Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines

2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.

A New Hereditarily l^2 Banach Space

2000 Mathematics Subject Classification: 46B20, 46B26.

External Characterization of I-Favorable Spaces

1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

An incremental multilinear system for human face learning and recognition

This dissertation establishes a novel system for human face learning and recognition based on incremental multilinear Principal Component Analysis (PCA). Most of the existing face recognition systems need training data during the learning process. The system as proposed in this dissertation utilizes an unsupervised or weakly supervised learning approach, in which the learning phase requires a minimal amount of training data. It also overcomes the inability of traditional systems to adapt to the testing phase as the decision process for the newly acquired images continues to rely on that same old training data set. Consequently when a new training set is to be used, the traditional approach will require that the entire eigensystem will have to be generated again. However, as a means to speed up this computational process, the proposed method uses the eigensystem generated from the old training set together with the new images to generate more effectively the new eigensystem in a so-called incremental learning process. In the empirical evaluation phase, there are two key factors that are essential in evaluating the performance of the proposed method: (1) recognition accuracy and (2) computational complexity. In order to establish the most suitable algorithm for this research, a comparative analysis of the best performing methods has been carried out first. The results of the comparative analysis advocated for the initial utilization of the multilinear PCA in our research. As for the consideration of the issue of computational complexity for the subspace update procedure, a novel incremental algorithm, which combines the traditional sequential Karhunen-Loeve (SKL) algorithm with the newly developed incremental modified fast PCA algorithm, was established. In order to utilize the multilinear PCA in the incremental process, a new unfolding method was developed to affix the newly added data at the end of the previous data. The results of the incremental process based on these two methods were obtained to bear out these new theoretical improvements. Some object tracking results using video images are also provided as another challenging task to prove the soundness of this incremental multilinear learning method.

Some near horizon studies onWeyl and Vaidya spacetimes

This thesis comprises some studies on the Weyl, Vaidya and Weyl distorted Schwarzschild (WDS) spacetimes. The main focal areas are : a) construction of near horizon metric(NHM) for WDS spacetime and subsequently a "stretched horizon" prescribed by the membrane formalism for black holes, b) application of membrane formalism and construction of stretched horizons for Vaidya spacetime and c) using the thin shell formalism to construct an asymptotically flat spacetime with a Weyl interior where the construction does not violate energy conditions. For a), a standard formalism developed in [1] has been used wherein the metric is expanded as a Taylor series in ingoing Gaussian null coordinates with the affine parameter as the expansion parameter. This expansion is used to construct a timelike "stretched horizon" just outside the true horizon to facilitate some membrane formalism studies, the theory for which was first introduced in [2]. b) applies the membrane formalism to Vaidya spacetime and also extends a part of the work done in [1] in which event horizon candidates were located perturbatively. Here, we locate stretched horizons in close proximity to every event horizon candidate located in [1]. c) is an attempt to induce Weyl distortions with a thin shell of matter in an asymptotically flat spacetime without violating energy conditions.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Oligocene to early Miocene benthic foraminifera in the eastern Equatorial Pacific

We investigated Oligocene and early Miocene benthic foraminiferal faunas (> 105 µm in size) from Ocean Drilling Program (Leg 199) Site 1218 (4826 m water depth and ~3300 to ~4000 m paleo-water depth) and Site 1219 (5063 m water depth and ~4200 to ~4400 m paleo-water depth) to understand the response of abyssal benthic foraminifera to mid-Oligocene glacial events in the eastern Equatorial Pacific Ocean. Two principal factor assemblages were recognized. The Factor 1 assemblage (common Nuttallides umbonifer) is related to either an influx of the Southern Component Water (SCW), possibly carbonate undersaturated, or a decrease in seasonality of the food supply from the surface ocean. The Factor 2 assemblage is characterized by typical deep-sea taxa living under variable trophic conditions, possibly with a seasonal component in food supply. The occurrence of abyssal benthic foraminifera faunas during the mid-Oligocene depends on either the effect of SCW or the seasonality of food resources. The Factor 1 assemblage was most common near 76Ol-C11r, 73Ol-C10rn and 67Ol-C9n (ca. 30.2, 29.1 and 26.8 Ma respectively by Pälike et al. (2006, doi:10.1126/science.1133822)). This indicates that the effect of SCW increased or the seasonal input of food from the surface ocean to benthic environments was weakened close to these glacial events. In contrast, the huge export flux of small biogenic carbonate particles close to these glacial events might be responsible for carbonate-rich sediments buffering carbonate undersaturation. Changes in deep-water masses or the periodicity of food supply from the surface ocean and variation in surface carbonate production affected by orbital forcing had an impact on the mid-Oligocene faunas of abyssal benthic foraminifera around the intervals of glacial events in the eastern Equatorial Pacific Ocean. The Factor 1 assemblage decreased sharply at ? 30 Ma (29.8 Ma by Pälike et al. (2006), 30.0 Ma by CK95) and returned to dominance after ? 29 Ma (28.6 Ma by Pälike et al. (2006), 28.8 Ma by CK95). It is likely that the effect of SCW (possibly carbonate undersaturated) has intensified since the late Oligocene. The faunal transition of benthic foraminifera in the eastern Equatorial Pacific Ocean at ~29 Ma might be attributable to the influence of Northern Component Water (NCW) input to the Southern Ocean and the subsequent formation of SCW at about that time.

Relative abundance of euphausiids (Crustacea) in water samples of the Arabian Sea (Table 2)

In the present paper, the ecology and feeding habits of euphausiids are described. The samples were taken at the time of the NE-monsoon (1964/65) by R. V. "Meteor" in the Arabian Sea and adjacent waters. 24 species were determined. According to distribution of the species, the following marine areas can be distinguished: Arabian Sea: 24 species, dominant are Euphausia diomedeae, E. tenera, E. distinguenda, Stylocheiron carinatum. Gulf of Aden: 10 species, dominant are Euphausia diomedeae, E. distinguenda. Red Sea: 6 species, dominant are Euphausia diomedeae, E. distinguenda. Gulf of Oman : 5 Species, dominant are Euphausia distinguenda, Pseudeupbaufia latifrons. Persian Gulf: 1 species - Pseudeuphausia latifrons. The total number of euphausiids indicate the biomass of this group. High densities of euphausiids (200-299 and > 300 individuals/100 m**3) occur in the innermost part of the Gulf cf Aden, in the area south of the equator near the African east coast, near Karachi (Indian west coast) and in the Persian Gulf. Comparison with data relating to production biology confirms that these are eutrophic zones which coincide with areas in which upwelling occurs at the time of the NE-monsoon. The central part of the Arabian Sea differs from adjacent waters by virtue of less dense euphausiid populations (> 199 individuals/100 m**3). Measurements relating to production biology demonstrate a relatively low concentration of primary food sources. Food material was ascertained by analysis of stomach content. The following omnivorous species were examined: Euphausia diomedeae, E. distinguenda, E. tenera, Pseudeuphausia latifrons and Thysanopoda tricuspidata. Apart from crustacean remains large numbers of Foraminifera, Radiolaria, tintinnids, dinoflagellates were found in the stomachs. Quantitatively crustaceans form the most important item in the diet. Food selection on the basis of size and form appears to be restricted to certain genera of tintinnids. The genera Stylocheiron and Nematoscelis are predators. Only crustacean remains were found in the stomachs of Stylocheiron abbreviatum, whereas Radiolaria, Foraminifera and tintinnids occurred to some extent in Nematasceli sp. Different euphausiids in the food chain in the Arabian Sea. In omnivorous species the position is variable, since they not only feed by filtering autotrophic and heterotrophic Protista, but also by predation on zooplankton. Carnivorous species without filtering apparatus feed exclusively on zooplankton of the size of copepods. Only these species are well established as occupying a higher position in the food chain. The parasitic protozoan Tbalassomyces fagei was found on Euphausia diomedeae, E. fenera, E. distinguenda and E. sanzoi.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.

Face recognition using a unified 3D morphable model

We address the problem of 3D-assisted 2D face recognition in scenarios when the input image is subject to degradations or exhibits intra-personal variations not captured by the 3D model. The proposed solution involves a novel approach to learn a subspace spanned by perturbations caused by the missing modes of variation and image degradations, using 3D face data reconstructed from 2D images rather than 3D capture. This is accomplished by modelling the difference in the texture map of the 3D aligned input and reference images. A training set of these texture maps then defines a perturbation space which can be represented using PCA bases. Assuming that the image perturbation subspace is orthogonal to the 3D face model space, then these additive components can be recovered from an unseen input image, resulting in an improved fit of the 3D face model. The linearity of the model leads to efficient fitting. Experiments show that our method achieves very competitive face recognition performance on Multi-PIE and AR databases. We also present baseline face recognition results on a new data set exhibiting combined pose and illumination variations as well as occlusion.

Data-Driven Dynamic Modeling of Coupled Thermal and Electric Outputs of Microturbines

Microturbines are among the most successfully commercialized distributed energy resources, especially when they are used for combined heat and power generation. However, the interrelated thermal and electrical system dynamic behaviors have not been fully investigated. This is technically challenging due to the complex thermo-fluid-mechanical energy conversion processes which introduce multiple time-scale dynamics and strong nonlinearity into the analysis. To tackle this problem, this paper proposes a simplified model which can predict the coupled thermal and electric output dynamics of microturbines. Considering the time-scale difference of various dynamic processes occuring within microturbines, the electromechanical subsystem is treated as a fast quasi-linear process while the thermo-mechanical subsystem is treated as a slow process with high nonlinearity. A three-stage subspace identification method is utilized to capture the dominant dynamics and predict the electric power output. For the thermo-mechanical process, a radial basis function model trained by the particle swarm optimization method is employed to handle the strong nonlinear characteristics. Experimental tests on a Capstone C30 microturbine show that the proposed modeling method can well capture the system dynamics and produce a good prediction of the coupled thermal and electric outputs in various operating modes.