Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members — that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph

Pulsed-Field Gradient NMR Self Diffusion and Ionic Conductivity Measurements for Liquid Electrolytes Containing LiBF₄ and Propylene Carbonate

Liquid electrolytes have been prepared using lithium tetrafluoroborate (LiBF₄) and propylene carbonate (PC). Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) measurements were taken for the cation, anion and solvent molecules using lithium (⁷Li), fluorine (¹⁹F) and hydrogen (¹H) nuclei, respectively. It was found that lithium diffusion was slow compared to the much larger fluorinated BF₄ anion likely resulting from a large solvation shell of the lithium. Ionic conductivity and viscosity have also been measured for a range of salt concentrations and temperatures. By comparing the measured conductivity with a ideal predicted conductivity derived from the Nernst-Einstein equation and self diffusion coefficients the degree of ionic association of the anion and cation was determined and was observed to increase with salt concentration and temperature. Using the measured viscosity and self diffusion coefficients the effective radius of each of the species was determined for various salt concentrations

Comparison between audio and tactile systems for delivering simple navigational information to visually impaired pedestrians

Many of the current GPS (Global Positioning Systems) navigation aids use an audio method to deliver navigation information to the user. For the visually impaired person this method can be problematic. The visually impaired pedestrian relies heavily on information contained within the ambient sound environment; for location and orientation information, navigation information, and importantly, safety information. In this paper we present the design of an innovative tactile interface and verification of results obtained through experimental trials. This pilot study compared the efficiency of the tactile interface, to an audio method of delivering simple navigational information. The findings indicate that the tactile interface could be used successfully by blind and sighted pedestrians and may offer advantages over auditory interfaces

Two distinct lithium diffusive species for polymer gel electrolytes containing LiBF₄, propylene carbonate (PC) and PVDF

Polymer gel electrolytes have been prepared using lithium tetrafluoroborate (LiBF₄), propylene carbonate (PC) and polyvinylidene fluoride (PVDF) at 20% and 30% concentration by mass. Self diffusion coefficients have been measured using pulse field gradient nuclear magnetic resonance (PFG-NMR) for the cation and anion using ⁷Li and ¹⁹F resonant frequencies respectively. It was found that lithium ion diffusion was slow compared to the much larger fluorine anion likely resulting from a large solvation shell of the lithium. Lithium ion diffusion measurements exhibited two distinct diffusive species, whereas the fluorine ions exhibited only a single diffusive species

Adsorption of DNA onto positively charged amidine colloidal spheres and the resultant bridging interaction

The complexation behaviour of duplex linear DNA (negatively charged) with amidine functionalised sub-micron latex spheres (positively charged) was studied using dynamic light scattering (DLS) and a PALS interferrometric zeta potential sizer. Four types of DNA-sphere complex were investigated as a function of component concentration by combining amidine functionalised polystyrene microspheres with radii of 10.5 nm and 60 nm, and herring DNA of lengths of 35 nm and 85 nm. At low DNA concentrations (cDNA), the undercharged complexes showed a small increase in measured hydrodynamic radius (Rh) and a decrease in zeta potential with increasing cDNA. Within a critical DNA concentration range Rh was seen to peak sharply, and the zeta potentials were 0 mV, corresponding to the formation of unstable neutral complexes. Immediately above this concentration region the measured Rh values became comparable with those at low cDNA, and the zeta potential became negative, indicating the formation of stable overcharged complexes. The small and large spheres formed multi-sphere and single sphere overcharged aggregates respectively, which is thought to be determined by the relative magnitude of the chain persistence length (50 nm) and the sphere radius, switching on or off the DNA bridging interaction

ScotGrid: Providing an Effective Distributed Tier-2 in the LHC Era

ScotGrid is a distributed Tier-2 centre in the UK with sites in Durham, Edinburgh and Glasgow. ScotGrid has undergone a huge expansion in hardware in anticipation of the LHC and now provides more than 4MSI2K and 500TB to the LHC VOs. Scaling up to this level of provision has brought many challenges to the Tier-2 and we show in this paper how we have adopted new methods of organising the centres, from fabric management and monitoring to remote management of sites to management and operational procedures, to meet these challenges. We describe how we have coped with different operational models at the sites, where Glagsow and Durham sites are managed "in house" but resources at Edinburgh are managed as a central university resource. This required the adoption of a different fabric management model at Edinburgh and a special engagement with the cluster managers. Challenges arose from the different job models of local and grid submission that required special attention to resolve. We show how ScotGrid has successfully provided an infrastructure for ATLAS and LHCb Monte Carlo production. Special attention has been paid to ensuring that user analysis functions efficiently, which has required optimisation of local storage and networking to cope with the demands of user analysis. Finally, although these Tier-2 resources are pledged to the whole VO, we have established close links with our local physics user communities as being the best way to ensure that the Tier-2 functions effectively as a part of the LHC grid computing framework..Comment: Preprint for 17th International Conference on Computing in High Energy and Nuclear Physics, 7 pages, 1 figur