A few remarks on time-frequency analysis of Gevrey, analytic and ultra-analytic functions

We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and time-frequency analysis of the corresponding pseudodifferential operators.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1209.094

Advancing image quantification methods and tools for analysis of nanoparticle electrokinetics

Image processing methods and techniques for high-throughput quantification of dielectrophoretic (DEP) collections onto planar castellated electrode arrays are developed and evaluated. Fluorescence-based dielectrophoretic spectroscopy is an important tool for laboratory investigations of AC electrokinetic properties of nanoparticles. This paper details new, first principle, theoretical and experimental developments of geometric feature recognition techniques that enable quantification of positive dielectrophoretic (pDEP) nanoparticle collections onto castellated arrays. As an alternative to the geometric-based method, novel statistical methods that do not require any information about array features, are also developed using the quantile and standard deviation functions. Data from pDEP collection and release experiments using 200 nm diameter latex nanospheres demonstrates that pDEP quantification using the statistic-based methods yields quantitatively similar results to the geometric-based method. The development of geometric- and statistic-based quantification methods enables high-throughput, supervisor-free image processing tools critical for dielectrophoretic spectroscopy and automated DEP technology development