Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Complexe d'épaule dans un contexte d'analyse tridimentionnel - Modélisation et mise en garde

L'épaule est un complexe articulaire formé par le thorax, la clavicule, la scapula et l'humérus. Alors que les orientation et position de ces derniers la rendent difficile à étudier, la compréhension approfondie de l'interrelation de ces segments demeure cliniquement importante. Ainsi, un nouveau modèle du membre supérieur est développé et présenté. La cinématique articulaire de 15 sujets sains est collectée et reconstruite à l'aide du modèle. Celle-ci s'avère être généralement moins variable et plus facilement interprétable que le modèle de référence. Parallèlement, l'utilisation de simplifications, issues de la 2D, sur le calcul d'amplitude de mouvement en 3D est critiquée. Cependant, des cas d'exception où ces simplifications s'appliquent sont dégagés et prouvés. Ainsi, ils sont une éventuelle avenue d'amélioration supplémentaire des modèles sans compromission de leur validé.

A influência das injunções de orientação relativa na calibração de um sistema dual de câmeras digitais

Image acquisition systems based on multi-head arrangement of digital frame cameras, such as the commercial systems DMC, UltraCam, besides others, are attractive alternatives enabling larger imaging area when compared to a single frame camera. Considering that in these systems, cameras are tightly attached to an external mount, it is assumed that relative position and orientation between cameras are stable during image acquisition and, consequently, these constraint can be included in the calibration step. This constraint is acceptable because estimates of the relative orientation (RO) parameters between cameras, from previously estimated exterior orientation parameters, present higher and significant deviations than the expected physical variations, due to error propagation. In order to solve this problem, this work presents an approach based on simultaneous calibration of two or more cameras using constraints that state that the relative rotation matrix and the distance between the cameras head are stable. Experiments with images acquired by an arrangement of two Hasselblad H2D cameras were accomplished, without and with the mentioned constraints. The experiments showed that the calibration process with RO constraints allows better results than the approach based on single camera calibration, provided that the estimation has included only images with good target distribution.

A photogrammetric method for single image orientation and measurement

The aim of this paper is to present a photogrammetric method for determining the dimensions of flat surfaces, such as billboards, based on a single digital image. A mathematical model was adapted to generate linear equations for vertical and horizontal lines in the object space. These lines are identified and measured in the image and the rotation matrix is computed using an indirect method. The distance between the camera and the surface is measured using a lasermeter, providing the coordinates of the camera perspective center. Eccentricity of the lasermeter center related to the camera perspective center is modeled by three translations, which are computed using a calibration procedure. Some experiments were performed to test the proposed method and the achieved results are within a relative error of about 1 percent in areas and distances in the object space. This accuracy fulfills the requirements of the intended applications. © 2005 American Society for Photogrammetry and Remote Sensing.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Automatic quantification of matrix cracking and fiber rotation by X-ray computed tomography in shear-deformed carbon fiber-reinforced laminates

The deformation and damage mechanisms of carbon fiber-reinforced epoxy laminates deformed in shear were studied by means of X-ray computed tomography. In particular, the evolution of matrix cracking, interply delamination and fiber rotation was ascertained as a function of the applied strain. In order to provide quantitative information, an algorithm was developed to automatically determine the crack density and the fiber orientation from the tomograms. The investigation provided new insights about the complex interaction between the different damage mechanisms (i.e. matrix cracking and interply delamination) as a function of the applied strain, ply thickness and ply location within the laminate as well as quantitative data about the evolution of matrix cracking and fiber rotation during deformation

The early Miocene rotation of the Corso-Sardinian block. New paleomagnetic constraints for the end of the motion

The paleomagnetic investigations carried out in the 70's on Oligo-Miocene volcanics of Sardinia have demonstrated that the island was turned by 35-30 degrees clockwise from 33 Ma up to 3-1-20.5 Ma and rotated counterclockwise in a few million years [De Jong et al., 1969, 1973; Bobier et Coulon, 1970; Coulon et al., 1974; Manzoni, 1974, 1975; Bellon rr nl.. 1977: Edel et Lortscher, 1977; Edel, 1979, 1980]. Since then, the end of the rotation fixed at 19 Ma by Montigny er al. [1981] was the subject of discussions and several studies associating paleomagnetism and radiometric dating were undertaken [Assorgia er al., 1994: Vigliotti et Langenheim, 1995: Deino et al., 1997; Gattacceca rt Deino, 1999]. This is a contribution to this debate that is hampered by thr important secular variation recorded in the volcanics. The only way to get our of this problem is to sample series of successive flows as completely as possible, and to reduce the effect of secular variation by the calculation of means. Sampling was performed north of Bonorva in 5 pyroclastic flows that belong to the upper ignimbritic series SI2 according to Coulon rr nl. [1974] or LBLS according to Assorgia et al. [1997] (fig. I). Ar-40/Ar-39 dating of biotites from the debris flow (MDF) has yielded an age or 18.35 +/- 0.03 Ma [Dubois, 2000]. Five of the investigated sites are located beneath the debris flow ITV, TVB, TVD, SPM85, SPM86), one site was cured in the matrix of the debris flow (MDF) and one in 4 metric blocks included in the flow (DFC). Another site was sampled in the upper ash flow (PDM) that marks the end of the pyroclastic activity, just before the marine transgression. According to micropaleontological and radiometric dating this transgression has occurred between 18.35 and 17.6 Ma [Dubois, 2000]. After removal of a soft viscous component, the thermal demagnetization generally shows a univectorial behaviour of the remanent magnetization (fig. 2a). The maximum unblocking temperatures of 580-620 degrees (tab. I) and a rapid saturation below 100 mT (fig. 3) indicate that the carrier of the characteristic magnetization is magnetite. The exception comes: from the upper site PDM in which were found two characteristic components, one with a normal polarity and low unblocking temperatures up to 350 degreesC and one with a reversed polarity and maximum unblocking temperatures at 580-600 degreesC of magnetite. After calculation of a mean direction for each flow, the mean << Al >> direction 4 degrees /57 degrees (alpha (95) = 13 degrees) computed with the mean directions for the 5 flows may be considered as weakly affected by secular variation. But the results require a more careful examination. The declinations are N to NNW beneath the debris flow. NNW in the debris flow. and NNE (or SSW) above the debris flow, The elongated distribution of the directions obtained at sites TVB and TVD. scattered from the mean direction of TV to the mean direction of MDF is interpreted as due to partial overprinting during the debris How volcanic episode, The low temperature component PDMa is likely related to the alteration seen on thin sections and is also viewed as an overprint. As NNE/SSW directions occur as well below (mean direction << B >> : 5 degrees /58 degrees) as above the debris flow (PDMb : 200 degrees/-58 degrees). the NNW directions (<< C >> : 337 degrees /64 degrees) associated with the debris flow volcanism may be interpreted as resulting from a magnetic field excursion. According to the polarity scale of Cande and Kent [1992, 1995] and the radiometric age of MDF, the directions with normal polarity (TV, TVB, TVD, SPM85. SPM86a. MDF. DFC) may represent the period 5En. while the directions with reversed polarity PDMb and SPM86b were likely acquired during the period 5Dr. Using the mean << Al >> direction, the mean << B >>, or the PDM direction (tab. I). the deviation in declination with the direction of stable Europe 6.4 degrees /58.7 degrees (alpha (95) = 8 degrees) for a selection of 4 middle Tertiary poles by Besse et Courtillot [1991] or 7 degrees /56 degrees (alpha (95) = 3 degrees) for 19 poles listed by Edel [1980] can be considered as negligible. Using the results from the uppermost ignimbritic layer of Anglona also emplaced around 18.3 Ma [Odin rt al.. 1994]. the mean direction << E >> (3 degrees /51.5 degrees) leads to the same conclusion. On the contrary, when taking into account all dated results available for the period 5En (mean direction << D >> 353 degrees /56 degrees for 45 sites) (tab. II). the deviation 13 degrees is much more significant. As the rotation of Sardinia started around 21-20.5 Ma. the assumption of a constant velocity of rotation and the deviations of the Sardinia directions with respect to the stable Europe direction locate the end of the motion between 18.3 and 17.2 or 16.7 Ma (fig. 4). During the interval 18.35-17.5 Ma, the marine transgression took place. At the same period a NE-SW shortening interpreted as resulting from the collision of Sardinia with Apulia affected different parts of the island [Letouzey et al., 1982]. Consequently, the new paleomagnetic results and the tectono-sedimentary evolution are in favour of an end of the rotation at 17.5-18 Ma.

Chiroptical measurement of chiral aggregates at liquid-liquid interface in centrifugal liquid membrane cell by Mueller matrix and conventional circular dichroism methods

The centrifugal liquid membrane (CLM) cell has been utilized for chiroptical studies of liquid-liquid interfaces with a conventional circular dichroism (CD) spectropolarimeter. These studies required the characterization of optical properties of the rotating cylindrical CLM glass cell, which was used under the high speed rotation. In the present study, we have measured the circular and linear dichroism (CD and LD) spectra and the circular and linear birefringence (CB and LB) spectra of the CLM cell itself as well as those of porphyrine aggregates formed at the liquid-liquid interface in the CLM cell, applying Mueller matrix measurement method. From the results, it was confirmed that the CLM-CD spectra of the interfacial porphyrin aggregates observed by a conventional CD spectropolarimeter should be correct irrespective of LD and LB signals in the CLM cell.

Analysis of Semi-solid Processing for Metal Matrix Composite Synthesis Using Factorial Design

The main goal in this work is to conduct a quantitative analysis of the mechanical stir casting process for obtaining particulate metal matrix composites. A combined route of stirring at semi-solid state followed by stirring at liquid state is proposed. A fractional factorial design was developed to investigate the influence and interactions of factors as: time, rotation, initial fraction and particle size, on the incorporated fraction. The best incorporations were obtained with all factors at high levels, as well as that very long stirring periods have no strong influence being particle size and rotation the most important factors on the incorporated fraction. Particle wetting occurs during stirring at semisolid state, highlighting the importance of the interactions between particles and the alloy globularized phase. The role of the alloying element Mg as a wettability-promoting agent is discussed. The shear forces resulting from the stirring system is emphasized and understood as the effect of rotation itself added to the propeller blade geometry.

Messung der paritätsverletzenden Neutronenspin-Rotation in 139 La unter Einsatz von 3 He-Neutronenspin-Filtern

Die Machbarkeit der Detektion einer P,T-Verletzung in der Neutron-Kern-p-Wellenresonanz von La-139 wird untersucht. Als experimentelleVerbesserung wurde der He-3- Neutronenspin- Filter (He-3-NSF) getestet. Mit einem He-3-NSF als Polarisationsanalysator wurde die rein P-verletzende Neutronenspin-Rotation in 139La erstmals mit guter Genauigkeit unmittelbar in der Resonanz bestimmt. Das schwache Matrixelement betrug v=1.51(5)stat(7)syst meV. Es wurde ein adiabatischer He-3-Spin-Rotator entwickelt und erfolgreich getestet, welcher es erlaubt, die Richtung der He-3-Polarisation einzustellen. Dies kann die bei Polarisationsmessungen üblichen Spinpräzessionsspulen ersetzen. Das Problem der Unterdrückung apparativer Falscheffekte während einer P,T-Detektion wird diskutiert und konnte jedoch noch nicht gelöst werden.

Interfering with the connection between the nucleus and the cytoskeleton affects nuclear rotation, mechanotransduction and myogenesis

Mechanical stress controls a broad range of cellular functions. The cytoskeleton is physically connected to the extracellular matrix via integrin receptors, and to the nuclear lamina by the LINC complex that spans both nuclear membranes. We asked here how disruption of this direct link from the cytoskeleton to nuclear chromatin affects mechanotransduction. Fibroblasts grown on flexible silicone membranes reacted to cyclic stretch by nuclear rotation. This rotation was abolished by inhibition of actomyosin contraction as well as by overexpression of dominant-negative versions of nesprin or sun proteins that form the LINC complex. In an in vitro model of muscle differentiation, cyclic strain inhibits differentiation and induces proliferation of C2C12 myoblasts. Interference with the LINC complex in these cells abrogated their stretch-induced proliferation, while stretch increased p38 MAPK and NFkappaB phosphorylation and the transcript levels of myogenic transcription factors MyoD and myogenin. We found that the physical link from the cytoskeleton to the nuclear lamina is crucial for correct mechanotransduction, and that disruption of the LINC complex perturbs the mechanical control of cell differentiation.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.