Age of infection epidemic models [1, 3], based on non-linear integro-dierential equations, naturally describe the evolution of diseases whose infectivity depends on the time since becoming infected. Here we consider a multi-group age of infection model [2] and we extend the investigations in [4], [5] and [6] to provide numerical solutions that retain the main properties of the continuous system. In particular, we use Direct Quadrature methods and prove that the numerical solution is positive and bounded. Furthermore, in order to study the asymptotic behavior of the numerical solution, we formulate discrete equivalents of the nal size relation and of the basic reproduction number and we prove that they converge to the continuous ones, as the step-size of the discretization goes to zero.

Cow's milk allergy (CMA) is a common condition in the pediatric population. CMA can induce a diverse range of symptoms of variable intensity. It occurs mainly in the first year of life, and if the child is not breastfed, hypoallergenic formula is the dietary treatment. Extensively hydrolyzed cow's milk formulas (eHF) with documented hypo-allergenicity can be recommended as the first choice, while amino acid-based formulas (AAF) are recommended for patients with more severe symptoms. Hydrolyzed rice-based formulas (HRFs) are a suitable alternative for infants with CMA that cannot tolerate or do not like eHF and in infants with severe forms of CMA. In the present paper, we reviewed the nutritional composition of HRFs as well as studies regarding their efficacy and tolerance in children, and we provided an updated overview of the recent evidence on the use of HRFs in CMA. The available studies provide evidence that HRFs exhibit excellent efficacy and tolerance and seem to be adequate in providing normal growth in healthy children as well as in children with CMA.

Background Diagnosis and treatment of 22q11.2 deletion syndrome (22q11.2DS) have led to improved life expectancy and achievement of adulthood. Limited data on long-term outcomes reported an increased risk of premature death for cardiovascular causes, even without congenital heart disease (CHD). The aim of this study was to assess the cardiac function in adolescents and young adults with 22q11.2DS without CHDs. Methods A total of 32 patients (20M, 12F; mean age 26.00 ± 8.08 years) and a healthy control group underwent transthoracic echocardiography, including Tissue Doppler Imaging (TDI) and 2-dimensional Speckle Tracking Echocardiography (2D-STE). Results Compared to controls, 22q11.2DS patients showed a significant increase of the left ventricle (LV) diastolic and systolic diameters (p = 0.029 and p = 0.035 respectively), interventricular septum thickness (p = 0.005), LV mass index (p < 0.001) and aortic root size (p < 0.001). 2D-STE analysis revealed a significant reduction of LV global longitudinal strain (p < 0.001) in 22q11.2DS than controls. Moreover, several LV diastolic parameters were significantly different between groups. Conclusions Our results suggest that an echocardiographic follow-up in 22q11.2DS patients without CHDs can help to identify subclinical impairment of the LV and evaluate a potential progression of aortic root dilation over time, improving outcomes, reducing long-term complications and allowing for a better prognosis.

We present a new method for assessing and measuring homophily in networks whose nodes have categorical attributes, namely when the nodes of networks come partitioned into classes (colors). We probe this method in two different classes of networks: (i) protein-protein interaction (PPI) networks, where nodes correspond to proteins, partitioned according to their functional role, and edges represent functional interactions between proteins (ii) Pokec on-line social network, where nodes correspond to users, partitioned according to their age, and edges respresent friendship between users.Similarly to other classical and well consolidated approaches, our method compares the relative edge density of the subgraphs induced by each class with the corresponding expected relative edge density under a null model. The novelty of our approach consists in prescribing an endogenous null model, namely, the sample space of the null model is built on the input network itself. This allows us to give exact explicit expression for the z-score of the relative edge density of each class as well as other related statistics. The z-scores directly quantify the statistical significance of the observed homophily via ?eby?ëv inequality. The expression of each z-score is entered by the network structure through basic combinatorial invariant such as the number of subgraphs with two spanning edges. Each z-score is computed in O(n+ m) time for a network with n nodes and m edges. This leads to an overall efficient computational method for assesing homophily. We complement the analysis of homophily/heterophily by considering z-scores of the number of isolated nodes in the subgraphs induced by each class, that are computed in O(nm) time. Theoretical results are then exploited to show that, as expected, both the analyzed network classes are significantly homophilic with respect to the considered node properties.

We compute the Euler equations of a functional useful for simultaneous video inpainting and motion estimation, which was obtained in [17] as the relaxation of a modified version of the functional proposed in [16]. The functional is defined on vectorial functions of bounded variations, therefore we also get the Euler equations holding on the singular sets of minimizers, highlighting in particular the conditions on the jump sets. Such conditions are expressed by means of traces of geometrically meaningful vector fields and characterized as pointwise limits of averages on cylinders with axes parallel to the unit normals to the jump sets.

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

The chapter surveys the magneto-quasistatic models for co-seismic electromagnetic signals

The dynamic behavior of a self-propelled semiflexible filament of length L is con- sidered under the action of a linear shear flow. The system is studied by using Brownian multi-particle collision dynamics. The system can be characterized in terms of the persistence length Lp of the chain, of the Peclet number, and of the Weissenberg number. The quantity Lp/L measures the bending rigidity of the polymer, the Peclet number Pe is the ratio of active force times L to thermal energy, and the Weissenberg number Wi characterizes the flow strength over thermal effects. In this presentation we will focus our attention to intermediate values of Pe corresponding to the weak spiral regime when no external flow is applied. The numerical results allow us to outline the main features of the physics underlying the considered system: o At low values of Wi, polymer is stretched by activity and aligned by shear along the flow direction. This effect is more marked in the case of more flexible chains. o At the intermediate values of Wi, polymer is prone to tumble due to shear and this promotes a contraction of the chain. o At very high values of Wi, activity sums up to shear enhancing polymer stretching and deformation.

The radical polymerization process of acrylate compounds is, nowadays, numerically investigated using classical force fields and reactive molecular dynamics, with the aim to probe the gel-point transition as a function of the initial radical concentration. In the present paper, the gel-point transition of the 1,6-hexanediol dimethacrylate (HDDMA) is investigated by a coarser force field which grants a reduction in the computational costs, thereby allowing the simulation of larger system sizes and smaller radical concentrations. Hence, the polymerization is investigated using reactive classical molecular dynamics combined with a dynamical approach of the nonequilibrium molecular dynamics (D-NEMD). The network structures in the polymerization process are probed by cluster analysis tools, and the results are critically compared with the similar all-atom system, showing a good agreement.

The SOC change index, defined as the normalized difference between the actual Soil Organic Carbon and the value assumed at an initial reference year, is here tailored to the RothC carbon model dynamics. It assumes as a baseline the value of the SOC equilibrium under constant environmental conditions. A sensitivity analysis is performed to evaluate the response of the model to changes in temperature, Net Primary Production (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximate the SOC change index in the Alta Murgia National Park, a protected area in the Italian Apulia region, selected as a test site. The SOC change index exhibits negative trends for all the land use considered without fertilizers. The negative trend in the arable class can be inverted by a suitable organic fertilization program here proposed.

We analyze a second-order accurate implicit-symplectic (IMSP) scheme for reaction-diffusion systems modeling spatiotemporal dynamics of predator-prey populations. We prove stability and errors estimates of the semi-discrete-in-time approximations, under positivity assumptions. The numerical simulations confirm the theoretically derived rates of convergence and show an improved accuracy in the second-order IMSP in comparison with the first-order IMSP, at same computational cost.

We report the regularization technique used in the inversion of the radiative transfer equation. The talk is intended for a general public, and does not require specialistic notions.

We report the results of the regularization of the surface emissivity for the FORUM instrument.

Amino acids (AAs) are well known to be involved in the regulation of glucose metabolism and, in particular, of insulin secretion. However, the effects of different AAs on insulin release and kinetics have not been completely elucidated. The aim of this study was to propose a mathematical model that includes the effect of AAs on insulin kinetics during a mixed meal tolerance test. To this aim, five different models were proposed and compared. Validation was performed using average data, derived from the scientific literature, regarding subjects with normal glucose tolerance (CNT) and with type 2 diabetes (T2D). From the average data of the CNT and T2D people, data for two virtual populations (100 for each group) were generated for further model validation. Among the five proposed models, a simple model including one first-order differential equation showed the best results in terms of model performance (best compromise between model structure parsimony, estimated parameters plausibility, and data fit accuracy). With regard to the contribution of AAs to insulin appearance/disappearance (k model parameter), model analysis of the average data from the literature yielded 0.0247 (confidence interval, CI: 0.0168 - 0.0325) and -0.0048 (CI: -0.0281 - 0.0185) ?U·ml/(?mol·l·min), for CNT and T2D, respectively. This suggests a positive effect of AAs on insulin secretion in CNT, and negligible effect in T2D. In conclusion, a simple model, including single first-order differential equation, may help to describe the possible AAs effects on insulin kinetics during a physiological metabolic test, and provide parameters that can be assessed in the single individuals.

An unsupervised segmentation/clustering algorithm is a method for modeling the generation of directly observable visible variables from hidden sources. Each hidden source coop- erates in activating a subset of visible variables, or parts, which, in turn, additively generate the whole. This project aims at applying the versatility of such a method to the semantic analysis of text documents, namely patent applications.

Overview on hydrodynamic stability and wave turbulence

A hidden defect D affecting the interface in a layered specimen is evaluated from temperature maps collected on its top side. An explicit formula that approximates thermal conductance of the damaged interface is derived by means of first order Thin Plate Approximation. This formula is used to obtain a geometrical description of D from experimental data.

The dynamical response of a tethered semiflexible polymer with self-attractive interactions and subjected to an external force field is numerically investigated by varying stiffness and self-interaction strength. The chain is confined in two spatial dimensions and placed in contact with a heat bath described by the Brownian multi-particle collision method. For strong self-attraction the equilibrium conformations range from compact structures to double-stranded chains, and to rods when increasing the stiffness. Under the external field at small rigidities, the initial close-packed chain is continuously unwound by the force before being completely elongated. For double-stranded conformations the transition from the folded state to the open one is sharp being steeper for larger stiffnesses. The discontinuity in the transition appears in the force-extension relation, as well as in the probability distribution function of the gyration radius. The relative deformation with respect to the equilibrium case along the direction normal to the force is found to decay as the inverse of the applied force.