Improved filters for gravitational waves from inspiralling compact binaries

The order of the post-Newtonian expansion needed, to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiralling compact binaries, is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) The introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of Pade approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available O(v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5% implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10-15 % that would be detectable using standard post-Newtonian approximants.Comment: Latex ([prd,aps,eqsecnum,epsf]{revtex}), 40 pages including 12 encapsulated figures. (The paper, together with all the figures and tables is available from ftp://carina.astro.cf.ac.uk/pub/incoming/sathya/dis97.uu

Improved filters for gravitational waves from inspiraling compact binaries

The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) the introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available (v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5%, implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10–15 % that would be detectable using standard post-Newtonian approximants

Experimental study of digital image processing techniques for LANDSAT data

The author has identified the following significant results. Results are reported for: (1) subscene registration, (2) full scene rectification and registration, (3) resampling techniques, (4) and ground control point (GCP) extraction. Subscenes (354 pixels x 234 lines) were registered to approximately 1/4 pixel accuracy and evaluated by change detection imagery for three cases: (1) bulk data registration, (2) precision correction of a reference subscene using GCP data, and (3) independently precision processed subscenes. Full scene rectification and registration results were evaluated by using a correlation technique to measure registration errors of 0.3 pixel rms thoughout the full scene. Resampling evaluations of nearest neighbor and TRW cubic convolution processed data included change detection imagery and feature classification. Resampled data were also evaluated for an MSS scene containing specular solar reflections

Learning Deep SPD Visual Representation for Image Classification

Symmetric positive definite (SPD) visual representations are effective due to their ability to capture high-order statistics to describe images. Reliable and efficient calculation of SPD matrix representation from small sized feature maps with a high number of channels in CNN is a challenging issue. This thesis presents three novel methods to address the above challenge. The first method, called Relation Dropout (ReDro), is inspired by the fact that eigen-decomposition of a block diagonal matrix can be efficiently obtained by eigendecomposition of each block separately. Thus, instead of using a full covariance matrix as in the literature, this thesis randomly group the channels and form a covariance matrix per group. ReDro is inserted as an additional layer preceding the matrix normalisation step and the random grouping is made transparent to all subsequent layers. ReDro can be seen as a dropout-related regularisation which discards some pair-wise channel relationships across each group. The second method, called FastCOV, exploits the intrinsic connection between eigensytems of XXT and XTX. Specifically, it computes position-wise covariance matrix upon convolutional feature maps instead of the typical channel-wise covariance matrix. As the spatial size of feature maps is usually much smaller than the channel number, conducting eigen-decomposition of the position-wise covariance matrix avoids rank-deficiency and it is faster than the decomposition of the channel-wise covariance matrix. The eigenvalues and eigenvectors of the normalised channel-wise covariance matrix can be retrieved by the connection of the XXT and XTX eigen-systems. The third method, iSICE, deals with the reliable covariance estimation from small sized and highdimensional CNN feature maps. It exploits the prior structure of the covariance matrix to estimate sparse inverse covariance which is developed in the literature to deal with the covariance matrix’s small sample issue. Given a covariance matrix, this thesis iteratively minimises its log-likelihood penalised by a sparsity with gradient descend. The resultant representation characterises partial correlation instead of indirect correlation characterised in covariance representation. As experimentally demonstrated, all three proposed methods improve the image classification performance, whereas the first two proposed methods reduce the computational cost of learning large SPD visual representations

The convolution theorem for the continuous wavelet tranform

We study the application of the continuous wavelet transform to perform signal 1ltering processes. We 1rst show that the convolution and correlation of two wavelet functions satisfy the required admissibility and regularity conditions. By using these new wavelet functions to analyze both convolutions and correlations, respectively, we derive convolution and correlation theorems for the continuous wavelet transform and show them to be similar to that of other joint spatial/spatial–frequency or time/frequency representations. We then investigate the e5ect of multiplying the continuous wavelet transform of a given signal by a related transfer function and show how to perform spatially variant 1ltering operations in the wavelet domain. Finally, we present numerical examples showing the usefulness of applying the convolution theorem for the continuous wavelet transform to perform signal restoration in the presence of additive noise

On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics

When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.Comment: 16 pages, 4 figure

SPIRE Map-Making Test Report

The photometer section of SPIRE is one of the key instruments on board of Herschel. Its legacy depends very much on how well the scanmap observations that it carried out during the Herschel mission can be converted to high quality maps. In order to have a comprehensive assessment on the current status of SPIRE map-making, as well as to provide guidance for future development of the SPIRE scan-map data reduction pipeline, we carried out a test campaign on SPIRE map-making. In this report, we present results of the tests in this campaign.Comment: This document has an executive summary, 6 chapters, and 102 pages. More information can be found at: https://nhscsci.ipac.caltech.edu/sc/index.php/Spire/SPIREMap-MakingTest201