Academic literature on the topic 'Topological selection'

We examine a new electrodynamic approach to target selection. The study shows that in the case of p-polarisation, a topological portrait of two types of angle reflectors is in a certain sense inverted in relation to that of the s-polarisation case, and consequently, evident polarisation dependence of angle reflector topological portraits may be traced.

<abstract> <p>Effectively selecting discriminative brain regions in multi-modal neuroimages is one of the effective means to reveal the neuropathological mechanism of end-stage renal disease associated with mild cognitive impairment (ESRDaMCI). Existing multi-modal feature selection methods usually depend on the <italic>Euclidean</italic> distance to measure the similarity between data, which tends to ignore the implied data manifold. A self-expression topological manifold based multi-modal feature selection method (SETMFS) is proposed to address this issue employing self-expression topological manifold. First, a dynamic brain functional network is established using functional magnetic resonance imaging (fMRI), after which the betweenness centrality is extracted. The feature matrix of fMRI is constructed based on this centrality measure. Second, the feature matrix of arterial spin labeling (ASL) is constructed by extracting the cerebral blood flow (CBF). Then, the topological relationship matrices are constructed by calculating the topological relationship between each data point in the two feature matrices to measure the intrinsic similarity between the features, respectively. Subsequently, the graph regularization is utilized to embed the self-expression model into topological manifold learning to identify the linear self-expression of the features. Finally, the selected well-represented feature vectors are fed into a multicore support vector machine (MKSVM) for classification. The experimental results show that the classification performance of SETMFS is significantly superior to several state-of-the-art feature selection methods, especially its classification accuracy reaches 86.10%, which is at least 4.34% higher than other comparable methods. This method fully considers the topological correlation between the multi-modal features and provides a reference for ESRDaMCI auxiliary diagnosis.</p> </abstract>

We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of T0 topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of ℵ1 Hechler reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 12.