On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Sequential extraction and single-step cold-acid extraction: A feasibility study for use with freshwater-canal sediments

This investigation examines metal release from freshwater sediment using sequential extraction and single-step cold-acid leaching. The concentrations of Cd, Cr, Cu, Fe, Ni, Pb and Zn released using a standard 3-step sequential extraction (Rauret et al., 1999) are compared to those released using a 0.5 M HCl; leach. The results show that the three sediments behave in very different ways when subject to the same leaching experiments: the cold-acid extraction appears to remove higher relative concentrations of metals from the iron-rich sediment than from the other two sediments. Cold-acid extraction appears to be more effective at removing metals from sediments with crystalline iron oxides than the "reducible" step of the sequential extraction. The results show that a single-step acid leach can be just as effective as sequential extractions at removing metals from sediment and are a great deal less time-consuming.

Scalability of efficient parallel K-Means

Clustering is defined as the grouping of similar items in a set, and is an important process within the field of data mining. As the amount of data for various applications continues to increase, in terms of its size and dimensionality, it is necessary to have efficient clustering methods. A popular clustering algorithm is K-Means, which adopts a greedy approach to produce a set of K-clusters with associated centres of mass, and uses a squared error distortion measure to determine convergence. Methods for improving the efficiency of K-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting a more efficient data structure, notably a multi-dimensional binary search tree (KD-Tree) to store either centroids or data points. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient K-Means techniques in parallel computational environments. In this work, we provide a parallel formulation for the KD-Tree based K-Means algorithm and address its load balancing issues.

The effect of consumption volume on profile and liking of oral nutritional supplements of varied sweetness: sequential profiling and boredom tests

Oral nutrition supplements (ONS) are routinely prescribed to those with, or at risk of, malnutrition. Previous research identified poor compliance due to taste and sweetness. This paper investigates taste and hedonic liking of ONS, of varying sweetness and metallic levels, over consumption volume; an important consideration as patients are prescribed large volumes of ONS daily. A sequential descriptive profile was developed to determine the perception of sensory attributes over repeat consumption of ONS. Changes in liking of ONS following repeat consumption were characterised by a boredom test. Certain flavour (metallic taste, soya milk flavour) and mouthfeel (mouthdrying, mouthcoating) attributes built up over increased consumption volume (p 0.002). Hedonic liking data from two cohorts, healthy older volunteers (n = 32, median age 73) and patients (n = 28, median age 85), suggested such build-up was disliked. Efforts made to improve the palatability of ONS must take account of the build up of taste and mouthfeel characteristics over increased consumption volume.

Species divergence and trait convergence in experimental plant community assembly

Despite decades of research, it remains controversial whether ecological communities converge towards a common structure determined by environmental conditions irrespective of assembly history. Here, we show experimentally that the answer depends on the level of community organization considered. In a 9-year grassland experiment, we manipulated initial plant composition on abandoned arable land and subsequently allowed natural colonization. Initial compositional variation caused plant communities to remain divergent in species identities, even though these same communities converged strongly in species traits. This contrast between species divergence and trait convergence could not be explained by dispersal limitation or community neutrality alone. Our results show that the simultaneous operation of trait-based assembly rules and species-level priority effects drives community assembly, making it both deterministic and historically contingent, but at different levels of community organization.