Geometry based visualization with OpenCL

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

In situ measured cross section geometry of old timber structures and its influence on structural safety

Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay, using a simplified probabilistic geometry model and considering a remaining capacity factor for the decayed areas. This model can be used for assessing the safety of the structure at present and for predicting future performance.

Mobile image processing to support educational geometry games

The mobile IT era is here, it is still growing and expanding at a steady rate and, most of all, it is entertaining. Mobile devices are used for entertainment, whether social through the so-called social networks, or private through web browsing, video watching or gaming. Youngsters make heavy use of these devices, and even small children show impressive adaptability and skill. However not much attention is directed towards education, especially in the case of young children. Too much time is usually spent in games which only purpose is to keep children entertained, time that could be put to better use such as developing elementary geometric notions. Taking advantage of this pocket computer scenario, it is proposed an application geared towards small children in the 6 – 9 age group that allows them to consolidate knowledge regarding geometric shapes, forming a stepping stone that leads to some fundamental mathematical knowledge to be exercised later on. To achieve this goal, the application will detect simple geometric shapes like squares, circles and triangles using the device’s camera. The novelty of this application will be a core real-time detection system designed and developed from the ground up for mobile devices, taking into account their characteristic limitations such as reduced processing power, memory and battery. User feedback was be gathered, aggregated and studied to assess the educational factor of the application.

A GIS extension model to calculate urban heat island intensity based on urban geometry

This paper presents a simulation model, which was incorporated into a Geographic Information System (GIS), in order to calculate the maximum intensity of urban heat islands based on urban geometry data. The method-ology of this study stands on a theoretical-numerical basis (Okeâ s model), followed by the study and selection of existing GIS tools, the design of the calculation model, the incorporation of the resulting algorithm into the GIS platform and the application of the tool, developed as exemplification. The developed tool will help researchers to simulate UHI in different urban scenarios.

Aortic stenosis. Gender influence on left ventricular geometry and function in patients under 70 years of age

OBJECTIVE: To verify if adaptive left ventricle (LV) characteristics are also present in individuals under 70 years of age with severe aortic stenosis (AS). METHODS: The study comprised 40 consecutive patients under 70 years of age with AS and no associated coronary artery disease, referred for valve surgery. Out of the 40 patients, 22 were men and 18 women, and the mean age was 49.8±14.3 years. Cardiac symptoms, presence of systemic hypertension (SH), functional class according to the New York Heart Association (NYHA), and valve lesion etiology were considered. LV cavity dimensions, ejection fraction (EF), fractional shortening (FS), mass (MS), and relative diastolic thickness (RDT) were examined by Doppler echocardiography. RESULTS: Fourteen (63.6%) men and 11 (61.6%) women were classified as NYHA class III/IV (p=0.70). There was no difference in the frequency of angina, syncope or dyspnea between genders. The incidence of SH was greater in women than in men (10 versus 2, p=0.0044). Women had a smaller LV end-diastolic diameter index (32.1±6.5 x 36.5±5.3mm/m², p=0.027), LV end-systolic diameter index (19.9±5.9 x 26.5±6.4mm/m², p=0.0022) and LV mass index (MS) (211.4±71.1 x 270.9±74.9g/m², p=0.017) when compared with men. EF (66.2±13.4 x 52.0±14.6%, p=0.0032), FS (37.6±10.7 x 27.9±9.6%, p=0.0046) and RDT (0.58±0.22 x 0.44±0.09, p=0.0095) were significantly greater in women than in men. CONCLUSION: It is the patient gender rather than age that influences left ventricular adaptive response to AS.

Left Ventricular Diastolic Function in Essential Hypertensive Patients: Influence of Age and Left Ventricular Geometry

PURPOSE - To evaluate diastolic dysfunction (DD) in essential hypertension and the influence of age and cardiac geometry on this parameter. METHODS - Four hundred sixty essential hypertensive patients (HT) underwent Doppler echocardiography to obtain E/A wave ratio (E/A), atrial deceleration time (ADT), and isovolumetric relaxation time (IRT). All patients were grouped according to cardiac geometric patterns (NG - normal geometry; CR - concentric remodeling; CH- concentric hypertrophy; EH - eccentric hypertrophy) and to age (<40; 40 - 60; >60 years). One hundred six normotensives (NT) persons were also evaluated. RESULTS - A worsening of diastolic function in the HT compared with the NT, including HT with NG (E/A: NT - 1.38±0.03 vs HT - 1.27±0.02, p<0.01), was observed. A higher prevalence of DD occurred parallel to age and cardiac geometry also in the prehypertrophic groups (CR). Multiple regression analysis identified age as the most important predictor of DD (r²=0.30, p<0.01). CONCLUSION - DD was prevalent in this hypertensive population, being highly affected by age and less by heart structural parameters. DD is observed in incipient stages of hypertensive heart disease, and thus its early detection may help in the risk stratification of hypertensive patients.

Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Ricci-flat complex geometry and its applications

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2010

Adelic convex geometry of numbers

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Wing geometry as a tool for studying the Lutzomyia longipalpis (Diptera: Psychodidae) complex

Toro Toro (T) and Yungas (Y) have been described as genetically well differentiated populations of the Lutzomyia longipalpis (Lutz & Neiva, 1912) complex in Bolivia. Here we use geometric morphometrics to compare samples from these populations and new populations (Bolivia and Nicaragua), representing distant geographical origins, qualitative morphological variation ("one-spot" or "two-spots" phenotypes), ecologically distinct traits (peridomestic and silvatic populations), and possibly different epidemiological roles (transmitting or nor transmitting Leishmania chagasi). The Nicaragua (N) (Somotillo) sample was "one-spot" phenotype and a possible peridomestic vector. The Bolivian sample of the Y was also "one-spot" phenotype and a demonstrated peridomestic vector of visceral leishmaniasis (VL). The three remaining samples were silvatic, "two-spots" phenotypes. Two of them (Uyuni and T) were collected in the highlands of Bolivian where VL never has been reported. The last one (Robore, R) came from the lowlands of Bolivia, where human cases of VL are sporadically reported. The decomposition of metric variation into size and shape by geometric morphometric techniques suggests the existence of two groups (N/Y/R, and U/T). Several arguments indicate that such subdivision of Lu. longipalpis could correspond to different evolutionary units.