Persistence Terrace for Topological Inference of Point Cloud Data

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online.     

Formation of a perylenetetracarboxylic diimide network film by post electrochemical treatment

Perylenetetracarboxylic diimide (PDI) derivatives bearing two or four peripheral pyrrole pendants (PDI-nPy, n=2 or 4) are cross-linkable materials by electro/phototreatment. In this paper, we introduce a new posttreatment technique to produce an insoluble film. Unlike the common solution-phase electrochemical deposition, we first spin-coated PDI-nPy on an electrode and then electrotreated the coated surface in a monomer-free electrolyte solution. This method gives the film a smooth surface with no granules, while the common method induces a rough film with a lot of granules. The post electrochemical treatment also provides a merit of higher resolution in a patterning process on a specific metal electrode. As one of the applications, we carried out an electrochromic study on the posttreated PDI-4Py film. It turned purple (lambdamax=590 nm) and sky blue (lambdamax=797 nm) at 0 and -1.9 V vs Ag/Ag+, respectively. We believe this method will broaden the patterning concept with the desired film morphology and resolution using PDI on a specific electrode.     

Complete NMR signal assignments of flavonol derivatives

Common substitution positions of flavonols are at C-5 and C-7; 6-substituted flavonol derivatives are rarely found in natural sources. Here, we report complete assignments of 1H and 13C chemical shifts of eight flavonol derivatives including four 6-substituted flavonols.     

Orbital-selective mass enhancements in multiband Ca(2-x)Sr(x)RuO4 systems analyzed by the extended Drude model

We investigated optical spectra of quasi-two-dimensional multiband systems. The extended Drude model analysis on the -plane optical conductivity spectra indicates that the effective mass should be enhanced near . Based on the sum rule argument, we showed that the orbital-selective Mott-gap opening for the bands, the widely investigated picture, could not be the origin of the mass enhancement. We exploited the multiband effects in the extended Drude model analysis, and demonstrated that the intriguing heavy mass state near should come from the renormalization of the band.     

How does distortion correction correlate with anisotropic indices? A diffusion tensor imaging study

PURPOSE: The purpose of this study was to determine a suitable registration algorithm for diffusion tensor imaging (DTI) using conventional preprocessing tools [statistical parametric mapping (SPM) and automated image registration (AIR)] and to investigate how anisotropic indices for clinical assessments are affected by these distortion corrections. MATERIALS AND METHODS: Brain DTI data from 15 normal healthy volunteers were used to evaluate four spatial registration schemes within subjects to correct image distortions: noncorrection, SPM-based affine registration, AIR-based affine registration and AIR-based nonlinear polynomial warping. The performance of each distortion correction was assessed using: (a) quantitative parameters: tensor-fitting error (Ef), mean dispersion index (MDI), mean fractional anisotropy (MFA) and mean variance (MV) within 11 regions of interest (ROI) defined from homogeneous fiber bundles; and (b) fiber tractography through the uncinate fasciculus and the corpus callosum. Fractional anisotropy (FA) and mean diffusivity (MD) were calculated to demonstrate the effects of distortion correction. Repeated-measures analysis of variance was used to investigate differences among the four registration paradigms. RESULTS: AIR-based nonlinear registration showed the best performance for reducing image distortions with respect to smaller Ef (P<.02), MDI (P<.01) and MV (P<.01) with larger MFA (P<.01). FA was decreased to correct distortions (P<.0001) whether the applied registration was linear or nonlinear and was lowest after nonlinear correction (P<.001). No significant differences were found in MD. CONCLUSION: In conventional DTI processing, anisotropic indices of FA can be misestimated by noncorrection or inappropriate distortion correction, which leads to an erroneous increase in FA. AIR-based nonlinear distortion correction would be required for a more accurate measurement of this diffusion parameter.     

Effects of temperature and carrier gas flow amount on the formation of GaN nanorods by the HVPE method

We fabricated one-dimensional GaN nanorods on AlN/Si (1 1 1) substrates at various temperatures, and carrier gas flow amount, using the hydride vapor phase epitaxy (HVPE) method. An AlN buffer layer of 50 nm thickness was deposited by RF sputtering for 25 min. Stalagmite-like GaN nanorods formed at a growth temperature of 650 °C. The diameters and lengths of GaN nanorods increase with growth time, whereas the density of nanorods decreases. And we performed the experiments by changing the carrier gas flow amount at a growth temperature of 650 °C and HCl:NH₃ flow ratio of 1:40. GaN nanorods, with an average diameter of 50 nm, were obtained at a carrier gas flow amount of 1340 sccm. The shape, structures, and optical characteristics of the nanorods were investigated by field-emission scanning electron microscopy, X-ray diffraction, and photoluminescence.     

A methodology for knowledge discovery to support product family design

This paper introduces a methodology for knowledge discovery related to product family design that integrates an ontology with data mining techniques. In the proposed methodology, the ontology represents attributes for the components of products in functional hierarchies. Fuzzy clustering is employed for data mining to first partition product functions into subsets for identifying modules in a given product family and then identify the similarity level of components in a module. Module categorization is introduced to support association rule mining for knowledge discovery related to platform design. We apply the proposed methodology to first develop and then utilize design knowledge for a family of power tools. Based on the developed design knowledge, a new platform is suggested to improve commonality in the power tool family.