Computing the persistent homology of range images with alpha shapes

Laser scanning is becoming an increasingly popular method for measuring 3D objects in industrial design. Laser scanners produce a cloud of 3D points. For CAD software to be able to use such data, however, this point cloud needs to be turned into a vector format. A popular way to do this is to triangulate the assumed surface of the point cloud using alpha shapes. Alpha shapes start from the convex hull of the point cloud and gradually refine it towards the true surface of the object. Often it is nontrivial to decide when to stop this refinement. One criterion for this is to do so when the homology of the object stops changing. This is known as the persistent homology of the object. The goal of this thesis is to develop a way to compute the homology of a given point cloud when processed with alpha shapes, and to infer from it when the persistent homology has been achieved. Practically, the computation of such a characteristic of the target might be applied to power line tower span analysis.

Occlusal and dentofacial characteristics of the deciduous dentition and treatment effects of the eruption guidance appliance in the early mixed dentition

The aim of this investigation was to analyze the dental occlusion in the deciduous dentition, and the effects of orthodontic treatment carried out in the early mixed dentition with the eruption guidance appliance. The deciduous occlusion and craniofacial morphology of 486 children (244 girls and 242 boys) were investigated at the onset of the mixed dentition period (mean age 5.1 years, range 4.0-7.8 years). Treatment in the treatment group and follow-up in the control group were started when the first deciduous incisor was exfoliated (T1) and ended when all permanent incisors and first molars were fully erupted (T2). The mean age of the children was 5.1 years (SD 0.5) at T1 and 8.4 years (SD 0.5) at T2. Treatment was carried out with the eruption guidance appliance. Occlusal changes that took place in 167 children were compared with those of 104 untreated control children. Pre- and post-treatment cephalometric radiographs were taken, and the craniofacial morphology of 115 consecutively treated children was compared with that of 104 control children. The prevalence of malocclusion in the deciduous dentition was 68% or 93% depending on how the cut-off value between the acceptable and non-acceptable occlusal characteristic was defined. The early dentofacial features of children with distal occlusion, large overjet and deepbite differed from those with normal occlusion. However, the skeletal pattern of these three malocclusions showed considerable similarity each being characterized by a retrusive mandible, small maxillo-mandibular difference, convex profile, retrusive lower incisors, and large interincisal angle. In the treatment group, overjet and overbite decreased significantly from T1 to T2. Following treatment, a tooth-to-tooth contact was found in 99% of the treated children but only in 24% of the controls. A Class I molar relationship was observed in 90% of the children in the treatment group, and in 48% in the control group. Good alignment of the incisors was observed in 98% of the treated children, whereas upper crowding was found in 32% and lower crowding in 47% of the controls. A significant difference between the groups was found in the mandibular length, midfacial length and maxillo-mandibular differential. The occlusal correction, brought about by the eruption guidance appliance, was achieved mainly through changes in the dentoalveolar region of the mandible. In addition, the appliance seemed to enhance the growth of the mandible. Treatment in the early mixed dentition using the eruption guidance appliance is an effective method to normalize occlusion and reduce further need of orthodontic treatment. Only few spontaneous corrective changes can be expected without active intervention.

A characterization of cooperative TU-games with large monotonic core

[cat] El concepte de joc cooperatiu amb large core és introduït per Sharkey (1982) i el de Population Monotonic Allocation Scheme és definit per Sprumont (1990). Inspirat en aquests conceptes, Moulin (1990) introdueix la noció de large monotonic core donant una caracterització per a jocs de tres jugadors. En aquest document provem que tots els jocs amb large monotonic core són convexes. A més, donem un criteri efectiu per determinar si un joc té large monotonic core o no, i daquí obtenim una caracterització pel cas de quatre jugadors.

A characterization of cooperative TU-games with large monotonic core

[cat] El concepte de joc cooperatiu amb large core és introduït per Sharkey (1982) i el de Population Monotonic Allocation Scheme és definit per Sprumont (1990). Inspirat en aquests conceptes, Moulin (1990) introdueix la noció de large monotonic core donant una caracterització per a jocs de tres jugadors. En aquest document provem que tots els jocs amb large monotonic core són convexes. A més, donem un criteri efectiu per determinar si un joc té large monotonic core o no, i daquí obtenim una caracterització pel cas de quatre jugadors.

Bifurcation of relative equilibria of the (1+3)-body problem

We study the relative equilibria of the limit case of the pla- nar Newtonian 4{body problem when three masses tend to zero, the so-called (1 + 3){body problem. Depending on the values of the in- nitesimal masses the number of relative equilibria varies from ten to fourteen. Always six of these relative equilibria are convex and the oth- ers are concave. Each convex relative equilibrium of the (1 + 3){body problem can be continued to a unique family of relative equilibria of the general 4{body problem when three of the masses are su ciently small and every convex relative equilibrium for these masses belongs to one of these six families.

Reconeixement de gestos de la mà amb el sensor Kinect

El reconeixement dels gestos de la mà (HGR, Hand Gesture Recognition) és actualment un camp important de recerca degut a la varietat de situacions en les quals és necessari comunicar-se mitjançant signes, com pot ser la comunicació entre persones que utilitzen la llengua de signes i les que no. En aquest projecte es presenta un mètode de reconeixement de gestos de la mà a temps real utilitzant el sensor Kinect per Microsoft Xbox, implementat en un entorn Linux (Ubuntu) amb llenguatge de programació Python i utilitzant la llibreria de visió artifical OpenCV per a processar les dades sobre un ordinador portàtil convencional. Gràcies a la capacitat del sensor Kinect de capturar dades de profunditat d’una escena es poden determinar les posicions i trajectòries dels objectes en 3 dimensions, el que implica poder realitzar una anàlisi complerta a temps real d’una imatge o d’una seqüencia d’imatges. El procediment de reconeixement que es planteja es basa en la segmentació de la imatge per poder treballar únicament amb la mà, en la detecció dels contorns, per després obtenir l’envolupant convexa i els defectes convexos, que finalment han de servir per determinar el nombre de dits i concloure en la interpretació del gest; el resultat final és la transcripció del seu significat en una finestra que serveix d’interfície amb l’interlocutor. L’aplicació permet reconèixer els números del 0 al 5, ja que s’analitza únicament una mà, alguns gestos populars i algunes de les lletres de l’alfabet dactilològic de la llengua de signes catalana. El projecte és doncs, la porta d’entrada al camp del reconeixement de gestos i la base d’un futur sistema de reconeixement de la llengua de signes capaç de transcriure tant els signes dinàmics com l’alfabet dactilològic.

Assessment of pelvic floor by three-dimensional-ultrasound in primiparous women according to delivery mode: initial experience from a single reference service in Brazil

PURPOSE: To evaluate changes to the pelvic floor of primiparous women with different delivery modes, using three-dimensional ultrasound. METHODS: A prospective cross-sectional study on 35 primiparae divided into groups according to the delivery mode: elective cesarean delivery (n=10), vaginal delivery (n=16), and forceps delivery (n=9). Three-dimensional ultrasound on the pelvic floor was performed on the second postpartum day with the patient in a resting position. A convex volumetric transducer (RAB4-8L) was used, in contact with the large labia, with the patient in the gynecological position. Biometric measurements of the urogenital hiatus were taken in the axial plane on images in the rendering mode, in order to assess the area, anteroposterior and transverse diameters, average thickness, and avulsion of the levator ani muscle. Differences between groups were evaluated by determining the mean differences and their respective 95% confidence intervals. The proportions of levator ani muscle avulsion were compared between elective cesarean section and vaginal birth using Fisher's exact test. RESULTS: The mean areas of the urogenital hiatus in the cases of vaginal and forceps deliveries were 17.0 and 20.1 cm², respectively, versus 12.4 cm² in the Control Group (elective cesarean). Avulsion of the levator ani muscle was observed in women who underwent vaginal delivery (3/25), however there was no statistically significant difference between cesarean section and vaginal delivery groups (p=0.5). CONCLUSION: Transperineal three-dimensional ultrasound was useful for assessing the pelvic floor of primiparous women, by allowing pelvic morphological changes to be differentiated according to the delivery mode.

Systematization, description and territory of the caudal cerebral artery of the brain in broad-snouted Caiman (Caiman latirostris)

Thirty heads with the neck segment of Caiman latirostris were used. The animals were provided from a creation center called Mister Caiman, under the authorization of the Brazilian Institute of Environment and Renewable Natural Resources (Ibama). Animals were sacrificed according to the slaughtering routine of the abattoir, and the heads were sectioned at the level of the third cervical vertebra. The arterial system was washed with cold saline solution, with drainage through jugular veins. Subsequently, the system was filled with red colored latex injection. Pieces were than fixed in 20% formaldehyde, for seven days. The brains were removed, with a spinal cord segment, the duramater removed and the arteries dissected. At the level of the hypophysis, the internal carotid artery gave off a rostral branch, and a short caudal branch, continuing, naturally, as the caudal cerebral artery. This artery projected laterodorsalwards and, as it overpassed the optic tract, gave off its I (the first) central branch. Penetrated in the cerebral transverse fissure, emitting the diencephalic artery and next its II (second) central branch. Still inside the fissure, originated occipital hemispheric branches and a pineal branch. Emerged from the cerebral transverse fissure, over the occipital pole of the cerebral hemisphere. Projected rostralwards, sagital to the cerebral longitudinal fissure, as interhemispheric artery. This artery gave off medial and convex hemispheric branches to the respective surfaces of the cerebral hemispheres, anastomosed with its contralateral homologous, forming the common ethmoidal artery. This artery entered the fissure between the olfactory peduncles, emerging ventrally and dividing into ethmoidal arteries, right and left, which progressed towards the nasal cavities, vascularizing them. The territory of the caudal cerebral artery included the most caudal area of the base of the cerebral hemisphere, its convex surface, the olfactory peduncles and bulbs, the choroid plexuses and the diencephalus with its parietal organs.

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.

Morphological characterization with image analysis of cocoa beverage powder agglomerated with steam

In this study, the morphological characteristics of cocoa beverage powder granules under minimal, average, and maximal process conditions of a steam agglomerator were studied. a stereoscopic microscope coupled to a digital camera was used for the morphological analysis. The images were analyzed to obtain shape and size descriptors. aiming to evaluate the descriptors, 150 particles were analyzed. The results showed that there was no difference between the shape descriptors - compacity, circularity, roughness, and aspect ratio - in the operating conditions evaluated. It was observed that the cocoa beverage powder granules are elongated in shape. The size descriptors, area, perimeter, perimeter of convex bounding polygon, minimal and maximal Feret diameter, were different in the process conditions for the granules of size above 600 μm. as for the minimal process conditions, especially due to low solid feed rates, there is an increase in the size descriptor values. In addition, under the minimum process conditions, in which there is low solid feed rate (400g/min) for a steam pressure of 1.0 bar, it was obtained a good granular condition with retention of 81.1% of granules on sieves with aperture size between 300 and 1190 μm.

Computational models for and from biology : simple gene assembly and reaction systems

The advancement of science and technology makes it clear that no single perspective is any longer sufficient to describe the true nature of any phenomenon. That is why the interdisciplinary research is gaining more attention overtime. An excellent example of this type of research is natural computing which stands on the borderline between biology and computer science. The contribution of research done in natural computing is twofold: on one hand, it sheds light into how nature works and how it processes information and, on the other hand, it provides some guidelines on how to design bio-inspired technologies. The first direction in this thesis focuses on a nature-inspired process called gene assembly in ciliates. The second one studies reaction systems, as a modeling framework with its rationale built upon the biochemical interactions happening within a cell. The process of gene assembly in ciliates has attracted a lot of attention as a research topic in the past 15 years. Two main modelling frameworks have been initially proposed in the end of 1990s to capture ciliates’ gene assembly process, namely the intermolecular model and the intramolecular model. They were followed by other model proposals such as templatebased assembly and DNA rearrangement pathways recombination models. In this thesis we are interested in a variation of the intramolecular model called simple gene assembly model, which focuses on the simplest possible folds in the assembly process. We propose a new framework called directed overlap-inclusion (DOI) graphs to overcome the limitations that previously introduced models faced in capturing all the combinatorial details of the simple gene assembly process. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs. We also introduce DOI graph-based rewriting rules that capture all the operations of the simple gene assembly model and prove that they are equivalent to the string-based formalization of the model. Reaction systems (RS) is another nature-inspired modeling framework that is studied in this thesis. Reaction systems’ rationale is based upon two main regulation mechanisms, facilitation and inhibition, which control the interactions between biochemical reactions. Reaction systems is a complementary modeling framework to traditional quantitative frameworks, focusing on explicit cause-effect relationships between reactions. The explicit formulation of facilitation and inhibition mechanisms behind reactions, as well as the focus on interactions between reactions (rather than dynamics of concentrations) makes their applicability potentially wide and useful beyond biological case studies. In this thesis, we construct a reaction system model corresponding to the heat shock response mechanism based on a novel concept of dominance graph that captures the competition on resources in the ODE model. We also introduce for RS various concepts inspired by biology, e.g., mass conservation, steady state, periodicity, etc., to do model checking of the reaction systems based models. We prove that the complexity of the decision problems related to these properties varies from P to NP- and coNP-complete to PSPACE-complete. We further focus on the mass conservation relation in an RS and introduce the conservation dependency graph to capture the relation between the species and also propose an algorithm to list the conserved sets of a given reaction system.

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.