We study the Stekloff eigenvalue problem for the so-called pseudo p-Laplacian operator. After proving the existence of an unbounded sequence of eigenvalues, we focus on the first nontrivial eigenvalue ?, providing various equivalent characterizations for it. We also prove an upper bound for ? in terms of geometric quantities. The latter can be seen as the nonlinear analogue of the Brock-Weinstock inequality for the first nontrivial Stekloff eigenvalue of the (standard) Laplacian. Such an estimate is obtained by exploiting a family of sharp weighted Wulff inequalities, which are here derived and appear to be interesting in themselves. © 2013 Springer Basel.

Given an open set ?, we consider the problem of providing sharp lower bounds for ? (?), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong-Krahn-Szego inequality, asserting that the disjoint unions of two equal balls minimize ? among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ? are considered as well. © 2012 Springer-Verlag Berlin Heidelberg.

A highly nonlinear eigenvalue problem is studied in a Sobolev space with variable exponent. The Euler-Lagrange equation for the minimization of a Rayleigh quotient of two Luxemburg norms is derived. The asymptotic case with a "variable infinity" is treated. Local uniqueness is proved for the viscosity solutions.

This chapter concerns the state-of-the-art of the research about non-local minimal surfaces and their phase-field approximations.

We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field. In confined samples, the anchoring at the walls and the geometry of the device lead to the stabilisation of further structures, including field-aligned disclination loops, splayed nematic patterns, and yet more metastable states. Our results are relevant to the understanding of the switching dynamics for a class of new, "superstable", blue phases which are composed of bimesogenic liquid crystals, as these materials combine anomalously large flexoelectric coefficients, and low or near-zero dielectric anisotropy.

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

In Mobile Unattended Wireless Sensor Networks (MUWSNs), nodes sense the environment and store the acquired data until the arrival of a trusted data sink. In this paper, we address the fundamental issue of quantifying to which extent secret sharing schemes, combined with nodes mobility, can help in assuring data availability and confidentiality. We provide accurate analytical results binding the fraction of the network accessed by the sink and the adversary to the amount of information they can successfully recover. Extensive simulations support our findings.

In Mobile Unattended Wireless Sensor Networks (MUWSNs), nodes sense the environment and store the acquired data until the arrival of a trusted data sink. MUWSNs, other than being a reference model for an increasing number of military and civilian applications, also capture a few important characteristics of emerging computing paradigms like Participatory Sensing (PS). In this paper, we start by identifying the main features and issues of MUWSNs, revising the related work in the area and highlighting their shortcomings. We then propose a new approach based on secret sharing and information diffusion to improve data integrity and confidentiality, and present experimental results confirming the effectiveness of this solution. The rationale is that information sharing among neighboring nodes, combined with nodes mobility, helps distributing the information into the network in a way that, at the same time, facilitates data recovering and is resilient to data loss or stealing. This is a first step towards the general objective of providing closed results about how secret sharing schemes and nodes mobility can help in assuring data security using local communications only, and understanding how to set system parameters to achieve the desired trade-off between confidentiality and availability.

An important problem in the context of wireless sensor networks is the Maximum Network Lifetime Problem (MLP): find a collection of subset of sensors (cover) each covering the whole set of targets and assign them an activation time so that network lifetime is maximized. In this paper we consider a variant of MLP, where we allow each cover to neglect a certain fraction (1 - ?) of the targets. We analyze the problem and show that the total network lifetime can be hugely improved by neglecting a very small portion of the targets. An exact approach, based on a Column Generation scheme, is presented and a heuristic solution algorithm is also provided to initialize the approach. The proposed approaches are tested on a wide set of instances. The experimentation shows the effectiveness of both the proposed problems and solution algorithms in extending network lifetime and improving target coverage time when some regularity conditions are taken into account. © 2011 Springer-Verlag.

In the colourful travelling salesman problem (CTSP), given a graph G with a (not necessarily distinct) label (colour) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types. We propose two new heuristics based on the deconstruction of a Hamiltonian tour into subpaths and their reconstruction into a new tour, as well as an adaptation of an existing approach. Extensive experimentation shows the effectiveness of the proposed approaches.

A technique for color quantization is described, which consists of two processes. The first process is based on the analysis of the histograms of the three color components of the RGB input image. The second process performs clustering of the colors quantized by the first process, based on their Euclidean distance. At the end of the second process, the output image is obtained by replacing the color of each pixel of the input image with the closest representative color. The obtained results are satisfactory from both the qualitative and the quantitative point of view.

We present a color image segmentation algorithm, RCRM, based on the detection of Representative Colors and on Region Merging. The 3D color histogram of the RGB input image is built. Colors are processed in decreasing frequency order and a grouping process is accomplished to gather in the same cluster all colors that are close enough to the current color. Colormapping is done to originate a preliminary image segmentation. Segmentation regions having small size undergo a merging process. Merging is actually accomplished only for adjacent regions whose colors do not significantly differ. The parameters involved by the algorithm are set automatically by taking into account color distribution in the input image and geometrical features of the regions into which the image is partitioned. The algorithm has been tested on a large number of RGB color images originating satisfactory results.

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate vf in a shear flow increases with compressibility intensity ?, following the relation ?vf??2. Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case. The effect has been quantitatively measured, and it turns out to be generally small. For the cellular flow, two extreme cases have been investigated, with the whole perturbation situated either in the center of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behavior in the two cases. The enhancing remains modest and is always less than 20%.

Breakup of small tracer-like aggregates is studied by means f numerical simulations in four different flows, namely homogeneous isotropic turbulence, smooth stochastic flow, turbulent channel flow, and developing boundary layer flow.

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori non-negativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case. © 2012 Springer-Verlag.

Periodic monitoring of biodiversity changes at a landscape scale constitutes a key issue for conservation managers. Earth Observation (EO) data offers a potential solution, through direct or indirect mapping of species or habitats. Most national and international programs rely on the use of Land Cover (LC) and/or Land Use (LU) classification systems. Yet, these are not as clearly relatable to biodiversity in comparison to habitat classifications, and provide less scope for monitoring. While a conversion from LC/LU classification to habitat classification can be of great utility, differences in definitions and criteria have so far limited the establishment of a unified approach for such translation between these two classification systems. Focusing on five Mediterranean NATURA 2000 sites, this paper considers the scope for three of the most commonly used global LC/LU taxonomies - CORINE Land Cover (CLC), the Food and Agricultural Organisation (FAO) Land Cover Classification System (LCCS) and the International Geosphere-Biosphere Programme (IGBP) to be translated to habitat taxonomies. Through both quantitative and expert knowledge based qualitative analysis of selected taxonomies, FAO-LCCS turns out to be the best candidate to cope with the complexity of habitat description and provides a framework for EO and in-situ data integration for habitat mapping, reducing uncertainties and class overlaps and bridging the gap between LC/LU and habitats domains for landscape monitoring - a major issue for conservation. This study also highlights the need to modify the FAO-LCCS hierarchical class description process to permit the addition of attributes based on class-specific expert knowledge to select multi-temporal (seasonal) EO data and improve classification. An application of LC/LU to habitat mapping is provided for a coastal Natura 2000 site with high classification accuracy as a result Key words: Mapping; land cover; land use; habitat; earth observation; taxonomies; Natura 2000; classification schemes

In this article we present evidence for a relationship between chromosome gene loci and the topological properties of the protein-protein interaction network corresponding to the set of genes under consideration. Specifically, for each chromosome of the Saccharomyces cerevisiae genome, the distribution of the intra-chromosome inter-gene distances was analyzed and a positive correlation with the distance among the corresponding proteins of the protein-protein interaction network was found. In order to study this relationship we used concepts based on non-parametric statistics and information theory. We provide statistical evidence that if two genes are closely located, then it is likely that their protein products are closely located in the protein-protein interaction network, or in other words, that they are involved in the same biological process.

We document the derivation and implementation of extensions to a two-dimensional, multicomponent lattice Boltzmann equation model, with Laplace law interfacial tension. The extended model behaves in such a way that the boundary between its immiscible drop and embedding fluid components can be shown to describe a vesicle of constant volume bounded by a membrane with conserved length, specified interface compressibility, bending rigidity, preferred curvature, and interfacial tension. We describe how to apply this result to several, independent vesicles. The extended scheme is completely Eulerian, and it represents a two-way coupled vesicle membrane and flow within a single framework. Unlike previous methods, our approach dispenses entirely with the need explicitly to track the membrane, or boundary, and makes no use whatsoever of computationally expensive and intricate interface tracking and remeshing. Validation data are presented, which demonstrate the utility of the method in the simulation of the flow of high volume fraction suspensions of deformable objects

We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ̄rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [10], where only the zeros of the orthogonal polynomials are used.