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

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

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

Product Differentiation Costs and Global Competition

The growing competitive intensity on the markets determines the emergence of competition costs that are expressed at a corporate level and have implicit repercussions for the supply system. This type of costs makes it possible to identify a close link between competition costs and supply differentiation costs. Classification by competitive intensity presupposes that the analysis performed identifies the classification of company costs as the discriminating element, in terms of the competitive pressure of the context in which the firm operates. The emergence of competition costs is linked to an attempt to squeeze them as an aspect of vertical, or more specifically, horizontal cooperation strategies.Product Differentiation; Differentiation Costs; Over-Supply; Global Competition; Marketing; Market-Driven Management; Global Corporations; Global Markets DOI:http://dx.doi.org/10.4468/2005.1.06garbelli