Abstract:
Coeliac Disease (CD) is a permanent gluten intolerance, whose pathogenesis involves multiple factors including genetics and environment. CD has different representations and non-specific symptoms such as diarrhea, bloating, pain, flatulence and constipation may sometimes be misleading. Once diagnosed of CD, patients must adhere to Gluten Free Diet, which consists in the lifelong avoidance of gluten containing foods and of those naturally gluten free but at risk of contamination. This dietary approach is considered the only therapy in order to avoid symptoms exacerbation and to reduce the digestive mucosa inflammation, which has been related to higher risks of lymphoproliferative malignancy and other immunological disorders. However, being on a Gluten Free Diet is not as resolving as it may seem since it has several criticalities. First of all, excluding gluten means limiting food variety so that coeliac patients may have unbalanced intake of several nutrients and develop clinical or subclinical deficiencies. This can be due to scarce attention to qualitative and quantitative composition of diets and poor information about gluten-containing foods, which only patient-tailored dietetic protocol and long-term follow-up can achieve. Secondly, Gluten Free Diet may not result in complete remission of mucosal damage or in resolution of symptoms. Unintentional contamination of gluten or poor adherence to diet are the main culprits of the incomplete mucosal healing but other triggers may be involved. Recent research has focused on the role of FODMAPs in changing gut microbiota and on the improvement of Irritable Bowel Syndrome (IBS) symptoms after their dietary avoidance or reduction. Since CD and IBS may share many clinical presentations, further studies are needed to evaluate if a subgroup of CD patients whose symptoms are not improved by Gluten Free Diet could benefit from a new therapeutic approach consisting in both gluten/wheat and FODMAPs avoidance.

Abstract:
the mandibular gland secretion (mgs) and the faecal fluid (ff) of the leaf-cutting ant atta sexdens rubropilosa forel affected the spore germination of selected microfungi isolated from nests of this insect. mgs was more effective than the ff, completely inhibiting the spore germination of four out of six microfungi species.

Abstract:
In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both classes can be completely analytically characterized in terms of the involved parameters. The proposed algorithms improve and extend the framework of weighted fractal networks recently proposed in (T. Carletti & S. Righi, in press Physica A, 2010)

Abstract:
The classical Lagrange inversion formula is extended to analytic and non--analytic inversion problems on non--Archimedean fields. We give some applications to the field of formal Laurent series in $n$ variables, where the non--analytic inversion formula gives explicit formal solutions of general semilinear differential and $q$--difference equations. We will be interested in linearization problems for germs of diffeomorphisms (Siegel center problem) and vector fields. In addition to analytic results, we give sufficient condition for the linearization to belong to some Classes of ultradifferentiable germs, closed under composition and derivation, including Gevrey Classes. We prove that Bruno's condition is sufficient for the linearization to belong to the same Class of the germ, whereas new conditions weaker than Bruno's one are introduced if one allows the linearization to be less regular than the germ. This generalizes to dimension $n> 1$ some results of [CarlettiMarmi]. Our formulation of the Lagrange inversion formula by mean of trees, allows us to point out the strong similarities existing between the two linearization problems, formulated (essentially) with the same functional equation. For analytic vector fields of $\C^2$ we prove a quantitative estimate of a previous qualitative result of [MatteiMoussu] and we compare it with a result of [YoccozPerezMarco].

Abstract:
We study the orbit behavior of a germ of an analytic vector field of $(C^n,0)$, $n \geq 2$. We prove that if its linear part is semisimple, non--resonant and verifies a Bruno--like condition, then the origin is effectively stable: stable for finite but exponentially long times.

Abstract:
We study the Siegel--Schr\"oder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey--$s$, $s>0$ category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey--$s$ formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin for the analytic germ.

Abstract:
We study the 1/2--Complex Bruno function and we produce an algorithm to evaluate it numerically, giving a characterization of the monoid $\hat{\mathcal{M}}=\mathcal{M}_T\cup \mathcal{M}_S$. We use this algorithm to test the Marmi--Moussa--Yoccoz Conjecture about the H\"older continuity of the function $z\mapsto -i\mathbf{B}(z)+ \log U(e^{2\pi i z})$ on $\{z\in \mathbb{C}: \Im z \geq 0 \}$, where $\mathbf{B}$ is the 1/2--complex Bruno function and $U$ is the Yoccoz function. We give a positive answer to an explicit question of S. Marmi et al [MMY2001].

Abstract:
In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.

Abstract:
We propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some specific molecules, belonging to the reactions set. This allows us to study the stochastic evolution of a protocell, whose volume increases because of the production of container molecules. Several protocell models are considered and compared with the deterministic models.

Abstract:
We study the dynamics of public opinion in a model in which agents change their opinions as a result of random binary encounters if the opinion difference is below their individual thresholds that evolve over time. We ground these thresholds in a simple individual cost-benefit analysis with linear benefits of diversity and quadratic communication costs. We clarify and deepen the results of earlier continuous-opinion dynamics models (Deffuant et al., Adv Complex Systems 2000; Weisbuch et al., Complexity 2002) and establish several new results regarding the patterns of opinions in the asymptotic state and the cluster formation time.