A novel local PCA-based method for detecting activation signals in fMRI.

A novel local principal component analysis (LPCA) technique is presented for activation signal detection in functional magnetic resonance imaging (fMRI) without explicit knowledge about the shape of the model activation signal. Unlike the traditional PCA methods, our LPCA algorithm is based on a measure of separation between two clusters formed by the signal segments in active periods and inactive periods, which is computed in an eigen-subspace. In addition, we only applied PCA to the temporal sequence of each individual voxel instead of applying PCA to the fMRI data set. In our algorithm, we first applied a linear regression procedure to alleviate the baseline drift artifact. Then, the baseline-corrected temporal signals were partitioned into active and inactive segments according to the paradigm used for the fMRI data acquisition. Principal components were computed from all these segments for each voxel by PCA. By projecting the segments of each voxel onto a linear subspace formed by the corresponding most dominant principal components, two separate clusters were formed from active and inactive segments. An activation measure was defined based on the degree of separation between these two clusters in the projection space. We show experimental results on the activation signal detection from various sets of fMRI data with different types of stimulation by using the proposed LPCA algorithm and the standard t-test method for comparison. Our experiments indicate that the LPCA algorithm in general provides substantial signal-to-noise ratio improvement over the t-test method.     

Undersampled Windowed Exponentials and Their Applications

We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form

$$ {\mathcal{F}}(g): =\bigl\{ e^{2\pi i n x}: n\ge 0\bigr\} \cup \bigl\{ g(x)e^{2\pi i nx}: n< 0\bigr\} $$

for \(L^{2}[-1/2,1/2]\) by the spectra of the Toeplitz operators with the symbol \(g\). Using this characterization, we classify all real-valued functions \(g\) such that \({\mathcal{F}}(g)\) is complete or forms a frame/basis. Conversely, we use the classical non-harmonic Fourier series theory to determine all \(\xi \) such that the Toeplitz operators with the symbol \(e^{2\pi i \xi x}\) is injective or invertible. These results demonstrate an elegant interaction between frame theory of windowed exponentials and Toeplitz operators. Finally, we use our results to answer some open questions in dynamical sampling, and derivative samplings on Paley-Wiener spaces of bandlimited functions.

     

Morphology–luminescence correlations in europium-doped ZnO nanomaterials

In order to investigate the correlations of morphologies and optical properties, different morphologies of Eu-doped ZnO were synthesized by different methods. Specifically, the structure of SiO₂/ZnO:Eu nanoflower was synthesized for the first time and has not been reported previously. One percent was chosen as the Eu doping concentration. The relations of the morphology, diameter, and uniformity with the PL intensity were examined. The PL intensity of ZOE samples has a close relationship with the morphology. The PL intensity order of the different morphologies of ZnO:Eu is as follows: nanorod arrays > thin film > nanospheres > nanoparticles > nanoflowers > nanorods. The PL intensity of nanomaterials is larger, if the diameter of the nanomaterials is larger. However, the size of diameter is not the most important reason. It was found that the sample uniformity plays a key role on ZnO:Eu PL intensity. ZnO:Eu with small particle diameters may have strong photoluminescence intensity, if the nanoparticles are uniform.     

Structure of the Polymer Obtained from Bisphenol-A and Cl 2 P(O)CH 3

Using the step-by-step build-up approach, the possible conformations of compound PhOP(O)(Me)OPh(Me) 2 Ph were constructed and geometrically optimized. Among the obtained structures 32 conformations belonging to low, comparable energy levels were used to construct the most stable dimers and tetramers of the title polymer. The results allowed us to estimate the geometrical structure of the polymer.     

Qualitative and quantitative analysis of the unsaponifiable fraction of vegetable oils by using comprehensive 2D GC with dual MS/FID detection

The present investigation is focused on the development of a comprehensive two-dimensional GC (GC?×?GC) method, with dual MS/FID detection, for the qualitative and quantitative analysis of the entire unsaponifiable fraction of vegetable oils. The unsaponifiable fraction forms a minor, highly specific part of a vegetable oil, and can be used as an indicator of genuineness. The column set used consisted of a low-polarity first dimension, and a medium-polarity secondary one, both characterized by a high thermal stability. The use of dual detection enabled the attainment of both mass spectral information and relative % FID data. The complexity of the fingerprint, generated by the unsaponifiable fraction, fully justified the employment of the two-dimensional GC technology. Furthermore, two other GC?×?GC benefits contributed greatly to the attainment of promising results, namely sensitivity enhancement and the formation of group-type patterns. The method herein proposed could potentially open a new opportunity for the more in-depth knowledge of the unsaponifiable fraction of vegetable oils.