Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Exploiting log files in video retrieval

While research into user-centered text retrieval is based on mature evaluation methodologies, user evaluation in multimedia retrieval is still in its infancy. User evaluations can be expensive and are also often non-repeatable. An alternative way of evaluating such systems is the use of simulations. In this poster, we present an evaluation methodology which is based on exploiting log files recorded from a user-study we conducted

Pilot study of vegetation in the Alchichica-Perote region by remote sensing

A study of the application of satellite images to the identification of vegetation in a small area corresponding to the arid zone of Veracruz and part of Puebla is presented. This study is accomplished by means of images from the LANDSAT satellite obtained on January 19 and May 23, 1973. The interpretation of the different maps is made on the basis of information from the data bank of the Flora de Veracruz program, and various surveys made by land and air

Static and Dynamic Nonlinearity of A/D Converters

The dynamic range of broadband digital system is mostly limited by harmonics and spurious arising from ADC nonlinearity. The nonlinearity may be described in several ways. The distinction between static and dynamic contributions has strong theoretical motivations but it is difficult to independently measure these contributions. A more practical approach is based upon analysis of the complex spectrum, which is well defined, easily measured, and may be used to optimize the ADC working point and to somehow characterize both static and dynamic nonlinearity. To minimize harmonics and spurious components we need a sufficient level of input noise (dither), which destroys the periodicity at multistage pipelined ADC, combined with a careful analysis of the different sources of nonlinearity

The Effects of Retrograde Reactions and of Diffusion on 40Ar-39Ar Ages of Micas

The effects of metamorphic reactions occurring during decompression were explored to understand their influence on the 40Ar-39Ar ages of micas. Monometamorphic metasediments from the Lepontine Alps (Switzerland) reached lower amphibolite facies during the Barrovian metamorphism related to the collision between European and African (Adria) continental plates. Mineral assemblages typically composed of garnet, plagioclase, biotite, muscovite and paragonite (or margarite) were screened for petrological equilibrium, to focus on samples that record a minimum degree of retrogression. X-ray diffraction data indicate that some mineral separates prepared for 40Ar-39Ar stepwise heating analysis are monomineralic, whereas others are composed of two white micas (muscovite with paragonite or margarite), or biotite and chlorite. In monomineralic samples 37Ar/39Ar and 38Ar/39Ar (proportional to Ca/K and Cl/K ratios) did not change and the resulting ages can be interpreted unambiguously. In mineral separates containing two white micas, Ca/K and Cl/K ratios were variable, reflecting non-simultaneous laboratory degassing of the two heterochemical Ar reservoirs. These ratios were used to identify each Ar reservoir and to unravel the age. In a chlorite-margarite-biotite calcschist equilibrated near 560°C and 0·65 GPa, biotite, margarite, and muscovite all yield ages around 18 Ma. At slightly higher grade (560-580°C, 0·8-0·9 GPa), the assemblage muscovite-paragonite-plagioclase is in equilibrium and remains stable during retrogression. In this case, muscovite and paragonite yield indistinguishable ages around 16·5 Ma. Above 590°C, paragonite was mostly consumed to form plagioclase >590°C, whereby the relict mica yields an age up to 5·6 Ma younger than muscovite. This partial or total resetting of the Ar clock in paragonite is interpreted to reflect plagioclase growth during decompression. Where biotite is present within this same assemblage, it systematically yields a younger age than muscovite, by 0·5-2 Ma. However, these biotites all show small amounts of retrograde chlorite formation. We conclude that even very minor chloritization of biotite is apparently a more effective process than temperature in resetting the Ar clock, as is the formation of plagioclase from paragonite decomposition. Multi-equilibrium thermobarometry is an excellent means to ensure that equilibrium in investigated samples is preserved, and this helps to obtain geologically meaningful metamorphic ages. However, even samples passing such equilibrium tests may still show retrograde effects that affect the Ar retention of micas. A more robust interpretation of such 40Ar-39Ar results may require use of a second geochronometer, such as U-Pb on monazit

A generalization of Osgood's test and a comparison criterion for integral equations with noise

In this work, we prove a generalization of Osgood's test for the explosion of the solutions of initial-value problems. We also establish a comparison criterion for the solution of integral equations with noise, and provide estimations of the time of explosion of problems arising in the investigation of crack failures where the noise is the absolute value of the Brownian motionComment: 10 page

Evolutionary Dynamics in Vascularised Tumours under Chemotherapy: Mathematical Modelling, Asymptotic Analysis and Numerical Simulations

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentangle the impact of different evolutionary parameters on the emergence of intra-tumour phenotypic heterogeneity and the development of resistance to chemotherapy, we construct explicit solutions to the equation for the phenotypic distribution of tumour cells and provide a detailed quantitative characterisation of the long-time asymptotic behaviour of such solutions. Analytical results are integrated with numerical simulations of a calibrated version of the model based on biologically consistent parameter values. The results obtained provide a theoretical explanation for the observation that the phenotypic properties of tumour cells in vascularised tumours vary with the distance from the blood vessels. Moreover, we demonstrate that lower oxygen levels may correlate with higher levels of phenotypic variability, which suggests that the presence of hypoxic regions supports intra-tumour phenotypic heterogeneity. Finally, the results of our analysis put on a rigorous mathematical basis the idea, previously suggested by formal asymptotic results and numerical simulations, that hypoxia favours the selection for chemoresistant phenotypic variants prior to treatment. Consequently, this facilitates the development of resistance following chemotherapy