Multicolored Dynamos on Toroidal Meshes

Detecting on a graph the presence of the minimum number of nodes (target set) that will be able to "activate" a prescribed number of vertices in the graph is called the target set selection problem (TSS) proposed by Kempe, Kleinberg, and Tardos. In TSS's settings, nodes have two possible states (active or non-active) and the threshold triggering the activation of a node is given by the number of its active neighbors. Dealing with fault tolerance in a majority based system the two possible states are used to denote faulty or non-faulty nodes, and the threshold is given by the state of the majority of neighbors. Here, the major effort was in determining the distribution of initial faults leading the entire system to a faulty behavior. Such an activation pattern, also known as dynamic monopoly (or shortly dynamo), was introduced by Peleg in 1996. In this paper we extend the TSS problem's settings by representing nodes' states with a "multicolored" set. The extended version of the problem can be described as follows: let G be a simple connected graph where every node is assigned a color from a finite ordered set C = {1, . . ., k} of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors. Given G, we study the initial distributions of colors leading the system to a k monochromatic configuration in toroidal meshes, focusing on the minimum number of initial k-colored nodes. We find upper and lower bounds to the size of a dynamo, and then special classes of dynamos, outlined by means of a new approach based on recoloring patterns, are characterized

Dynamic Monopolies in Colored Tori

The {\em information diffusion} has been modeled as the spread of an information within a group through a process of social influence, where the diffusion is driven by the so called {\em influential network}. Such a process, which has been intensively studied under the name of {\em viral marketing}, has the goal to select an initial good set of individuals that will promote a new idea (or message) by spreading the "rumor" within the entire social network through the word-of-mouth. Several studies used the {\em linear threshold model} where the group is represented by a graph, nodes have two possible states (active, non-active), and the threshold triggering the adoption (activation) of a new idea to a node is given by the number of the active neighbors. The problem of detecting in a graph the presence of the minimal number of nodes that will be able to activate the entire network is called {\em target set selection} (TSS). In this paper we extend TSS by allowing nodes to have more than two colors. The multicolored version of the TSS can be described as follows: let $G$ be a torus where every node is assigned a color from a finite set of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors. We study the initial distributions of colors leading the system to a monochromatic configuration of color $k$, focusing on the minimum number of initial $k$-colored nodes. We conclude the paper by providing the time complexity to achieve the monochromatic configuration

Strong Subadditivity, Null Energy Condition and Charged Black Holes

Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area surfaces that determine the entanglement entropy for the boundary theory, can penetrate into this forbidden region only for certain choices for the mass and the charge functions in the background. This penetration is then perceived as the violation of SSA in the boundary theory. We also find that this happens only when the critical surface lies above the apparent horizon, but not otherwise. We conjecture that SSA, which is thus non-trivially related to NEC, also characterizes the entire time-evolution process along which the dual field theory may thermalize.Comment: 27 pages, v3 matches the published versio

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving 2D Voronoi meshes that are regenerated at each time step and which explicitly allow topology changes in time. The Voronoi tessellations are obtained from a set of generator points that move with the local fluid velocity. We employ an AREPO-type approach, which rapidly rebuilds a new high quality mesh rearranging the element shapes and neighbors in order to guarantee a robust mesh evolution even for vortex flows and very long simulation times. The old and new Voronoi elements associated to the same generator are connected to construct closed space--time control volumes, whose bottom and top faces may be polygons with a different number of sides. We also incorporate degenerate space--time sliver elements, needed to fill the space--time holes that arise because of topology changes. The final ALE FV-DG scheme is obtained by a redesign of the fully discrete direct ALE schemes of Boscheri and Dumbser, extended here to moving Voronoi meshes and space--time sliver elements. Our new numerical scheme is based on the integration over arbitrary shaped closed space--time control volumes combined with a fully-discrete space--time conservation formulation of the governing PDE system. In this way the discrete solution is conservative and satisfies the GCL by construction. Numerical convergence studies as well as a large set of benchmarks for hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and robustness of the proposed method. Our numerical results clearly show that the new combination of very high order schemes with regenerated meshes with topology changes lead to substantial improvements compared to direct ALE methods on conforming meshes

Comparación de técnicas de clasificación deductivas para estimar la distribución potencial de insectos cuarentenarios

El objetivo de este trabajo fue comparar el desempeño de los criterios de clasificación nítidos y difusos en la construcción de modelos deductivos de la distribución potencial de insectos exóticos. Considerando criterios de clasificación binaria nítida y difusa, de capas ráster de temperatura máxima, media y mínima diaria, se generó un índice de riesgo bioclimático relativo, considerando el número de días con condiciones óptimas para el desarrollo de Bactrocera oleae (Gmelin) (Diptera: Tephritidae) y Cerotoma arcuatus (Olivier) (Coleoptera: Chrysomelidae). Se realizaron análisis de sensibilidad de los modelos. Los modelos deductivos de distribución potencial de especies realizados mediante clasificación difusa, serían más robustos y menos restrictivos en la determinación de áreas de riesgo fitosanitario potencial que aquellos realizados con criterios de clasificación nítidos. Estos últimos serían más sensibles y tendrían mayor capacidad de discriminar áreas con diferentes perfiles de riesgo ambiental.The objective of this paper was to evaluate the performance of crisp and fuzzy classification criteria in the construction of deductive potential distribution models of exotic insects. As case studies, Bactrocera oleae (Gmelin) (Diptera: Tephritidae) and Cerotoma arcuatus (Olivier) (Coleoptera: Chrysomelidae) were selected. Considering crisp and fuzzy classification for raster layers of maximum, average and minimum daily temperature, a relative bioclimatic risk index was generated. The number of days with optimal conditions for pests’ development was considered. Sensitivity analyses of both models were performed. Considering each case evaluated and the variables used, deductive pest distribution models made by fuzzy classification was more robust and less conservative in the determination of potential phytosanitary risk areas than those made with crisp classification criteria. This last case was more sensitive and would have a greater capacity to discriminate areas with different environmental risk profiles.Fil: Heit, Guillermo Eugenio. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Vegetal. Cátedra de Zoología Agrícola; ArgentinaFil: Sione, Walter Fabian. Universidad Autónoma de Entre Rí­os. Facultad de Ciencia y Tecnología. Centro Regional de Geomática; Argentina. Universidad Nacional de Luján; ArgentinaFil: Claps, Lucia Elena. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo. Instituto Superior de Entomología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Aceñolaza, Pablo Gilberto. Provincia de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Universidad Autónoma de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción; Argentin

Continuous finite element subgrid basis functions for Discontinuous Galerkin schemes on unstructured polygonal Voronoi meshes

We propose a new high order accurate nodal discontinuous Galerkin (DG) method for the solution of nonlinear hyperbolic systems of partial differential equations (PDE) on unstructured polygonal Voronoi meshes. Rather than using classical polynomials of degree N inside each element, in our new approach the discrete solution is represented by piecewise continuous polynomials of degree N within each Voronoi element, using a continuous finite element basis defined on a subgrid inside each polygon. We call the resulting subgrid basis an agglomerated finite element (AFE) basis for the DG method on general polygons, since it is obtained by the agglomeration of the finite element basis functions associated with the subgrid triangles. The basis functions on each sub-triangle are defined, as usual, on a universal reference element, hence allowing to compute universal mass, flux and stiffness matrices for the subgrid triangles once and for all in a pre-processing stage for the reference element only. Consequently, the construction of an efficient quadrature-free algorithm is possible, despite the unstructured nature of the computational grid. High order of accuracy in time is achieved thanks to the ADER approach, making use of an element-local space-time Galerkin finite element predictor. The novel schemes are carefully validated against a set of typical benchmark problems for the compressible Euler and Navier-Stokes equations. The numerical results have been checked with reference solutions available in literature and also systematically compared, in terms of computational efficiency and accuracy, with those obtained by the corresponding modal DG version of the scheme

Opinions within Media, Power and Gossip

Despite the increasing diffusion of the Internet technology, TV remains the principal medium of communication. People's perceptions, knowledge, beliefs and opinions about matter of facts get (in)formed through the information reported on by the mass-media. However, a single source of information (and consensus) could be a potential cause of anomalies in the structure and evolution of a society. Hence, as the information available (and the way it is reported) is fundamental for our perceptions and opinions, the definition of conditions allowing for a good information to be disseminated is a pressing challenge. In this paper starting from a report on the last Italian political campaign in 2008, we derive a socio-cognitive computational model of opinion dynamics where agents get informed by different sources of information. Then, a what-if analysis, performed trough simulations on the model's parameters space, is shown. In particular, the scenario implemented includes three main streams of information acquisition, differing in both the contents and the perceived reliability of the messages spread. Agents' internal opinion is updated either by accessing one of the information sources, namely media and experts, or by exchanging information with one another. They are also endowed with cognitive mechanisms to accept, reject or partially consider the acquired information

Effect of Indian clubbell exercises on cricket fast bowlers’ shoulder kinematics

Background: The glenohumeral joint’s rotational range of motion (ROM) and muscle strength are essential to execute the cricket bowling action. Performing shoulder rotation exercises may increase the rotator cuff muscle strength and rotational ROM.  Objectives: The aim of this study was to test the effect of a six-week exercise programme on shoulder rotational ROM and muscle strength. Methods: Twenty-one healthy male cricket fast bowlers were recruited, ranked and pair-matched on initial shoulder rotator muscle strength and assigned to either a shoulder exercise (SE) group or cricket training (CT) only group. The SE group incorporated Indian clubbell exercises in addition to their cricket training. Results: Bowlers in both groups displayed a large increase on the dominant shoulder’s internal rotation (IR) ROM, but only the SE group’s bowlers displayed ROM improvements (p<0.001) bilaterally for both internal and external rotation. The CT group’s fast bowler’s non-dominant shoulder IR ROM significantly decreased (p=0.02) during the six weeks. Between groups, only the SE group’s bowler’s internal rotator muscle strength improved (p<0.001) bilaterally. The observed kinematic changes were statistically significantly greater at a 5% level for the SE group’s bowlers (bilateral internal rotators muscle strength, non-dominant shoulder IR ROM and horizontal adduction ROM). Conclusion: Maintenance of the shoulder’s rotational ROM and muscle strength is vital for a fast bowler. Cricket bowlers who perform regular clubbell exercises might increase their shoulder’s ROM and internal rotator cuffs’ muscle strength, which may aid in stabilising their glenohumeral joint while bowling.