A likelihood method to cross-calibrate air-shower detectors

We present a detailed statistical treatment of the energy calibration of hybrid air-shower detectors, which combine a surface detector array and a fluorescence detector, to obtain an unbiased estimate of the calibration curve. The special features of calibration data from air showers prevent unbiased results, if a standard least-squares fit is applied to the problem. We develop a general maximum-likelihood approach, based on the detailed statistical model, to solve the problem. Our approach was developed for the Pierre Auger Observatory, but the applied principles are general and can be transferred to other air-shower experiments, even to the cross-calibration of other observables. Since our general likelihood function is expensive to compute, we derive two approximations with significantly smaller computational cost. In the recent years both have been used to calibrate data of the Pierre Auger Observatory. We demonstrate that these approximations introduce negligible bias when they are applied to simulated toy experiments, which mimic realistic experimental conditions.Comment: 10 pages, 7 figure

An apple-to-apple comparison of Learning-to-rank algorithms in terms of Normalized Discounted Cumulative Gain

International audienceThe Normalized Discounted Cumulative Gain (NDCG) is a widely used evaluation metric for learning-to-rank (LTR) systems. NDCG is designed for ranking tasks with more than one relevance levels. There are many freely available, open source tools for computing the NDCG score for a ranked result list. Even though the definition of NDCG is unambiguous, the various tools can produce different scores for ranked lists with certain properties, deteriorating the empirical tests in many published papers and thereby making the comparison of empirical results published in different studies difficult to compare. In this study, first, we identify the major differences between the various publicly available NDCG evaluation tools. Second, based on a set of comparative experiments using a common benchmark dataset in LTR research and 6 different LTR algorithms, we demonstrate how these differences affect the overall performance of different algorithms and the final scores that are used to compare different systems

Theoretical insights into the electronic structure of nickel(0)-diphosphine-carbon dioxide complexes

The coordination properties of carbon dioxide bound to Ni(0) with various phosphines have been inves- tigated by means of DFT calculations. Reasonable linear correlation has been found between Tolman’s electronic parameters (TEPs) and the asymmetric stretching frequency of the coordinated CO2. Two de- scriptors from EDA-NOCV calculations, namely the interaction energy and the Hirshfeld charge associated with the back donation component gave acceptable linear correlation as well with the TEPs. The coordination strength, as well as the C = O bond order in coordinated carbon dioxide can be tuned by varying the substituents on phosphorus: in the presence of electron withdrawing groups the C = O bond remains stronger and Ni-C interaction is weaker, moreover, a new Ni-O bond path is formed; whereas for more basic diphosphines the Ni –C bond order is higher and the coordinated carbon dioxide possess a weaker C = O bond

Elastic principal manifolds and their practical applications

Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through "the middle" of data distribution. We propose an algorithm for fast construction of grid approximations of principal manifolds with given topology. It is based on analogy of principal manifold and elastic membrane. The first advantage of this method is a form of the functional to be minimized which becomes quadratic at the step of the vertices position refinement. This makes the algorithm very effective, especially for parallel implementations. Another advantage is that the same algorithmic kernel is applied to construct principal manifolds of different dimensions and topologies. We demonstrate how flexibility of the approach allows numerous adaptive strategies like principal graph constructing, etc. The algorithm is implemented as a C++ package elmap and as a part of stand-alone data visualization tool VidaExpert, available on the web. We describe the approach and provide several examples of its application with speed performance characteristics.Comment: 26 pages, 10 figures, edited final versio

Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization

Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing non-linear principal manifolds were proposed, including our elastic maps approach which is based on a physical analogy with elastic membranes. We have developed a general geometric framework for constructing ``principal objects'' of various dimensions and topologies with the simplest quadratic form of the smoothness penalty which allows very effective parallel implementations. Our approach is implemented in three programming languages (C++, Java and Delphi) with two graphical user interfaces (VidaExpert http://bioinfo.curie.fr/projects/vidaexpert and ViMiDa http://bioinfo-out.curie.fr/projects/vimida applications). In this paper we overview the method of elastic maps and present in detail one of its major applications: the visualization of microarray data in bioinformatics. We show that the method of elastic maps outperforms linear PCA in terms of data approximation, representation of between-point distance structure, preservation of local point neighborhood and representing point classes in low-dimensional spaces.Comment: 35 pages 10 figure

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-

Operations of and Future Plans for the Pierre Auger Observatory

Technical reports on operations and features of the Pierre Auger Observatory, including ongoing and planned enhancements and the status of the future northern hemisphere portion of the Observatory. Contributions to the 31st International Cosmic Ray Conference, Lodz, Poland, July 2009.Comment: Contributions to the 31st ICRC, Lodz, Poland, July 200

A search for point sources of EeV photons

Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10^17.3 eV to 10^18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm^-2 s^-1, and no celestial direction exceeds 0.25 eV cm^-2 s^-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.Comment: 28 pages, 10 figures, accepted for publication in The Astrophysical Journa

The Pierre Auger Observatory III: Other Astrophysical Observations

Astrophysical observations of ultra-high-energy cosmic rays with the Pierre Auger ObservatoryComment: Contributions to the 32nd International Cosmic Ray Conference, Beijing, China, August 201