Space partitioning for scalable K-means

K-Means is a popular clustering algorithm which adopts an iterative refinement procedure to determine data partitions and to compute their associated centres of mass, called centroids. The straightforward implementation of the algorithm is often referred to as `brute force' since it computes a proximity measure from each data point to each centroid at every iteration of the K-Means process. Efficient implementations of the K-Means algorithm have been predominantly based on multi-dimensional binary search trees (KD-Trees). A combination of an efficient data structure and geometrical constraints allow to reduce the number of distance computations required at each iteration. In this work we present a general space partitioning approach for improving the efficiency and the scalability of the K-Means algorithm. We propose to adopt approximate hierarchical clustering methods to generate binary space partitioning trees in contrast to KD-Trees. In the experimental analysis, we have tested the performance of the proposed Binary Space Partitioning K-Means (BSP-KM) when a divisive clustering algorithm is used. We have carried out extensive experimental tests to compare the proposed approach to the one based on KD-Trees (KD-KM) in a wide range of the parameters space. BSP-KM is more scalable than KDKM, while keeping the deterministic nature of the `brute force' algorithm. In particular, the proposed space partitioning approach has shown to overcome the well-known limitation of KD-Trees in high-dimensional spaces and can also be adopted to improve the efficiency of other algorithms in which KD-Trees have been used.

Peroxy radical partitioning during the AMMA radical intercomparison exercise

Peroxy radicals were measured onboard two scientific aircrafts during the AMMA (African Monsoon Multidisciplinary Analysis) campaign in summer 2006. This paper reports results from the flight on 16 August 2006 during which measurements of HO2 by laser induced fluorescence spectroscopy at low pressure (LIF-FAGE) and total peroxy radicals (RO2* = HO2+ΣRO2, R = organic chain) by two similar instruments based on the peroxy radical chemical amplification (PeRCA) technique were subject of a blind intercomparison. The German DLR-Falcon and the British FAAM-BAe-146 flew wing tip to wing tip for about 30 min making concurrent measurements on 2 horizontal level runs at 697 and 485 hPa over the same geographical area in Burkina Faso. A full set of supporting measurements comprising photolysis frequencies, and relevant trace gases like CO, NO, NO2, NOy, O3 and a wider range of VOCs were collected simultaneously. Results are discussed on the basis of the characteristics and limitations of the different instruments used. Generally, no data bias are identified and the RO2* data available agree quite reasonably within the instrumental errors. The [RO2*]/[HO2] ratios, which vary between 1:1 and 3:1, as well as the peroxy radical variability, concur with variations in photolysis rates and in other potential radical precursors. Model results provide additional information about dominant radical formation and loss processes.

Biomass partitioning and growth efficiency in four naturally regenerated forest tree species

Current forest growth models and yield tables are almost exclusively based on data from mature trees, reducing their applicability to young and developing stands. To address this gap, young European beech, sessile oak, Scots pine and Norway spruce trees approximately 0 to 10 years old were destructively sampled in a range of naturally regenerated forest stands in Central Europe. Diameter at base and height were first measured in situ for up to 175 individuals per species. Subsequently, the trees were excavated and dry biomass of foliage, branches, stems and roots was measured. Allometric relations were then used to calculate biomass allocation coefficients (BAC) and growth efficiency (GE) patterns in young trees. We found large differences in BAC and GE between broadleaves and conifers, but also between species within these categories. Both BAC and GE are strongly age-specific in young trees, their rapidly changing values reflecting different growth strategies in the earliest stages of growth. We show that linear relationships describing biomass allocation in older trees are not applicable in young trees. To accurately predict forest biomass and carbon stocks, forest growth models need to include species and age specific parameters of biomass allocation patterns.

Blind equalisation of multilevel PAM data for nonminimum phase channels via second- and fourth-order cumulants

This paper introduces a new blind equalisation algorithm for the pulse amplitude modulation (PAM) data transmitted through nonminimum phase (NMP) channels. The algorithm itself is based on a noncausal AR model of communication channels and the second- and fourth-order cumulants of the received data series, where only the diagonal slices of cumulants are used. The AR parameters are adjusted at each sample by using a successive over-relaxation (SOR) scheme, a variety of the ordinary LMS scheme, but with a faster convergence rate and a greater robustness to the selection of the ‘step-size’ in iterations. Computer simulations are implemented for both linear time-invariant (LTI) and linear time-variant (LTV) NMP channels, and the results show that the algorithm proposed in this paper has a fast convergence rate and a potential capability to track the LTV NMP channels.

A simple, coherent framework for partitioning uncertainty in climate predictions

A simple and coherent framework for partitioning uncertainty in multi-model climate ensembles is presented. The analysis of variance (ANOVA) is used to decompose a measure of total variation additively into scenario uncertainty, model uncertainty and internal variability. This approach requires fewer assumptions than existing methods and can be easily used to quantify uncertainty related to model-scenario interaction - the contribution to model uncertainty arising from the variation across scenarios of model deviations from the ensemble mean. Uncertainty in global mean surface air temperature is quantified as a function of lead time for a subset of the Coupled Model Intercomparison Project phase 3 ensemble and results largely agree with those published by other authors: scenario uncertainty dominates beyond 2050 and internal variability remains approximately constant over the 21st century. Both elements of model uncertainty, due to scenario-independent and scenario-dependent deviations from the ensemble mean, are found to increase with time. Estimates of model deviations that arise as by-products of the framework reveal significant differences between models that could lead to a deeper understanding of the sources of uncertainty in multi-model ensembles. For example, three models are shown diverging pattern over the 21st century, while another model exhibits an unusually large variation among its scenario-dependent deviations.

An isotope dilution model for partitioning phenylalanine uptake by the liver of lactating dairy cows

An isotope dilution model for partitioning phenylalanine uptake by the liver of the lactating dairy cow was constructed and solved in the steady state. If assumptions are made, model solution permits calculation of the rate of phenylalanine uptake from portal vein and hepatic arterial blood supply, phenylalanine release into the hepatic vein, phenylalanine oxidation and synthesis, and degradation of hepatic constitutive and export proteins. The model requires the measurement of plasma fow rate through the liver in combination with phenylalanine concentrations and plateau isotopic enrichments in arterial, portal and hepatic plasma during a constant infusion of [1-13C]phenylalanine tracer. The model can be applied to other amino acids with similar metabolic fates and will provide a means for assessing the impact of hepatic metabolism on amino acid availability to peripheral tissues. This is of particular importance for the dairy cow when considering the requirements for milk protein synthesis and the negative environmental impact of excessive nitrogen excretion.

Mineral partitioning in milk and milk permeates at high temperature

The soluble phase of milk was separated at 20 and 80°C using ultrafiltration. The resulting permeates were then subjected to further ultrafiltration and dialysis at close to these two temperatures. It was found that pH, Ca2+ and soluble Ca decreased as the separation temperature increased both in original UF permeates and in dialysates obtained from these permeates, but P decreased only slightly. The major reason for these changes was due to the precipitation of calcium phosphate/citrate complexes onto the casein micelle with concomitant release of H+. The pH of both permeates and dialysates from milk at 20°C were slightly higher than for milk. When UF permeates collected at 20 and 80°C, were each dialysed at both these temperatures, the dialysate collected at 80°C showed much less temperature dependence for pH and ionic calcium compared with that collected at 20°C. This is in contrast to milk, which shows considerable temperature dependence for pH and ionic calcium. Further experiments revealed that the pH and Ca2+ concentration of permeates showed high temperature dependence above the temperature at which they were separated, but a much lower temperature dependence below that temperature. These findings suggest that dialysis and UF of milk at high temperature provide the best means yet for estimating the pH and ionic calcium of milk at that temperature.

Modeling data with structural and temporal correlation using lower level and higher level multilevel models

Novel imaging techniques are playing an increasingly important role in drug development, providing insight into the mechanism of action of new chemical entities. The data sets obtained by these methods can be large with complex inter-relationships, but the most appropriate statistical analysis for handling this data is often uncertain - precisely because of the exploratory nature of the way the data are collected. We present an example from a clinical trial using magnetic resonance imaging to assess changes in atherosclerotic plaques following treatment with a tool compound with established clinical benefit. We compared two specific approaches to handle the correlations due to physical location and repeated measurements: two-level and four-level multilevel models. The two methods identified similar structural variables, but higher level multilevel models had the advantage of explaining a greater proportion of variation, and the modeling assumptions appeared to be better satisfied.

Development of a semantic graph-based scene description

Software representations of scenes, i.e. the modelling of objects in space, are used in many application domains. Current modelling and scene description standards focus on visualisation dimensions, and are intrinsically limited by their dependence upon their semantic interpretation and contextual application by humans. In this paper we propose the need for an open, extensible and semantically rich modelling language, which facilitates a machine-readable semantic structure. We critically review existing standards and techniques, and highlight a need for a semantically focussed scene description language. Based on this defined need we propose a preliminary solution, based on hypergraph theory, and reflect on application domains.

RAMI4PILPS: An intercomparison of formulations for the partitioning of solar radiation in land surface models

[1] Remotely sensed, multiannual data sets of shortwave radiative surface fluxes are now available for assimilation into land surface schemes (LSSs) of climate and/or numerical weather prediction models. The RAMI4PILPS suite of virtual experiments assesses the accuracy and consistency of the radiative transfer formulations that provide the magnitudes of absorbed, reflected, and transmitted shortwave radiative fluxes in LSSs. RAMI4PILPS evaluates models under perfectly controlled experimental conditions in order to eliminate uncertainties arising from an incomplete or erroneous knowledge of the structural, spectral and illumination related canopy characteristics typical for model comparison with in situ observations. More specifically, the shortwave radiation is separated into a visible and near-infrared spectral region, and the quality of the simulated radiative fluxes is evaluated by direct comparison with a 3-D Monte Carlo reference model identified during the third phase of the Radiation transfer Model Intercomparison (RAMI) exercise. The RAMI4PILPS setup thus allows to focus in particular on the numerical accuracy of shortwave radiative transfer formulations and to pinpoint to areas where future model improvements should concentrate. The impact of increasing degrees of structural and spectral subgrid variability on the simulated fluxes is documented and the relevance of any thus emerging biases with respect to gross primary production estimates and shortwave radiative forcings due to snow and fire events are investigated.

Genetic variability in partitioning to the yield component of cacao (Theobroma cacao L.)

Biomass partitioning of cacao (Theobroma cacao L.) was studied in seven clones and five hybrids in a replicated experiment in Bahia, Brazil. Over an eighteen month period, a seven- fold difference in dry bean yield was demonstrated between genotypes, ranging from the equivalent of 200 to 1389 kg.ha-1. During the same interval, the increase in trunk cross-sectional area ranged from 11.1 cm2 for clone EEG-29 to 27.6 cm2 for hybrid PA-150 * MA-15. Yield efficiency increment (the ratio of cumulative yield to the increase in trunk circumference), which indicated partitioning between the vegetative and reproductive components, ranged from 0.008 kg.cm-2 for clone CP-82 to 0.08 kg.cm-2 for clone EEG-29. An examination of biomass partitioning within the pod of the seven clones revealed that the beans accounted for between 32.0% (CP-82) and 44.5% (ICS-9) of the pod biomass. The study demonstrated the potential for yield improvement in cacao by selectively breeding for more efficient partitioning to the yield component.