An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Plant Functional Type (PFT) map over Siberia derived from GlobCover 2005 dataset, link to dataset in NetCDF format

High-latitude ecosystems play an important role in the global carbon cycle and in regulating the climate system and are presently undergoing rapid environmental change. Accurate land cover data sets are required to both document these changes as well as to provide land-surface information for benchmarking and initializing Earth system models. Earth system models also require specific land cover classification systems based on plant functional types (PFTs), rather than species or ecosystems, and so post-processing of existing land cover data is often required. This study compares over Siberia, multiple land cover data sets against one another and with auxiliary data to identify key uncertainties that contribute to variability in PFT classifications that would introduce errors in Earth system modeling. Land cover classification systems from GLC 2000, GlobCover 2005 and 2009, and MODIS collections 5 and 5.1 are first aggregated to a common legend, and then compared to high-resolution land cover classification systems, vegetation continuous fields (MODIS VCFs) and satellite-derived tree heights (to discriminate against sparse, shrub, and forest vegetation). The GlobCover data set, with a lower threshold for tree cover and taller tree heights and a better spatial resolution, tends to have better distributions of tree cover compared to high-resolution data. It has therefore been chosen to build new PFT maps for the ORCHIDEE land surface model at 1 km scale. Compared to the original PFT data set, the new PFT maps based on GlobCover 2005 and an updated cross-walking approach mainly differ in the characterization of forests and degree of tree cover. The partition of grasslands and bare soils now appears more realistic compared with ground truth data. This new vegetation map provides a framework for further development of new PFTs in the ORCHIDEE model like shrubs, lichens and mosses, to represent the water and carbon cycles in northern latitudes better. Updated land cover data sets are critical for improving and maintaining the relevance of Earth system models for assessing climate and human impacts on biogeochemistry and biophysics.

Spatial data mining for enhanced soil map modelling

The principle of using induction rules based on spatial environmental data to model a soil map has previously been demonstrated Whilst the general pattern of classes of large spatial extent and those with close association with geology were delineated small classes and the detailed spatial pattern of the map were less well rendered Here we examine several strategies to improve the quality of the soil map models generated by rule induction Terrain attributes that are better suited to landscape description at a resolution of 250 m are introduced as predictors of soil type A map sampling strategy is developed Classification error is reduced by using boosting rather than cross validation to improve the model Further the benefit of incorporating the local spatial context for each environmental variable into the rule induction is examined The best model was achieved by sampling in proportion to the spatial extent of the mapped classes boosting the decision trees and using spatial contextual information extracted from the environmental variables.

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

Elements of Non-Linear Hamiltonian Dynamics

In this paper we present a set of generic results on Hamiltonian non-linear dynamics. We show the necessary conditions for a Hamiltonian system to present a non-twist scenario and from that we introduce the isochronous resonances. The generality of these resonances is shown from the Hamiltonian given by the Birkhof-Gustavson normal form, which can be considered a toy model, and from an optic system governed by the non-linear map of the annular billiard. We also define a special kind of transport barrier called robust torus. The meanders and shearless curves are also presented and we show the most robust shearless barrier associated with the rotation numbers.

Visualization of oligonucleotide probes and point mutations in interphase nuclei and DNA fibers using rolling circle DNA amplification

Rolling circle amplification (RCA) is a surface-anchored DNA replication reaction that can be exploited to visualize single molecular recognition events. Here we report the use of RCA to visualize target DNA sequences as small as 50 nts in peripheral blood lymphocytes or in stretched DNA fibers. Three unique target sequences within the cystic fibrosis transmembrane conductance regulator gene could be detected simultaneously in interphase nuclei, and could be ordered in a linear map in stretched DNA. Allele-discriminating oligonucleotide probes in conjunction with RCA also were used to discriminate wild-type and mutant alleles in the cystic fibrosis transmembrane conductance regulator, p53, BRCA-1, and Gorlin syndrome genes in the nuclei of cultured cells or in DNA fibers. These observations demonstrate that signal amplification by RCA can be coupled to nucleic acid hybridization and multicolor fluorescence imaging to detect single nucleotide changes in DNA within a cytological context or in single DNA molecules. This provides a means for direct physical haplotyping and the analysis of somatic mutations on a cell-by-cell basis.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

The influence of off-screen landmarks on user orientation

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Estudos dos agrupamentos vegetativos relacionados com as áreas onde foram efetuadas as pesquisas sôbre a febre amarela silvestre no Município de Passos, Estado de Minas Gerais

The work reported here was carried-out on the invitation of Dr. Henry Kumm, Director of the Rockefeller Foundation, and by appointment from Dr. Henrique Aragão, Director of the Instituto Oswaldo Cruz. It was done during the investigation of sylvan yellow fever, in June 1947, with a view to establishing the phyto-ecological conditions of the county of Passos. The pe¬riod was, however, too short for definite conclusions to be reached. Thanks are due to Dr. O. R. Causey, Chief of Research on Yellow Fever for transpor¬tation and other help. THE REGIONAL VEGETATION. Aerial photographs of the county of Passos shoto that it is covered by three great types of vegetation: Rain Forest, Secondary Pasture Land and Scrub.1 Detailed investigation, however, brings out the fact that these correspond to different seres; furthermore, each type presents not only the specific, characteristics of the biological form dominant for the climate, but also are at various stages, which express HABITATS differing from those of the normal sere. The phytogeographic survey of the region shows that most of it is now covered by secondary pasture land (disclimax) in which Melinis minutiflora, v. "fat grass" (fig. 1), predominates. The mosaic of Rain Forest and of small patches of Scrub reveals the effects of human intervention (BARRETO, H. L. de Mello 1); consequently, all the formations have to be regarded as secon¬dary, though some of them probably include relicts of the primitive climax (WARMING, E. 2). On close examination, the Scrub cannot be considered as the climax, because of the following facts: 1. In the zone of Rain-Forest stretches of forest are present in very varied topographic conditions and the reconstitution of the associations show that man has destroyed an ecological unit (fig. 2). 2. In the zone of Scrub the characteristic patches are small. The banks of rivers and brooks, the valleys and ravine and whatever the soil has retained some humidity, is being invaded fry Rain Forest, which seems to be growing under optimum conditions. The Scrub is thus limited to small belts on the calcareous mountains and on sandy soils with alcaline depths (pH abo¬ve 7) which do not retain enough moisture for the Rain Forest that is progres¬sively restricting the area occupied by Scrub. In view of the topographic and present climatic conditions the Rain Forest must consequently be regarded as the regional climax. The presence of ecologically contradictory elements and associations shows that the real problem is that of the fluctuations of the climate of Passos or even of Minas Geraes during the quaternary and recent periods (DAN-SEREAU, P. : 3), a subject on which little is known and which is tied to the evolution of the climate of Brazil (OLIVEIRA, E. : 4) . The transformation of Scrub into Rain Forest has been - observed by the author before, in other parts of Brazil (VELOSO, PL P.: 5) . It seems probable that the Rio Grande has also greatly influenced the change of the regional vegetation, by invading areas of Scrub and dislocating the limit of the Pluvial climate towards the Canastra Range, though there are remnants of Scrub (postclimax) transfor¬med into secondary open country (disclimax, fig. 5) by human devastation and the setting of fire to the land. VEGETATION GROUPS OF THE PLUVIAL TYPE. The map of the region also shows that at the present time the small patches of forest (whether devasted or intact) occupy the least accessible places, such as valleys, peaks and abrupt slopes (fig. 2). Even these are now being destroyed, so that in the near future this forested region will be en¬tirely reduced to poor pasture land unless energetic measures of conservation are undertaken in time. The Special Service for Prophylaxis against Yellow Fever installed two of their four Stations for the Capture of Mosquitos in this area, one of them at Batatal and the other at Cachoeira, which have separate formations each of them composed of several associations. Other vegetation formations were also analysed, from the synecological point of view, so as to ascertain of which degree of succession their associations belong. These phytosociological sur¬veys give an idea of the principal characteristics of each station. BATATAL FORMATION. The abrupt nature of the valley has rendered this location inappropriate for agricultural purposes since colonial times. The relict of the primitive forest climax saved by this circumstance has expanded gradually to zones whose paedologic conditions favour the eatablishment of mesophilous species. The aerial photograph shows two small stretches of forest, one apparently primi¬tive, the other composed of associations belonging to the subclimax of the subsere. CACHOEIRA FORMATION. Aerial photographs show that this station is crossed by a small river, which divides it into two separate parts. The first, which presents ecological conditions similar, though not identical to those of Batatal, is favoured by topography and apparently remains primitive forest. Though the topography of the other, on the whole, favours the establishment of groups belonging to the normal sere of the climax, is has been partly devastated recently and the aspect of the associations has been completely modified. It was is this part that the four posts for the capturing of mosquitos were set up. The first forest is favoured by deposition of organic matter, washed out from the nearby devasted areas by torrential rains, and thus provides, an appropriate HABITAT for the climax species with certain hygrophilous trends of the ecological quasiclimax type. This association seems to have reached a biological equilibrium, as the dominates. Gallesia gorarema and Cariniana legalis (fig. 10), present an optimum vitality with a vigorous habit and a normal evolutionary cycle. The Cariniantum legalis Gallesiosum equilibrium, corresponds however, to a provisory association, because if the moving of soil by torrential rains should cease it would become possible…

Simulation des fonctions de texture bidirectionnelles

Le réalisme des objets en infographie exige de simuler adéquatement leur apparence sous divers éclairages et à différentes échelles. Une solution communément adoptée par les chercheurs consiste à mesurer avec l’aide d’appareils calibrés la réflectance d’un échantillon de surface réelle, pour ensuite l’encoder sous forme d’un modèle de réflectance (BRDF) ou d’une texture de réflectances (BTF). Malgré des avancées importantes, les données ainsi mises à la portée des artistes restent encore très peu utilisées. Cette réticence pourrait s’expliquer par deux raisons principales : (1) la quantité et la qualité de mesures disponibles et (2) la taille des données. Ce travail propose de s’attaquer à ces deux problèmes sous l’angle de la simulation. Nous conjecturons que le niveau de réalisme du rendu en infographie produit déjà des résultats satisfaisants avec les techniques actuelles. Ainsi, nous proposons de précalculer et encoder dans une BTF augmentée les effets d’éclairage sur une géométrie, qui sera par la suite appliquée sur les surfaces. Ce précalcul de rendu et textures étant déjà bien adopté par les artistes, il pourra mieux s’insérer dans leurs réalisations. Pour nous assurer que ce modèle répond aussi aux exigences des représentations multi-échelles, nous proposons aussi une adaptation des BTFs à un encodage de type MIP map.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

Chirikov diffusion in the asteroidal three-body resonance (5,-2,-2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the NesvornA1/2-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, -2, -2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to 10(8) years.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.