The Berlekamp-Massey Algorithm revisited

We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation. partially supported by the Galois Theory and Explicit Methods in Arithmetic Project HPRN-CT-2000-00114 partially supported by the European Union funded project RAAG CT-2001-00271     

Fast in situ 3D nanoimaging: a new tool for dynamic characterization in materials science

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Mapping inland water carbon content with Landsat 8 data

Landsat 8 is the first Earth observation satellite with sufficient radiometric and spatial resolution to allow global mapping of lake CDOM and DOC (coloured dissolved organic matter and dissolved organic carbon, respectively) content. Landsat 8 is a multispectral sensor however, the number of potentially usable band ratios, or more sophisticated indices, is limited. In order to test the suitability of the ratio most commonly used in lake carbon content mapping, the green–red band ratio, we carried out fieldwork in Estonian and Brazilian lakes. Several atmospheric correction methods were also tested in order to use image data where the image-to-image variability due to illumination conditions would be minimal. None of the four atmospheric correction methods tested, produced reflectance spectra that matched well with in situ measured reflectance. Nevertheless, the green–red band ratio calculated from the reflectance data was in correlation with measured CDOM values. In situ data show that there is a strong correlation between CDOM and DOC concentrations in Estonian and Brazilian lakes. Thus, mapping the global CDOM and DOC content from Landsat 8 is plausible but more data from different parts of the world are needed before decisions can be made about the accuracy of such global estimation.     

A Wildland–Urban Interface Typology for Forest Fire Risk Management in Mediterranean Areas

The transitional areas that lie between wildlands and urbanized spaces, generally defined as wildland–urban interfaces (WUI), represent an increasing risk factor in Mediterranean areas; these define a new scenario in forest fire fighting and prevention. We have developed a methodological approach in order to assess the hazard and vulnerability of WUI which is based on landscape analysis, on the use of Geographic Information Systems (GIS) techniques and remote sensing. Unlike traditional approaches which are based on local scale characterization of WUI, we propose a progressive multi-scale approach. In order to reach an operative classification of the WUI the methodology was developed in three stages: a regional urban development model, a landscape character assessment and finally, a WUI typology. The last WUI typology has been based on the identification of different urban morphologies and their context within the type of landscape in which they occur.     

Natural and human forcing in recent geomorphic change; case studies in the Rio de la Plata basin

An analysis of geomorphic system's response to change in human and natural drivers in some areas within the Río de la Plata basin is presented. The aim is to determine whether an acceleration of geomorphic processes has taken place in recent years and, if so, to what extent it is due to natural (climate) or human (land-use) drivers. Study areas of different size, socio-economic and geomorphic conditions have been selected: the Río de la Plata estuary and three sub-basins within its watershed. Sediment cores were extracted and dated (²¹⁰Pb) to determine sedimentation rates since the end of the 19th century. Rates were compared with time series on rainfall as well as human drivers such as population, GDP, livestock load, crop area, energy consumption or cement consumption, all of them related to human capacity to disturb land surface. Data on river discharge were also gathered. Results obtained indicate that sedimentation rates during the last century have remained essentially constant in a remote Andean basin, whereas they show important increases in the other two, particularly one located by the São Paulo metropolitan area. Rates in the estuary are somewhere in between. It appears that there is an intensification of denudation/sedimentation processes within the basin.Rainfall remained stable or varied very slightly during the period analysed and does not seem to explain increases of sedimentation rates observed. Human drivers, particularly those more directly related to capacity to disturb land surface (GDP, energy or cement consumption) show variations that suggest human forcing is a more likely explanation for the observed change in geomorphic processes. It appears that a marked increase in denudation, of a “technological” nature, is taking place in this basin and leading to an acceleration of sediment supply. This is coherent with similar increases observed in other regions.     

Conformational properties of poly(diallyldimethyl ammonium chloride) (PDDA) determined by combination of molecular dynamics, rotational isomeric states and Monte Carlo procedures

A theoretical model describing the conformational properties of poly(diallyldimethyl ammonium chloride) (PDDA) is developed with the following strategy: molecular dynamics simulations are performed on model molecules representing dimers of PDDA. The results are employed to formulate a rotational isomeric state model for these molecules in terms of short-range interactions. Furthermore, the MD trajectories permit the evaluation of conformational energies and probabilities for the 27 conformations allowed to the three bonds sequence contained in the dimers. These probabilities are then employed to generate single chains of PDDA in vacuo according to standard Monte Carlo procedures and their main squared end to end distance 〈r²〉 are computed. The procedure (MD simulations, evaluation of energies and probabilities and MC calculations) is then repeated for two more realistic systems obtained by fitting into a cubic box, having side length L and periodic boundary conditions, a forty repeating units oligomer of PDDA together with 40 Cl⁻ as counterions and 500 water molecules (referred to as water system, ) or the oligomer with its counterions, 500 water molecules and 20 NaCl molecules (referred to as salt system, ). The behavior of the three systems is noticeably different and the value of unperturbed dimensions computed for the realistic systems are in good agreement with preliminary results of experimental measurements being carried out in our laboratory.     

Using implicit equations of parametric curves and surfaces without computing them: Polynomial algebra by values

The availability of the implicit equation of a plane curve or of a 3D surface can be very useful in order to solve many geometric problems involving the considered curve or surface: for example, when dealing with the point position problem or answering intersection questions. On the other hand, it is well known that in most cases, even for moderate degrees, the implicit equation is either difficult to compute or, if computed, the high degree and the big size of the coefficients makes extremely difficult its use in practice.We will show that, for several problems involving plane curves, 3D surfaces and some of their constructions (for example, offsets), it is possible to use the implicit equation (or, more precisely, its properties) without needing to explicitly determine it. We replace the computation of the implicit equation with the evaluation of the considered parameterizations in a set of points. We then translate the geometric problem in hand, into one or several generalized eigenvalue problems on matrix pencils (depending again on several evaluations of the considered parameterizations).This is the so-called “polynomial algebra by values” approach where the huge polynomial equations coming from Elimination Theory (e.g., using resultants) are replaced by big structured and sparse numerical matrices. For these matrices there are well-known numerical techniques allowing to provide the results we need to answer the geometric questions on the considered curves and surfaces.