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Distance-Sensitive Planar Point Location

Let $\mathcal{S}$ be a connected planar polygonal subdivision with $n$ edges that we want to preprocess for point-location queries, and where we are given the probability $\gamma_i$ that the query point lies in a polygon $P_i$ of $\mathcal{S}$. We show how to preprocess $\mathcal{S}$ such that the query time for a point~$p\in P_i$ depends on~$\gamma_i$ and, in addition, on the distance from $p$ to the boundary of~$P_i$---the further away from the boundary, the faster the query. More precisely, we show that a point-location query can be answered in time $O\left(\min \left(\log n, 1 + \log \frac{\mathrm{area}(P_i)}{\gamma_i \Delta_{p}^2}\right)\right)$, where $\Delta_{p}$ is the shortest Euclidean distance of the query point~$p$ to the boundary of $P_i$. Our structure uses $O(n)$ space and $O(n \log n)$ preprocessing time. It is based on a decomposition of the regions of $\mathcal{S}$ into convex quadrilaterals and triangles with the following property: for any point $p\in P_i$, the quadrilateral or triangle containing~$p$ has area $\Omega(\Delta_{p}^2)$. For the special case where $\mathcal{S}$ is a subdivision of the unit square and $\gamma_i=\mathrm{area}(P_i)$, we present a simpler solution that achieves a query time of $O\left(\min \left(\log n, \log \frac{1}{\Delta_{p}^2}\right)\right)$. The latter solution can be extended to convex subdivisions in three dimensions

Функционирование маркетинговых терминов в английском языке и способы их перевода на русский язык

Целью исследования является определение способов перевода английской терминологии на русский язык

Exploration of new multivariate spectral calibration algorithms.

A variety of multivariate calibration algorithms for quantitative spectral analyses were investigated and compared, and new algorithms were developed in the course of this Laboratory Directed Research and Development project. We were able to demonstrate the ability of the hybrid classical least squares/partial least squares (CLSIPLS) calibration algorithms to maintain calibrations in the presence of spectrometer drift and to transfer calibrations between spectrometers from the same or different manufacturers. These methods were found to be as good or better in prediction ability as the commonly used partial least squares (PLS) method. We also present the theory for an entirely new class of algorithms labeled augmented classical least squares (ACLS) methods. New factor selection methods are developed and described for the ACLS algorithms. These factor selection methods are demonstrated using near-infrared spectra collected from a system of dilute aqueous solutions. The ACLS algorithm is also shown to provide improved ease of use and better prediction ability than PLS when transferring calibrations between near-infrared calibrations from the same manufacturer. Finally, simulations incorporating either ideal or realistic errors in the spectra were used to compare the prediction abilities of the new ACLS algorithm with that of PLS. We found that in the presence of realistic errors with non-uniform spectral error variance across spectral channels or with spectral errors correlated between frequency channels, ACLS methods generally out-performed the more commonly used PLS method. These results demonstrate the need for realistic error structure in simulations when the prediction abilities of various algorithms are compared. The combination of equal or superior prediction ability and the ease of use of the ACLS algorithms make the new ACLS methods the preferred algorithms to use for multivariate spectral calibrations

Integrated immunovirological profiling validates plasma SARS-CoV-2 RNA as an early predictor of COVID-19 mortality.

peer reviewedDespite advances in COVID-19 management, identifying patients evolving toward death remains challenging. To identify early predictors of mortality within 60 days of symptom onset (DSO), we performed immunovirological assessments on plasma from 279 individuals. On samples collected at DSO11 in a discovery cohort, high severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral RNA (vRNA), low receptor binding domain–specific immunoglobulin G and antibody-dependent cellular cytotoxicity, and elevated cytokines and tissue injury markers were strongly associated with mortality, including in patients on mechanical ventilation. A three-variable model of vRNA, with predefined adjustment by age and sex, robustly identified patients with fatal outcome (adjusted hazard ratio for log-transformed vRNA = 3.5). This model remained robust in independent validation and confirmation cohorts. Since plasma vRNA’s predictive accuracy was maintained at earlier time points, its quantitation can help us understand disease heterogeneity and identify patients who may benefit from new therapies

Interface Hamiltonians and bulk critical behavior

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