We are concerned with the discretization of optimal control problems when a Runge-Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian's first order conditions on the discrete model, require a symplectic partitioned Runge-Kutta scheme for state-costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian. We prove that a correct numerical treatment of the state-current costate system needs Lawson exponential schemes for the costate approximation. In the numerical tests a shooting strategy is employed in order to verify the accuracy, up to the fourth order, of the innovative procedure we propose.

Heavy or light particles introduced into a liquid trigger motion due to their buoyancy, with the potential to drive flow to a turbulent state. In the case of vapor bubbles present in a liquid near its boiling point, thermal coupling between the liquid and vapor can moderate this additional motion by reducing temperature gradients in the liquid. Whether the destabilizing mechanical feedback or stabilizing thermal feedback will dominate the system response depends on the number of bubbles present and the properties of the phase change. Here we study thermal convection with phase change in a cylindrical Rayleigh-Benard cell to examine this competition. Using the Reynolds number of the flow as a signature of turbulence and the intensity of the flow, we show that in general the rising vapor bubbles destabilize the system and lead to higher velocities. The exception is a limited regime corresponding to phase change with a high latent heat of vaporization (corresponding to low Jakob number), where the vapor bubbles can eliminate the convective flow by smoothing temperature differences of the fluid.

Clustering is one of the most important unsupervised learning problems and it consists of finding a common structure in a collection of unlabeled data. However, due to the ill-posed nature of the problem, different runs of the same clustering algorithm applied to the same data-set usually produce different solutions. In this scenario choosing a single solution is quite arbitrary. On the other hand, in many applications the problem of multiple solutions becomes intractable, hence it is often more desirable to provide a limited group of ''good'' clusterings rather than a single solution. In the present paper we propose the least squares consensus clustering. This technique allows to extrapolate a small number of different clustering solutions from an initial (large) ensemble obtained by applying any clustering algorithm to a given data-set. We also define a measure of quality and present a graphical visualization of each consensus clustering to make immediately interpretable the strength of the consensus. We have carried out several numerical experiments both on synthetic and real data-sets to illustrate the proposed methodology.

Automatic estimation of current dipoles from biomagnetic data is still a problematic task. This is due not only to the ill-posedness of the inverse problem but also to two intrinsic difficulties introduced by the dipolar model: the unknown number of sources and the nonlinear relationship between the source locations and the data. Recently, we have developed a new Bayesian approach, particle filtering, based on dynamical tracking of the dipole constellation. Contrary to many dipole-based methods, particle filtering does not assume stationarity of the source configuration: the number of dipoles and their positions are estimated and updated dynamically during the course of the MEG sequence. We have now developed a Matlab-based graphical user interface, which allows nonexpert users to do automatic dipole estimation from MEG data with particle filtering. In the present paper, we describe the main features of the software and show the analysis of both a synthetic data set and an experimental dataset. © 2011 C. Campi et al.

: Multidomain proteins are composed of rigid domains connected by (flexible) linkers. Therefore, the domains may experience a large degree of reciprocal reorientation. Pseudocontact shifts and residual dipolar couplings arising from one or more paramagnetic metals successively placed in a single metal binding site in the protein can be used as restraints to assess the degree of mobility of the different domains. They can be used to determine the maximum occurrence (MO) of each possible protein conformation, i.e. the maximum weight that such conformations can have independently of the real structural ensemble, in agreement with the provided restraints. In the case of two-domain proteins, the metal ions can be placed all in the same domain, or distributed between the two domains. It has been demonstrated that the quantity of independent information for the characterization of the system is larger when all metals are bound in the same domain. At the same time, it has been shown that there are practical advantages in placing the metals in different domains. Here, it is shown that distributing the metals between the domains provides a tool for defining a coefficient of compatibility among the restraints obtained from different metals, without a significant decrease of the capability of the MO values to discriminate among conformations with different weights.

For Ω R 2 a bounded open set with C 1 boundary, we study the regularity of the variational solution v ε W 1,2 0 (Ω) to the quasilinear elliptic equation of Leray-Lions -divA(x;δv) = f when f belongs to the Zygmund space L(log L) δ(Ω), 1/2 ≤ δ δ 1. We prove that |δv| belongs to the Lorentz space L 2,1/δ(Ω).

inglese

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re-lambda similar to 200 and Re-lambda similar to 400, corresponding to resolutions of 512(3) and 2048(3) grid points, respectively. Particles Stokes number values range from St approximate to 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv:1012.1789v1 [physics.fludyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.