting the outcomes from novel diseases in real-time, as a disease is progressing.
Abstract. Given a quintic number field K/Q, we study the set of irreducible trinomials, polynomials of the form x 5 + ax + b, that have a root in K. We show that there is a genus four curve C K whose rational points are in bijection with such trinomials. This curve C K maps to an elliptic curve defined over a number field, and using this map, we are able (in some cases) to determine all the rational points on C K using elliptic curve Chabauty.
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