This dissertation reports a study of the fungi and 'protists' (Labyrinthulids, Thraustochytrids, Hyalochlorella marina) associated with the intertidal red algae Rhodoglossum affine and Gelidium coulteri. Research focused on laboratory isolations from algal thalli collected from in situ populations. Different isolation techniques and isolation media were employed to evaluate the abundance and diversity of fungi and protists associated with these red algae. Algal tissue surface sterilization and rigorous rinsing procedures were used to remove and/or enumerate surface-associated microbes. The results obtained from the different isolation techniques and algal tissue pretreatment procedures are compared and discussed in terms of their usefulness for each member of the algal-associated microbiota. Natural populations of affine and coulteri support a rich fauna of marine protists. The most prevalent members of this protist fauna were Labyrinthula spp. resembling the "Vishniac Strains" and Thraustochytrium motivum. Schizochytrium aggregatum, a new species of Labyrinthulid designated Labyrinthuloides sp. 1, and Hyalochlorella marina were also common depending upon the isolation method utilized. These protists appear to be associated with the surfaces of the algal thalli, and exist as saprobes and/or perthophytes rather than biotrophic parasites of the algal tissues. Isolations from field-collected algal tissues also yielded actinomycetes, yeasts, and a high diversity of imperfect fungi. Overall isolation frequencies for individual fungal taxa were low. Most of the mycelial fungi isolated are considered to be of terrestrial origin and of questionable 'significance' in the intertidal habitat. Only four, possibly five, are presently considered marine. The mycelial fungi most commonly isolated include: Acremonium sp. 019-78, Cladosporium cladosporioides, Dendryphiella salina, Penicillium spp., Phoma sp. (Group 1), Sigmoidea littoralis sp. nov., and Unidentified hyphomycete 044-78. Certain of these fungi may grow saprobically (as pertho-phytes) on reproductive and/or senescing algal tissues in the intertidal habitat, but their activities appear to be limited. Field-collected thalli of Rhodoglossum affine and Gelidium coulteri were allowed to decompose in mesh bags placed in the intertidal. The succession of higher fungi associated with the decomposing algae was followed by plating representative bimonthly subsamples of the algal tissues onto a Base Mineral Medium. Rhodoglossum affine deteriorated completely after 52 days of exposure, while a small amount of Gelidium coulteri remained after 71 days. Qualitative aspects of the mycobiota associated with the two algal species were similar, however fungi were isolated more frequently from coulteri. A dominant mycobiota was apparent after 36 days of exposure on the beach. Acremonium sp. 019-78, Dendryphiella salina and Sigmoidea littoralis sp. nov. were active colonizers of the decomposing algal tissues, and their isolation frequencies increased as decomposition proceeded. Several species of bacteria capable of utilizing the cell wall polysaccharides of red algae (agar, carrageenan) were also present on the decomposing algae. It is possible that the activities of these bacteria enhanced fungal development. Thraustochytrium motivum, Schizochytrium aggregatum and Ulkenia sp. RC02-80 were placed into sterile seawater cultures with surface-sterilized tissues of Rhodoglossum affine and Gelidium coulteri. After 72 hours of incubation, positive growth associations were examined using scanning electron microscopy. The three Thraustochytrids displayed luxuriant growth on all algal tissue types, and produced extensive ectoplasmic networks on the algal surfaces which functioned in attachment and, presumably, in the absorption of dissolved nutrients. Ectoplasmic net elements were resolved down to 0.02 pm in diameter, but no obvious 'penetration' of the algal tissues could be discerned. All of the protists (Labyrinthulids, Thraustochytrids, Hyalochlore11a marina) isolated from these red algae are described and illustrated. Certain commonly encountered and/or poorly known mycelial fungi are also described, including a new species of marine hyphomycete, Sigmoidea littoralis sp. nov. / Science, Faculty of / Botany, Department of / Graduate

archives@tulane.edu / This thesis examines the geometry and combinatorics of Borel subgroup orbits in classical symmetric spaces G/L where G is complex linear algebraic group and L is a Levi factor of a maximal parabolic subgroup P in G. In these cases, known as symmetric spaces of Hermitian type, we show that the canonical projection map $\pi : G/L \to G/P$ has the structure of an affine bundle. This fact yields a cell decomposition of G/L as well as isomorphisms of the cohomology and Chow rings of G/L and G/P, and motivates the study of the Borel orbits of G/L in relation to their images under the equivariant map $\pi$. For all of the cases of interest (symmetric spaces of types AIII, CI, DIII and BDI), G/P is a Grassmannian variety with Borel orbits called Schubert cells. Borel orbits of most of these symmetric spaces are parametrized by combinatorial objects called clans. This thesis provides enumerative formulae for the orbits in type CI, DIII and BDI , and gives bijections between sets of clans and other families of objects such as (fixed-point free) partial involutions, rook placements, and set partitions. Clans come with a poset structure given by the closure containment relation of the corresponding Borel orbits, and we supply rank polynomials for these posets in types CI and DIII. We give a combinatorial description of the closure order relations in types AIII, CI, and DIII which allows us to resolve part of a conjecture of Wyser on the restriction of this order from type AIII to other types. In the course of this description, we identify the preimages of Schubert cells under the map \pi as collections of clans called “sects.” Our combinatorial description of the sects identifies Borel orbits whose closures generate the Chow ring of G/L and reveals additional structure in the closure poset of clans. In particular, the preimage of the largest Schubert cell coincides variously with well-known posets of matrix Schubert varieties and congruence Borel orbit closures. Furthermore, we show that in type AIII the closure order restricted to a given sect can be described combinatorially in terms of “rank tableaux.” / 0 / Aram Bingham

The first two chapters provide the necessary prerequisites. In the third and fourth chapters we demonstrate than an affine Hjelmslev plane (or A. H. plane) is coordinatized by a biternary ring; and that given a biternary ring, one can construct an affine Hjelmslev plane. In the fifth and sixth chapters we introduce the notions of an ordering of an A. H. plane and an ordering of a biternary ring. In the seventh chapter we show that an ordering of an A. H. plane H induces an ordering on the coordinate biternary ring. In the eighth chapter we show that a given ordering of a biternary ring M induces an ordering on the A.H. plane constructed over M. In the remaining chapters we examine the associated ordinary affine plane of an A. H. plane, the case where an A. H. plane is Desarguesian, and give an example of an ordered non-Desarguesian A. H. plane. / Thesis / Master of Science (MSc)

<p> In this thesis we examine a generalized notion of ordinary two dimensional affine and projective geometries The first six chapters deal very generally with coordinatization methods for these geometries and a direct construction of the analytic model for the affine case. The last two chapters are concerned with a discussion of these structures viewed as topological geometries. </p> / Thesis / Doctor of Philosophy (PhD)

No description available.

Schubert calculus has become an indispensable tool for enumerative geometry. It concerns the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The polynomials that represent the Schubert classes are called Schubert polynomials. An ongoing project in Schubert calculus has been to provide geometric foundations for the combinatorics. An example is the recovery by Knutson and Miller of the Schubert polynomials for finite flag varieties as the equivariant cohomology classes of matrix Schubert varieties. The present thesis is the start of a project to recover Schubert polynomials for the Borel-Moore homology of the (special linear) affine Grassmannian by an analogous process. This requires finitizing an affine Schubert variety to produce a matrix affine Schubert variety. This involves a choice of ``window'', so one must then identify a class representative that is independent of this choice. Examples lead us to conjecture that this representative is a k-Schur function. Concluding the discussion is a preliminary investigation into the combinatorics of Gröbner degenerations of matrix affine Schubert varieties, which should lead to a combinatorial proof of the conjecture. / Ph. D.

In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module. / Master of Science / The Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-Hecke Algebra corresponds to a linear transformation. Then, for each element we can find eigenvalues and eigenvectors. The transformations that we are considering all have the same eigenvalues. So, we consider the intersection of all the eigenspaces that correspond to the same eigenvalue. I.e. vectors that are eigenvectors of all of the elements. We find an algorithm that generates a basis for said vectors.

Face recognition algorithms has in the past few years become a very active area of research in the fields of computer vision, image processing, and cognitive psychology. This has spawned various algorithms of different complexities. The concept of principal component analysis(PCA) is a popular mode of face recognition algorithm and has often been used to benchmark other face recognition algorithms for identification and verification scenarios. However in this thesis, we try to analyze different face recognition algorithms at a deeper level. The objective is to model the distances output by any face recognition algorithm as a function of the input images. We achieve this by creating an affine eigen space from the PCA space such that it can approximate the results of the face recognition algorithm under consideration as closely as possible. Holistic template matching algorithms like the Linear Discriminant Analysis algorithm( LDA), the Bayesian Intrapersonal/Extrapersonal classifier(BIC), as well as local feature based algorithms like the Elastic Bunch Graph Matching algorithm(EBGM) and a commercial face recognition algorithm are selected for our experiments. We experiment on two different data sets, the FERET data set and the Notre Dame data set. The FERET data set consists of images of subjects with variation in both time and expression. The Notre Dame data set consists of images of subjects with variation in time. We train our affine approximation algorithm on 25 subjects and test with 300 subjects from the FERET data set and 415 subjects from the Notre Dame data set. We also analyze the effect of different distance metrics used by the face recognition algorithm on the accuracy of the approximation. We study the quality of the approximation in the context of recognition for the identification and verification scenarios, characterized by cumulative match score curves (CMC) and receiver operator curves (ROC), respectively. Our studies indicate that both the holistic template matching algorithms as well as feature based algorithms can be well approximated. We also find the affine approximation training can be generalized across covariates. For the data with time variation, we find that the rank order of approximation performance is BIC, LDA, EBGM, and commercial. For the data with expression variation, the rank order is LDA, BIC, commercial, and EBGM. Experiments to approximate PCA with distance measures other than Euclidean also performed very well. PCA+Euclidean distance is best approximated followed by PCA+MahL1, PCA+MahCosine, and PCA+Covariance.

In order to foster the maturity of face recognition analysis as a science, a well implemented baseline algorithm and good performance metrics are highly essential to benchmark progress. In the past, face recognition algorithms based on Principal Components Analysis(PCA) have often been used as a baseline algorithm. The objective of this thesis is to develop a strategy to estimate the best affine transformation, which when applied to the eigen space of the PCA face recognition algorithm can approximate the results of any given face recognition algorithm. The affine approximation strategy outputs an optimal affine transform that approximates the similarity matrix of the distances between a given set of faces generated by any given face recognition algorithm. The affine approximation strategy would help in comparing how close a face recognition algorithm is to the PCA based face recognition algorithm. This thesis work shows how the affine approximation algorithm can be used as a valuable tool to evaluate face recognition algorithms at a deep level. Two test algorithms were choosen to demonstrate the usefulness of the affine approximation strategy. They are the Linear Discriminant Analysis(LDA) based face recognition algorithm and the Bayesian interpersonal and intrapersonal classifier based face recognition algorithm. Our studies indicate that both the algorithms can be approximated well. These conclusions were arrived based on the results produced by analyzing the raw similarity scores and by studying the identification and verification performance of the algorithms. Two training scenarios were considered, one in which both the face recognition and the affine approximation algorithm were trained on the same data set and in the other, different data sets were used to train both the algorithms. Gross error measures like the average RMS error and Stress-1 error were used to directly compare the raw similarity scores. The histogram of the difference between the similarity matrixes also clearly showed that the error spread is small for the affine approximation algorithm. The performance of the algorithms in the identification and the verification scenario were characterized using traditional CMS and ROC curves. The McNemar's test showed that the difference between the CMS and the ROC curves generated by the test face recognition algorithms and the affine approximation strategy is not statistically significant. The results were statistically insignificant at rank 1 for the first training scenario but for the second training scenario they became insignificant only at higher ranks. This difference in performance can be attributed to the different training sets used in the second training scenario.

La thèse consiste de deux parties. Dans la première partie, on montre la pureté des fibres de Springer affines pour $\gl_{4}$ dans le cas non-ramifié. Plus précisément, on construit une famille de pavages non standard en espaces affines de la grassmannienne affine, qui induisent des pavages en espaces affines de la fibre de Springer affine. Dans la deuxième partie, on introduit une notion de $\xi$-stabilité sur la grassmannienne affine $\xx$ pour le groupe $\gl_{d}$, et on calcule le polynôme de Poincaré du quotient $\xx^{\xi}/T$ de la partie $\xi$-stable $\xxs$ par le tore maximal $T$ par une processus analogue de la réduction de Harder-Narasimhan.