Multiscale Geometric Methods for Data Sets I: Multiscale SVD, Noise and Curvature

Large data sets are often modeled as being noisy samples from probability distributions in R^D, with D large. It has been noticed that oftentimes the support M of these probability distributions seems to be well-approximated by low-dimensional sets, perhaps even by manifolds. We shall consider sets that are locally well approximated by k-dimensional planes, with k << D, with k-dimensional manifolds isometrically embedded in R^D being a special case. Samples from this distribution; are furthermore corrupted by D-dimensional noise. Certain tools from multiscale geometric measure theory and harmonic analysis seem well-suited to be adapted to the study of samples from such probability distributions, in order to yield quantitative geometric information about them. In this paper we introduce and study multiscale covariance matrices, i.e. covariances corresponding to the distribution restricted to a ball of radius r, with a fixed center and varying r, and under rather general geometric assumptions we study how their empirical, noisy counterparts behave. We prove that in the range of scales where these covariance matrices are most informative, the empirical, noisy covariances are close to their expected, noiseless counterparts. In fact, this is true as soon as the number of samples in the balls where the covariance matrices are computed is linear in the intrinsic dimension of M. As an application, we present an algorithm for estimating the intrinsic dimension of M

The Impact of Model and Rainfall Forcing Errors on Characterizing Soil Moisture Uncertainty in Land Surface Modeling

The contribution of rainfall forcing errors relative to model (structural and parameter) uncertainty in the prediction of soil moisture is investigated by integrating the NASA Catchment Land Surface Model (CLSM), forced with hydro-meteorological data, in the Oklahoma region. Rainfall-forcing uncertainty is introduced using a stochastic error model that generates ensemble rainfall fields from satellite rainfall products. The ensemble satellite rain fields are propagated through CLSM to produce soil moisture ensembles. Errors in CLSM are modeled with two different approaches: either by perturbing model parameters (representing model parameter uncertainty) or by adding randomly generated noise (representing model structure and parameter uncertainty) to the model prognostic variables. Our findings highlight that the method currently used in the NASA GEOS-5 Land Data Assimilation System to perturb CLSM variables poorly describes the uncertainty in the predicted soil moisture, even when combined with rainfall model perturbations. On the other hand, by adding model parameter perturbations to rainfall forcing perturbations, a better characterization of uncertainty in soil moisture simulations is observed. Specifically, an analysis of the rank histograms shows that the most consistent ensemble of soil moisture is obtained by combining rainfall and model parameter perturbations. When rainfall forcing and model prognostic perturbations are added, the rank histogram shows a U-shape at the domain average scale, which corresponds to a lack of variability in the forecast ensemble. The more accurate estimation of the soil moisture prediction uncertainty obtained by combining rainfall and parameter perturbations is encouraging for the application of this approach in ensemble data assimilation systems

Model-Based Image Signal Processors via Learnable Dictionaries

Digital cameras transform sensor RAW readings into RGB images by means of their Image Signal Processor (ISP). Computational photography tasks such as image denoising and colour constancy are commonly performed in the RAW domain, in part due to the inherent hardware design, but also due to the appealing simplicity of noise statistics that result from the direct sensor readings. Despite this, the availability of RAW images is limited in comparison with the abundance and diversity of available RGB data. Recent approaches have attempted to bridge this gap by estimating the RGB to RAW mapping: handcrafted model-based methods that are interpretable and controllable usually require manual parameter fine-tuning, while end-to-end learnable neural networks require large amounts of training data, at times with complex training procedures, and generally lack interpretability and parametric control. Towards addressing these existing limitations, we present a novel hybrid model-based and data-driven ISP that builds on canonical ISP operations and is both learnable and interpretable. Our proposed invertible model, capable of bidirectional mapping between RAW and RGB domains, employs end-to-end learning of rich parameter representations, i.e. dictionaries, that are free from direct parametric supervision and additionally enable simple and plausible data augmentation. We evidence the value of our data generation process by extensive experiments under both RAW image reconstruction and RAW image denoising tasks, obtaining state-of-the-art performance in both. Additionally, we show that our ISP can learn meaningful mappings from few data samples, and that denoising models trained with our dictionary-based data augmentation are competitive despite having only few or zero ground-truth labels.Comment: AAAI 202

A new experimental snow avalanche test site at Seehore peak in Aosta Valley (NW Italian Alps) - Part II: Engineering aspects

The estimate of the effects produced by the impact of a snow avalanche against an obstacle is of the utmost importance in designing safe mountain constructions. For this purpose, an ad-hoc instrumented obstacle was designed and built in order to measure impact forces of small and medium snow avalanches at Seehore peak (NW Italian Alps). The structural design had to consider several specific and unusual demands dictated by the difficult environment. In this article, the new test facility is described from the engineering point of view, discussing the most important aspects of the analyzed problems which were solved before and after the construction. The performance of the instrumented obstacle in the first two operating seasons, and some proposals for future upgrading are eventually illustrate

Selection of new markers for animal by-products characterization by classical microscopy

The aim of this study was to identify possible markers to distinguish differences between land animals by using the microscopic method in association with computer image analysis. For this purpose bone fragments from poultry and mammals were obtained and analysed by microscopic method. Through a digital camera and an image analysis software 85 bone lacunae images have been processed and elaborated in order to obtain for each lacuna a monochrome mask on which several measurements were performed. Data were analysed by ANOVA and LDA. Results obtained in the present study indicated that of 32 descriptors processed by image analysis software, only 12 were significantly (P<0.001) different between mammalian and poultry. However, when morphometric measurements were analysed by LDA, 86% of lacunae were correctly classified into the animal class of origin (i.e. mammalian as mammalian and poultry as poultry). By contrast 14% of lacunae were incorrectly classified. In conclusion, data here presented indicate that some of descriptors used by image analysis appears promising not only for a reliable distinction between the different origins of animal meal at the level of vertebrate classes, but also for further characterisation and identification of processed animal proteins in animal feeds

Tuning Polyamidoamine Design to Increase Uptake and Efficacy of Ruthenium Complexes for Photodynamic Therapy

Nanomedicine holds great promises to change the way drugs are delivered to their target, owing to the use of nano-sized drug carriers capable to enter cells and be trafficked intracellularly via energy dependent pathways [1, 2]. This is very different from the way most drugs arrive to their target, often based simply on their solubility and partition coefficients in lipids and water. Despite some valuable successes, drug delivery remains rather challenging and several factors are still limiting its potential. Among such factors, it has emerged, for instance, that most nano-sized carriers entering cells via endocytosis are later trafficked along the endolysosomal pathway to the lysosomes, where the low pH and abundant proteases can degrade and destroy the internalised cargo. Strategies to escape the endosomes and lysosomes are being investigated. Among the many polymer species employed as drug delivery vectors, linear polyamidoamines (PAAs) are very interesting and promising materials. In this communication it will be presented a new polycationic PAA endowed with a luminescent Ru complex (Ru-PhenAN) and its ability to target the cell nucleus. It shows unique trafficking to the cell nucleus of all the treated cells, also at polymer doses as low as cytotoxicity is very low. Also, it will be shown the efficacy of Ru-PhenAN as photosensitizers for photodynamic therapy (PDT), a treatment of pathological conditions based on the photo-activation of a bioactive compound, which is not harmful in the absence of light irradiation [3]

Robotic modified radical hysterectomy with pelvic lymphadenectomy

Radical hysterectomy, the complete removal of a woman’s uterus, is usually performed via an abdominal incision that requires a 3–5 day hospital stay and a 6–8 week recovery period. Now, in a handful of hospitals around the world, new robotic technology allows doctors to perform this procedure through small incisions that require a recovery time of only one night in the hospital and a significantly shorter recovery period at home. Watch such a procedure being carried out at the European Institute of Oncology

PA6 and halloysite nanotubes composites with improved hydrothermal ageing resistance : role of filler physicochemical properties, functionalization and dispersion technique

Polyamide 6 (PA6) suffers from fast degradation in humid conditions due to hydrolysis of amide bonds, which limits its durability. The addition of nanotubular fillers represents a viable strategy for overcoming this issue, although the additive/polymer interface at high filler content can become privileged site for moisture accumulation. As a cost-effective and versatile material, halloysite nanotubes (HNT) were investigated to prepare PA6 nanocomposites with very low loadings (1-45% w/w). The roles of the physicochemical properties of two differently sourced HNT, of filler functionalization with (3-aminopropyl)triethoxysilane and of dispersion techniques (in situ polymerization vs. melt blending) were investigated. The aspect ratio (5 vs. 15) and surface charge (-31 vs.-59 mV) of the two HNT proved crucial in determining their distribution within the polymer matrix. In situ polymerization of functionalized HNT leads to enclosed and well-penetrated filler within the polymer matrix. PA6 nanocomposites crystal growth and nucleation type were studied according to Avrami theory, as well as the formation of different crystalline structures (\u3b1 and \u3b3 forms). After 1680 h of ageing, functionalized HNT reduced the diffusion of water into polymer, lowering water uptake after 600 h up to 90%, increasing the materials durability also regarding molecular weights and rheological behavior

Spectrum of turbulent Kelvin-waves cascade in superfluid helium

To explain the observed decay of superfluid turbulence at very low temperature, it has been proposed that a cascade of Kelvin waves (analogous to the classical Kolmogorov cascade) transfers kinetic energy to length scales which are small enough that sound can be radiated away. We report results of numerical simulations of the interaction of quantized vortex filaments. We observe the development of the Kelvin-waves cascade, and compute the statistics of the curvature, the amplitude spectrum (which we compare with competing theories) and the fractal dimension.Comment: 32 pages, 22 figure

Snow Avalanche Impact Measurements at the Seehore Test Site in Aosta Valley (NW Italian Alps)

In full-scale snow avalanche test sites, structures such as pylons, plates, or dams have been used to measure impact forces and pressures from avalanches. Impact pressures are of extreme importance when dealing with issues such as hazard mapping and the design of buildings exposed to avalanches. In this paper, we present the force measurements recorded for five selected avalanches that occurred at the Seehore test site in Aosta Valley (NW Italian Alps). The five avalanches were small to medium-sized and cover a wide range in terms of snow characteristics and flow dynamics. Our aim was to analyze the force and pressure measurements with respect to the avalanche characteristics. We measured pressures in the range of 2 to 30 kPa. Though without exhaustive measurements of the avalanche flows, we found indications of different flow regimes. For example, we could appreciate some differences in the vertical profile of the pressures recorded for wet dense avalanches and powder ones. Being aware of the fact that more complete measurements are necessary to fully describe the avalanche flows, we think that the data of the five avalanches triggered at the Seehore test site might add some useful information to the ongoing scientific discussion on avalanche flow regimes and impact pressure