Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation

We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates. The first test is constructed by carrying out thresholding to remove the non-signal bearing dimensions. The second test combines data transformation via the precision matrix with the thresholding. The benefits of the thresholding and the data transformations are showed by a reduced variance of the test thresholding statistics, the improved power and a wider detection region of the tests. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.Comment: 64 page

Harmonic coordinates in the string and membrane equations

In this note, we first show that the solutions to Cauchy problems for two versions of relativistic string and membrane equations are diffeomorphic. Then we investigate the coordinates transformation presented in Ref. [9] (see (2.20) in Ref. [9]) which plays an important role in the study on the dynamics of the motion of string in Minkowski space. This kind of transformed coordinates are harmonic coordinates, and the nonlinear relativistic string equations can be straightforwardly simplified into linear wave equations under this transformation

Direct Detection of Thrombin Binding to 8-Bromodeoxyguanosine-Modified Aptamer: Effects of Modification on Affinity and Kinetics

The affinity of an 8-bromodeoxyguanosine- (8-BrdG-) substituted thrombin-binding aptamer (TBA-Br), which has the 1st and 10th guanosine residues replaced with 8-BrdG, was estimated using reflectometric interference spectroscopy (RIfS). When comparing TBA-Br with unmodified TBA (TBA-H), it was demonstrated that the modification effectively improved the affinity of TBA; dissociation constants (KD) of TBA-H and TBA-Br were 45.4 nM and 1.99 nM, respectively. These values, which were obtained by direct observation of thrombin binding using RIfS, have the same order of magnitude as those obtained in our previous study utilizing conformational changes in TBA to detect thrombin binding, thus confirming the validity of the obtained KD values. RIfS measurements also revealed that the 8-BrdG modification resulted in a lower dissociation rate constant (kd), which suggests that the enhancement of affinity can be attributed to the stabilization of the G-quadruplex structure on introduction of 8-BrdG