On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

An oblivious shortest-path routing algorithm for fully connected cubic networks

Fully connected cubic networks (FCCNs) are a class of newly proposed hierarchical interconnection networks for multicomputer systems, which enjoy the strengths of constant node degree and good expandability. The shortest path routing in FCCNs is an open problem. In this paper, we present an oblivious routing algorithm for n-level FCCN with N = 8(n) nodes, and prove that this algorithm creates a shortest path from the source to the destination. At the costs of both an O(N)-parallel-step off-line preprocessing phase and a list of size N stored at each node, the proposed algorithm is carried out at each related node in O(n) time. In some cases the proposed algorithm is superior to the one proposed by Chang and Wang in terms of the length of the routing path. This justifies the utility of our routing strategy. (C) 2006 Elsevier Inc. All rights reserved.

Largest connected component of a star graph with faulty vertices

In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n >= 3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.

'Everything is connected, and everything matters': relationships in I ♥ Huckabees

An analysis of two paired moments, both involving bicycle rides, which enables a discussion of the relationships which the film establishes formally between these moments (and other elements of the film) and establishes the parallel between these structures and the film's interest in exploring coincidences, and seeking out a range of economic, political and metaphysical relationships. It explores the way the film dramatises philosophical debates through action.

Winter floods in Britain are connected to atmospheric rivers

Damage from flooding in the winter and fall seasons has been widespread in the United Kingdom (UK) and Western Europe over recent decades. Here we show that winter flood events in the UK are connected to Atmospheric Rivers (ARs), narrow ribbons along which a large flux of moisture is transported from the subtropics to the mid-latitudes. Combining river flow records with rainfall measurements, satellite data and model simulations, we demonstrate that ARs occur simultaneously with the 10 largest winter flood events since 1970 in a range of British river basins, suggesting that ARs are persistently critical in explaining extreme winter flooding in the UK. Understanding the physical processes that determine the persistence of AR events will be of importance in assessing the risk of future flooding over north-western Europe and other mid-latitude regions.

Space heating and hot water demand analysis of dwellings connected to district heating scheme in UK

To achieve CO2 emissions reductions the UK Building Regulations require developers of new residential buildings to calculate expected CO2 emissions arising from their energy consumption using a methodology such as Standard Assessment Procedure (SAP 2005) or, more recently SAP 2009. SAP encompasses all domestic heat consumption and a limited proportion of the electricity consumption. However, these calculations are rarely verified with real energy consumption and related CO2 emissions. This paper presents the results of an analysis based on weekly head demand data for more than 200 individual flats. The data is collected from recently built residential development connected to a district heating network. A methodology for separating out the domestic hot water use (DHW) and space heating demand (SH) has been developed and compares measured values to the demand calculated using SAP 2005 and 2009 methodologies. The analysis shows also the variance in DHW and SH consumption between both size of the flats and tenure (privately owned or housing association). Evaluation of the space heating consumption includes also an estimation of the heating degree day (HDD) base temperature for each block of flats and its comparison to the average base temperature calculated using the SAP 2005 methodology.

Constrained principal component analysis reveals functionally connected load-dependent networks involved in multiple stages of working memory

Constrained principal component analysis (CPCA) with a finite impulse response (FIR) basis set was used to reveal functionally connected networks and their temporal progression over a multistage verbal working memory trial in which memory load was varied. Four components were extracted, and all showed statistically significant sensitivity to the memory load manipulation. Additionally, two of the four components sustained this peak activity, both for approximately 3 s (Components 1 and 4). The functional networks that showed sustained activity were characterized by increased activations in the dorsal anterior cingulate cortex, right dorsolateral prefrontal cortex, and left supramarginal gyrus, and decreased activations in the primary auditory cortex and "default network" regions. The functional networks that did not show sustained activity were instead dominated by increased activation in occipital cortex, dorsal anterior cingulate cortex, sensori-motor cortical regions, and superior parietal cortex. The response shapes suggest that although all four components appear to be invoked at encoding, the two sustained-peak components are likely to be additionally involved in the delay period. Our investigation provides a unique view of the contributions made by a network of brain regions over the course of a multiple-stage working memory trial.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Testing substorm theories: The need for multipoint observations

The requirement for multipoint observations to test theories of magnetospheric substorms is reviewed. A wide variety of such theories have been proposed, but these cannot be properly evaluated because we do not understand how the various features of a substorm are causally linked. In terms of explaining certain substorm features, some theories may be mutually-exclusive rivals. But this is not always the case, making it possible that theories may be either combined into a synthesis model or loosely connected in a more modular view of substorms. Some key questions are defined which require multipoint in-situ measurements, combined with remote sensing observations, of the development and relationship of the major substorm features.

The impact of location and type on the performance of Low-Voltage network connected Battery Energy Storage Systems

This paper assesses the impact of the location and configuration of Battery Energy Storage Systems (BESS) on Low-Voltage (LV) feeders. BESS are now being deployed on LV networks by Distribution Network Operators (DNOs) as an alternative to conventional reinforcement (e.g. upgrading cables and transformers) in response to increased electricity demand from new technologies such as electric vehicles. By storing energy during periods of low demand and then releasing that energy at times of high demand, the peak demand of a given LV substation on the grid can be reduced therefore mitigating or at least delaying the need for replacement and upgrade. However, existing research into this application of BESS tends to evaluate the aggregated impact of such systems at the substation level and does not systematically consider the impact of the location and configuration of BESS on the voltage profiles, losses and utilisation within a given feeder. In this paper, four configurations of BESS are considered: single-phase, unlinked three-phase, linked three-phase without storage for phase-balancing only, and linked three-phase with storage. These four configurations are then assessed based on models of two real LV networks. In each case, the impact of the BESS is systematically evaluated at every node in the LV network using Matlab linked with OpenDSS. The location and configuration of a BESS is shown to be critical when seeking the best overall network impact or when considering specific impacts on voltage, losses, or utilisation separately. Furthermore, the paper also demonstrates that phase-balancing without energy storage can provide much of the gains on unbalanced networks compared to systems with energy storage.