Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

The effect of non-uniform radiative damping on the zonal-mean dynamics of the extratropical middle atmosphere

The effect of spatial and temporal variations in the radiative damping rate on the response to an imposed forcing or diabatic heating is examined in a zonal-mean model of the middle atmosphere. Attention is restricted to the extratropics, where a linear approach is viable. It is found that regions with weak radiative damping rates are more sensitive in terms of temperature to the remote influence of the diabatic circulation. The delay in the response in such regions can mean that ‘downward’ control is not achieved on seasonal time-scales. A seasonal variation in the radiative damping rate modulates the evolution of the response and leaves a transient-like signature in the annual mean temperature field. Several idealized examples are considered, motivated by topical questions. It is found that wave drag outside the polar vortex can significantly affect the temperatures in its interior, so that high-latitude, high-altitude gravity-wave drag is not the only mechanism for warming the southern hemisphere polar vortex. Diabatic mass transport through the 100 hPa surface is found to lag the seasonal evolution of the wave drag that drives the transport, and thus cannot be considered to be in the downward control regime. On the other hand, the seasonal variation of the radiative damping rate is found to make only a weak contribution to the annual mean temperature increase that has been observed above the ozone hole. Copyright © 2002 Royal Meteorological Society.

The financial effects of uniform and mixed corporate social performance

Firms typically present a mixed picture of corporate social performance (CSP), with positive and negative indicators exhibited by the same firm. Thus, stakeholders’ judgements of corporate social responsibility (CSR) typically evaluate positives in the context of negatives, and vice versa. Building on social judgement theory, we present two alternative accounts of how stakeholders respond to such complexity, which provide differing implications for the financial effects of CSP: reciprocal dampening and rewarding uniformity. Echoing notable findings on strategic consistency, our US panel study finds that firms that exhibit uniformly positive or uniformly negative indicators in particular dimensions of CSP outperform firms that exhibit a mixed picture of positives and negatives, which supports the notion that stakeholders’ judgements of CSR reward uniformity.

Effects of non-uniform crosswind fields on scintillometry measurements

The effects of a non-uniform wind field along the path of a scintillometer are investigated. Theoretical spectra are calculated for a range of scenarios where the crosswind varies in space or time and compared to the ‘ideal’ spectrum based on a constant uniform crosswind. It is verified that the refractive-index structure parameter relation with the scintillometer signal remains valid and invariant for both spatially and temporally-varying crosswinds. However, the spectral shape may change significantly preventing accurate estimation of the crosswind speed from the peak of the frequency spectrum and retrieval of the structure parameter from the plateau of the power spectrum. On comparison with experimental data, non-uniform crosswind conditions could be responsible for previously unexplained features sometimes seen in observed spectra. By accounting for the distribution of crosswind, theoretical spectra can be generated that closely replicate the observations, leading to a better understanding of the measurements. Spatial variability of wind speeds should be expected for paths other than those that are parallel to the surface and over flat, homogenous areas, whilst fluctuations in time are important for all sites.

The influence of plant species number on productivity, ground coverage and floral performance in grass-free lawns

The grass-free lawn is a novel development in modern ornamental horticulture where the traditional monoculture of grass is replaced by a variety of mowing-tolerant clonal forbs. It brings floral aesthetics and a diverse species approach to the use of lawn space. How the number of constituent forb species affects the aesthetic and structural performance of grass-free lawns was investigated using grass-free lawns composed of four, six and twelve British native clonal perennial forb species. Lawn productivity was seen to increase with increasing species number but the relationship was not linear. Plant cover was dynamic in all lawn types, varied between years and was not representative of individual species' floral performance. The behaviour of component species common to all lawns suggested that lawns with 12 species show greater structural stability than the lawns with a lower species number. Visual performance in lawns with the greatest species number was lower than in lawns with fewer species, with increasing variety in floral size and individual species floral productivity leading to a trade-off between diversity and floral performance. Individual species were seen to have different aesthetic functions in grass-free lawns either by providing flowers, ground coverage or both.

Coverage-dependent structural evolution in the interaction of NO2 with Au{111}

We have used low-temperature STM, together with DFT calculations incorporating the effects of dispersion forces, to study from a structural point of view the interaction of NO2 with Au{111} surfaces. NO2 adsorbs molecularly on Au{111} at 80 K, initially as small, disordered clusters at the elbows of the type-x reconstruction lines of the clean-surface herringbone reconstruction, and then as larger, ordered islands on the fcc regions. Within the islands, the NO2 molecules define a (√3 × 2)rect. superlattice, for which we evaluate structural models. By around 0.25 ML coverage, the herringbone reconstruction has been lifted, accompanied by the formation of Au nanoclusters, and the islands have coalesced. At this stage, essentially the whole surface is covered with an overlayer consisting predominantly of domains of the (√3 × 2)rect. structure, but also containing less wellordered regions. With further exposure, the degree of disorder in the overlayer increases; saturation occurs close to 0.43 ML.

Intercomparison of methods of coupling between convection and large-scale circulation: 1. Comparison over uniform surface conditions

As part of an international intercomparison project, a set of single column models (SCMs) and cloud-resolving models (CRMs) are run under the weak temperature gradient (WTG) method and the damped gravity wave (DGW) method. For each model, the implementation of the WTG or DGW method involves a simulated column which is coupled to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. The simulated column has the same surface conditions as the reference state and is initialized with profiles from the reference state. We performed systematic comparison of the behavior of different models under a consistent implementation of the WTG method and the DGW method and systematic comparison of the WTG and DGW methods in models with different physics and numerics. CRMs and SCMs produce a variety of behaviors under both WTG and DGW methods. Some of the models reproduce the reference state while others sustain a large-scale circulation which results in either substantially lower or higher precipitation compared to the value of the reference state. CRMs show a fairly linear relationship between precipitation and circulation strength. SCMs display a wider range of behaviors than CRMs. Some SCMs under the WTG method produce zero precipitation. Within an individual SCM, a DGW simulation and a corresponding WTG simulation can produce different signed circulation. When initialized with a dry troposphere, DGW simulations always result in a precipitating equilibrium state. The greatest sensitivities to the initial moisture conditions occur for multiple stable equilibria in some WTG simulations, corresponding to either a dry equilibrium state when initialized as dry or a precipitating equilibrium state when initialized as moist. Multiple equilibria are seen in more WTG simulations for higher SST. In some models, the existence of multiple equilibria is sensitive to some parameters in the WTG calculations.

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

Sampling uncertainty in gridded sea surface temperature products and Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data

Sea surface temperature (SST) data are often provided as gridded products, typically at resolutions of order 0.05 degrees from satellite observations to reduce data volume at the request of data users and facilitate comparison against other products or models. Sampling uncertainty is introduced in gridded products where the full surface area of the ocean within a grid cell cannot be fully observed because of cloud cover. In this paper we parameterise uncertainties in SST as a function of the percentage of clear-sky pixels available and the SST variability in that subsample. This parameterisation is developed from Advanced Along Track Scanning Radiometer (AATSR) data, but is applicable to all gridded L3U SST products at resolutions of 0.05-0.1 degrees, irrespective of instrument and retrieval algorithm, provided that instrument noise propagated into the SST is accounted for. We also calculate the sampling uncertainty of ~0.04 K in Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) products, using related methods.

Intercomparison of methods of coupling between convection and large-scale circulation. 2: Comparison over non-uniform surface conditions

As part of an international intercomparison project, the weak temperature gradient (WTG) and damped gravity wave (DGW) methods are used to parameterize large-scale dynamics in a set of cloud-resolving models (CRMs) and single column models (SCMs). The WTG or DGW method is implemented using a configuration that couples a model to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. We investigated the sensitivity of each model to changes in SST, given a fixed reference state. We performed a systematic comparison of the WTG and DGW methods in different models, and a systematic comparison of the behavior of those models using the WTG method and the DGW method. The sensitivity to the SST depends on both the large-scale parameterization method and the choice of the cloud model. In general, SCMs display a wider range of behaviors than CRMs. All CRMs using either the WTG or DGW method show an increase of precipitation with SST, while SCMs show sensitivities which are not always monotonic. CRMs using either the WTG or DGW method show a similar relationship between mean precipitation rate and column-relative humidity, while SCMs exhibit a much wider range of behaviors. DGW simulations produce large-scale velocity profiles which are smoother and less top-heavy compared to those produced by the WTG simulations. These large-scale parameterization methods provide a useful tool to identify the impact of parameterization differences on model behavior in the presence of two-way feedback between convection and the large-scale circulation.