An approach to teach Calculus/Mathematical Analysis (for engineering students) using computers and active learning – its conception, development of materials and evaluation

Dissertação para obtenção do Grau de Doutor em Ciências da Educação

Participatory Surveillance and Mathematical Models in Epidemiologic Research: Successes and Challenges

Theoretical epidemiology aims to understand the dynamics of diseases in populations and communities. Biological and behavioral processes are abstracted into mathematical formulations which aim to reproduce epidemiological observations. In this thesis a new system for the self-reporting of syndromic data — Influenzanet — is introduced and assessed. The system is currently being extended to address greater challenges of monitoring the health and well-being of tropical communities.(...)

Mathematical and numerical methods for inverse problems using fundamental solutions techniques

Fundação para a Ciência e a Tecnologia - SFRH/BD/27914/2006

Formação de professores no programa nacional para a alfabetização na idade certa com uso das TIC: um estudo de caso no ensino fundamental

Dissertação de mestrado em Ciências da Educação (área de especialização em Tecnologia Educativa)

Mathematical and numerical analysis for coagulation-fragmentation equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Mathematical model to analyze the heat transfer in tunnel kilns for burning of ceramics

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2013

Mathematical modeling and evolution of signal transduction pathways and networks

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2013

Mathematical models of influenza A virus infection : from intracellular replication to virus growth in cell populations

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2015

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work.

A mathematical model to describe fat oxidation kinetics during graded exercise.

PURPOSE: The purpose of this study was to develop a mathematical model (sine model, SIN) to describe fat oxidation kinetics as a function of the relative exercise intensity [% of maximal oxygen uptake (%VO2max)] during graded exercise and to determine the exercise intensity (Fatmax) that elicits maximal fat oxidation (MFO) and the intensity at which the fat oxidation becomes negligible (Fatmin). This model included three independent variables (dilatation, symmetry, and translation) that incorporated primary expected modulations of the curve because of training level or body composition. METHODS: Thirty-two healthy volunteers (17 women and 15 men) performed a graded exercise test on a cycle ergometer, with 3-min stages and 20-W increments. Substrate oxidation rates were determined using indirect calorimetry. SIN was compared with measured values (MV) and with other methods currently used [i.e., the RER method (MRER) and third polynomial curves (P3)]. RESULTS: There was no significant difference in the fitting accuracy between SIN and P3 (P = 0.157), whereas MRER was less precise than SIN (P < 0.001). Fatmax (44 +/- 10% VO2max) and MFO (0.37 +/- 0.16 g x min(-1)) determined using SIN were significantly correlated with MV, P3, and MRER (P < 0.001). The variable of dilatation was correlated with Fatmax, Fatmin, and MFO (r = 0.79, r = 0.67, and r = 0.60, respectively, P < 0.001). CONCLUSIONS: The SIN model presents the same precision as other methods currently used in the determination of Fatmax and MFO but in addition allows calculation of Fatmin. Moreover, the three independent variables are directly related to the main expected modulations of the fat oxidation curve. SIN, therefore, seems to be an appropriate tool in analyzing fat oxidation kinetics obtained during graded exercise.

Conceptions et représentations comparées du "héros" : une catégorie complexe : étude comparative des données épiques grecques et vétérotestamentaires

Ce travail traite de la catégorie du « héros » et s'articule autour d'une comparaison entre les récits de la Grèce antique, principalement la poésie épique, et le Proche-Orient ancien, essentiellement les textes vétérotestamentaires - une étude dont l'objet est dès lors principalement textuel. Partant du constat, si simple mais lourd de conséquence, que le mot français « héros » vient du substantif grec rjpcoç, le texte débute par un travail de décentrement face aux référents contemporains liés à l'emploi du terme dans nos langues modernes : le « héros » n'est pas forcément le rjpcoç. Riche de cette analyse, la deuxième partie du travail se tourne vers l'Antiquité grecque, et plus précisément vers les poésies homérique et hésiodique. L'analyse de l'emploi du vocabulaire héroïque au sein de ces récits permet de cerner plus précisément les diverses figures appelées rjpcoç - figures qui semblent si différentes les unes des autres alors qu'elles partagent un qualificatif commun. Fort de cet apport quant à la compréhension du rjpcoç épique grec, une troisième partie questionne la présence de la catégorie du « héros » dans la Bible hébraïque mais aussi dans ses traductions en langues modernes. Constatant que le mot « héros » n 'apparaît jamais dans les langues anciennes que sont le grec de la LXX ou le latin de la Vulgate, les figures vétérotestamentaires sont repensées dans leur contexte proche- oriental, les voyant sous la lumière du Levant - lumière qui est la leur - et ce grâce au vocabulaire somme toute fort précis de la langue hébraïque. Finalement, une partie conclusive tente de mettre en exergue ce que la comparaison des récits grecs épiques et vétérotestamentaires a permis de soulever quant à leurs catégories « héroïques » respectives. L'enjeu est également de penser de manière critique ce que les cultures occidentales contemporaines nomment « héros », s'appuyant si souvent sur un « double héritage » gréco-romain et judéo-chrétien.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.