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

Efficient and Accurate Coded Target Decoding for 3D Reconstruction of Soil Specimens in Triaxial Test

Coded Targets Have Been Widely Used for Solving the Corresponding Problem in Photogrammetry for High-Accuracy Three-Dimensional Measurements. Accurate and Efficient Recognition and Identification of Coded Targets Are of Great Importance in Coded Target-Based Photogrammetry. in This Paper, an Efficient and Accurate Method for Coded Target Decoding Was Developed. in This Method, Blob Analysis Was Performed to Recognize the Coded Targets. Then, Image Processing, the RANSAC Algorithm, and the Interpolation Technique Were Applied Respectively to Decode the Coded Targets, Identify Falsely Identified Coded Targets, and Recover Missing Coded Targets. Interpolation Was Also Performed on the Membrane, Which Can Significantly Increase the Density of the Points on the Membrane and Produce More Representative 3D Results for the Soils Specimen. This Method Was Implemented into a MATLAB Program and All Computation Was Done Automatically by the Computer Program. This Method Takes Advantage of the Prior Knowledge of the Geometric Arrangement of the Coded Targets. the Effectiveness and Accuracy of the Proposed Method Are Validated by Implementing It into Three-Dimensional Reconstruction of Soil Specimens during Triaxial Testing in Geotechnical Engineering. Experimental Validation Results Indicate that the Proposed Method Can Achieve Accurate and Efficient Coded Target Recognition and Identification Results