Power assignment problems in wireless communication

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in (Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\`o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts

Deflation techniques for finding distinct solutions of nonlinear partial differential equations

Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find starting points that lie in different basins of attraction. In this paper, we present an infinite-dimensional deflation algorithm for systematically modifying the residual of a nonlinear PDE problem to eliminate known solutions from consideration. This enables the Newton-Kantorovitch iteration to converge to several different solutions, even starting from the same initial guess. The deflated Jacobian is dense, but an efficient preconditioning strategy is devised, and the number of Krylov iterations are observed not to grow as solutions are deflated. The power of the approach is demonstrated on several problems from special functions, phase separation, differential geometry and \ud fluid mechanics that permit distinct solutions

A human macrophage – hepatocyte co-culture model for comparative studies of infection and replication of Francisella tularensis LVS strain and subspecies holarctica and mediasiatica

Detection of intracellular LPS in macrophage / hepatocyte co-cultures infected with LVS (open bars), spp. holarctica (grey filled bars) or spp. mediasiatica (black filled bars) and untreated control (hatched bars). A) Different amounts of macrophages in the co-culture were tested (6, 12 and 22 % of macrophages on total cell count). Flow cytometric detection of intracellular LPS in macrophages (MFI mean fluorescence intensity); B-D) percentage of remaining detectable macrophages after infection of the co-cultures with B) 6 % macrophages/94 % hepatocytes, C) 12 % macrophages/ 88 % hepatocytes and D) 22 % macrophages/ 88 % hepatocytes 72 h post infection. (TIF 32735 kb

Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum \phi^4_2

We perform a Monte Carlo simulation calculation of the critical coupling constant for the continuum {\lambda \over 4} \phi^4_2 theory. The critical coupling constant we obtain is [{\lambda \over \mu^2}]_crit=10.24(3).Comment: 11 pages, 4 figures, LaTe

The Grothendieck group of polytopes and norms

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Surrogate-based optimization of tidal turbine arrays: a case study for the Faro-Olhão inlet

This paper presents a study for estimating the size of a tidal turbine array for the Faro-Olhão Inlet (Potugal) using a surrogate optimization approach. The method compromises problem formulation, hydro-morphodynamic modelling, surrogate construction and validation, and constraint optimization. A total of 26 surrogates were built using linear RBFs as a function of two design variables: number of rows in the array and Tidal Energy Converters (TECs) per row. Surrogates describe array performance and environmental effects associated with hydrodynamic and morphological aspects of the multi inlet lagoon. After validation, surrogate models were used to formulate a constraint optimization model. Results evidence that the largest array size that satisfies performance and environmental constraints is made of 3 rows and 10 TECs per row.Eduardo González-Gorbeña has received funding for the OpTiCA project (http://msca-optica.eu/) from the Marie Skłodowska-Curie Actions of the European Union's H2020-MSCA-IF-EF-RI-2016 / GA#: 748747. The paper is a contribution to the SCORE pro-ject, funded by the Portuguese Foundation for Science and Technology (FCT–PTDC/AAG-TEC/1710/2014). André Pacheco was supported by the Portuguese Foun-dation for Science and Technology under the Portuguese Researchers’ Programme 2014 entitled “Exploring new concepts for extracting energy from tides” (IF/00286/2014/CP1234).info:eu-repo/semantics/publishedVersio