No abstract

The current research study is concerned with the automated differentiation between histopathological slides from colon tissues with respect to four classes (healthy tissue and cancerous of grades 1, 2 or 3) through an optimized ensemble of predictors. Six distinct classifiers with prediction accuracies ranging from 87% to 95% are considered for the task. The proposed method of combining them takes into account the probabilities of the individual classifiers for each sample to be assigned to any of the four classes, optimizes weights for each technique by differential evolution and attains an accuracy that is significantly better than the individual results. Moreover, a degree of confidence is defined that would allow the pathologists to separate the data into two distinct sets, one that is correctly classified with a high level of confidence and the rest that would need their further attention. The tandem is also validated on other benchmark data sets. The proposed methodology proves to be efficient in improving the classification accuracy of each algorithm taken separately and performs reasonably well on other data sets, even with default weights. In addition, by establishing a degree of confidence the method becomes more viable for use by actual practitioners.

BackgroundAlignment-free methods of genomic comparison offer the possibility of scaling to large data sets of nucleotide sequences comprised of several thousand or more base pairs. Such methods can be used for purposes of deducing “nearby” species in a reference data set, or for constructing phylogenetic trees.ResultsWe describe one such method that gives quite strong results. We use the Frequency Chaos Game Representation (FCGR) to create images from such sequences, We then reduce dimension, first using a Fourier trig transform, followed by a Singular Values Decomposition (SVD). This gives vectors of modest length. These in turn are used for fast sequence lookup, construction of phylogenetic trees, and classification of virus genomic data. We illustrate the accuracy and scalability of this approach on several benchmark test sets.ConclusionsThe tandem of FCGR and dimension reductions using Fourier-type transforms and SVD provides a powerful approach for alignment-free genomic comparison. Results compare favorably and often surpass best results reported in prior literature. Good scalability is also observed.

The SARS-CoV-2 pandemic has caused significant mortality and morbidity worldwide, sparing almost no community. As the disease will likely remain a threat for years to come, an understanding of the precise influences of human demographics and settlement, as well as the dynamic factors of climate, susceptible depletion, and intervention, on the spread of localized epidemics will be vital for mounting an effective response. We consider the entire set of local epidemics in the United States; a broad selection of demographic, population density, and climate factors; and local mobility data, tracking social distancing interventions, to determine the key factors driving the spread and containment of the virus. Assuming first a linear model for the rate of exponential growth (or decay) in cases/mortality, we find that population-weighted density, humidity, and median age dominate the dynamics of growth and decline, once interventions are accounted for. A focus on distinct metropolitan areas suggests that some locales benefited from the timing of a nearly simultaneous nationwide shutdown, and/or the regional climate conditions in mid-March; while others suffered significant outbreaks prior to intervention. Using a first-principles model of the infection spread, we then develop predictions for the impact of the relaxation of social distancing and local climate conditions. A few regions, where a significant fraction of the population was infected, show evidence that the epidemic has partially resolved via depletion of the susceptible population (i.e., "herd immunity"), while most regions in the United States remain overwhelmingly susceptible. These results will be important for optimal management of intervention strategies, which can be facilitated using our online dashboard.

Strong Gröbner bases over Euclidean domains and even more general rings were first defined in the 1980s. Since that time, efficient ways to compute them, and a variety of applications, have appeared. In this note we show, via simple examples, applications to solving equations in quotient rings, Hensel lifting, Hermite normal form computations, reduction of univariate polynomial lattices, and finding small generators in quadratic number rings.