Cosa ha cambiato maggiormente la nostra vita negli ultimi 60 anni? Sicuramente il computer. Un'idea antica di uomini geniali come Pascal e Leibniz, tra gli altri. ...E di un signore forse meno conosciuto, Charles Babbage, che nella Londra vittoriana, in compagnia della brillante discepola Ada Lovelace, aveva progettato una "macchina analitica" che forse già assomigliava ai computer di oggi.

Laure Saint-Raymond is a French mathematician working in partial differential equations, fluid mechanics and statistical mechanics. She is a professor at École Normale Supérieure de Lyon. In 2008, she was awarded the EMS Prize and, in 2013, when she was 38 years old, she became the youngest member of the French Academy of Sciences.

Difficoltà di comunicare la matematica

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.

Risultati di un sondaggio sulla rivista Archimede

In this paper, we propose a new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks. This model describes salt and water transport, and crystal formation in a one dimensional symmetry. This is a preliminary study that takes into account mathematically the effects of inhibitors inside a porous stone. To this aim, we introduce two model parameters: the crystallization rate coefficient, which depends on the nucleation rate, and the specific volume of precipitated salt. These two parameters are determined by numerical fitting of our model for both the case of the brick treated with PC and non treated one.

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behaviour using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-decay estimates of the local truncation error, it is possible to design schemes, based on the standard upwind approximation, which are increasingly accurate for large times when approximating small perturbations of constant asymptotic states. Numerical tests show their better performances with respect to those of other schemes.

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [3] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in an open neighborhood of the physical parameters, the system is totally dissipative near its unique non-vanishing equilibrium point. Using this property, we are able to prove existence and uniqueness of global smooth solutions to the Cauchy problem on the whole line for small perturbations of this equilibrium point and the solutions are shown to converge exponentially in time at the equilibrium state.

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells during the course of time and provide a Cell Index which is proportional to cellular morphology, spreading, ruffling and adhesion quality as well as cell number. In this paper we propose a macroscopic mathematical model, based on advection-reaction-diffusion partial differential equations, describing the cell migration assay using the real-time technology. We carried out numerical simulations to compare simulated model dynamics with data of observed biological experiments on three different cell lines and in two experimental settings: absence of chemotactic signals (basal migration) and presence of a chemoattractant. Overall we conclude that our minimal mathematical model is able to describe the phenomenon in the real time scale and numerical results show a good agreement with the experimental evidences.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these elements enable us to control and to validate the model we have already derived and to present some numerical simulations in the 2D and the 3D cases.

In this paper some recent mathematical models applied to material damage are reviewed. The complexity of damage processes related to Cultural Heritage materials creates the necessity of developing predictive tools in order to monitor and detect surface alterations even before they are visible by naked eyes. The proposed models, elaborated by a research group of the Institute of Applied Mathematics - Research Council of Italy, are based on partial differential equations and well capture the main features of chemical processes (copper corrosion and salt crystallization), which occur on different materials such as stone and copper.

We prove global existence and uniqueness of smooth solutions to a nonlinear system of parabolic-elliptic equations, which describes the chemical aggression of a permeable material, like calcium carbonate rocks, in presence of acid atmosphere. This model applies when convective flows are not negligible, due to the high permeability of the material. The global (in time) result is proven by using a weak continuation principle for the local solutions.

In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed of oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable transmission conditions at nodes.

In this paper we study the effect of rare mutations, driven by a marked point process, on the evolutionary behavior of a population. We derive a Kolmogorov equation describing the expected values of the different frequencies and prove some rigorous analytical results about their behavior. Finally, in a simple case of two different quasispecies, we are able to prove that the rarity of mutations increases the survival opportunity of the low fitness species.

Il 14 dicembre del 1955, presso la sede Centrale del CNR, il Presidente della Repubblica, Giovanni Gronchi, inaugurava il calcolatore elettronico Ferranti Mark1* dell'Istituto Nazionale per le Applicazioni del Calcolo, alla presenza del fondatore e direttore dell'Istituto, il matematico Mauro Picone. Dal nome del costruttore e dalla sigla dell'istituto, la macchina venne denominata FINAC. Si trattava del secondo calcolatore elettronico installato in Italia, preceduto di pochi mesi dal CRC-102A del Politecnico di Milano. L'acquisto era avvenuto grazie agli sforzi di Picone per dotare il suo istituto di una delle 'potenti macchine calcolatrici elettroniche', all'epoca solo anglo-americane. Negli anni precedenti Picone era giunto più volte ad un passo dal realizzare il suo intento di costruire quello che, sarebbe stato il primo calcolatore italiano. Aveva maturato questo proposito viaggiando negli USA, dove l'analisi numerica progrediva enormemente con lo sviluppo di progetti su 'macchine calcolatrici a cifre ad alta velocità'. Poiché una serie di impedimenti, internazionali e interni, rischiavano di prolungare eccessivamente i tempi, Picone scelse di acquistare un'apparecchiatura già in commercio, che sarebbe poi stata la FINAC, che per alcuni anni rimase il più potente computer italiano. Con esso vennero sviluppate molte ricerche sui temi più svariati, dal modello econometrico della Banca d'Italia ai calcoli per la progettazione di ponti e dighe. Un lavoro, particolarmente significativo per lo sviluppo dell'informatica italiana, fu la realizzazione di un simulatore della CEP, futura Calcolatrice Elettronica Pisana. Con questo anniversario si vuole celebrare, tra le altre cose, l'intuizione di Mauro Picone, la sua capacità innovativa e la scelta di investire generosamente nel futuro, conferendo grande impulso alla soluzione di problemi reali attraverso la modellizzazione matematica, creando anche in Italia i presupposti per lo sviluppo della moderna matematica applicata e dell'informatica

Gene therapy is a promising approach for treating a wide range of human pathologies such as genetic disorders as well as diseases acquired over time. Viral and non-viral vectors are used to convey sequences of genes that can be expressed for therapeutic purposes. Plasmid DNA is receiving considerable attention for intramuscular gene transfer due to its safety, simplicity and low cost of production. Nevertheless, strategies to improve DNA uptake into the nucleus of cells for its expression are required. Cytoskeleton plays an important role in the intracellular trafficking. The mechanism regulating this process must be elucidated. Here, we propose a new methodological approach based on the coupling of biology assays and predictive mathematical models, in order to clarify the mechanism of the DNA uptake and its expression into the cells. Once these processes are better clarified, we will be able to propose more efficient therapeutic gene transfer protocols for the treatment of human patients.

A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (SO2) pollution. This model is characterized by the movement of a double free boundary. Numerical simulations show a nice agreement with experimental result. (C) 2014 Elsevier Inc. All rights reserved.