On the Infinite Dual Goldie Dimension

We analyze how the properties of Goldie dimension continue to hold or not in the infinite case, with particular interest for the dual Goldie dimension of the lattice of right ideals of a ring R. In this setting we underline the important role played by maximal ideals and we compute the dual Goldie dimension of any Boolean ring and of any endomorphism ring of an infinite dimensional vector space over a division ring

Nonparametric ridge estimation

We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249-1286]. Some numerical experiments verify that the algorithm is accurate.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1218 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spinal cord gray matter segmentation using deep dilated convolutions

Gray matter (GM) tissue changes have been associated with a wide range of neurological disorders and was also recently found relevant as a biomarker for disability in amyotrophic lateral sclerosis. The ability to automatically segment the GM is, therefore, an important task for modern studies of the spinal cord. In this work, we devise a modern, simple and end-to-end fully automated human spinal cord gray matter segmentation method using Deep Learning, that works both on in vivo and ex vivo MRI acquisitions. We evaluate our method against six independently developed methods on a GM segmentation challenge and report state-of-the-art results in 8 out of 10 different evaluation metrics as well as major network parameter reduction when compared to the traditional medical imaging architectures such as U-Nets.Comment: 13 pages, 8 figure

Nonparametric Inference For Density Modes

We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified using the first half of the data and inference is done with the second half of the data. To get valid confidence sets for the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial (ESP) transformation. This leads to valid bootstrap confidence sets regardless of any multiplicities in the eigenvalues. We also suggest a new method for bandwidth selection, namely, choosing the bandwidth to maximize the number of significant modes. We show by example that this method works well. Even when the true distribution is singular, and hence does not have a density, (in which case cross validation chooses a zero bandwidth), our method chooses a reasonable bandwidth

AxonDeepSeg: automatic axon and myelin segmentation from microscopy data using convolutional neural networks

Segmentation of axon and myelin from microscopy images of the nervous system provides useful quantitative information about the tissue microstructure, such as axon density and myelin thickness. This could be used for instance to document cell morphometry across species, or to validate novel non-invasive quantitative magnetic resonance imaging techniques. Most currently-available segmentation algorithms are based on standard image processing and usually require multiple processing steps and/or parameter tuning by the user to adapt to different modalities. Moreover, only few methods are publicly available. We introduce AxonDeepSeg, an open-source software that performs axon and myelin segmentation of microscopic images using deep learning. AxonDeepSeg features: (i) a convolutional neural network architecture; (ii) an easy training procedure to generate new models based on manually-labelled data and (iii) two ready-to-use models trained from scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Results show high pixel-wise accuracy across various species: 85% on rat SEM, 81% on human SEM, 95% on mice TEM and 84% on macaque TEM. Segmentation of a full rat spinal cord slice is computed and morphological metrics are extracted and compared against the literature. AxonDeepSeg is freely available at https://github.com/neuropoly/axondeepsegComment: 14 pages, 7 figure

Impacts of Greenhouse and Local Gases Mitigation Options on Air Pollution in the Buenos Aires Metropolitan Area: Valuation of Human Health Effects

The objective of this work is to assess through the "avoided health cost method" what would be the economic benefits of undertaking greenhouse (and local) gases mitigation policies in the Buenos Aires Metropolitan Area. To do so, we have developed six steps: Mitigation Scenarios (which policies to undertake), Emissions Inventory according to those, an Ambient Air Pollution Model to calculate the physical impacts, Health Effects Estimation to assess the health consequences of reducing air pollution, and Economic Valuation of those health impacts. The mitigation measures valued have to do with the transportation sector (greater penetration of compressed natural gas, consumption improvements, and some mode substitution) and the energy sector (the introduction of new dams and the rational use of energy by reducing energy consumption in residential, commercial and public buildings). There are three scenarios: a Baseline or Business-as-Usual scenario, a scenario that considers GHG mitigation options for Argentina with impacts in terms of local pollution, and an Integrated scenario which in addition to GHG mitigation includes policies related to local air quality and rational use of energy programs. All scenarios were built up to the year 2012. Particulate matter is the pollutant whose impact is valued.