Search results for " statistics"
showing 10 items of 1891 documents
On the fusion problem for degenerate elliptic equations
1995
Let F be a relatively closed subset of a Euclidean domain Ω. We investigate when solutions u to certain elliptic equations on Ω/F are restrictions of solutions on all of Ω. Specifically, we show that if ∂F is not too large, and u has a suitable decay rate near F, then u can be so extended.
Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering
2017
Clustering is an unsupervised machine learning and pattern recognition method. In general, in addition to revealing hidden groups of similar observations and clusters, their number needs to be determined. Internal clustering validation indices estimate this number without any external information. The purpose of this article is to evaluate, empirically, characteristics of a representative set of internal clustering validation indices with many datasets. The prototype-based clustering framework includes multiple, classical and robust, statistical estimates of cluster location so that the overall setting of the paper is novel. General observations on the quality of validation indices and on t…
The ALHAMBRA survey: reliable morphological catalogue of 22 051 early- and late-type galaxies
2013
Advanced Large Homogeneous Area Medium Band Redshift Astronomical (ALHAMBRA) is photometric survey designed to trace the cosmic evolution and cosmic variance. It covers a large area of ~4 deg2 in eight fields, where seven fields overlap with other surveys, allowing us to have complementary data in other wavelengths. All observations were carried out in 20 continuous, medium band (30 nm width) optical and 3 near-infrared (JHK) bands, providing the precise measurements of photometric redshifts. In addition, morphological classification of galaxies is crucial for any kind of galaxy formation and cosmic evolution studies, providing the information about star formation histories, their environme…
The ALHAMBRA survey: An empirical estimation of the cosmic variance for merger fraction studies based on close pairs
2014
[Aims]: Our goal is to estimate empirically the cosmic variance that affects merger fraction studies based on close pairs for the first time. [Methods]: We compute the merger fraction from photometric redshift close pairs with 10 h−1 kpc ≤ rp ≤ 50 h−1 kpc and Δv ≤ 500 km s−1 and measure it in the 48 sub-fields of the ALHAMBRA survey. We study the distribution of the measured merger fractions that follow a log-normal function and estimate the cosmic variance σv as the intrinsic dispersion of the observed distribution. We develop a maximum likelihood estimator to measure a reliable σv and avoid the dispersion due to the observational errors (including the Poisson shot noise term). [Results]: …
The ALHAMBRA survey: accurate merger fractions derived by PDF analysis of photometrically close pairs
2015
[Aims]: Our goal is to develop and test a novel methodology to compute accurate close-pair fractions with photometric redshifts. [Methods]: We improved the currently used methodologies to estimate the merger fraction fm from photometric redshifts by (i) using the full probability distribution functions (PDFs) of the sources in redshift space; (ii) including the variation in the luminosity of the sources with z in both the sample selection and the luminosity ratio constrain; and (iii) splitting individual PDFs into red and blue spectral templates to reliably work with colour selections.We tested the performance of our new methodology with the PDFs provided by the ALHAMBRA photometric survey.…
Accurate representation of the distributions of the 3D Poisson-Voronoi typical cell geometrical features
2019
Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for ev…
Solutions for parametric double phase Robin problems
2021
We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .
Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate va…
2021
Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of ‘instantaneous’ effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index…
Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy
2020
A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x &isin
Random cutout sets with spatially inhomogeneous intensities
2015
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.