Filament bifurcations in a one-dimensional model of reacting excitable fluid flow

Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the filament-like structures observed in the system. Here, we perform a bifurcation analysis of this one-dimensional approximation as a function of the {\it Damk{\"o}hler} number, the ratio between the chemical and the strain rates. Different branches of stable solutions are calculated, and a Hopf bifurcation, leading to an oscillating filament, identified.Comment: 9 pages, 4 figures; elsart.cls styl

Shedding light on El Farol

We mathematize El Farol bar problem and transform it into a workable model. We find general conditions under which the convergence of the average attendance to the resource level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies leads this problem to a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.El Farol, Minority Game, resource level, biased strategies

Evolutionary dynamics of incubation periods

The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected people take much longer than average to show symptoms, leading to a distribution of incubation periods that is right skewed and often approximately lognormal. Although this statistical pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.Comment: 24 pages, 8 figures, 1 tabl

Ottimizzazione della mucoadesivita' di miscele di polisaccaridi come veicoli oftalmici

Polisaccaridi mucomimetici, come xiloglucano (tamarind seed polysaccaride TSP) e acido ialuronico (HA), attualmente utilizzati in sostituti lacrimali possono prolungare la residenza dei farmaci nell'area precorneale grazie alle loro proprietà mucoadesive. Inoltre, in recenti test chimico-fisici, si è osservata un’interazione tra TSP e HA in soluzione nella proporzione TSP-HA 3:2. A tale scopo sono state preparate e studiate quattro miscele dei due polimeri: TSP-HA(1:4), TSP-HA(2:3), TSP-HA(3:2), TSP-HA(1:4) in tampone fosfato pH 7.4, isotonico (TF), che sono state medicate con KEF (0.07%) o con DS (0.3%) In questo lavoro di tesi le soluzioni TSP-HA sono state confrontate per il tempo di residenza medio nel fluido lacrimale dei conigli (MRT) e per la capacità di prolungare il tempo di residenza di KEF o di DS in tale fluido.Poi e’ stato studiato in vitro con dialisi dinamica il binding in soluzione tra KEF o DS, e le miscele polimeriche allo studio. E' stato confrontato, inoltre, l’ordine dei valori di MRT con quello dell’interattività mucina-polimero, quest’ultima determinata in base all’aumento della viscosità di una dispersione di mucina causato dall’interazione mucina-polimero(metodo Hassan-Gallo). La presente tesi ha mostrato che c'è un effeto sinergico tra i due polimeri TSP-HA e in virtù della sua mucoadesività, TSP-HA(3:2) si suppone stabilizzi il film lacrimale. I presenti risultati hanno mostrato che formulazioni oftalmiche di KF e DS contenenti TSP hanno la potenzialità di diminuire la frequenza delle instillazioni