Normalized Frobenius condition number of the orthogonal projections of the identity

[EN]This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A ? Rn×n, S being an arbitrary subspace of Rn×n). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S ? Rn×n, a new index bF (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed...

Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

[EN]We analyze the best approximation

Chemische und enzymatische Synthese von orthogonal stabil geschützten Kohlenhydrat-Scaffolds für kombinatorische Anwendungen

Auf der Suche nach potenten pharmakologischen Wirkstoffen hat die Kombinatorische Chemie in der letzten Dekade eine große Bedeutung erlangt, um innerhalb kurzer Zeit ein breites Spektrum von Verbindungen für biologische Tests zu erzeugen. Kohlenhydrate stellen als Scaffolds interessante Kandidaten für die kombinatorische Synthese dar, da sie mehrere Derivatisierungspositionen in stereochemisch definierter Art und Weise zur Verfügung stellen. So ist die räumlich eindeutige Präsentation angebundener pharmakophorer Gruppen möglich, wie es für den Einsatz als Peptidmimetika wünschenswert ist. Zur gezielten Derivatisierung einzelner Hydroxylfunktionen ist der Einsatz eines orthogonalen Schutz-gruppenmusters erforderlich, das gegenüber den im Lauf der kombinatorischen Synthese herrschenden Reaktionsbedingungen hinreichend stabil ist. Weiterhin ist ein geeignetes Ankersystem zu finden, um eine Festphasensynthese und damit eine Automatisierung zu ermöglichen.Zur Minimierung der im Fall von Hexosen wie Galactose benötigten fünf zueinander orthogonal stabilen Schutzgruppen wurde bei der vorliegenden Arbeit von Galactal ausgegangen, bei dem nur noch drei Hydroxylfunktionen zu differenzieren sind. Das Galactose-Gerüst kann anschließend wiederhergestellt werden. Die Differenzierung wurde über den Einsatz von Hydrolasen durch regioselektive Acylierungs- und Deacylierungs-reaktionen erreicht, wobei auch immobilisierte Enzyme Verwendung fanden. Dabei konnte ein orthogonales Schutzgruppenmuster sequentiell aufgebaut werden, das auch die nötigen Stabilitäten gegenüber sonstigen, teilweise geeignet modifizierten Reaktionsbedingungen aufweist. Für die Anbindung an eine Festphase wurde ein metathetisch spaltbarer Anker entwickelt, der über die anomere Position unter Wiederherstellung des Galactose-Gerüsts angebunden wurde. Auch ein oxidativ spaltbares und ein photolabiles Ankersystem wurden erprobt.

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

The performance of the parallel vector implementation of the one- and two-dimensional orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform (FFT) kernels. The factors considered in comparing the speed-up of these vectorized digital signal processing algorithms are discussed and it is shown that the traditional way of comparing th execution speed of digital signal processing algorithms by the ratios of the number of multiplications and additions is no longer effective for vector implementation; the structure of the algorithm must also be considered as a factor when comparing the execution speed of vectorized digital signal processing algorithms. Simulation results on the Cray X/MP with the following orthogonal transforms are presented: discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh transform (DWHT), and discrete Hadamard transform (DHDT). A comparison between the DHT and the fast Hartley transform is also included.(34 refs)

Orthogonal polarization spectroscopy to detect mesenteric hypoperfusion

OBJECTIVE: Orthogonal polarization spectral (OPS) imaging is used to assess mucosal microcirculation. We tested sensitivity and variability of OPS in the assessment of mesenteric blood flow (Q (sma)) reduction. SETTING: University Animal Laboratory. INTERVENTIONS: In eight pigs, Q (sma) was reduced in steps of 15% from baseline; five animals served as controls. Jejunal mucosal microcirculatory blood flow was recorded with OPS and laser Doppler flowmetry at each step. OPS data from each period were collected and randomly ordered. Samples from each period were individually chosen by two blinded investigators and quantified [capillary density (number of vessels crossing predefined lines), number of perfused villi] after agreement on the methodology. MEASUREMENT AND RESULTS: Interobserver coefficient of variation (CV) for capillary density from samples representing the same flow condition was 0.34 (0.04-1.41) and intraobserver CV was 0.10 (0.02-0.61). Only one investigator observed a decrease in capillary density [to 62% (48-82%) of baseline values at 45% Q (sma) reduction; P = 0.011], but comparisons with controls never revealed significant differences. In contrast, reduction in perfused villi was detected by both investigators at 75% of mesenteric blood flow reduction. Laser Doppler flow revealed heterogeneous microcirculatory perfusion. CONCLUSIONS: Assessment of capillary density did not reveal differences between animals with and without Q (sma) reduction, and evaluation of perfused villi revealed blood flow reduction only when Q (sma) was very low. Potential explanations are blood flow redistribution and heterogeneity, and suboptimal contrast of OPS images. Despite agreement on the method of analysis, interobserver differences in the quantification of vessel density on gut mucosa using OPS are high.

Agrin defines polarized distribution of orthogonal arrays of particles in astrocytes

Accumulating evidence indicates that agrin, a heparan sulphate proteoglycan of the extracellular matrix, plays a role in the organization and maintenance of the blood-brain barrier. This evidence is based on the differential effects of agrin isoforms on the expression and distribution of the water channel protein, aquaporin-4 (AQP4), on the swelling capacity of cultured astrocytes of neonatal mice and on freeze-fracture data revealing an agrin-dependent clustering of orthogonal arrays of particles (OAPs), the structural equivalent of AQP4. Here, we show that the OAP density in agrin-null mice is dramatically decreased in comparison with wild-types, by using quantitative freeze-fracture analysis of astrocytic membranes. In contrast, anti-AQP4 immunohistochemistry has revealed that the immunoreactivity of the superficial astrocytic endfeet of the agrin-null mouse is comparable with that in wild-type mice. Moreover, in vitro, wild-type and agrin-null astrocytes cultured from mouse embryos at embryonic day 19.5 differ neither in AQP4 immunoreactivity, nor in OAP density in freeze-fracture replicas. Analyses of brain tissue samples and cultured astrocytes by reverse transcription with the polymerase chain reaction have not demonstrated any difference in the level of AQP4 mRNA between wild-type astrocytes and astrocytes from agrin-null mice. Furthermore, we have been unable to detect any difference in the swelling capacity between wild-type and agrin-null astrocytes. These results clearly demonstrate, for the first time, that agrin plays a pivotal role for the clustering of OAPs in the endfoot membranes of astrocytes, whereas the mere presence of AQP4 is not sufficient for OAP clustering.

Nucleic acid sensing by an orthogonal reporter system based on homo-DNA

We have developed an assay for single strand DNA or RNA detection which is based on the homo-DNA templated Staudinger reduction of the profluorophore rhodamine-azide. The assay is based on a three component system, consisting of a homo-DNA/DNA hybrid probe, a set of homo-DNA reporter strands and the target DNA or RNA. We present two different formats of the assay (Omega probe and linear probe) in which the linear probe was found to perform best with catalytic turnover of the reporter strands (TON: 8) and a match/mismatch discrimination of up to 19. The advantage of this system is that the reporting (homo-DNA) and sensing (DNA) domain are decoupled from each other since the two pairing systems are bioorthogonal. This allows independent optimization of either domain which may lead to higher selectivity in in vivo imaging.

THE NATURAL AND ORTHOGONAL INTERACTION (NOIA) MODELS FOR QUANTITATIVE TRAITS (QTs) AND COMPLEX DISEASES

My dissertation focuses on developing methods for gene-gene/environment interactions and imprinting effect detections for human complex diseases and quantitative traits. It includes three sections: (1) generalizing the Natural and Orthogonal interaction (NOIA) model for the coding technique originally developed for gene-gene (GxG) interaction and also to reduced models; (2) developing a novel statistical approach that allows for modeling gene-environment (GxE) interactions influencing disease risk, and (3) developing a statistical approach for modeling genetic variants displaying parent-of-origin effects (POEs), such as imprinting. In the past decade, genetic researchers have identified a large number of causal variants for human genetic diseases and traits by single-locus analysis, and interaction has now become a hot topic in the effort to search for the complex network between multiple genes or environmental exposures contributing to the outcome. Epistasis, also known as gene-gene interaction is the departure from additive genetic effects from several genes to a trait, which means that the same alleles of one gene could display different genetic effects under different genetic backgrounds. In this study, we propose to implement the NOIA model for association studies along with interaction for human complex traits and diseases. We compare the performance of the new statistical models we developed and the usual functional model by both simulation study and real data analysis. Both simulation and real data analysis revealed higher power of the NOIA GxG interaction model for detecting both main genetic effects and interaction effects. Through application on a melanoma dataset, we confirmed the previously identified significant regions for melanoma risk at 15q13.1, 16q24.3 and 9p21.3. We also identified potential interactions with these significant regions that contribute to melanoma risk. Based on the NOIA model, we developed a novel statistical approach that allows us to model effects from a genetic factor and binary environmental exposure that are jointly influencing disease risk. Both simulation and real data analyses revealed higher power of the NOIA model for detecting both main genetic effects and interaction effects for both quantitative and binary traits. We also found that estimates of the parameters from logistic regression for binary traits are no longer statistically uncorrelated under the alternative model when there is an association. Applying our novel approach to a lung cancer dataset, we confirmed four SNPs in 5p15 and 15q25 region to be significantly associated with lung cancer risk in Caucasians population: rs2736100, rs402710, rs16969968 and rs8034191. We also validated that rs16969968 and rs8034191 in 15q25 region are significantly interacting with smoking in Caucasian population. Our approach identified the potential interactions of SNP rs2256543 in 6p21 with smoking on contributing to lung cancer risk. Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting affects several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we propose a NOIA framework for a single locus association study that estimates both main allelic effects and POEs. We develop statistical (Stat-POE) and functional (Func-POE) models, and demonstrate conditions for orthogonality of the Stat-POE model. We conducted simulations for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.

Wet and dry resistivities along three orthogonal directions of ODP Holes 185-801C and 185-1149B

The results of shore-based three-axis resistivity and X-ray computed tomography (CT) measurements on cube-shaped samples recovered during Leg 185 are presented along with moisture and density, P-wave velocity, resistivity, and X-ray CT measurements on whole-round samples of representative lithologies from Site 1149. These measurements augment the standard suite of physical properties obtained during Leg 185 from the cube samples and samples obtained adjacent to the cut cubes. Both shipboard and shore-based measurements of physical properties provide information that assists in characterizing lithologic units, correlating cored material with downhole logging data, understanding the nature of consolidation, and interpreting seismic reflection profiles.