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Aims The aim of this work was to assess the effects of a probiotic diet on well-being of healthy seniors living in boarding and private homes in Marche Region, Italy. In particular, we focused on the modulation of high-sensitivity C-reactive protein (HsCRP), intestinal microbiota and short-chain fatty acids (SCFAs). Methods and Results Ninety-seven healthy seniors took part in a double-blind, placebo-controlled feeding study (59 fed probiotics, 38 fed placebo) for 6 months. Each volunteer ingested daily one food product or a dietary supplement enriched with Synbio® blend (Synbiotec Srl, Camerino, Italy) or the placebo (control group). Blood and faecal samples were collected before and at the end of the intervention period to perform biochemical and microbiological analyses. The serum HsCRP difference value after 6 months of treatment was significantly higher in the probiotic group than placebo (p < 0.05). After the intervention, a significant increase in faecal lactobacilli and a bifidobacteria increase in more participants were observed in the probiotic group. The 16S NGS analysis on the probiotic group showed a decreasing trend of Proteobacteria at the end of the treatment and conversely, an increasing trend of Actinobacteria and Verrucomicrobia phyla, to which the increase of Akkermansiaceae and Bifidobacteriaceae contributes at the family level. Finally, total short-chain fatty acids (SCFAs) and butyric acid were significantly higher in the probiotic group at the end of the treatment respect to the beginning. Conclusions Overall, this study emphasizes the beneficial anti-inflammageing effect of a prolonged diet based on functional foods enriched with Synbio® through the modulation of the intestinal microbiota and the consequent increase in the SCFA production. Significance and Impact of the Study Synbio® integration in elderly daily diet may be a preventive strategy to support healthy ageing.

New algorithms for the numerical solution of optimization problems involving the $$l_{0}$$ pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral $$\textcircled {1}$$ (grossone) and indicating the number of elements of the set $${\text {I}}\!{\text {N}}$$ , of natural numbers. We show how the numerical system built upon $$\textcircled {1}$$ and the proposed approximation of the $$l_0$$ pseudo-norm in terms of $$\textcircled {1}$$ can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems.

Numerical simulation models of water flow in variably saturated soils are important tools in water resource management, assessment of water-related disasters and agriculture. Richards equation is o...

A new numerical method to solve two-point boundary value problems for second order differential equations is proposed. This method is based on the singular value expansion of an integral formulation of the derivative operator. Here, we outline such an expansion and we propose a method to build new algebraic schemes able to solve boundary value problems. The performances of the presented method are tested by numerical experiments on boundary value problems that have known solutions.

The derivative operator is reformulated as a Volterra integral operator of the first kind. So, the singular value expansion (SVE) of the kernel of such integral operator can be used to obtain new numerical methods to solve differential equations. We present such ideas in the solution of initial value problems for ordinary differential equations of first order. In particular, we develop an iterative scheme where global error in the solution of this problem is gradually reduced at each step. The global error is approximated by using the system of the singular functions in the aforementioned SVE.

The best approximation problem is a classical topic of the approximation theory and the Remez algorithm is one of the most famous methods for computing minimax polynomial approximations. We present a slight modification of the (second) Remez algorithm where a new approach to update the trial reference is considered. In particular at each step, given the local extrema of the error function of the trial polynomial, the proposed algorithm replaces all the points of the trial reference considering some “ad hoc” oscillating local extrema and the global extremum (with its adjacent) of the error function. Moreover at each step the new trial reference is chosen trying to preserve a sort of equidistribution of the nodes at the ends of the approximation interval. Experimentally we have that this method is particularly appropriate when the number of the local extrema of the error function is very large. Several numerical experiments are performed to assess the real performance of the proposed method in the approximation of continuous and Lipschitz continuous functions. In particular, we compare the performance of the proposed method for the computation of the best approximant with the algorithm proposed in [17] where an update of the Remez ideas for best polynomial approximation in the context of the chebfun software system is studied.

In this study, we propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier–Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger.

We consider an initial–boundary value problem for the two-dimensional Burgers equation on the plane. This problem is reformulated by an equivalent integral equation on the Fourier transform space. For the solution of this integral equation, two numerical methods are proposed. One of these two methods is based on the properties of the Gaussian function, whereas the other one is based on the FFT algorithm. Finally, the Galerkin method with Gaussian basis functions is applied to the original initial–boundary value problem, in order to compare the performances of the proposed methods with a standard numerical procedure. Some numerical examples are given to evaluate the efficiency of the proposed methods. The performances obtained from these numerical experiments promise that these methods can be applied effectively to more complex problems, such as the Navier–Stokes equation and the turbulence flows.

We consider the Volterra integral equation of the first kind for the derivative of a given function with one-side boundary conditions. We give a method to obtain the singular value expansion for the corresponding integral kernel. This singular value expansion can be used to give algorithms for the solution of the numerical differentiation problem. A numerical experiment shows the results obtained by a simple version of such algorithms.

Matter of this paper is the study of the flow and the corresponding heat transfer in a U-shaped heat exchanger. We propose a mathematical model that is formulated as a forced convection problem for incompressible and Newtonian fluids and results in the unsteady Navier-Stokes problem. In order to get a solution, we discretise the equations with both the Finite Elements Method and the Finite Volumes Method. These procedures give rise to a non-symmetric indefinite quadratic system of equations. Thus, three regularisation techniques are proposed to make approximations effective and ideas to compare their results are provided.

We study the cooling system for submersible electric pumps. This study aims to provide some guidelines to improve the existing cooling system of these electric pumps when they work partially or totally not immersed in the service fluid. Note that inefficient cooling systems cannot prevent the rise in temperature of the alternating current (AC) motor of the pump, and the consequent reduction of the service factor. We propose a three-dimensional model to describe the fluid flow in the cooling circuit and the heat transfer among the engine of the electric pump, the cooling system and the external environment. This model is discretized by using a finite element method, and the resulting algorithm has been implemented in a FORTRAN code. We show some preliminary results obtained by this code using two different geometries for the cooling circuit, and we compare these results with experimental data and with other numerical results obtained in a previous work, by using a two-dimensional model.

We consider a time-harmonic electromagnetic scattering problem for an inhomogeneous medium. Some symmetry hypotheses on the refractive index of the medium and on the electromagnetic fields allow to reduce this problem to a two-dimensional scattering problem. This boundary value problem is defined on an unbounded domain, so its numerical solution cannot be obtained by a straightforward application of usual methods, such as for example finite difference methods, and finite element methods. A possible way to overcome this difficulty is given by an equivalent integral formulation of this problem, where the scattered field can be computed from the solution of a Fredholm integral equation of second kind. The numerical approximation of this problem usually produces large dense linear systems. We consider usual iterative methods for the solution of such linear systems, and we study some preconditioning techniques to improve the efficiency of these methods. We show some numerical results obtained with two well known Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

An algorithm for the generation of quadrilateral grids on planar domains is presented. This algorithm is given by an iterative procedure, where, starting from an initial grid on the domain under consideration, the coordinates of the grid vertices are iteratively adjusted by using a local discrete variational approach. This procedure resembles the explicit difference scheme for a perturbed heat equation, where the perturbation can be dropped for convex domains. Experimental results on benchmark domains are presented, and show an interesting behavior of the proposed method.

The estimation of age of adult individuals usually employs methods based on age-related changes in the human skeleton. The main aim of this study was to assess dental age through analysis of images from peri-apical x-rays based on a new algorithm for automatic estimation of pulp and tooth area. The algorithm was tested on a sample of 40 canines of males and 30 of females from subjects between the ages of 20 and 70.

We propose a new direct method to solve linear systems. This method is based on the Sherman–Morrison formula and uses a finite iterative formula. To compare our method with the Restarted Generalized Minimum Residual Method and the Gaussian Elimination Method with Partial Pivoting, we use two classes of test problems: linear systems having Pascal, Cauchy, and Vandermonde matrices as coefficient matrices, and randomly generated linear systems.

Let u be a real function defined on a rectangular grid. The (two-dimensional) phase unwrapping problem consists in the reconstruction of u from the knowledge of its values modulus [email protected] We study two different methods for the solution of this problem: the Fourier transform method and the network optimization method. We show that these methods do not compute the same solution, so that we introduce a revised version of the Fourier transform method which is equivalent to the network optimization method. These results are based on an explicit expression for a singular value decomposition of A, where A is the matrix that defines the linear constraints of the optimization problem arising in the network optimization method.

We consider the scattering of time-harmonic electromagnetic waves by penetrable inhomogeneous obstacles. In particular, we study the numerical solution of an inverse scattering problem, where the refractive index of the obstacle is computed from some knowledge of the scattered waves, generated by the obstacle itself, and known incident waves. This problem can be formulated by a pair of non-linear integral equations, and its numerical solution is usually a time-consuming computation. We propose an efficient solution of this problem by taking into account a linearization of the integral equation under consideration. The proposed method is tested by a numerical experiment, where the inverse scattering problem is numerically solved for different obstacles.

We consider the problem of the generation of adaptive grids, where, for a given domain @W, we have to compute a partition that depends on a given map f providing the desired local mesh size. We propose a numerical method for the solution of this problem in the case of planar quadrilateral grids. In particular, a block decomposition method is proposed, by which @W is first decomposed in several blocks depending on the shape of the domain and on the size map f, and then the whole grid is obtained as the union of the quadrilateral grids on each block. The algorithm concludes with a smoothing step that depends on the size map f. We present some simple numerical examples to test the proposed method.

We consider the problem of the quadrangular and triangular grid generation. The algorithm proposed for the solution of this problem is based on a generalization of the so called variational method. In particular, this generalization takes into account a combination of length and area functionals for a given triangular grid related to the quadrangular grid under consideration. As a consequence of this generalization high quality triangular grids of a given domain are obtained in a straightforward way from the quadrangular grids computed by this algorithm. We test the proposed algorithm on standard numerical examples.