On a question of Babadi and Tarokh

In a recent remarkable paper, Babadi and Tarokh proved the "randomness" of sequences arising from binary linear block codes in the sense of spectral distribution, provided that their dual distances are sufficiently large. However, numerical experiments conducted by the authors revealed that Gold sequences which have dual distance 5 also satisfy such randomness property. Hence the interesting question was raised as to whether or not the stringent requirement of large dual distances can be relaxed in the theorem in order to explain the randomness of Gold sequences. This paper improves their result on several fronts and provides an affirmative answer to this question

Development of a Computer Vision-Based Three-Dimensional Reconstruction Method for Volume-Change Measurement of Unsaturated Soils during Triaxial Testing

Problems associated with unsaturated soils are ubiquitous in the U.S., where expansive and collapsible soils are some of the most widely distributed and costly geologic hazards. Solving these widespread geohazards requires a fundamental understanding of the constitutive behavior of unsaturated soils. In the past six decades, the suction-controlled triaxial test has been established as a standard approach to characterizing constitutive behavior for unsaturated soils. However, this type of test requires costly test equipment and time-consuming testing processes. To overcome these limitations, a photogrammetry-based method has been developed recently to measure the global and localized volume-changes of unsaturated soils during triaxial test. However, this method relies on software to detect coded targets, which often requires tedious manual correction of incorrectly coded target detection information. To address the limitation of the photogrammetry-based method, this study developed a photogrammetric computer vision-based approach for automatic target recognition and 3D reconstruction for volume-changes measurement of unsaturated soils in triaxial tests. Deep learning method was used to improve the accuracy and efficiency of coded target recognition. A photogrammetric computer vision method and ray tracing technique were then developed and validated to reconstruct the three-dimensional models of soil specimen

Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori

This paper deals with the operator-valued Hardy spaces introduced and studied by Tao Mei. Our principal result shows that the Poisson kernel in Mei's definition of these spaces can be replaced by any reasonable test function. As an application, we get a general characterization of Hardy spaces on quantum tori. The latter characterization plays a key role in our recent study of Triebel-Lizorkin spaces on quantum tori

Carbon Nanotube-based Ultra-sensitive Breath Acetone Sensor for Non-invasive Diabetes Diagnosis

In this project, the design and theoretical analysis of an ultra-high sensitive breath acetone sensor based on carbon nanotube (CNT) structure is proposed. In this device, a carbon nanotube is anchored to a substrate in one end, and the other end is coated by -WO3. As a ferroelectric material, -WO3 has high selectivity in acetone absorption. The end tip of carbon nanotube is coated with -WO3 material to absorb minute acetone molecules in breath sample. Piezoelectric activation is used to activate the vibration of carbon nanotube cantilever structure. When acetone molecules are absorbed by the coated -WO3, the resonant frequency of the cantilever will be changed for a certain amount. By sensing this certain resonant frequency change, the existence of a single acetone molecule can be detected. A theoretical model is developed to describe the vibration of the carbon nanotube cantilever structure. The resonant frequency change of the cantilever due to attached mass is analyzed. The proposed breath acetone sensor can achieve extremely high sensitivity in molecular level. It can be potentially used for non-invasive diabetic's diagnosis, which leads to a quick, convenient, accurate and painless breath diagnosis of diabetics