Hyperbolic type metrics and distortion of quasiconformal map pings

This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.

Systematization, distribution and territory of the caudal cerebral artery on the brain's surface of the turkey (Meleagris gallopavo)

Thirty Meleagris gallopavo heads with their neck segments were used. Animals were contained and euthanized with the association of mebezonium iodide, embutramide and tetracaine hydrochloride (T 61, Intervet ) by intravenous injection. The arterial system was rinsed with cold saline solution (15°C), with 5000IU heparin and filled with red-colored latex. The samples were fixed in 20% formaldehyde for seven days. The brains were removed with a segment of cervical spinal cord and after, the dura-mater was removed and the arteries dissected. The cerebral carotid arteries, after the intercarotid anastomosis, were projected around the hypophysis, until they reached the tuber cinereum and divided into their terminal branches, the caudal branch and the rostral branch. The rostral branch was projected rostrolateralwards and gave off, in sequence, two collateral branches, the caudal cerebral and the middle cerebral arteries and the terminal branch was as cerebroethmoidal artery. The caudal cerebral artery of one antimere formed the interhemispheric artery, which gave off dorsal hemispheric branches to the convex surface of both antimeres. Its dorsal tectal mesencephalic branch, of only one antimere, originated the dorsal cerebellar artery. In the interior of the cerebral transverse fissure, after the origin of the dorsal tectal mesencephalic artery, the caudal cerebral artery emitted occipital hemispheric branches, pineal branches and medial hemispheric branches, on both antimeres. The caudal cerebral artery's territory comprehended the entire surface of the dorsal hemioptic lobe, the rostral surface of the cerebellum, the diencephalic structures, the caudal pole and the medial surface of the cerebral hemisphere and in the convex surface, the sagittal eminence except for its most rostral third. Due to the asymmetry found in the caudal cerebral arteries' ramifications, the models were classified into three types and their respective subtypes.

The Shadow Moiré method using the phase shifting technique and digital image processing: computational implementation and application to the 3D-reconstruction of a buckled plate

The Shadow Moiré fringe patterns are level lines of equal depth generated by interference between a master grid and its shadow projected on the surface. In simplistic approach, the minimum error is about the order of the master grid pitch, that is, always larger than 0,1 mm, resulting in an experimental technique of low precision. The use of a phase shift increases the accuracy of the Shadow Moiré technique. The current work uses the phase shifting method to determine the surfaces three-dimensional shape using isothamic fringe patterns and digital image processing. The current study presents the method and applies it to images obtained by simulation for error evaluation, as well as to a buckled plate, obtaining excellent results. The method hands itself particularly useful to decrease the errors in the interpretation of the Moiré fringes that can adversely affect the calculations of displacements in pieces containing many concave and convex regions in relatively small areas.

Leaf anatomy of two Anemia Sw. species (Schizaeaceae-Pteridophyte) from a rocky outcrop in Niterói, Rio de Janeiro, Brazil

The ferns Anemia tomentosa (Sav.) Sw. var. anthriscifolia (Schrad.) Mickel and Anemia villosa Humb. & Bonpl. ex Willd. are widely associated with vegetation islands on rocky outcrops in Rio de Janeiro. Both species are desiccation tolerant. The leaf anatomy of these species was examined aiming to identify morphological characteristics that would allow the establishment of these species in water-scarce environments. The plants were harvested on "Pedra de Itacoatiara" and prepared according to the usual procedures. The petiole has a uniseriate epidermis with lignified cell walls, conical stegmata, and uniseriate multicelular and glandular trichomes. In A. villosa, the stomata protrude in a respiratory line. Under the epidermis the cells have thick, lignified walls. The parenchyma has phenolic compounds and starch grains. The petiole vascular bundles are surrounded by endodermis with Casparian strips and the xylem is V-shaped (A. villosa) or arc-shaped (A. tomentosa var. anthriscifolia). The leaf blades have a uniseriate epidermis with sinuous anticlinal and convex periclinal walls, conical stegmata and chloroplasts on both surfaces. The leaf margins of A. villosa have lignified cells. The guard cells of the stomata on the abaxial surface are on the same level or are raised above ordinary epidermal cells. Multicelular uniseriate trichomes and glandular hairs were observed. The dorsiventral mesophyll has loosely packed chlorenchyma with arm-shaped and H-shaped cells. The vascular bundles are surrounded by endodermis with Casparian strips and with parenchymatic extensions towards the epidermis. Anatomical results were analyzed considering the interaction of these plants with abiotic factors.

Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

Sedimentology and taphonomy of storm-generated shell beds from the Verulam formation (Ordovician), Lakefield and Gamebridge quarries, Southern Ontario, Canada /

The Verulam Formation (Middle Ordovician) at the Lakefield Quarry and Gamebridge Quarry, southern Ontario, is comprised of five main lithofacies. These include shoal deposits consisting of Lithofacies 1, winnowed crinoidal grainstones and, shelf deposits consisting of: Lithofacies 2, wackestones, packstones, grainstones, and rudstones; Lithofacies 3, laminated calcisiltites; Lithofacies 4, nodular wackestones and mudstones; and, Lithofacies 5, laminated mudstones and shales. The distribution of the lithofacies was influenced by variations in storm frequency and intensity during a relative sea level fall. Predominant convex-up attitudes of concavo-convex shells within shell beds suggest syndepositional reworking during storm events. The bimodal orientations of shell axes on the upper surfaces of the shell beds indicates deposition under wave-generated currents. The sedimentary features and shell orientations indicate that the shell beds were deposited during storm events and not by the gradual accumulation of shelly material. Cluster and principal component analysis of relative abundance data of the taxa in the shell beds, interbedded nodular wackestones and mudstones, and laminated mudstones and shales, indicates one biofacies comprised of three main assemblages: a strophomenid (Sowerbyelladominated) assemblage, a transitional mixed strophomenid-atrypid assemblage and an atrypid (Zygospira-dominatQd) assemblage. The occurrence of the strophomenid, the strophomenid-atrypid and atrypid assemblages were controlled by storm-driven allogenic taphonomic feedback.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with our problem is convex : its core is therefore large and easily described. Next, we propose the following fairness requirement : no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare vector in the core satisfies this condition : it is the marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Some Implications of the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy

In an economy where cash can be stored costlessly (in nominal terms), the nominal interest rate is bounded below by zero. This paper derives the implications of this nonnegativity constraint for the term structure and shows that it induces a nonlinear and convex relation between short- and long-term interest rates. As a result, the long-term rate responds asymmetrically to changes in the short-term rate, and by less than predicted by a benchmark linear model. In particular, a decrease in the short-term rate leads to a decrease in the long-term rate that is smaller in magnitude than the increase in the long-term rate associated with an increase in the short-term rate of the same size. Up to the extent that monetary policy acts by affecting long-term rates through the term structure, its power is considerably reduced at low interest rates. The empirical predictions of the model are examined using data from Japan.

Solidarity in Choosing a Location on a Cycle

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.

Oligarchies in Spatial Environments

In spatial environments we consider social welfare functions satisfying Arrow’s requirements, i.e. weak Pareto and independence of irrelevant alternatives. Individual preferences measure distances between alternatives according to the Lp-norm (for a fixed p => 1). When the policy space is multi-dimensional and the set of alternatives has a non-empty interior and it is compact and convex, any quasi-transitive welfare function must be oligarchic. As a corollary we obtain that for transitive welfare functions weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

L’étude de l’interaction entre les chondrocytes et le collagène modifié par le 4-Hydroxynonénal : implication dans le développement de l’arthrose

OBJECTIF: Récemment, nous avons démontré que la modification du collagène type II (Col II) par le 4-hydroxynonénal (HNE), un produit de la peroxydation lipidique, est augmentée dans le cartilage arthrosique sans qu’on sache la signification de cette augmentation dans la pathogenèse de l’arthrose. L’objectif de cette étude vise à démontrer que cette modification affecte l’interaction chondrocytes/matrice extracellulaire (MEC) et en conséquence induit des changements phénotypiques et fonctionnels de ces cellules. METHODES: Des plaques de culture ont été préalablement cotées avec du Col II puis traitées avec du HNE (0.1-2 mM) excepté le puits contrôle. Les chondrocytes ont été ensuite ensemencés puis incubés pendant 48 heures. La viabilité des cellules est évaluée par le test MTT. Le Western blot est utilisé pour mesurer l’expression des molécules d’adhésion (l’ICAM-1 et l’intégrine α1β1), de la cyclooxygenase-2 (COX-2), du Col II ainsi que la phosphorylation de la p38 MAPK, ERK1/2 et NF-κB-p65. La RT-PCR en temps réel est utilisée pour mesurer l’expression de l’ARNm de l’ICAM-1, des intégrines α1β1, de la COX-2 et de la métalloprotéinases-13 (MMP-13). La détermination de l’expression de l’ICAM-1 à la surface des cellules est réalisée par cytométrie de flux. Des kits commerciaux ont servi pour mesurer le niveau de la MMP-13, de la prostaglandine E2 (PGE2), de l’activité de la caspase-8 et de la phosphorylation de la p38 MAPK, ERK1/2 et NF-κB-p65. RESULTATS: La modification du Col II par 0.2 mM HNE induit significativement l’expression des molécules d’adhésion telles que l’ICAM-1 et l’intégrine α1β1, de la MMP-13 sans avoir un effet sur la morphologie, la survie et le phénotype cellulaires. Nos résultats montrent aussi une forte augmentation de la phosphorylation de la p38 MAPK, d’ERK1/2 et de NF-κB-p65. Cependant, la modification du Col II par 2 mM HNE affecte la morphologie et la viabilité cellulaires et induit l’activité de la caspase-8. Elle inhibe fortement l’expression des integrines α1β1 et du Col II ainsi que la phosphorylation de l’ERK1/2 et de NF-κB-p65, mais par contre, induit significativement la production de la COX-2 et son produit la PGE2 ainsi que la phosphorylation de la p38 MAPK. Fait intéressant, le prétraitement des complexes HNE/Col II par 0.1 mM de carnosine empêche les changements phénotypiques et fonctionnels des chondrocytes. CONCLUSION : Ces nouveaux résultats suggèrent le rôle important de la modification du Col II par le HNE dans l’arthrose, en affectant le phénotype et le fonctionnement cellulaires des chondrocytes. La carnosine, par sa capacité de neutraliser le HNE, a révélé d’être un agent promoteur dans le traitement de l’arthrose.

Asset Pricing in a Production Economy with Chew–Dekel Preferences

In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with Chew–Dekel risk preferences and convex capital adjustment costs. When households display levels of disappointment aversion consistent with the experimental evidence, a version of the model parameterized to match the volatility of output and consumption growth generates unconditional expected asset returns and price of risk in line with the historical data. For the model with Epstein–Zin preferences to generate similar statistics, the relative risk aversion coefficient needs to be about 55, two orders of magnitude higher than the available estimates. We argue that this is not surprising, given the limited risk imposed on agents by a reasonably calibrated stochastic growth model.