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Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling
Authors:
Euclid Collaboration,
G. Congedo,
L. Miller,
A. N. Taylor,
N. Cross,
C. A. J. Duncan,
T. Kitching,
N. Martinet,
S. Matthew,
T. Schrabback,
M. Tewes,
N. Welikala,
N. Aghanim,
A. Amara,
S. Andreon,
N. Auricchio,
M. Baldi,
S. Bardelli,
R. Bender,
C. Bodendorf,
D. Bonino,
E. Branchini,
M. Brescia,
J. Brinchmann,
S. Camera
, et al. (217 additional authors not shown)
Abstract:
LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies…
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LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. We quantified the scientific performance through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images; realistic clustering with a mean surface number density of 250 arcmin$^{-2}$ ($I_{\rm E}<29.5$) for galaxies, and 6 arcmin$^{-2}$ ($I_{\rm E}<26$) for stars; and a diffraction-limited chromatic PSF with a full width at half maximum of $0.^{\!\prime\prime}2$ and spatial variation across the field of view. LensMC measured objects with a density of 90 arcmin$^{-2}$ ($I_{\rm E}<26.5$) in 4500 deg$^2$. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We found measurement multiplicative and additive biases of $m_1=(-3.6\pm0.2)\times10^{-3}$, $m_2=(-4.3\pm0.2)\times10^{-3}$, $c_1=(-1.78\pm0.03)\times10^{-4}$, $c_2=(0.09\pm0.03)\times10^{-4}$; a large detection bias with a multiplicative component of $1.2\times10^{-2}$ and an additive component of $-3\times10^{-4}$; and a measurement PSF leakage of $α_1=(-9\pm3)\times10^{-4}$ and $α_2=(2\pm3)\times10^{-4}$. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies ($-5\times10^{-3}$). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at https://gitlab.com/gcongedo/LensMC
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Submitted 2 December, 2024; v1 submitted 1 May, 2024;
originally announced May 2024.
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The temporalized Massey's method
Authors:
Massimo Franceschet,
Enrico Bozzo
Abstract:
We propose and throughly investigate a temporalized version of the popular Massey's technique for rating actors in sport competitions. The method can be described as a dynamic temporal process in which team ratings are updated at every match according to their performance during the match and the strength of the opponent team. Using the Italian soccer dataset, we empirically show that the method h…
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We propose and throughly investigate a temporalized version of the popular Massey's technique for rating actors in sport competitions. The method can be described as a dynamic temporal process in which team ratings are updated at every match according to their performance during the match and the strength of the opponent team. Using the Italian soccer dataset, we empirically show that the method has a good foresight prediction accuracy.
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Submitted 2 February, 2017;
originally announced February 2017.
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The Massey's method for sport rating: a network science perspective
Authors:
Massimo Franceschet,
Enrico Bozzo
Abstract:
We revisit the Massey's method for rating and ranking in sports and contextualize it as a general centrality measure in network science.
We revisit the Massey's method for rating and ranking in sports and contextualize it as a general centrality measure in network science.
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Submitted 12 January, 2017;
originally announced January 2017.
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Arbitrarily regularizable graphs
Authors:
Massimo Franceschet,
Enrico Bozzo
Abstract:
A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative regularizable graphs have been thoroughly investigated in the literature. In this work, we propose and study arbitrarily regularizable graphs. In particular, we…
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A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative regularizable graphs have been thoroughly investigated in the literature. In this work, we propose and study arbitrarily regularizable graphs. In particular, we investigate necessary and sufficient regularization conditions on the topology of the graph and of the corresponding adjacency matrix. Moreover, we study the computational complexity of the regularization problem and characterize it as a linear programming model.
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Submitted 30 June, 2017; v1 submitted 23 August, 2016;
originally announced August 2016.
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A theory on power in networks
Authors:
Massimo Franceschet,
Enrico Bozzo
Abstract:
The eigenvector centrality equation $λx = A \, x$ is a successful compromise between simplicity and expressivity. It claims that central actors are those connected with central others. For at least 70 years, this equation has been explored in disparate contexts, including econometrics, sociometry, bibliometrics, Web information retrieval, and network science. We propose an equally elegant counterp…
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The eigenvector centrality equation $λx = A \, x$ is a successful compromise between simplicity and expressivity. It claims that central actors are those connected with central others. For at least 70 years, this equation has been explored in disparate contexts, including econometrics, sociometry, bibliometrics, Web information retrieval, and network science. We propose an equally elegant counterpart: the power equation $x = A x^÷$, where $x^÷$ is the vector whose entries are the reciprocal of those of $x$. It asserts that power is in the hands of those connected with powerless others. It is meaningful, for instance, in bargaining situations, where it is advantageous to be connected to those who have few options. We tell the parallel, mostly unexplored story of this intriguing equation.
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Submitted 10 March, 2016; v1 submitted 28 October, 2015;
originally announced October 2015.
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The effect of the displacement damage on the Charge Collection Efficiency in Silicon Drift Detectors for the LOFT satellite
Authors:
E. Del Monte,
Y. Evangelista,
E. Bozzo,
F. Cadoux,
A. Rachevski,
G. Zampa,
N. Zampa,
M. Feroci,
M. Pohl,
A. Vacchi
Abstract:
The technology of Silicon Drift Detectors (SDDs) has been selected for the two instruments aboard the Large Observatory For X-ray Timing (LOFT) space mission. LOFT underwent a three year long assessment phase as candidate for the M3 launch opportunity within the "Cosmic Vision 2015 -- 2025" long-term science plan of the European Space Agency. During the LOFT assessment phase, we studied the displa…
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The technology of Silicon Drift Detectors (SDDs) has been selected for the two instruments aboard the Large Observatory For X-ray Timing (LOFT) space mission. LOFT underwent a three year long assessment phase as candidate for the M3 launch opportunity within the "Cosmic Vision 2015 -- 2025" long-term science plan of the European Space Agency. During the LOFT assessment phase, we studied the displacement damage produced in the SDDs by the protons trapped in the Earth's magnetosphere. In a previous paper we discussed the effects of the Non Ionising Energy Losses from protons on the SDD leakage current. In this paper we report the measurement of the variation of Charge Collection Efficiency produced by displacement damage caused by protons and the comparison with the expected damage in orbit.
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Submitted 26 March, 2015;
originally announced March 2015.
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Radiation tests of the Silicon Drift Detectors for LOFT
Authors:
E. Del Monte,
P. Azzarello,
E. Bozzo,
S. Bugiel,
S. Diebold,
Y. Evangelista,
E. Kendziorra,
F. Muleri,
E. Perinati,
A. Rachevski,
G. Zampa,
N. Zampa,
M. Feroci,
M. Pohl,
A. Santangelo,
A. Vacchi
Abstract:
During the three years long assessment phase of the LOFT mission, candidate to the M3 launch opportunity of the ESA Cosmic Vision programme, we estimated and measured the radiation damage of the silicon drift detectors (SDDs) of the satellite instrumentation. In particular, we irradiated the detectors with protons (of 0.8 and 11 MeV energy) to study the increment of leakage current and the variati…
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During the three years long assessment phase of the LOFT mission, candidate to the M3 launch opportunity of the ESA Cosmic Vision programme, we estimated and measured the radiation damage of the silicon drift detectors (SDDs) of the satellite instrumentation. In particular, we irradiated the detectors with protons (of 0.8 and 11 MeV energy) to study the increment of leakage current and the variation of the charge collection efficiency produced by the displacement damage, and we "bombarded" the detectors with hypervelocity dust grains to measure the effect of the debris impacts. In this paper we describe the measurements and discuss the results in the context of the LOFT mission.
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Submitted 27 August, 2014;
originally announced August 2014.
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Measurement of the effect of Non Ionising Energy Losses on the leakage current of Silicon Drift Detector prototypes for the LOFT satellite
Authors:
E. Del Monte,
A. Rachevski,
G. Zampa,
N. Zampa,
P. Azzarello,
E. Bozzo,
R. Campana,
S. Diebold,
Y. Evangelista,
E. Perinati,
M. Feroci,
M. Pohl,
A. Vacchi
Abstract:
The silicon drift detectors are at the basis of the instrumentation aboard the Large Observatory For x-ray Timing (LOFT) satellite mission, which underwent a three year assessment phase within the "Cosmic Vision 2015 - 2025" long-term science plan of the European Space Agency. Silicon detectors are especially sensitive to the displacement damage, produced by the non ionising energy losses of charg…
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The silicon drift detectors are at the basis of the instrumentation aboard the Large Observatory For x-ray Timing (LOFT) satellite mission, which underwent a three year assessment phase within the "Cosmic Vision 2015 - 2025" long-term science plan of the European Space Agency. Silicon detectors are especially sensitive to the displacement damage, produced by the non ionising energy losses of charged and neutral particles, leading to an increase of the device leakage current and thus worsening the spectral resolution.
During the LOFT assessment phase, we irradiated two silicon drift detectors with a proton beam at the Proton Irradiation Facility in the accelerator of the Paul Scherrer Institute and we measured the increase in leakage current. In this paper we report the results of the irradiation and we discuss the impact of the radiation damage on the LOFT scientific performance.
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Submitted 24 June, 2014; v1 submitted 21 May, 2014;
originally announced May 2014.
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Vulnerability and power on networks
Authors:
Enrico Bozzo,
Massimo Franceschet,
Franca Rinaldi
Abstract:
Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fr…
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Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fresh notions of vulnerability and power at node level defined in terms of the corresponding measures at group level. We investigate the computational complexity of computing the defined measures, both at group and node levels, and provide effective methods to quantify them. Finally we test vulnerability and power on both artificial and real networks.
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Submitted 19 December, 2014; v1 submitted 19 December, 2013;
originally announced December 2013.
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Accelerator experiments with soft protons and hyper-velocity dust particles: application to ongoing projects of future X-ray missions
Authors:
E. Perinati,
S. Diebold,
E. Kendziorra,
A. Santangelo,
C. Tenzer,
J. Jochum,
S. Bugiel,
R. Srama,
E. Del Monte,
M. Feroci,
A. Rubini,
A. Rachevski,
G. Zampa,
N. Zampa,
I. Rashevskaya,
A. Vacchi,
P. Azzarello,
E. Bozzo,
J. -W. den Herder,
S. Zane,
S. Brandt,
M. Hernanz,
M. A. Leutenegger,
R. L. Kelley,
C. A. Kilbourne
, et al. (9 additional authors not shown)
Abstract:
We report on our activities, currently in progress, aimed at performing accelerator experiments with soft protons and hyper-velocity dust particles. They include tests of different types of X-ray detectors and related components (such as filters) and measurements of scattering of soft protons and hyper-velocity dust particles off X-ray mirror shells. These activities have been identified as a goal…
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We report on our activities, currently in progress, aimed at performing accelerator experiments with soft protons and hyper-velocity dust particles. They include tests of different types of X-ray detectors and related components (such as filters) and measurements of scattering of soft protons and hyper-velocity dust particles off X-ray mirror shells. These activities have been identified as a goal in the context of a number of ongoing space projects in order to assess the risk posed by environmental radiation and dust and qualify the adopted instrumentation with respect to possible damage or performance degradation. In this paper we focus on tests for the Silicon Drift Detectors (SDDs) used aboard the LOFT space mission. We use the Van de Graaff accelerators at the University of Tübingen and at the Max Planck Institute for Nuclear Physics (MPIK) in Heidelberg, for soft proton and hyper-velocity dust tests respectively. We present the experimental set-up adopted to perform the tests, status of the activities and some very preliminary results achieved at present time.
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Submitted 14 September, 2012;
originally announced September 2012.
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Effective and efficient approximations of the generalized inverse of the graph Laplacian matrix with an application to current-flow betweenness centrality
Authors:
Enrico Bozzo,
Massimo Franceschet
Abstract:
We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which is resource demanding in terms of consumed time and memory and hence impractical whenever the graph is relatively large. Our approximations use only few eigenp…
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We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which is resource demanding in terms of consumed time and memory and hence impractical whenever the graph is relatively large. Our approximations use only few eigenpairs of the Laplacian matrix and are parametric with respect to this number, so that the user can compromise between effectiveness and efficiency of the approximated solution. We apply the devised approximations to the problem of computing current-flow betweenness centrality on a graph. However, given the generality of the Laplacian matrix, many other applications can be sought. We experimentally demonstrate that the approximations are effective already with a constant number of eigenpairs. These few eigenpairs can be stored with a linear amount of memory in the number of nodes of the graph and, in the realistic case of sparse networks, they can be efficiently computed using one of the many methods for retrieving few eigenpairs of sparse matrices that abound in the literature.
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Submitted 22 May, 2012;
originally announced May 2012.