A Kind of Affine Weighted Moment Invariants

A new kind of geometric invariants is proposed in this paper, which is called affine weighted moment invariant (AWMI). By combination of local affine differential invariants and a framework of global integral, they can more effectively extract features of images and help to increase the number of low-order invariants and to decrease the calculating cost. The experimental results show that AWMIs have good stability and distinguishability and achieve better results in image retrieval than traditional moment invariants. An extension to 3D is straightforward

Generalization of polynomial chaos for estimation of angular random variables

“The state of a dynamical system will rarely be known perfectly, requiring the variable elements in the state to become random variables. More accurate estimation of the uncertainty in the random variable results in a better understanding of how the random variable will behave at future points in time. Many methods exist for representing a random variable within a system including a polynomial chaos expansion (PCE), which expresses a random variable as a linear combination of basis polynomials. Polynomial chaos expansions have been studied at length for the joint estimation of states that are purely translational (i.e. described in Cartesian space); however, many dynamical systems also include non-translational states, such as angles. Many methods of quantifying the uncertainty in a random variable are not capable of representing angular random variables on the unit circle and instead rely on projections onto a tangent line. Any element of any space V can be quantified with a PCE if V is spanned by the expansion’s basis polynomials. This implies that, as long as basis polynomials span the unit circle, an angular random variable (either real or complex) can be quantified using a PCE. A generalization of the PCE is developed allowing for the representation of complex valued random variables, which includes complex representations of angles. Additionally, it is proposed that real valued polynomials that are orthogonal with respect to measures on the real valued unit circle can be used as basis polynomials in a chaos expansion, which reduces the additional numerical burden imposed by complex valued polynomials. Both complex and real unit circle PCEs are shown to accurately estimate angular random variables in independent and correlated multivariate dynamical systems”--Abstract, page iii

Moment transport equations for non-Gaussianity

We present a novel method for calculating the primordial non-Gaussianity produced by super-horizon evolution during inflation. Our method evolves the distribution of coarse-grained inflationary field values using a transport equation. We present simple evolution equations for the moments of this distribution, such as the variance and skewness. This method possesses some advantages over existing techniques. Among them, it cleanly separates multiple sources of primordial non-Gaussianity, and is computationally efficient when compared with popular alternatives, such as the "delta N" framework. We adduce numerical calculations demonstrating that our new method offers good agreement with those already in the literature. We focus on two fields and the fNL parameter, but we expect our method will generalize to multiple scalar fields and to moments of arbitrarily high order. We present our expressions in a field-space covariant form which we postulate to be valid for any number of fields.Comment: 24 pages, 4 colour figures; uses iopart.cls. v2: Erroneous statements about delta N method in Sec. 2 removed. Correction to gauge transformation in Eq. (12) brings numerical results of Sec. 4 into better agreement with the delta N formula. Conclusions remain the same. v3: minor change

B-Spline based uncertainty quantification for stochastic analysis

The consideration of uncertainties has become inevitable in state-of-the-art science and technology. Research in the field of uncertainty quantification has gained much importance in the last decades. The main focus of scientists is the identification of uncertain sources, the determination and hierarchization of uncertainties, and the investigation of their influences on system responses. Polynomial chaos expansion, among others, is suitable for this purpose, and has asserted itself as a versatile and powerful tool in various applications. In the last years, its combination with any kind of dimension reduction methods has been intensively pursued, providing support for the processing of high-dimensional input variables up to now. Indeed, this is also referred to as the curse of dimensionality and its abolishment would be considered as a milestone in uncertainty quantification. At this point, the present thesis starts and investigates spline spaces, as a natural extension of polynomials, in the field of uncertainty quantification. The newly developed method 'spline chaos', aims to employ the more complex, but thereby more flexible, structure of splines to counter harder real-world applications where polynomial chaos fails. Ordinarily, the bases of polynomial chaos expansions are orthogonal polynomials, which are replaced by B-spline basis functions in this work. Convergence of the new method is proved and emphasized by numerical examples, which are extended to an accuracy analysis with multi-dimensional input. Moreover, by solving several stochastic differential equations, it is shown that the spline chaos is a generalization of multi-element Legendre chaos and superior to it. Finally, the spline chaos accounts for solving partial differential equations and results in a stochastic Galerkin isogeometric analysis that contributes to the efficient uncertainty quantification of elliptic partial differential equations. A general framework in combination with an a priori error estimation of the expected solution is provided

The Hyper Suprime-Cam Software Pipeline

In this paper, we describe the optical imaging data processing pipeline developed for the Subaru Telescope's Hyper Suprime-Cam (HSC) instrument. The HSC Pipeline builds on the prototype pipeline being developed by the Large Synoptic Survey Telescope's Data Management system, adding customizations for HSC, large-scale processing capabilities, and novel algorithms that have since been reincorporated into the LSST codebase. While designed primarily to reduce HSC Subaru Strategic Program (SSP) data, it is also the recommended pipeline for reducing general-observer HSC data. The HSC pipeline includes high level processing steps that generate coadded images and science-ready catalogs as well as low-level detrending and image characterizations.Comment: 39 pages, 21 figures, 2 tables. Submitted to Publications of the Astronomical Society of Japa