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Set Approach (set + approach)
Kinds of Set Approach Selected AbstractsCoping With Missing Attribute Values Based on Closest Fit in Preterm Birth Data: A Rough Set ApproachCOMPUTATIONAL INTELLIGENCE, Issue 3 2001Jerzy W. Grzymala-Busse Data mining is frequently applied to data sets with missing attribute values. A new approach to missing attribute values, called closest fit, is introduced in this paper. In this approach, for a given case (example) with a missing attribute value we search for another case that is as similar as possible to the given case. Cases can be considered as vectors of attribute values. The search is for the case that has as many as possible identical attribute values for symbolic attributes, or as the smallest possible value differences for numerical attributes. There are two possible ways to conduct a search: within the same class (concept) as the case with the missing attribute values, or for the entire set of all cases. For comparison, we also experimented with another approach to missing attribute values, where the missing values are replaced by the most common value of the attribute for symbolic attributes or by the average value for numerical attributes. All algorithms were implemented in the system OOMIS. Our experiments were performed on the preterm birth data sets provided by the Duke University Medical Center. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd. [source] On surface tension modelling using the level set methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2009Sergey V. Shepel Abstract The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface-tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two-phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching-off of interfaces, the traditional level set model of surface tension produces an error that results in non-converging solutions for film-like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first-order convergence. Copyright © 2008 John Wiley & Sons, Ltd. [source] Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005A. H. Coppola-Owen Abstract In this paper we present a problem we have encountered using a stabilized finite element method on fixed grids for flows with interfaces modelled with the level set approach. We propose a solution based on enriching the pressure shape functions on the elements cut by the interface. The enrichment is used to enable the pressure gradient to be discontinuous at the interface, thus improving the ability to simulate the behaviour of fluids with different density under a gravitational force. The additional shape function used is local to each element and the corresponding degree of freedom can therefore be condensed prior to assembly, making the implementation quite simple on any existing finite element code. Copyright © 2005 John Wiley & Sons, Ltd. [source] Effect of NSAIDs on the recurrence of nonmelanoma skin cancerINTERNATIONAL JOURNAL OF CANCER, Issue 3 2006Maria V. Grau Experimental studies have consistently shown a protective effect of nonsteroidal antiinflammatory drugs (NSAIDs) against nonmelanoma skin cancers (NMSC). However, little human epidemiological research has been done in this regard. We used data from the Skin Cancer Chemoprevention Study to explore the association of NSAID use and with the risk of basal-cell carcinoma (BCC) and squamous-cell carcinoma (SCC). 1,805 subjects with a recent history of NMSC were randomized to placebo or 50 mg of daily ,-carotene. Participants were asked about their use of over-the-counter and prescription medications at baseline and every 4 months during the trial. Skin follow-up examinations were scheduled annually with a study dermatologist; confirmed lesions were the endpoints in the study. We used a risk set approach to the analysis of grouped times survival data and unconditional logistic regression to compute odds ratios [ORs] for various exposures to NSAIDs. The use of NSAIDs was reported in over 50% of questionnaires. For BCC, NSAIDs exhibited a weak protective effect in crude analyses, which attenuated markedly after adjustment. For SCC, the use of NSAIDs in the year previous to diagnosis reduced the odds by almost 30% (adjusted OR= 0.71, 95% CI 0.48,1.04). When we accounted for frequency of use, results for BCC were not striking, and there were inconsistent suggestions of an inverse association with SCC. There were some indications of a modest, nonsignificant reduction on the number of BCCs and SCCs with NSAID use. Our data suggest a weak and inconsistent chemopreventive effect of NSAIDs on BCC and SCC. © 2006 Wiley-Liss, Inc. [source] Rough approximation by dominance relationsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2002Salvatore Greco In this article we are considering a multicriteria classification that differs from usual classification problems since it takes into account preference orders in the description of objects by condition and decision attributes. To deal with multicriteria classification we propose to use a dominance-based rough set approach (DRSA). This approach is different from the classic rough set approach (CRSA) because it takes into account preference orders in the domains of attributes and in the set of decision classes. Given a set of objects partitioned into pre-defined and preference-ordered classes, the new rough set approach is able to approximate this partition by means of dominance relations (instead of indiscernibility relations used in the CRSA). The rough approximation of this partition is a starting point for induction of if-then decision rules. The syntax of these rules is adapted to represent preference orders. The DRSA keeps the best properties of the CRSA: it analyses only facts present in data, and possible inconsistencies are not corrected. Moreover, the new approach does not need any prior discretization of continuous-valued attributes. In this article we characterize the DRSA as well as decision rules induced from these approximations. The usefulness of the DRSA and its advantages over the CRSA are presented in a real study of evaluation of the risk of business failure. © 2002 John Wiley & Sons, Inc. [source] Measuring the effects of human impact on vegetation by integrating phytosociology and remote sensing in a fuzzy set approachJOURNAL OF VEGETATION SCIENCE, Issue 5 2003Enrico Feoli Anon. 1954 , Abstract. The response of fragmented vegetation to human impact has been analysed in degraded and degrading areas in Tanzania (Lake Manyara). Phytosociology was integrated with GIS and remote sensing data as follows: (1) a land cover/land use map was obtained by analysing remote sensing data and conducting field verification; (2) phytosociological relevés were randomly sampled in woodland vegetation patches using the map; (3) the pattern of land cover/land use around the relevés was described; (4) gradients of land use intensity (human impact) were obtained based on the descriptions; (5) the response of vegetation types to impacts of gradients was calculated using fuzzy set theory. Two complementary gradients of human impact were defined based on land cover/land use analysis of the remotely sensed data: one related to cultivation intensity and the other to grazing intensity. Response functions of vegetation types (defined by numerical classification) to these gradients demonstrated that the vegetation types are strongly related to the degree of human impact and that the corresponding vegetation patches show different degrees of permeability to the species of the surrounding landscape. [source] Perturbation theory and excursion set estimates of the probability distribution function of dark matter, and a method for reconstructing the initial distribution functionMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008Tsz Yan Lam ABSTRACT Non-linear evolution is sometimes modelled by assuming there is a deterministic mapping from initial to final values of the locally smoothed overdensity. However, if an underdense region is embedded in a denser one, then it is possible that its evolution is determined by its surroundings, so the mapping between initial and final overdensities is not as ,local' as one might have assumed. If this source of non-locality is not accounted for, then it appears as stochasticity in the mapping between initial and final densities. Perturbation theory methods ignore this ,cloud-in-cloud' effect, whereas methods based on the excursion set approach do account for it; as a result, one may expect the two approaches to provide different estimates of the shape of the non-linear counts in cells distribution. We show that, on scales where the rms fluctuation is small, this source of non-locality has only a small effect, so the predictions of the two approaches differ only on the small scales on which perturbation theory is no longer expected to be valid anyway. We illustrate our results by comparing the predictions of these approaches when the initial,final mapping is given by the spherical collapse model. Both are in reasonably good agreement with measurements in numerical simulations on scales where the rms fluctuation is of the order of unity or smaller. If the deterministic mapping from initial conditions to final density depends on quantities other than the initial density, then this will also manifest as stochasticity in the mapping from initial density to final. For example, the Zeldovich approximation and the ellipsoidal collapse model both assume that the initial shear field plays an important role in determining the evolution. We compare the predictions of these approximations with simulations, both before and after accounting for the ,cloud-in-cloud' effect. Our analysis accounts approximately for the fact that the shape of a cell at the present time is different from its initial shape; ignoring this makes a noticeable difference on scales where the rms fluctuation in a cell is of the order of unity or larger. On scales where the rms fluctuation is 2 or less, methods based on the spherical model are sufficiently accurate to permit a rather accurate reconstruction of the shape of the initial distribution from the non-linear one. This can be used as the basis for a method for constraining the statistical properties of the initial fluctuation field from the present-day field, under the hypothesis that the evolution was purely gravitational. We illustrate by showing how the highly non-Gaussian non-linear density field in a numerical simulation can be transformed to provide an accurate estimate of the initial Gaussian distribution from which it evolved. [source] RANS-simulation of premixed turbulent combustion using the level set approachPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005A. Kurenkov A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described with the help of the level set approach [1] which is used for tracking of propagating interfaces in free-surface flows, geodesics, grid generation and combustion. The fluid properties are conditioned on the flame front position using a burntunburnt probability function across the flame front. Computations are performed using the code FASTEST-3D which is a flow solver for a non-orthogonal, block-structured grid. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||