Iterative estimation of mutual information with error bounds

Mutual Information (MI) is an established measure for linear and nonlinear dependencies between two variables. Estimating MI is nontrivial and requires notable computation power for high estimation quality. While some estimation techniques allow trading result quality for lower runtimes, this tradeoff is fixed per task and cannot be adjusted. If the available time is unknown in advance or is overestimated, one may need to abort the estimation without any result. Conversely, when there are several estimation tasks, and one wants to budget computation time between them, there currently is no efficient way to adjust it dynamically based on certain targets, e.g., high MI values or MI values close to a constant. In this article, we present an iterative estimator of MI. Our method offers an estimate with low quality near-instantly and improves this estimate in fine grained steps with more computation time. The estimate also converges towards the result of a conventional estimator. We prove that the time complexity for this convergence is only slightly slower than non-iterative estimation. Additionally, with each step our estimator also tightens statistical guarantees regarding the convergence result, i.e., confidence intervals, progressively. These also serve as quality indicators for early estimates and allow to reliably discern between attribute pairs with weak and strong dependencies. Our experiments show that these guarantees can also be used to execute threshold queries faster compared to non-iterative estimation

Deriving Bounds on the Size of Spatial Areas

Many application domains such as surveillance, environmental monitoring or sensor-data processing need upper and lower bounds on areas that are covered by a certain feature. For example, a smart-city infrastructure might need bounds on the size of an area polluted with fine-dust, to re-route combustion-engine traffic. Obtaining such bounds is challenging, because in almost any real-world application, information about the region of interest is incomplete, e.g., the database of sensor data contains only a limited number of samples. Existing approaches cannot provide upper and lower bounds or depend on restrictive assumptions, e.g., the area must be convex. Our approach in turn is based on the natural assumption that it is possible to specify a minimal diameter for the feature in question. Given this assumption, we formally derive bounds on the area size, and we provide algorithms that compute these bounds from a database of sensor data, based on geometrical considerations. We evaluate our algorithms both with a real-world case study and with synthetic data

NLTE effects on Fe I/II in the atmospheres of FGK stars and application to abundance analysis of their spectra

We describe the first results from our project aimed at large-scale calculations of NLTE abundance corrections for important astrophysical atoms and ions. In this paper, the focus is on Fe which is a proxy of stellar metallicity and is commonly used to derive effective temperature and gravity. We present a small grid of NLTE abundance corrections for Fe I lines and discuss how NLTE effects influence determination of effective temperature, surface gravity, and metallicity for late-type stars.Comment: 6 pages, to be published in IOP The Journal of Physics: Conference Series, proceedings of the Workshop: 'Stellar Atmospheres in the Gaia Era: Quantitative Spectroscopy and Comparative Spectrum Modelling', Brussels, June 201

Robust Multi-Image HDR Reconstruction for the Modulo Camera

Photographing scenes with high dynamic range (HDR) poses great challenges to consumer cameras with their limited sensor bit depth. To address this, Zhao et al. recently proposed a novel sensor concept - the modulo camera - which captures the least significant bits of the recorded scene instead of going into saturation. Similar to conventional pipelines, HDR images can be reconstructed from multiple exposures, but significantly fewer images are needed than with a typical saturating sensor. While the concept is appealing, we show that the original reconstruction approach assumes noise-free measurements and quickly breaks down otherwise. To address this, we propose a novel reconstruction algorithm that is robust to image noise and produces significantly fewer artifacts. We theoretically analyze correctness as well as limitations, and show that our approach significantly outperforms the baseline on real data.Comment: to appear at the 39th German Conference on Pattern Recognition (GCPR) 201

Hysteresis of Backflow Imprinted in Collimated Jets

We report two different types of backflow from jets by performing 2D special relativistic hydrodynamical simulations. One is anti-parallel and quasi-straight to the main jet (quasi-straight backflow), and the other is bent path of the backflow (bent backflow). We find that the former appears when the head advance speed is comparable to or higher than the local sound speed at the hotspot while the latter appears when the head advance speed is slower than the sound speed bat the hotspot. Bent backflow collides with the unshocked jet and laterally squeezes the jet. At the same time, a pair of new oblique shocks are formed at the tip of the jet and new bent fast backflows are generated via these oblique shocks. The hysteresis of backflow collisions is thus imprinted in the jet as a node and anti-node structure. This process also promotes broadening of the jet cross sectional area and it also causes a decrease in the head advance velocity. This hydrodynamic process may be tested by observations of compact young jets.Comment: 9 pages, 5 figures, accepted for publication in ApJ

Secrecy and performance models for query processing on outsourced graph data

Database outsourcing is a challenge concerning data secrecy. Even if an adversary, including the service provider, accesses the data, she should not be able to learn any information from the accessed data. In this paper, we address this problem for graph-structured data. First, we define a secrecy notion for graph-structured data based on the concepts of indistinguishability and searchable encryption. To address this problem, we propose an approach based on bucketization. Next to bucketization, it makes use of obfuscated indexes and encryption. We show that finding an optimal bucketization tailored to graph-structured data is NP-hard; therefore, we come up with a heuristic. We prove that the proposed bucketization approach fulfills our secrecy notion. In addition, we present a performance model for scale-free networks which consists of (1) a number-of-buckets model that estimates the number of buckets obtained after applying our bucketization approach and (2) a query-cost model. Finally, we demonstrate with a set of experiments the accuracy of our number-of-buckets model and the efficiency of our approach with respect to query processing

The Enigmatic HH 255

To gain insight into the nature of the peculiar Herbig-Haro object HH 255 (also called Burnham's nebula), we use previously published observations to derive information about the emission line fluxes as a function of position within HH 255 and compare them with the well-studied, and relatively well-behaved bow shock HH 1. There are some qualitative similarities in the H$\alpha$ and [O III] 5007 lines in both objects. However, in contrast to the expectation of the standard bow shock model, the fluxes of the [O I] 6300, [S II] 6731, and [N II] 6583 lines are essentially constant along the axis of the flow, while the electron density decreases, over a large distance within HH 255. We also explore the possibility that HH 255 represents the emission behind a standing or quasi-stationary shock. The shock faces upwind, and we suggest, using theoretical arguments, that it may be associated with the collimation of the southern outflow from T Tauri. Using a simplified magnetohydrodynamic simulation to illustrate the basic concept, we demonstrate that the existence of such a shock at the north edge of HH 255 could indeed explain its unusual kinematic and ionization properties. Whether or not such a shock can explain the detailed emission line stratification remains an open question.Comment: Accepted by PASP, 12 pages including 8 figure