Search for: All records

In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, our method provides a natural way of numerosity data reduction. We establish the theoretical guarantees of the proposed method, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. We also introduce a bootstrap method to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction. 

In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, our method provides a natural way of numerosity data reduction. We establish the theoretical guarantees of the proposed method, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. We also introduce a bootstrap method to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction. 

Over the past few months, the outbreak of Coronavirus disease (COVID-19) has been expanding over the world. A reliable and accurate dataset of the cases is vital for scientists to conduct related research and policy-makers to make better decisions. We collect the United States COVID-19 daily reported data from four open sources: the New York Times, the COVID-19 Data Repository by Johns Hopkins University, the COVID Tracking Project at the Atlantic, and the USAFacts, then compare the similarities and differences among them. To obtain reliable data for further analysis, we first examine the cyclical pattern and the following anomalies, which frequently occur in the reported cases: (1) the order dependencies violation, (2) the point or period anomalies, and (3) the issue of reporting delay. To address these detected issues, we propose the corresponding repairing methods and procedures if corrections are necessary. In addition, we integrate the COVID-19 reported cases with the county-level auxiliary information of the local features from official sources, such as health infrastructure, demographic, socioeconomic, and environmental information, which are also essential for understanding the spread of the virus. 

Abstract Optical antenna resonators enable control of light‐matter interactions on the nano‐scale via electron–photon hybrid states in strong coupling. Specifically, mid‐infrared (MIR) nano‐antennas coupled to saturable intersubband transitions in multi‐quantum‐well (MQW) semiconductor heterostructures allow for the coupling strength to be tuned through antenna resonance and field intensity. Here, tip‐enhanced nano‐scale variation of antenna‐MQW coupling across the antenna is demonstrated, with a spatially‐dependent coupling strength varying from 73 (strong coupling) to 24 (weak coupling). This behavior is modeled based on the spatially dependent local constructive and destructive interference between tip and antenna fields. Using a quantum‐mechanical density‐matrix model of the MQW system with its designed values of transition dipole moment, doping density, and population decay time, the picosecond IR pulse coupling to intersubband transitions and the associated tip induced strong‐field saturation effects are described. These results present a new regime of nonlinear IR light‐matter control based on the dynamic manipulation of quantum hybrid states on the nanoscale and in the infrared, with a perspective regarding extension to molecular vibrations. 

Background: Fluid intelligence (FI) involves abstract problem-solving without prior knowledge. Greater age-related FI decline increases Alzheimer’s disease (AD) risk, and recent studies suggest that certain dietary regimens may influence rates of decline. However, it is uncertain how long-term food consumption affects FI among adults with or without familial history of AD (FH) or APOE4 (ɛ4). Objective: Observe how the total diet is associated with long-term cognition among mid- to late-life populations at-risk and not-at-risk for AD. Methods: Among 1,787 mid-to-late-aged adult UK Biobank participants, 10-year FI trajectories were modeled and regressed onto the total diet based on self-reported intake of 49 whole foods from a Food Frequency Questionnaire (FFQ). Results: Daily cheese intake strongly predicted better FIT scores over time (FH-: β= 0.207, p < 0.001; ɛ4–: β= 0.073, p = 0.008; ɛ4+: β= 0.162, p = 0.001). Alcohol of any type daily also appeared beneficial (ɛ4+: β= 0.101, p = 0.022) and red wine was sometimes additionally protective (FH+: β= 0.100, p = 0.014; ɛ4–: β= 0.59, p = 0.039). Consuming lamb weekly was associated with improved outcomes (FH-: β= 0.066, p = 0.008; ɛ4+: β= 0.097, p = 0.044). Among at risk groups, added salt correlated with decreased performance (FH+: β= –0.114, p = 0.004; ɛ4+: β= –0.121, p = 0.009). Conclusion: Modifying meal plans may help minimize cognitive decline. We observed that added salt may put at-risk individuals at greater risk, but did not observe similar interactions among FH- and AD- individuals. Observations further suggest in risk status-dependent manners that adding cheese and red wine to the diet daily, and lamb on a weekly basis, may also improve long-term cognitive outcomes.