Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Reconstruction of spatiotemporal capture data by means of orthogonal functions: the case of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic

[EN] The information provided by the International Commission for the Conservation of Atlantic Tunas (ICCAT) on captures of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic has a number of limitations, such as gaps in the statistics for certain fleets and the level of spatiotemporal detail at which catches are reported. As a result, the quality of these data and their effectiveness for providing management advice is limited. In order to reconstruct missing spatiotemporal data of catches, the present study uses Data INterpolating Empirical Orthogonal Functions (DINEOF), a technique for missing data reconstruction, applied here for the first time to fisheries data. DINEOF is based on an Empirical Orthogonal Functions decomposition performed with a Lanczos method. DINEOF was tested with different amounts of missing data, intentionally removing values from 3.4% to 95.2% of data loss, and then compared with the same data set with no missing data. These validation analyses show that DINEOF is a reliable methodological approach of data reconstruction for the purposes of fishery management advice, even when the amount of missing data is very high.

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.

Frobenius polynomials for Calabi-Yau equations

Sei $\pi:X\rightarrow S$ eine \"uber $\Z$ definierte Familie von Calabi-Yau Varietaten der Dimension drei. Es existiere ein unter dem Gauss-Manin Zusammenhang invarianter Untermodul $M\subset H^3_{DR}(X/S)$ von Rang vier, sodass der Picard-Fuchs Operator $P$ auf $M$ ein sogenannter {\em Calabi-Yau } Operator von Ordnung vier ist. Sei $k$ ein endlicher K\"orper der Charaktetristik $p$, und sei $\pi_0:X_0\rightarrow S_0$ die Reduktion von $\pi$ \uber $k$. F\ur die gew\ohnlichen (ordinary) Fasern $X_{t_0}$ der Familie leiten wir eine explizite Formel zur Berechnung des charakteristischen Polynoms des Frobeniusendomorphismus, des {\em Frobeniuspolynoms}, auf dem korrespondierenden Untermodul $M_{cris}\subset H^3_{cris}(X_{t_0})$ her. Sei nun $f_0(z)$ die Potenzreihenl\osung der Differentialgleichung $Pf=0$ in einer Umgebung der Null. Da eine reziproke Nullstelle des Frobeniuspolynoms in einem Teichm\uller-Punkt $t$ durch $f_0(z)/f_0(z^p)|_{z=t}$ gegeben ist, ist ein entscheidender Schritt in der Berechnung des Frobeniuspolynoms die Konstruktion einer $p-$adischen analytischen Fortsetzung des Quotienten $f_0(z)/f_0(z^p)$ auf den Rand des $p-$adischen Einheitskreises. Kann man die Koeffizienten von $f_0$ mithilfe der konstanten Terme in den Potenzen eines Laurent-Polynoms, dessen Newton-Polyeder den Ursprung als einzigen inneren Gitterpunkt enth\alt, ausdr\ucken,so beweisen wir gewisse Kongruenz-Eigenschaften unter den Koeffizienten von $f_0$. Diese sind entscheidend bei der Konstruktion der analytischen Fortsetzung. Enth\alt die Faser $X_{t_0}$ einen gew\ohnlichen Doppelpunkt, so erwarten wir im Grenz\ubergang, dass das Frobeniuspolynom in zwei Faktoren von Grad eins und einen Faktor von Grad zwei zerf\allt. Der Faktor von Grad zwei ist dabei durch einen Koeffizienten $a_p$ eindeutig bestimmt. Durchl\auft nun $p$ die Menge aller Primzahlen, so erwarten wir aufgrund des Modularit\atssatzes, dass es eine Modulform von Gewicht vier gibt, deren Koeffizienten durch die Koeffizienten $a_p$ gegeben sind. Diese Erwartung hat sich durch unsere umfangreichen Rechnungen best\atigt. Dar\uberhinaus leiten wir weitere Formeln zur Bestimmung des Frobeniuspolynoms her, in welchen auch die nicht-holomorphen L\osungen der Gleichung $Pf=0$ in einer Umgebung der Null eine Rolle spielen.

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)

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

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.