It is known that symplectic algorithms do not necessarily conserve energy even for the harmonic oscillator. However, for separable Hamiltonian systems, splitting and composition schemes have the advantage to be explicit and can be constructed to preserve energy. In this paper we describe and test an integrator built on a one-parameter family of symplectic symmetric splitting methods, where the parameter is chosen at each time step so as to minimize the energy error. For second-degree polynomial Hamiltonian functions as the one describing the linear oscillator, we build up second and fourth order symmetric methods which are symplectic, energy-preserving and explicit. For non-linear examples, it is possible to construct schemes with minimum error on energy conservation. The methods are semi-explicit in the sense that they require, as additional computational effort, the search for a zero of a scalar function with respect to a scalar variable. Therefore, our approach may represent an effective alternative to energy-preserving implicit methods whenever multi-dimensional problems are dealt with as is the case of many applications of interest.

Recurrent focal neuropathy with liability to pressure palsies is a relatively frequent autosomal-dominant demyelinating neuropathy linked to peripheral myelin protein 22 (PMP22) gene deletions. The combination of PMP22 gene mutations with other genetic variants is known to cause a more severe phenotype than expected. We present the case of a patient with severe orthostatic hypotension since 12 years of age, who inherited a PMP22 gene deletion from his father. Genetic double trouble was suspected because of selective sympathetic autonomic disturbances. Through exome-sequencing analysis, we identified two novel mutations in the dopamine beta hydroxylase gene. Moreover, with interactome analysis, we excluded a further influence on the origin of the disease by variants in other genes. This case increases the number of unique patients presenting with dopamine-?-hydroxylase deficiency and of cases with genetically proven double trouble. Finding the right, complete diagnosis is crucial to obtain adequate medical care and appropriate genetic counseling.

Stable, predictive biomarkers and interpretable disease signatures are seen as a signi cant step towards personalized medicine. In this per- spective, integration of multi-omic data com- ing from genomics, transcriptomics, glycomics, proteomics, metabolomics is a powerful strat- egy to reconstruct and analyse complex mul- ti-dimensional interactions, enabling deeper mechanistic and medical insight. At the same time, there is a rising concern that much of such different omic data -although often publicly and freely available- lie in data- bases and repositories underutilised or not used at all. Issues coming from lack of stand- ardisation and shared biological identities are also well-known. From these considerations, a novel, pressing request arises from the life sciences to design methodologies and approaches that allow for these data to be interpreted as a whole, i.e. as inter- twined molecular signatures containing genes, proteins, mRNAs and miRNAs, able to capture inter-layers connections and complexity. Papers discuss data integration approaches and methods of several types and extents, their application in understanding the pathogenesis of speci c diseases or in identifying candidate biomarkers to exploit the full bene t of multi-omic datasets and their intrinsic information content. Topics of interest include, but are not limited to: o Methods for the integration of layered data, including, but not limited to, genomics, transcrip- tomics, glycomics, proteomics, metabolomics; o Application of multi-omic data integration approaches for diagnostic biomarker discovery in any eld of the life sciences; o Innovative approaches for the analysis and the visualization of multi-omic datasets; o Methods and applications for systematic measurements from single/undivided samples (com- prising genomic, transcriptomic, proteomic, metabolomic measurements, among others); o Multi-scale approaches for integrated dynamic modelling and simulation; o Implementation of applications, computational resources and repositories devoted to data integration including, but not limited to, data warehousing, database federation, semantic integration, service-oriented and/or wiki integration; o Issues related to the de nition and implementation of standards, shared identities and seman- tics, with particular focus on the integration problem.

MUSCL extensions (Monotone Upstream-centered Schemes for Conservation Laws) of the Godunov numerical scheme for scalar conservation laws are shown to admit a rather simple reformulation when recast in the formalism of the Haar multi-resolution analysis of L²(R). By pursuing this wavelet reformulation, a seemingly new MUSCL-WB scheme is derived for advection-reaction equations which is stable for a Courant number up to 1 (instead of roughly 1/2 ). However these highorder reconstructions aren't likely to improve the handling of delicate nonlinear wave interactions in the involved case of systems of Conservation/Balance laws.

An elementary model of (1 + 1)-dimensional general relativity, known as "R = T " and mainly developed by Mann and coworkers in the early 1990s, is set up in various contexts. Its formulation, mostly in isothermal coordinates, is derived and a relativistic Euler system of selfgravitating gas coupled to a Liouville equation for the metric's conformal factor is deduced. First, external field approximations are carried out: both a Klein-Gordon equation is studied along with its corresponding density, and a Dirac one inside a hydrostatic gravitational field induced by a static, piecewise constant mass repartition. Finally, the coupled Euler-Liouville system is simulated, by means of a locally inertial Godunov scheme: the gravitational collapse of a static random initial distribution of density is displayed. Well-balanced discretizations rely on the treatment of source terms at each interface of the computational grid, hence the metric remains flat in every computational cell.

This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

Abstract The hydrodynamic characterization of control appendages for ship hulls is of paramount importance for the assessment of maneuverability characteristics. However, the accurate numerical simulation of turbulent flow around a fully appended maneuvering vessel is a challenging task, because of the geometrical complexity of the appendages and of the complications connected to their movement during the computation. In addition, the accurate description of the flow within the boundary layer is important in order to estimate correctly the forces acting on each portion of the hull. To this aim, the use of overlapping multi-block body fitted grids can be very useful to obtain both a proper description of each particular region in the computational domain and an accurate prediction of the boundary layer, retaining, at the same time, a good mesh quality. Moreover, block-structured grids with partial overlapping can be fruitfully exploited to control grid spacing close to solid walls, without propagation of undesired clustering of grid cells in the interior of the domain. This approach proved to be also very useful in reducing grid generation time. In the present paper, some details of the flow simulation around a fully appended submarine is reported, with emphasis on the issues related to the complexities of the geometry to be used in the simulations and to the need to move the appendages in order to change the configuration of the various appendages.

Breakup of small aggregates in fully developed turbulence is studied by means of direct numerical simulations in a series of typical bounded and unbounded flow configurations, such as a turbulent channel flow, a developing boundary layer and homogeneous isotropic turbulence. The simplest criterion for breakup is adopted, whereby aggregate breakup occurs when the local hydrodynamic stress "1=2, with " being the energy dissipation at the position of the aggregate, overcomes a given threshold cr, which is characteristic for a given type of aggregate. Results show that the breakup rate decreases with increasing threshold. For small thresholds, it develops a scaling behaviour among the different flows. For high thresholds, the breakup rates show strong differences between the different flow configurations, highlighting the importance of non-universal mean-flow properties. To further assess the effects of flow inhomogeneity and turbulent fluctuations, the results are compared with those obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and applicability of a set of independent proxies.

This chapter presents some speculations focused on the design of a System Sociology approach. A key feature of that approach consists in the modeling of social and economical systems viewed as living complex systems subject to dynamical evolution. At the technical level, the mathematical techniques proposed to the modeling of social and economic systems make use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to game-theoretical tools. Applications focus on the interplay between individual competition for wealth distribution that, when coupled with political stances coming from support or opposition to the government, may give rise to strongly self-enhanced effects resulting in the onset of extreme conflicts. The latter may be thought of as describing early stages of massive, unpredictable events known as Black Swans.

Application of interpolation/approximation techniques (metamodels, for brevity) is commonly adopted in numerical optimization, typically to reduce the overall execution time of the optimization process. A limited number of trial solution are computed, cov- ering the design variable space: those trial points are then used for the determination of an estimate of the objective function in any desired location of the design space. The behaviour of the prediction of the objective function in between two trial points depends on the structure of the adopted metamodel, and there is no possibility, in principle, to determine a priori if one method is preferable to another. Nevertheless, some metamodels require the adjustment of a set of tuning parameters, and this operation is critical for the prevision qualities of the metamodel. In this paper, some base parameters of the kernel of the kriging metamodel are tuned in order to improve the overall quality of the prediction.

In this paper, multi-disciplinary optimization techniques are applied to sail design. Two different mathematical models, providing the solution of the fluid-dynamic and the structural problems governing the behaviour of a complete sailplan, are coupled in a fluid-structure interaction (FSI) scheme, in order to determine the real flying shape of the sails and the forces acting on them. A numerical optimization algorithm is then applied, optimizing the structural pattern of the sailplan in order to maximize the driving force or other significant quantities.

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and \emph{speed} diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models. In this paper, resting on the methods of kinetic theory, we introduce a new traffic model which takes into account the heterogeneous nature of the flow of vehicles along a road. In more detail, the model considers traffic as a mixture of two or more populations of vehicles (e.g., cars and trucks) with different microscopic characteristics, in particular different lengths and/or maximum speeds. With this approach we gain some insights into the scattering of the data in the regime of congested traffic clearly shown by actual measurements.

The paper presents a novel method for color quantization (CQ) of dermoscopic images. The proposed method consists of an iterative procedure that selects image regions in a hierarchical way, according to the visual importance of their colors. Each region provides a color for the palette which is used for quantization. The method is automatic, image dependent and computationally not demanding. Preliminary results show that the mean square error of quantized dermoscopic images is competitive with existing CQ approaches.

In the last two decades, PSO (Particle Swarm Optimization) gained a lot of attention among the different derivative-free algorithms for global optimization. The simplicity of the implementation, compact memory usage and parallel structure represent some key features, largely appreciated. On the other hand, the absence of local information about the objective function slow down the algorithm when one or more constraints are violated, even if a penalty approach is applied. This situation becomes critical when the feasible set reduces to a small portion of the space in which the objective function needs to be investigated, and then the probability to find a feasible point by uniform sampling is small. In the present paper, a modification of the original PSO algorithm is proposed that both avoids the evaluation of the objective function outside the feasible set and preserves the parallel structure of the algorithm. Particular attention is dedicated to the parallel structure of the algorithm, in the view of its implementation on parallel architectures.

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

Tropospheric ozone is a key species for tropospheric chemistry and air quality. Its monitoring is essential to quantify sources, transport, chemical transformation and sinks of atmospheric pollution. Accurate data are required for understanding and predicting chemical weather. Space-borne observations are very promising for these concerns, especially those from IASI/MetOp. However, their sensitivity near the surface remains limited and advanced retrieval methods are needed to access to the information from the lowest troposphere. Ill-conditioning is a well-known issue of the retrieval of vertical atmospheric profiles. It produces oscillations in the retrieved profiles beyond the error margins defined by the mapping of the measurement noise onto the solution. Tikhonov regularization is often used to improve the conditioning of the inversion. As for any regularization scheme, a crucial step is the choice of the strength of the applied constraint. This choice depends on the measurement errors and on the sensitivity of the measurements to the target parameters at the different altitudes. For this reason a self-adapting and altitude-dependent regularization scheme is likely preferable over a fixed strength determined apriori, on the basis of sensitivity tests. Such a scheme was already introduced in 2009 and applied to atmospheric profiles retrieved from MIPAS/ENVISAT. The implementation of this method on nadir IASI retrievals required the appropriated definition of the target function used to optimize the constraint for lower tropospheric retrievals. The challenge for this new retrieval algorithm is to limit the use of a priori constraints to the minimal amount needed to perform the inversion. Since the sensitivity of the observations to the ozone amount in the lowest layers depends on the atmospheric and surface conditions, it is crucial for the inversion algorithm to tune accordingly the contribution of the a priori information. We apply the method first on simulated observations of tropospheric ozone for August 20th, 2009 over Europe. A first evaluation of the method is discussed in the paper. Significant improvements in terms of degrees of freedom (DOF) for the solution are achieved with a 15% increase on average. The error estimate during the retrieval is in better agreement with the true error, calculated as the difference between the retrieved ozone and the true ozone. The spatial distribution and the dispersion of the error are better described. Finally, a first attempt to apply the method to actual IASI measurements is presented.

One of the greatest challenges in biomedicine is to get a unified view of observations made from the molecular up to the organism scale. Towards this goal, multiscale models have been highly instrumental in contexts such as the cardiovascular field, angiogenesis, neurosciences and tumour biology. More recently, such models are becoming an increasingly important resource to address immunological questions as well. Systematic mining of the literature in multiscale modelling led us to identify three main fields of immunological applications: host-virus interactions, inflammatory diseases and their treatment and development of multiscale simulation platforms for immunological research and for educational purposes. Here, we review the current developments in these directions, which illustrate that multiscale models can consistently integrate immunological data generated at several scales, and can be used to describe and optimize therapeutic treatments of complex immune diseases.

In this work a Discrete Boltzmann Model for the solution of transcritical 2D shallow water flows is presented and validated. In order to provide the model with transcritical capabilities, a particular multispeed velocity set has been employed for the discretization of the Boltzmann equation. It is shown that this particular set naturally yields a simple and closed procedure to determine higher order equilibrium distribution functions needed to simulate transcritical flow. The model is validated through several classical benchmarks and is proven to correctly and accurately simulate both 1D and 2D transitions between the two flow regimes.

Motivated by the observation that electrons in graphene, in the hydrodynamic regime of transport, can be treated as a two-dimensional ultrarelativistic gas with very low shear viscosity, we examine the existence of the Rayleigh-Bénard instability in a massless electron-hole plasma. First, we perform a linear stability analysis, derive the leading contributions to the relativistic Rayleigh number, and calculate the critical value above which the instability develops. By replacing typical values for graphene, such as thermal conductivity, shear viscosity, temperature, and sample sizes, we find that the instability might be experimentally observed in the near future. Additionally, we have performed simulations for vanishing reduced chemical potential and compare the measured critical Rayleigh number with the theoretical prediction, finding good agreement.