913 resultados para Strong Convexity


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This brief consumer marketing case study was published in a consumer marketing text book.

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1. A diverse array of patterns has been reported regarding the spatial extent of population genetic structure and effective dispersal in freshwater macroinvertebrates. In river systems, the movements of many taxa can be restricted to varying degrees by the natural stream channel hierarchy. 2. In this study, we sampled populations of the non-biting freshwater midge Echinocladius martini in the Paluma bioregion of tropical northeast Queensland to investigate fine scale patterns of within- and among-stream dispersal and gene flow within a purported historical refuge. We amplified a 639 bp fragment of mitochondrial COI and analysed genetic structure using pairwise ΦST, hierarchical AMOVA, Mantel tests and a parsimony network. Genetic variation was partitioned among stream sections using Streamtree to investigate the effect of potential instream dispersal barriers. 3. The data revealed strong natal site fidelity and significant differentiation among neighbouring, geographically proximate streams. We found evidence for only episodic adult flight among sites on separate stream reaches. Overall, however, our data suggested that both larval and adult dispersal was largely limited to within a stream channel. 4. This may arise from a combination of the high density of riparian vegetation physically restricting dispersal and from the joint effects of habitat stability and large population sizes. Together these may mitigate the requirement for movement among streams to avoid inbreeding and local extinction due to habitat change and may thus enable persistence of upstream populations in the absence of regular compensatory upstream flight. Taken together, these data suggest that dispersal of E. martini is highly restricted, to the scale of only a few kilometres, and hence occurs predominantly within the natal stream.

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Crystal growth of bulk CdTe in short-duration microgravity is performed by the unidirectional cooling method. The largest growth grains in microgravity samples are 4X2mm. The cooling profiles indicate undercooling melts in microgravity. Cooling melt samples in microgravity generate strong gradient of temperature due to stop thermal convections. Temperature distribution in the melt is calculated by the one-dimensional equation of heat conduction, and about 100 K-undercooling is considered to occur at the cooling surface.

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Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

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The paper "the importance of convexity in learning with squared loss" gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

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In this article, an enriched radial point interpolation method (e-RPIM) is developed for computational mechanics. The conventional radial basis function (RBF) interpolation is novelly augmented by the suitable basis functions to reflect the natural properties of deformation. The performance of the enriched meshless RBF shape functions is first investigated using the surface fitting. The surface fitting results have proven that, compared with the conventional RBF, the enriched RBF interpolation has a much better accuracy to fit a complex surface than the conventional RBF interpolation. It has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF interpolation, but also can accurately reflect the deformation properties of problems. The system of equations for two-dimensional solids is then derived based on the enriched RBF shape function and both of the meshless strong-form and weak-form. A numerical example of a bar is presented to study the effectiveness and efficiency of e-RPIM. As an important application, the newly developed e-RPIM, which is augmented by selected trigonometric basis functions, is applied to crack problems. It has been demonstrated that the present e-RPIM is very accurate and stable for fracture mechanics problems.

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A series of solid strong acid catalysts were synthesised from fibrous ZrO2/Al2O3 core and shell nanocomposites. In this series, the zirconium molar percentage was varied from 2 % to 50 %. The ZrO2/Al2O3 nanocomposites and their solid strong acid counterparts were characterised by a variety of techniques including 27Al magic angle spinning nuclear magnetic resonance (MAS-NMR), scanned electronic microscopy (SEM), transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), Nitrogen adsorption and infrared emission spectroscopy (IES). NMR results show that the interaction between zirconia species and alumina strongly correlates with pentacoordinated aluminium sites. This can also be detected by the change in binding energy of the 3d electrons of the zirconium. The acidity of the obtained solid acids was tested by using them as catalysts for the benzolyation of toluene. It was found that a sample with a 50 % zirconium molar percentage possessed the highest surface acidity equalling that of pristine sulfated zirconia despite the reduced mass of zirconia.

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Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.