On a general extending and constraining procedure for linear iterative methods

Algebraic Reconstruction Techniques (ART), on their both successive or simultaneous formulation, have been developed since early 70's as efficient ''row action methods'' for solving the image reconstruction problem in Computerized Tomography. In this respect, two important development directions were concerned with, firstly their extension to the inconsistent case of the reconstruction problem, and secondly with their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of our paper we introduce extending and constraining procedures for a general iterative method of ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimmino's simultaneous reflections method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also considered hard thresholding constraining used in sparse approximation problems and applied it successfully to a 3D particle image reconstruction problem

Constrained superfields in Supergravity

We analyze constrained superfields in supergravity. We investigate the consistency and solve all known constraints, presenting a new class that may have interesting applications in the construction of inflationary models. We provide the superspace Lagrangians for minimal supergravity models based on them and write the corresponding theories in component form using a simplifying gauge for the goldstino couplings.Comment: 24 pages. v2: JHEP final version (fixed typos, references added

Precision Measurements of the Cluster Red Sequence using an Error Corrected Gaussian Mixture Model

The red sequence is an important feature of galaxy clusters and plays a crucial role in optical cluster detection. Measurement of the slope and scatter of the red sequence are affected both by selection of red sequence galaxies and measurement errors. In this paper, we describe a new error corrected Gaussian Mixture Model for red sequence galaxy identification. Using this technique, we can remove the effects of measurement error and extract unbiased information about the intrinsic properties of the red sequence. We use this method to select red sequence galaxies in each of the 13,823 clusters in the maxBCG catalog, and measure the red sequence ridgeline location and scatter of each. These measurements provide precise constraints on the variation of the average red galaxy populations in the observed frame with redshift. We find that the scatter of the red sequence ridgeline increases mildly with redshift, and that the slope decreases with redshift. We also observe that the slope does not strongly depend on cluster richness. Using similar methods, we show that this behavior is mirrored in a spectroscopic sample of field galaxies, further emphasizing that ridgeline properties are independent of environment.Comment: 33 pages, 14 Figures; A typo in Eq.A11 is fixed. The C++/Python codes for ECGMM can be downloaded from: https://sites.google.com/site/jiangangecgmm