Robot and insect navigation by polarized skylight

A study of a large number of published experiments on the behaviour of insects navigating by skylight has led to the design of a system for navigation in lightly clouded skies, suitable for a robot or drone. The design is based on the measurement of the directions in the sky at which the polarization angle, i.e. the angle χ between the polarized E-vector and the meridian, equals ±π/4 or ±(π/4 + π/3) or ±(π/4 - π/3). For any one of these three options, at any given elevation, there are usually 4 such directions and these directions can give the azimuth of the sun accurately in a few short steps, as an insect can do. A simulation shows that this compass is accurate as well as simple and well suited for an insect or robot. A major advantage of this design is that it is close to being invariant to variable cloud cover. Also if at least two of these 12 directions are observed the solar azimuth can still be found by a robot, and possibly by an insect.

Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.