Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Simplification, approximation and deformation of large models

The high level of realism and interaction in many computer graphic applications requires techniques for processing complex geometric models. First, we present a method that provides an accurate low-resolution approximation from a multi-chart textured model that guarantees geometric fidelity and correct preservation of the appearance attributes. Then, we introduce a mesh structure called Compact Model that approximates dense triangular meshes while preserving sharp features, allowing adaptive reconstructions and supporting textured models. Next, we design a new space deformation technique called *Cages based on a multi-level system of cages that preserves the smoothness of the mesh between neighbouring cages and is extremely versatile, allowing the use of heterogeneous sets of coordinates and different levels of deformation. Finally, we propose a hybrid method that allows to apply any deformation technique on large models obtaining high quality results with a reduced memory footprint and a high performance.

Visibility and proximity on triangulated surfaces

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem: punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmes de geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada per calcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Com a aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntes sobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos.

Estructura i ultraestructura testicular del mascle reproductor porcí (Sus domesticus)

El present treball analitza al microscopi òptic i al microscopi electrònic de transmissió el testicle de Sus domesticus (raça Landrace - varietat anglesa) a partir de mascles reproductors porcins adults i sans. L'objectiu principal de tots els centres d'Inseminació Artificial Porcina i de les Explotacions de Selecció i Multiplicació Porcina és garantir una excel·lent qualitat espermàtica al llarg de la vida reproductiva útil d'un mascle reproductor porcí. Així doncs, un millor coneixement dels patrons estructural i ultraestructural normals del testicle permetrà diagnosticar amb facilitat quina ha estat l'estructura o funció testicular afectada quan s'observa una disminució de la qualitat del semen. Les anàlisis seminals i hormonals són certament crucials en la valoració d'aquests mascles, però, no són totalment informatives de les alteracions testiculars, ja que és necessari conèixer l'organització microscòpica. Diversos estudis sobre testicle han demostrat que els marcadors més sensibles per a l'avaluació de la funció testicular són els següents: (1) la grandària testicular, (2) el gruix i l'organització de la càpsula testicular, (3) el percentatge de túbuls seminífers i de teixit intersticial en el parènquima testicular, (4) el diàmetre dels túbuls seminífers, (5) l'alçada i la composició de cèl·lules germinals de l'epiteli seminífer, (6) el gruix i l'organització de la làmina pròpia i, (7) la morfologia i la grandària de les cèl·lules de Leydig. El primer objectiu concret del present estudi ha estat, per tant, caracteritzar tots aquests paràmetres testiculars en mascles porcins sans i adults. L'organització estructural del testicle i les mesures quantitatives utilitzades com a marcadors no mostren diferències significatives ni entres els mascles porcins (P > 0,01), ni entre el testicle dret i l'esquerre (P > 0,01). Els testicles, de 330,80  16,99 g de pes, estan envoltats per una càpsula, de 2.375,13  246,68 m de gruix, la qual es divideix en tres capes: la túnica vaginalis constitueix l'1,82  0,78 % de la càpsula i està composta per una capa mesotelial externa i una capa interna de teixit conjuntiu dens; la túnica albuginea representa el 37,31  3,27 % i és de teixit conjuntiu dens i, la túnica vasculosa constitueix el 64,24 4,40 % i és de teixit conjuntiu lax. En el parènquima testicular els túbuls seminífers i el teixit intersticial representen el 72,44  2,12 % i el 27,46  2,12 %, respectivament. Els túbuls seminífers, de 226,23  18,08 m de diàmetre, es troben fortament recargolats i empaquetats, i estan compostos per la làmina pròpia i l'epiteli seminífer. La làmina pròpia, de 4-4,5 m de gruix, està formada per la làmina basal i dues capes de cèl·lules peritubulars. L'epiteli seminífer, amb una alçada mitjana de 66,11  10,62 m, és columnar i estratificat amb cèl·lules de Sertoli i diferents generacions d'espermatogònies, espermatòcits i espermàtides. El teixit intersticial és un teixit conjuntiu lax amb abundants cèl·lules de Leydig polièdriques fortament empaquetades (ca. 15 x 12 m). El segon objectiu concret d'aquest estudi ha estat estudiar des del punt de vista morfològic i morfomètric (alçada, longitud, freqüència relativa d'aparició i durada) els estadis del cicle de l'epiteli seminífer en els mascles porcins de la raça Landrace (varietat anglesa), classificats d'acord amb el mètode de la morfologia tubular. Els estadis premeiòtics ( I, II i III) ocupen el 31,9 % del cicle espermatogènic i es caracteritzen, principalment, per la presència de cèl·lules en les fase inicials de la meiosi I. Les primeres etapes de la meiosi I no afecten els paràmetres morfomètrics de l'epiteli seminífer ja que els valors obtinguts per l'alçada de l'epiteli seminífer, la freqüència relativa, la longitud i la durada d'aquests estadis són molt variables. Els estadis meiòtics (IV i V) representen el 16,4 % del cicle espermatogènic i estan constituïts, principlament, per cèl·lules en un estat avançat de la meiosi I i /o cèl·lules en meiosi II. Les últimes fases de la meiosi I i també de la meiosi II tenen lloc ràpidament, la qual cosa resulta en una baixa freqüència relativa d'aparició i, per tant, en una baixa durada dels estadis meiòtics. Els estadis postmeiòtics (VI, VII i VIII) ocupen el 50,6 % del cicle espermatogènic. L'esdeveniment més important que té lloc en aquests estadis és la fase de maduració de l'espermiogènesi. En la fase de maduració, les espermàtides experimenten diverses modificacions morfològiques i estructurals que donen lloc, finalment, als espermatozoides. La complexitat d'aquests processos fa que els estadis postmeiòtics presentin valors més grans de freqüència relativa, longitud i durada. El tercer objectiu concret d'aquest treball ha estat descriure a nivell ultraestructural el procés d'espermiogènesi, i relacionar les transformacions que experimenten les espermàtides en fase d'elongació amb els canvis ultraestructurals que tenen lloc en les diferents cèl·lules que constitueixen el testicle (cèl·lules germinals, de Sertoli i de Leydig, principalment). L'espermiogènesi del mascle porcí de la raça Landrace (varietat anglesa) s'ha dividit en 9 passos que vénen definits per 9 tipus diferents d'espermàtides. Al llarg de l'espermiogènesi no s'observen diferències ultraestructurals significatives (P > 0,01) ni entre els mascles porcins ni entre el testicle esquerre i dret en les cèl·lules que constitueixen el testicle.

The four major N- and C-terminal splice variants of the excitatory amino acid transporter GLT-1 form cell surface homomeric and heteromeric assemblies

The L-glutamate transporter GLT-1 is an abundant CNS membrane protein of the excitatory amino acid transporter (EAAT) family which controls extracellular L-glutamate levels and is important in limiting excitotoxic neuronal death. Using RT-PCR, we have determined that four mRNAs encoding GLT-1 exist in mouse brain, with the potential to encode four GLT-1 isoforms that differ in their N- and C-termini. We expressed all four isoforms (termed MAST-KREK, MPK-KREK, MAST-DIETCI and MPK-DIETCI according to amino acid sequence) in a range of cell lines and primary astrocytes and show that each isoform can reach the cell surface. In transfected HEK-293 or COS-7 cells, all four isoforms support high-affinity sodium-dependent L-glutamate uptake with identical pharmacological and kinetic properties. Inserting a viral epitope (V5, HA or FLAG) into the second extracellular domain of each isoform allowed co-immunoprecipitation and tr-FRET studies using transfected HEK-293 cells. Here we show for the first time that each of the four isoforms are able to combine to form homomeric and heteromeric assemblies, each of which are expressed at the cell surface of primary astrocytes. After activation of protein kinase C by phorbol ester, V5-tagged GLT-1 is rapidly removed from the cell surface of HEK-293 cells and degraded. This study provides direct biochemical evidence for oligomeric assembly of GLT-1 and reports the development of novel tools to provide insight into the trafficking of GLT-1.

Bacterial polysaccharides suppress induced innate immunity by calcium chelation

Bacterial pathogens and symbionts must suppress or negate host innate immunity. However, pathogens release conserved oligomeric and polymeric molecules or MAMPs (Microbial Associated Molecular Patterns), which elicit host defenses [1], [2] and [3]. Extracellular polysaccharides (EPSs) are key virulence factors in plant and animal pathogenesis, but their precise function in establishing basic compatibility remains unclear [4], [5], [6] and [7]. Here, we show that EPSs suppress MAMP-induced signaling in plants through their polyanionic nature [4] and consequent ability to chelate divalent calcium ions [8]. In plants, Ca2+ ion influx to the cytosol from the apoplast (where bacteria multiply [4], [5] and [9]) is a prerequisite for activation of myriad defenses by MAMPs [10]. We show that EPSs from diverse plant and animal pathogens and symbionts bind calcium. EPS-defective mutants or pure MAMPs, such as the flagellin peptide flg22, elicit calcium influx, expression of host defense genes, and downstream resistance. Furthermore, EPSs, produced by wild-type strains or purified, suppress induced responses but do not block flg22-receptor binding in Arabidopsis cells. EPS production was confirmed in planta, and the amounts in bacterial biofilms greatly exceed those required for binding of apoplastic calcium. These data reveal a novel, fundamental role for bacterial EPS in disease establishment, encouraging novel control strategies.

Ribonucleocapsid formation of severe acute respiratory syndrome coronavirus through molecular action of the N-terminal domain of N protein

Conserved among all coronaviruses are four structural proteins: the matrix (M), small envelope (E), and spike (S) proteins that are embedded in the viral membrane and the nucleocapsid phosphoprotein (N), which exists in a ribonucleoprotein complex in the lumen. The N-terminal domain of coronaviral N proteins (N-NTD) provides a scaffold for RNA binding, while the C-terminal domain (N-CTD) mainly acts as oligomerization modules during assembly. The C terminus of the N protein anchors it to the viral membrane by associating with M protein. We characterized the structures of N-NTD from severe acute respiratory syndrome coronavirus (SARS-CoV) in two crystal forms, at 1.17 A (monoclinic) and at 1.85 A (cubic), respectively, resolved by molecular replacement using the homologous avian infectious bronchitis virus (IBV) structure. Flexible loops in the solution structure of SARS-CoV N-NTD are now shown to be well ordered around the beta-sheet core. The functionally important positively charged beta-hairpin protrudes out of the core, is oriented similarly to that in the IBV N-NTD, and is involved in crystal packing in the monoclinic form. In the cubic form, the monomers form trimeric units that stack in a helical array. Comparison of crystal packing of SARS-CoV and IBV N-NTDs suggests a common mode of RNA recognition, but they probably associate differently in vivo during the formation of the ribonucleoprotein complex. Electrostatic potential distribution on the surface of homology models of related coronaviral N-NTDs suggests that they use different modes of both RNA recognition and oligomeric assembly, perhaps explaining why their nucleocapsids have different morphologies.

Investigation of cooperativity in the binding of ligands to the D-2 dopamine receptor

The D 2 dopamine receptor exists as dimers or as higher-order oligomers, as determined from data from physical experiments. In this study, we sought evidence that this oligomerization leads to cooperativity by examining the binding of three radioligands ([H-3] nemonapride, [H-3] raclopride, and [H-3] spiperone) to D 2 dopamine receptors expressed in membranes of Sf9 cells. In saturation binding experiments, the three radioligands exhibited different B-max values, and the B-max values could be altered by the addition of sodium ions to assays. Despite labeling different numbers of sites, the different ligands were able to achieve full inhibition in competition experiments. Some ligand pairs also exhibited complex inhibition curves in these experiments. In radioligand dissociation experiments, the rate of dissociation of [H-3] nemonapride or [H-3] spiperone depended on the sodium ion concentration but was independent of the competing ligand. Although some of the data in this study are consistent with the behavior of a cooperative oligomeric receptor, not all of the data are in agreement with this model. It may, therefore, be necessary to consider more complex models for the behavior of this receptor.

Structure of the snake-venom toxin convulxin

Snake venoms contain a number of proteins that interact with components of the haemostatic system that promote or inhibit events leading to blood- clot formation. The snake- venom protein convulxin ( Cvx) binds glycoprotein ( GP) VI, the platelet receptor for collagen, and triggers signal transduction. Here, the 2.7 Angstrom resolution crystal structure of Cvx is presented. In common with other members of this snake-venom protein family, Cvx is an alphabeta- heterodimer and conforms to the C- type lectin- fold topology. Comparison with other family members allows a set of Cvx residues that form a concave surface to be putatively implicated in GPVI binding. Unlike other family members, with the exception of flavocetin- A ( FL- A), Cvx forms an (alphabeta)(4) tetramer. This oligomeric structure is consistent with Cvx clustering GPVI molecules on the surface of platelets and as a result promoting signal transduction activity. The Cvx structure and the location of the putative binding sites suggest a model for this multimeric signalling assembly.

Flavonoid supplement improves leg health and reduces fluid retention in pre-menopausal women in a double-blind, placebo-controlled study

Flavonoid extracts derived from plant foods have been shown to benefit certain types of fluid retention. However, no studies have investigated these compounds for use in premenstrual fluid retention, a complaint common among women with otherwise normal menstrual cycles. Therefore, we conducted a double-blind, placebo-controlled, pilot study into the effect of a daily flavonoid extract (Colladeen(R), 320 mg oligomeric procyanidins) on premenstrual fluid retention. Fluid retention was assessed at baseline and throughout 4 menstrual cycles of the intervention using validated questionnaires. Leg girth was also measured at baseline and at the end of the study. Thirty subjects completed the study (n = 18 active treatment; n = 12 placebo). Although no significant changes in leg girth measurements were noted, there was a significant improvement in subjective "leg health" scores after flavonoid treatment compared to placebo (p = 0.013). Furthermore, this was accompanied by an improvement in reported premenstrual fluid retention nearing significance (p = 0.066). We conclude that flavonoids supplements may provide a new therapeutic direction to counter premenstrual fluid retention and improve leg health. A larger study is now warranted.

Flavonoid supplement improves leg health and reduces fluid retention in pre-menopausal women in a double-blind, placebo-controlled study

Flavonoid extracts derived from plant foods have been shown to benefit certain types of fluid retention. However, no studies have investigated these compounds for use in premenstrual fluid retention, a complaint common among women with otherwise normal menstrual cycles. Therefore, we conducted a double-blind, placebo-controlled, pilot study into the effect of a daily flavonoid extract (Colladeen(R), 320 mg oligomeric procyanidins) on premenstrual fluid retention. Fluid retention was assessed at baseline and throughout 4 menstrual cycles of the intervention using validated questionnaires. Leg girth was also measured at baseline and at the end of the study. Thirty subjects completed the study (n = 18 active treatment; n = 12 placebo). Although no significant changes in leg girth measurements were noted, there was a significant improvement in subjective "leg health" scores after flavonoid treatment compared to placebo (p = 0.013). Furthermore, this was accompanied by an improvement in reported premenstrual fluid retention nearing significance (p = 0.066). We conclude that flavonoids supplements may provide a new therapeutic direction to counter premenstrual fluid retention and improve leg health. A larger study is now warranted.

Investigation of cooperativity in the binding of ligands to the D-2 dopamine receptor

The D 2 dopamine receptor exists as dimers or as higher-order oligomers, as determined from data from physical experiments. In this study, we sought evidence that this oligomerization leads to cooperativity by examining the binding of three radioligands ([H-3] nemonapride, [H-3] raclopride, and [H-3] spiperone) to D 2 dopamine receptors expressed in membranes of Sf9 cells. In saturation binding experiments, the three radioligands exhibited different B-max values, and the B-max values could be altered by the addition of sodium ions to assays. Despite labeling different numbers of sites, the different ligands were able to achieve full inhibition in competition experiments. Some ligand pairs also exhibited complex inhibition curves in these experiments. In radioligand dissociation experiments, the rate of dissociation of [H-3] nemonapride or [H-3] spiperone depended on the sodium ion concentration but was independent of the competing ligand. Although some of the data in this study are consistent with the behavior of a cooperative oligomeric receptor, not all of the data are in agreement with this model. It may, therefore, be necessary to consider more complex models for the behavior of this receptor.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Tools for regularizing Array Designs

This paper makes a contribution in bridging the theory and practice of the polyhedral model for designing parallel algorithms. Although the theory of polyhedral model is well developed, designers of massively parallel algorithms are unable to benefit from the theory due to the lack of software tools that incorporate the wide range of transformations that are possible in the model. The Uniformization tool that we developed was the first to integrate a number of techniques and to completely automate the transformation step allowing designers to explore a wide range of feasible designs from high-level specifications.