Mapping the Similarities of Spectra: Global and Locally-biased Approaches to SDSS Galaxy Data [IMA]

We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and we illustrate how this approach can be used in an exploratory manner to highlight both large-scale global as well as small-scale local structure in Sloan Digital Sky Survey (SDSS) data. We use this method in a way that simultaneously takes into account the measurements of spectral lines as well as the continuum shape. Unlike Principal Component Analysis, this method does not assume that the Euclidean distance between galaxy spectra is a good global measure of similarity between all spectra, but instead it only assumes that local difference information between similar spectra is reliable. Moreover, unlike other nonlinear dimensionality methods, this method can be used to characterize very finely both small-scale local as well as large-scale global properties of realistic noisy data. The power of the method is demonstrated on the SDSS Main Galaxy Sample by illustrating that the derived embeddings of spectra carry an unprecedented amount of information. By using a straightforward global or unsupervised variant, we observe that the main features correlate strongly with star formation rate and that they clearly separate active galactic nuclei. Computed parameters of the method can be used to describe line strengths and their interdependencies. By using a locally-biased or semi-supervised variant, we are able to focus on typical variations around specific objects of astronomical interest. We present several examples illustrating that this approach can enable new discoveries in the data as well as a detailed understanding of very fine local structure that would otherwise be overwhelmed by large-scale noise and global trends in the data.

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D. Lawlor, T. Budavari and M. Mahoney
Wed, 14 Sep 16

Comments: 34 pages. A modified version of this paper has been accepted to The Astrophysical Journal

A fast algorithm for identifying Friends-of-Friends halos [IMA]

We describe a simple and fast algorithm for identifying friends-of-friends clusters and prove its correctness. The algorithm avoids unnecessary expensive neighbor queries, uses minimal memory overhead, and rejects slowdown in high over-density regions. We define our algorithm formally based on pair enumeration, a problem that has been heavily studied in fast 2-point correlation codes and our reference implementation employs a dual KD-tree correlation function code. We construct halos in a hierarchical merger tree, and use a splay operation to reduce the average cost of identifying the root of a cluster from $O[\log L]$ to $O[1]$ ($L$ is the size of a cluster) without additional memory costs. This reduces the overall time complexity of merging trees form $O[L\log L]$ to $O[L]$, reducing the number of operations per by orders of magnitude. We next introduce a pruning operation that skips pair enumeration between two fully self-connected KD-tree nodes. This improves the robustness of the algorithm, reducing cost of exploring to high density peaks from $O[\delta^2]$ to $O[\delta]$. We show that for cosmological data set the algorithm eliminates more than half of enumerations for typically used linking lengths $b \sim 0.2$, and empirically scales as $O[\log b]$ at large $b$ (linking length) limit. Furthermore, our algorithm is extremely simple and easy to implement on top of an existing pair enumeration code, reusing the optimization effort that has been invested in fast correlation function codes.

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Y. Feng and C. Modi
Wed, 13 Jul 16

Comments: 9 pages, 3 figures. Submitting to Astronomy and Computing

Mathematical Foundations of the GraphBLAS [CL]

The GraphBLAS standard ( is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix mul- tiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

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J. Kepner, P. Aaltonen, D. Bader, et. al.
Tue, 21 Jun 16

Comments: 9 pages; 11 figures; accepted to IEEE High Performance Extreme Computing (HPEC) conference 2016

GTOC8: Results and Methods of ESA Advanced Concepts Team and JAXA-ISAS [CL]

We consider the interplanetary trajectory design problem posed by the 8th edition of the Global Trajectory Optimization Competition and present the end-to-end strategy developed by the team ACT-ISAS (a collaboration between the European Space Agency’s Advanced Concepts Team and JAXA’s Institute of Space and Astronautical Science). The resulting interplanetary trajectory won 1st place in the competition, achieving a final mission value of $J=146.33$ [Mkm]. Several new algorithms were developed in this context but have an interest that go beyond the particular problem considered, thus, they are discussed in some detail. These include the Moon-targeting technique, allowing one to target a Moon encounter from a low Earth orbit; the 1-$k$ and 2-$k$ fly-by targeting techniques, enabling one to design resonant fly-bys while ensuring a targeted future formation plane% is acquired at some point after the manoeuvre ; the distributed low-thrust targeting technique, admitting one to control the spacecraft formation plane at 1,000,000 [km]; and the low-thrust optimization technique, permitting one to enforce the formation plane’s orientations as path constraints.

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D. Izzo, D. Hennes, M. Martens, et. al.
Wed, 3 Feb 16

Comments: Presented at the 26th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA

An Integer Linear Programming Solution to the Telescope Network Scheduling Problem [IMA]

Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of scheduling them completely or even semi-manually disappears. In an earlier paper, a step towards software telescope scheduling was made with the specification of the Reservation formalism, through the use of which astronomers can express their complex observation needs and preferences. In this paper we build on that work. We present a solution to the discretized version of the problem of scheduling a telescope network. We derive a solvable integer linear programming (ILP) model based on the Reservation formalism. We show computational results verifying its correctness, and confirm that our Gurobi-based implementation can address problems of realistic size. Finally, we extend the ILP model to also handle the novel observation requests that can be specified using the more advanced Compound Reservation formalism.

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S. Lampoudi, E. Saunders and J. Eastman
Thu, 26 Mar 15

Comments: Accepted for publication in the refereed conference proceedings of the International Conference on Operations Research and Enterprise Systems (ICORES 2015)