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Identifying complex sources in large astronomical data using a coarse-grained complexity measure

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 Added by David Parkinson
 Publication date 2018
  fields Physics
and research's language is English




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The volume of data that will be produced by the next generation of astrophysical instruments represents a significant opportunity for making unplanned and unexpected discoveries. Conversely, finding unexpected objects or phenomena within such large volumes of data presents a challenge that may best be solved using computational and statistical approaches. We present the application of a coarse-grained complexity measure for identifying interesting observations in large astronomical data sets. This measure, which has been termed apparent complexity, has been shown to model human intuition and perceptions of complexity. Apparent complexity is computationally efficient to derive and can be used to segment and identify interesting observations in very large data sets based on their morphological complexity. We show, using data from the Australia Telescope Large Area Survey, that apparent complexity can be combined with clustering methods to provide an automated process for distinguishing between images of galaxies which have been classified as having simple and complex morphologies. The approach generalizes well when applied to new data after being calibrated on a smaller data set, where it performs better than tested classification methods using pixel data. This generalizability positions apparent complexity as a suitable machine-learning feature for identifying complex observations with unanticipated features.



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To date, the only way to argue polynomial lower bounds for dynamic algorithms is via fine-grained complexity arguments. These arguments rely on strong assumptions about specific problems such as the Strong Exponential Time Hypothesis (SETH) and the Online Matrix-Vector Multiplication Conjecture (OMv). While they have led to many exciting discoveries, dynamic algorithms still miss out some benefits and lessons from the traditional ``coarse-grained approach that relates together classes of problems such as P and NP. In this paper we initiate the study of coarse-grained complexity theory for dynamic algorithms. Below are among questions that this theory can answer. What if dynamic Orthogonal Vector (OV) is easy in the cell-probe model? A research program for proving polynomial unconditional lower bounds for dynamic OV in the cell-probe model is motivated by the fact that many conditional lower bounds can be shown via reductions from the dynamic OV problem. Since the cell-probe model is more powerful than word RAM and has historically allowed smaller upper bounds, it might turn out that dynamic OV is easy in the cell-probe model, making this research direction infeasible. Our theory implies that if this is the case, there will be very interesting algorithmic consequences: If dynamic OV can be maintained in polylogarithmic worst-case update time in the cell-probe model, then so are several important dynamic problems such as $k$-edge connectivity, $(1+epsilon)$-approximate mincut, $(1+epsilon)$-approximate matching, planar nearest neighbors, Chans subset union and 3-vs-4 diameter. The same conclusion can be made when we replace dynamic OV by, e.g., subgraph connectivity, single source reachability, Chans subset union, and 3-vs-4 diameter. Lower bounds for $k$-edge connectivity via dynamic OV? (see the full abstract in the pdf file).
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