2,394 research outputs found
Measurement dependent locality
The demonstration and use of Bell-nonlocality, a concept that is
fundamentally striking and is at the core of applications in device independent
quantum information processing, relies heavily on the assumption of measurement
independence, also called the assumption of free choice. The latter cannot be
verified or guaranteed. In this paper, we consider a relaxation of the
measurement independence assumption. We briefly review the results of Phys.
Rev. Lett. 113, 190402 (2014), which show that with our relaxation, the set of
so-called measurement dependent local (MDL) correlations is a polytope, i.e. it
can be fully described using a finite set of linear inequalities. Here we
analyze this polytope, first in the simplest case of 2 parties with binary
inputs and outputs, for which we give a full characterization. We show that
partially entangled states are preferable to the maximally entangled state when
dealing with measurement dependence in this scenario. We further present a
method which transforms any Bell-inequality into an MDL inequality and give
valid inequalities for the case of arbitrary number of parties as well as one
for arbitrary number of inputs. We introduce the assumption of independent
sources in the measurement dependence scenario and give a full analysis for the
bipartite scenario with binary inputs and outputs. Finally, we establish a link
between measurement dependence and another strong hindrance in certifying
nonlocal correlations: nondetection events.Comment: 16+7 pages, 2 figure
Spatial Smoothing for Diffusion Tensor Imaging with low Signal to Noise Ratios
Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for different DTI variables in low SNR situations. Based on this study a strategy for spatial smoothing, which demands essentially uniform noise, is derived. To construct a convenient filter the weights of the nonlinear Aurich chain are adapted to DTI. This edge preserving three dimensional filter is then validated in different variants via a quasi realistic model and is applied to very new data with isotropic voxels of the size 1x1x1 mm3 which correspond to a spatial mean SNR of approximately 3
DTI denoising for data with low signal to noise ratios
Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1×1×1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable
La Ley valenciana de Uniones de Hecho a la luz del art. 149.1.8. CE
Ley valenciana 1/2001, de 6 de abril, por la que se regulan las uniones de hecho, publicada en el Diari Oficial de la Generalitat Valenciana (DOGV), núm. 3.978, 11 de abril de 2011, pp. 7871 y ss
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