Search for: All records

Abstract The evolution of the COVID-19 pandemic is described through a time-dependent stochastic dynamic model in discrete time. The proposed multi-compartment model is expressed through a system of difference equations. Information on the social distancing measures and diagnostic testing rates are incorporated to characterize the dynamics of the various compartments of the model. In contrast with conventional epidemiological models, the proposed model involves interpretable temporally static and dynamic epidemiological rate parameters. A model fitting strategy built upon nonparametric smoothing is employed for estimating the time-varying parameters, while profiling over the time-independent parameters. Confidence bands of the parameters are obtained through a residual bootstrap procedure. A key feature of the methodology is its ability to estimate latent unobservable compartments such as the number of asymptomatic but infected individuals who are known to be the key vectors of COVID-19 spread. The nature of the disease dynamics is further quantified by relevant epidemiological markers that make use of the estimates of latent compartments. The methodology is applied to understand the true extent and dynamics of the pandemic in various states within the United States (US). 

Making statistical inference on quantities defining various characteristics of a temporally measured biochemical process and analyzing its variability across different experimental conditions is a core challenge in various branches of science. This problem is particularly difficult when the amount of data that can be collected is limited in terms of both the number of replicates and the number of time points per process trajectory. We propose a method for analyzing the variability of smooth functionals of the growth or production trajectories associated with such processes across different experimental conditions. Our modeling approach is based on a spline representation of the mean trajectories. We also develop a bootstrap-based inference procedure for the parameters while accounting for possible multiple comparisons. This methodology is applied to study two types of quantities—the “time to harvest” and “maximal productivity”—in the context of an experiment on the production of recombinant proteins. We complement the findings with extensive numerical experiments comparing the effectiveness of different types of bootstrap procedures for various tests of hypotheses. These numerical experiments convincingly demonstrate that the proposed method yields reliable inference on complex characteristics of the processes even in a data-limited environment where more traditional methods for statistical inference are typically not reliable. 

Abstract “Paintings fade like flowers”: van Gogh’s prediction on the impact of age on paintings came true for most of his paintings. We have studied the consequences of this aging on the Sunflowers in a vase with a yellow background series, namely its original, F454, currently in London, and two replicates, F457, in Tokyo, and F458, in Amsterdam, which van Gogh painted using the original as a model. The background and flower renditions in those paintings have faded and turned brown, making them less vibrant that van Gogh had most likely intended. We have attempted to restore van Gogh’s intent using a computational approach based on data science. After identifications of regions of interest (ROI) within the three paintings F454, F457, and F458 that capture the flowers, stems of the flowers, and background, respectively, we studied the geometry of the color space (in RGB representation) occupied by those ROIs. By comparing those color spaces with those occupied by similar ROIs in photographs of real sunflowers, we identified shifts in all three color coordinates, R, G, and B, with the positive shift in the blue coordinate being the more salient. We have proposed two algorithms, PCR-1 and PCR-2, for correcting that shift in blue and generate representations of the paintings that aim to restore their original conditions. The reduction of the blue component in the yellow hues has lead to more vibrant and less brownish digital rendition of the three Sunflowers in a vase with a yellow background . 

Our computational developments and analyses on experimental images are designed to evaluate the effectiveness of chemical spraying via unmanned aerial vehicle (UAV). Our evaluations are in accord with the two perspectives of color-complexity: color variety within a color system and color distributional geometry on an image. First, by working within RGB and HSV color systems, we develop a new color-identification algorithm relying on highly associative relations among three color-coordinates to lead us to exhaustively identify all targeted color-pixels. A color-dot is then identified as one isolated network of connected color-pixel. All identified color-dots vary in shapes and sizes within each image. Such a pixel-based computing algorithm is shown robustly and efficiently accommodating heterogeneity due to shaded regions and lighting conditions. Secondly, all color-dots with varying sizes are categorized into three categories. Since the number of small color-dot is rather large, we spatially divide the entire image into a 2D lattice of rectangular. As such, each rectangle becomes a collective of color-dots of various sizes and is classified with respect to its color-dots intensity. We progressively construct a series of minimum spanning trees (MST) as multiscale 2D distributional spatial geometries in a decreasing-intensity fashion. We extract the distributions of distances among connected rectangle-nodes in the observed MST and simulated MSTs generated under the spatial uniformness assumption. We devise a new algorithm for testing 2D spatial uniformness based on a Hierarchical clustering tree upon all involving MSTs. This new tree-based p -value evaluation has the capacity to become exact.