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.

Payoff-dependent balancedness and cores (revised version)

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

"Vegeu el resum a l´inici del document del fitxer adjunt."

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

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.

Amener à l'existence : la fragile naissance des nanosystèmes

En partant d'une étude ethnographique dans un laboratoire engagés dans la conception et la réalisation de micro et nanosystèmes, l'article rend compte de la manière dont ces objets sont amenés à l'existence, mais aussi de la fragilité de cette existence d'être technologique. Confronté à de nombreux échecs, les chercheurs en viennent à douter de leur faisabilité technologique, de leur capacité à maintenir l'intérêt des industriels pour ces objets, voire même du sens de l' histoire technologique. Cette histoire, qu' ils croyaient évoluer inéluctablement des microsystèmes vers les nanosystèmes, semble brutalement s'arrêter, voir s'inverser. Les nanosystèmes ne seraient alors qu'un leurre, une illusion plutôt qu'une nouvelle catégorie de technologie. L'existence-même de l'objet est devenue problématique. En suivant les chercheurs, ingénieurs et techniciens au travail, l'article rend compte de la technogénèse comme exploration des modes d'existence des êtres technologiques.

" Laennec CD-ROM " Dix ans d'existence d'un outil multimédia pour l'enseignement des gestes cliniques en pneumologie

Résumé « Laennec CD-ROM » est un programme d'enseignement assisté par ordinateur (EAO) pour l'apprentissage de la sémiologie en pneumologie. Son idée de base était de fournir aux étudiants et aux enseignants un outil d'apprentissage interactif et richement illustré des différents gestes cliniques en pneumologie. Primé en 1994 pour la meilleure contribution multimédia à la European Academie Software Award (EASA-94), il représente un bon exemple de ce qui pouvait être réalisé alors. Mais l'histoire de l'EAO remonte aux années 1960. Un bref historique de l'EAO permet de mieux situer ce programme dans le temps. Et comme tout outil pédagogique, celui-ci s'appuie sur une représentation de comment l'apprentissage se fait. Trois courants pédagogiques majeurs sont présentés. Le behaviorisme ou comportementalisme pour qui le savoir est transmis pour être stocké tel quel par l'apprenant. Pour le cognitivisme, par contre, le contenu est retravaillé par l'apprenant avant d'être stocké, et ce traitement de l'information peut être influencé. Quant au constructivisme, celui-ci prédit que le savoir est construit à l'aide des contenus mis à disposition, mettant en avant l'importance du contexte dans lequel l'apprentissage se fait. Mais indépendamment des orientations pédagogiques, une des question fondamentale est : un enseignement assisté par ordinateur est-il meilleur qu'un enseignement traditionnel ? Étonnamment, il n'est pas facile de répondre à cette question, malgré de . nombreuses études sur le sujet. « Laennec CD-ROM » est constitué de trois parties. Un tutoriel présentant de manière didactique l'inspection, la palpation, la percussion et l'auscultation pulmonaire. Il est richement illustré par des dessins, photos, vidéo et sons d'auscultation. La deuxième partie présente sept patients souffrant de maladies pulmonaires fréquentes. Ce volet du cd-rom permet d'appliquer à des cas les principes de sémiologie appris dans le tutoriel. Pour chaque patient, une anamnèse, un examen clinique (avec des sons d'auscultation) et une série d'examens para-cliniques (imagerie, laboratoire) permettent à l'utilisateur de poser un diagnostic différentiel et un traitement. La troisième partie du cd-rom est un petit historique sur René, Théophile, Hyacinthe Laennec, l'inventeur du stéthoscope. Pour terminer, la conception et la réalisation du programme sont présentées en détail ainsi que sa validation et son utilisation.

On the existence of hysteresis in the Kuramoto model with bimodal frequency distributions

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

On the current existence of a coccidial line of development in the malaria parasites: a theory

Most opinion favors the origin of the malaria parasites from a coccidial ancestor. It is assumed that whatever the process through which the coccidia differentiated into a Plasmodium this phenomenon very probably occured millions of year ago, and during that differentiation process the original coccidia vanished. Therefore it has never repeated. At the light of some experiments the existence, at the present time, of a coccidial cycle of development in the malaria parasites, is proposed. The conection routes and mechanisms through which the malaria parasite changes to a coccidial life, and the routes in reverse are exposed. Transmission of the malaria-coccidial forms is suggested.

Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

Existence of a sex pheromone in Triatoma infestans (Hemiptera: Reduviidae): I. Behavioural evidence

Assembling behaviour associated with mating was investigated in Triatoma infestans. The spatial distribution of both sexes was observed by video films, in the presence or absence of a copulating pair. Males aggregated around copulating pairs. Females did not exhibit this behaviour and their mean spatial density remained unaffected. Spontaneous aggregation tendency was observed in males in the absence of a copulating pair, but the temporal course significantly differed from that observed in the presence of a mating pair. Results support the existence of an aggregation signal that is released during mating, affecting the behaviour of males.