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O. Fors, A. Richichi, Xavier Otazu, & J. Nuñez. (2008). A new wavelet-based approach for the automated treatment of large sets of lunar occultation data. Astronomy and Astrohysics, 297–304.
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Olivier Penacchio. (2011). Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane. MN - Mathematische Nachrichten, 284(4), 526–542.
Abstract: We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords: Mixed Hodge structures, equivariant sheaves, MSC (2010) Primary: 14C30, Secondary: 14F05, 14M25
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T. Widemann, & Xavier Otazu. (2009). Titanias radius and an upper limit on its atmosphere from the September 8, 2001 stellar occultation. International Journal of Solar System Studies, 199(2), 458–476.
Abstract: On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V=7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: View the MathML source (1-σ error bar). This implies a density of View the MathML source using the value View the MathML source derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362–374]. We do not detect any significant difference between equatorial and polar radii, in the limit View the MathML source, in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: ΔαTcos(δT)=−108±13 mas and ΔδT=−62±7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: View the MathML source and ΔδU=−85±25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of ΔαTcos(δT)=−127±20 mas and ΔδT=−97±13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10–20 nbar. More specifically, we find an upper limit of 13 nbar (1-σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO2 atmosphere. We also provide an upper limit of 8 nbar for a possible CH4 atmosphere, and 22 nbar for pure N2, again at the 1-σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54±0.03 mas (corresponding to View the MathML source projected at Titania). With a distance of 170±25 parsecs, this corresponds to a radius of 9.8±0.2 solar radii for HIP 106829, typical of a K0 III giant.
Keywords: Occultations; Uranus, satellites; Satellites, shapes; Satellites, dynamics; Ices; Satellites, atmospheres
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Ivet Rafegas, & Maria Vanrell. (2018). Color encoding in biologically-inspired convolutional neural networks. VR - Vision Research, 151, 7–17.
Abstract: Convolutional Neural Networks have been proposed as suitable frameworks to model biological vision. Some of these artificial networks showed representational properties that rival primate performances in object recognition. In this paper we explore how color is encoded in a trained artificial network. It is performed by estimating a color selectivity index for each neuron, which allows us to describe the neuron activity to a color input stimuli. The index allows us to classify whether they are color selective or not and if they are of a single or double color. We have determined that all five convolutional layers of the network have a large number of color selective neurons. Color opponency clearly emerges in the first layer, presenting 4 main axes (Black-White, Red-Cyan, Blue-Yellow and Magenta-Green), but this is reduced and rotated as we go deeper into the network. In layer 2 we find a denser hue sampling of color neurons and opponency is reduced almost to one new main axis, the Bluish-Orangish coinciding with the dataset bias. In layers 3, 4 and 5 color neurons are similar amongst themselves, presenting different type of neurons that detect specific colored objects (e.g., orangish faces), specific surrounds (e.g., blue sky) or specific colored or contrasted object-surround configurations (e.g. blue blob in a green surround). Overall, our work concludes that color and shape representation are successively entangled through all the layers of the studied network, revealing certain parallelisms with the reported evidences in primate brains that can provide useful insight into intermediate hierarchical spatio-chromatic representations.
Keywords: Color coding; Computer vision; Deep learning; Convolutional neural networks
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Ivet Rafegas, Maria Vanrell, Luis A Alexandre, & G. Arias. (2020). Understanding trained CNNs by indexing neuron selectivity. PRL - Pattern Recognition Letters, 136, 318–325.
Abstract: The impressive performance of Convolutional Neural Networks (CNNs) when solving different vision problems is shadowed by their black-box nature and our consequent lack of understanding of the representations they build and how these representations are organized. To help understanding these issues, we propose to describe the activity of individual neurons by their Neuron Feature visualization and quantify their inherent selectivity with two specific properties. We explore selectivity indexes for: an image feature (color); and an image label (class membership). Our contribution is a framework to seek or classify neurons by indexing on these selectivity properties. It helps to find color selective neurons, such as a red-mushroom neuron in layer Conv4 or class selective neurons such as dog-face neurons in layer Conv5 in VGG-M, and establishes a methodology to derive other selectivity properties. Indexing on neuron selectivity can statistically draw how features and classes are represented through layers in a moment when the size of trained nets is growing and automatic tools to index neurons can be helpful.
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