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Variances in spectral analysis of membrane noise

Francesco Andrietti, Carla Canegallo (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Le fluttuazioni di conduttanza di un modello di canale del potassio di una fibra muscolare che segue una cinetica di Hodgkin e Huxley sono state analizzate attraverso l'analisi spettrale indiretta. Sono state confrontate due diverse stime della densità spettrale e le loro rispettive varianze: quella della prima stima considerata è già nota, mentre quella della seconda stima è stata ricavata da noi nelle medesime ipotesi (distribuzione normale). I risultati teorici sono stati confrontati con quelli...

Variational Framework for Assessment of the Left Ventricle Motion

J. Garcia-Barnés, D. Gil, S. Pujadas, F. Carreras (2008)

Mathematical Modelling of Natural Phenomena

Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from...

Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model

S. Boujena, A. Chiboub, J. Pousin (2010)

Mathematical Modelling of Natural Phenomena

Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work,...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Volume Filling Effect in Modelling Chemotaxis

D. Wrzosek (2010)

Mathematical Modelling of Natural Phenomena

The oriented movement of biological cells or organisms in response to a chemical gradient is called chemotaxis. The most interesting situation related to self-organization phenomenon takes place when the cells detect and response to a chemical which is secreted by themselves. Since pioneering works of Patlak (1953) and Keller and Segel (1970) many particularized models have been proposed to describe the aggregation phase of this process. Most of...

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