Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods

Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen--Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University, London, U

Systematic study of Ga1−x_{1-x}Inx_xAs self-assembled quantum wires with different interfacial strain relaxation

A systematic theoretical study of the electronic and optical properties of Ga$_{1-x}$In$_x$As self-assembled quantum-wires (QWR's) made of short-period superlattices (SPS) with strain-induced lateral ordering is presented. The theory is based on the effective bond-orbital model (EBOM) combined with a valence-force field (VFF) model. Valence-band anisotropy, band mixing, and effects due to local strain distribution at the atomistic level are all taken into account. Several structure models with varying degrees of alloy mixing for lateral modulation are considered. A valence force field model is used to find the equilibrium atomic positions in the QWR structure by minimizing the lattice energy. The strain tensor at each atomic (In or Ga) site is then obtained and included in the calculation of electronic states and optical properties. It is found that different local arrangement of atoms leads to very different strain distribution, which in turn alters the optical properties. In particular, we found that in model structures with thick capping layer the electron and hole are confined in the Ga-rich region and the optical anisotropy can be reversed due to the variation of lateral alloying mixing, while for model structures with thin capping layer the electron and hole are confined in the In-rich region, and the optical anisotropy is much less sensitive to the lateral alloy mixing.Comment: 23 pages, and 8 figure

Modeling the Radio Background from the First Black Holes at Cosmic Dawn: Implications for the 21 cm Absorption Amplitude

We estimate the 21 cm Radio Background from accretion onto the first intermediate-mass Black Holes between $z\approx 30$ and $z\approx 16$. Combining potentially optimistic, but plausible, scenarios for black hole formation and growth with empirical correlations between luminosity and radio-emission observed in low-redshift active galactic nuclei, we find that a model of black holes forming in molecular cooling halos is able to produce a 21 cm background that exceeds the Cosmic Microwave Background (CMB) at $z \approx 17$ though models involving larger halo masses are not entirely excluded. Such a background could explain the surprisingly large amplitude of the 21 cm absorption feature recently reported by the EDGES collaboration. Such black holes would also produce significant X-ray emission and contribute to the $0.5-2$ keV soft X-ray background at the level of $\approx 10^{-13}-10^{-12}$ erg sec$^{-1}$ cm$^{-2}$ deg$^{-2}$, consistent with existing constraints. In order to avoid heating the IGM over the EDGES trough, these black holes would need to be obscured by Hydrogen column depths of $N_\text{H} \sim 5 \times 10^{23} \text{cm}^{-2}$. Such black holes would avoid violating contraints on the CMB optical depth from Planck if their UV photon escape fractions were below $f_{\text{esc}} \lesssim 0.1$, which would be a natural result of $N_\text{H} \sim 5 \times 10^{23} \text{cm}^{-2}$ imposed by an unheated IGM.Comment: 10 pages, 7 figures, accepted to ApJ, replacement to match submitted versio

The far field diffraction pattern for corner reflectors with complex reflection coefficients

The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern

Personalized Pancreatic Tumor Growth Prediction via Group Learning

Tumor growth prediction, a highly challenging task, has long been viewed as a mathematical modeling problem, where the tumor growth pattern is personalized based on imaging and clinical data of a target patient. Though mathematical models yield promising results, their prediction accuracy may be limited by the absence of population trend data and personalized clinical characteristics. In this paper, we propose a statistical group learning approach to predict the tumor growth pattern that incorporates both the population trend and personalized data, in order to discover high-level features from multimodal imaging data. A deep convolutional neural network approach is developed to model the voxel-wise spatio-temporal tumor progression. The deep features are combined with the time intervals and the clinical factors to feed a process of feature selection. Our predictive model is pretrained on a group data set and personalized on the target patient data to estimate the future spatio-temporal progression of the patient's tumor. Multimodal imaging data at multiple time points are used in the learning, personalization and inference stages. Our method achieves a Dice coefficient of 86.8% +- 3.6% and RVD of 7.9% +- 5.4% on a pancreatic tumor data set, outperforming the DSC of 84.4% +- 4.0% and RVD 13.9% +- 9.8% obtained by a previous state-of-the-art model-based method

Divergence and Shannon information in genomes

Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length-independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.Comment: 4 pages, 3 tables, 2 figure