Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Some Unique Features of Egg Laying and Reproduction in Ichthyophis Malabarensis (Taylor) (Apoda:Amphibia)

The paper describes egg laying and reproduction in ICHTHYOPHIS MALABARENSIS. 100 eggs, the largest ever in Apoda, are laid in a single string and manipulated by the female into a massive clutch. The reproductive strategies in the species are discussed.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Laminar and turbulent natural convection in rectangular cavities

A computer program has been developed for the prediction of buoyancy-driven laminar and turbulent flow in rectangular air-filled two-dimensional cavities with differentially heated side walls. Laminar flow predictions for a square cavity and Rayleigh numbers from Ra = 10^3 up to the onset of unsteady flow have been obtained. Accurate solutions for Ra = 5 x 10^6, 10^7, 5 x 10^7 and 10^8 are presented and an estimate for the critical Rayleigh number at which the steady laminar flow becomes unsteady is given for this geometry. Numerical predictions of turbulent flow have been obtained for RaH~0(10^9 -10^11 ) and compared with existing experimental data. A previously developed second moment closure model (Behnia et al. 1987) has been used to model the turbulence. Results indicate that a second moment closure model is capable of predicting the observed flow features.

Vibration of generally orthotropic skew plates

Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Computation of turbulent flow in an IFRF quarl burner

A computational model for isothermal axisymmetric turbulent flow in a quarl burner is set up using the CFD package FLUENT, and numerical solutions obtained from the model are compared with available experimental data. A standard k-e model and and two versions of the RNG k-e model are used to model the turbulence. One of the aims of the computational study is to investigate whether the RNG based k-e turbulence models are capable of yielding improved flow predictions compared with the standard k-e turbulence model. A difficulty is that the flow considered here features a confined vortex breakdown which can be highly sensitive to flow behaviour both upstream and downstream of the breakdown zone. Nevertheless, the relatively simple confining geometry allows us to undertake a systematic study so that both grid-independent and domain-independent results can be reported. The systematic study includes a detailed investigation of the effects of upstream and downstream conditions on the predictions, in addition to grid refinement and other tests to ensure that numerical error is not significant. Another important aim is to determine to what extent the turbulence model predictions can provide us with new insights into the physics of confined vortex breakdown flows. To this end, the computations are discussed in detail with reference to known vortex breakdown phenomena and existing theories. A major conclusion is that one of the RNG k-e models investigated here is able to correctly capture the complex forward flow region inside the recirculating breakdown zone. This apparently pathological result is in stark contrast to the findings of previous studies, most of which have concluded that either algebraic or differential Reynolds stress modelling is needed to correctly predict the observed flow features. Arguments are given as to why an isotropic eddy-viscosity turbulence model may well be able to capture the complex flow structure within the recirculating zone for this flow setup. With regard to the flow physics, a major finding is that the results obtained here are more consistent with the view that confined vortex breakdown is a type of axisymmetric boundary layer separation, rather than a manifestation of a subcritical flow state.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

Characterization of sequence and structural features of the Candida krusei Enolase

The incidence of human infections by the fungal pathogen Candida species has been increasing in recent years. Enolase is an essential protein in fungal metabolism. Sequence data is available for human and a number of medically important fungal species. An understanding of the structural and functional features of fungal enolases may provide the structural basis for their use as a target for the development of new anti-fungal drugs. We have obtained the sequence of the enolase of Candida krusei (C. krusei), as it is a significant medically important fungal pathogen. We have then used multiple sequence alignments with various enolase isoforms in order to identify C. krusei specific amino acid residues. The phylogenetic tree of enolases shows that the C. krusei enolase assembles on the tree with the fungal genes. Importantly, C. krusei lacks four amino acids in the active site compared to human enolase, as revealed by multiple sequence alignments. These differences in the substrate binding site may be exploited for the design of new anti-fungal drugs to selectively block this enzyme. The lack of the important amino acids in the active site also indicates that C. krusei enolase might have evolved as a member of a mechanistically diverse enolase superfamily catalying somewhat different reactions.

Human genetic variation in the Baltic Sea region: Features of population history and natural selection

In this thesis, the genetic variation of human populations from the Baltic Sea region was studied in order to elucidate population history as well as evolutionary adaptation in this region. The study provided novel understanding of how the complex population level processes of migration, genetic drift, and natural selection have shaped genetic variation in North European populations. Results from genome-wide, mitochondrial DNA and Y-chromosomal analyses suggested that the genetic background of the populations of the Baltic Sea region lies predominantly in Continental Europe, which is consistent with earlier studies and archaeological evidence. The late settlement of Fennoscandia after the Ice Age and the subsequent small population size have led to pronounced genetic drift, especially in Finland and Karelia but also in Sweden, evident especially in genome-wide and Y-chromosomal analyses. Consequently, these populations show striking genetic differentiation, as opposed to much more homogeneous pattern of variation in Central European populations. Additionally, the eastern side of the Baltic Sea was observed to have experienced eastern influence in the genome-wide data as well as in mitochondrial DNA and Y-chromosomal variation – consistent with linguistic connections. However, Slavic influence in the Baltic Sea populations appears minor on genetic level. While the genetic diversity of the Finnish population overall was low, genome-wide and Y-chromosomal results showed pronounced regional differences. The genetic distance between Western and Eastern Finland was larger than for many geographically distant population pairs, and provinces also showed genetic differences. This is probably mainly due to the late settlement of Eastern Finland and local isolation, although differences in ancestral migration waves may contribute to this, too. In contrast, mitochondrial DNA and Y-chromosomal analyses of the contemporary Swedish population revealed a much less pronounced population structure and a fusion of the traces of ancient admixture, genetic drift, and recent immigration. Genome-wide datasets also provide a resource for studying the adaptive evolution of human populations. This study revealed tens of loci with strong signs of recent positive selection in Northern Europe. These results provide interesting targets for future research on evolutionary adaptation, and may be important for understanding the background of disease-causing variants in human populations.

Ultrastructural features of the early secretory pathway in Trichoderma reesei

We have systematically analysed the ultra structure of the early secretory pathway in the Trichoderma reesei hyphae in the wild-type QM6a, cellulase overexpressing Rut-C30 strain and a Rut-C30 transformant BV47 overexpressing a recombinant BiP1-VenusYFP fusion protein with an endoplasmic reticulum (ER) retention signal. The hyphae were studied after 24h of growth using transmission electron microscopy, confocal microscopy and quantitative stereological techniques. All three strains exhibited different spatial organisation of the ER at 24h in both a cellulase-inducing medium and a minimal medium containing glycerol as a carbon source (non-cellulase-inducing medium). The wild-type displayed a number of ER subdomains including parallel tubular/cisternal ER, ER whorls, ER-isolation membrane complexes with abundant autophagy vacuoles and dense bodies. Rut-C30 and its transformant BV47 overexpressing the BiP1-VenusYFP fusion protein also contained parallel tubular/cisternal ER, but no ER whorls; also, there were very few autophagy vacuoles and an increasing amount of punctate bodies where particularly the recombinant BiP1-VenusYFPfusion protein was localised. The early presence of distinct strain-specific features such as the dominance of ER whorls in the wild type and tub/cis ER in Rut-C30 suggests that these are inherent traits and not solely a result of cellular response mechanisms by the high secreting mutant to protein overload.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Mulibrey nanism : Clinical characteristics and pathophysiologic features of growth restriction, insulin resistance and tumour development

Background: Mulibrey nanism (MUL; Muscle-liver-brain-eye nanism; OMIM 253250) is an autosomal recessive growth disorder more prevalent in Finland than elsewhere in the world. Clinical characteristics include severe prenatal onset growth restriction, cardiopathy, multiple organ manifestations but no major neurological handicap. MUL is caused by mutations in the TRIM37 gene on chromosome 17q22-23, encoding a peroxisomal protein TRIM37 with ubiquitin E3-ligase activity. Nineteen different mutations have been detected, four of them present in the Finnish patients. Objective: This study aimed to characterize clinical and histopathological features of MUL in the national cohort of Finnish patients. Patients and methods: A total of 92 Finnish patients (age 0.7 to 77 years) participated in the clinical follow-up study. Patients hospital records and growth charts were reviewed. Physical, radiographic and laboratory examinations were performed according to a clinical protocol. Thirty patients (18 females) were treated with recombinant human GH for a median period of 5.7 years. Biopsies and autopsy samples were used for the histopathological and immunohistochemical analyses. Results: MUL patients were born small for gestational age (SGA) with immature craniofacial features after prenatal-onset growth restriction. They experienced a continuous deceleration in both height SDS and weight-for-height (WFH) postnatally. In infancy feeding difficulties and frequent pneumonias were common problems. At the time of diagnosis (median age 2.1 years) characteristic craniofacial, radiological and ocular features were the most constant findings. MUL patients showed a dramatic change in glucose metabolism with increasing age. While the children had low fasting glucose and insulin levels, 90% of the adults were insulin resistant, half had type 2 diabetes and an additional 42% showed impaired glucose tolerance (IGT). Seventy percent fulfilled the National Cholesterol Education Program (NCEP) Adult Treatment Panel III criteria for metabolic syndrome as adults. GH therapy improved pre-pubertal growth but had only minor impact on adult height (+5 cm). Interestingly, treated subjects were slimmer and had less frequent metabolic concerns as young adults. MUL patients displayed histologically a disturbed architecture with ectopic tissues and a high frequency of both benign and malignant tumours present in several internal organs. A total of 232 tumorous lesions were detected in our patient cohort. The majority of the tumours showed strong expression of endothelial cell marker CD34 as well as α-smooth muscle actin (α-SMA). Fifteen of the tumours were malignant and seven of them (five Wilms tumours) occurred in the kidney. Conclusions: MUL patients present a distinct postnatal growth pattern. Short-term response of GH treatment is substantial but the long-term impact remains modest. Although MUL patients form a distinct clinical and diagnostic entity, their clinical findings vary considerably from infancy to adulthood. While failure to thrive dominates early life, MUL adults develop metabolic syndrome and have a tendency for malignancies and vascular lesions in several organs. This speaks for a central role of TRIM37 in regulation of key cellular functions, such as proliferation, migration, angiogenesis and insulin signalling.