Invariant assertions play an important role in the analysis and documentation of while loops of imperative programs. Invariant functions and invariant relations are alternative analysis tools that are distinct from invariant assertions but are related to them. In this paper we discuss these three concepts and analyze their relationships. The study of invariant functions and invariant relations ...

0. Introduction. M. M. Day has shown that an abelian group has only one invariant mean if, and only if, the group is finite [3, Theorem 4, p. 534]. Knowing this we now ask to what extent the invariant means on a given abelian group are alike. In this paper we shall show that they all have the same "measure-theoretic character." An invariant mean on an abelian group G is a normalized, positive, ...

We present an approach to determine the category and location of objects in images. It performs very fast categorization of each pixel in an image, a brute-force approach made feasible by three key developments: First, our method reduces the size of a large generic dictionary (on the order of ten thousand words) to the low hundreds while increasing classification performance compared to k-means...

http://research.microsoft.com/enus/projects/objectclassrecognition http://www-nlpir.nist.gov/projects/trecvid/ http://lms.comp.nus.edu.sg/research/NUSWIDE.htm For the auxiliary image data set and the three target data sets described above, following (Gehler & Nowozin, 2009), we extract SIFT descriptors for the experimental images, which are computed on a regular grid on the image with a spacing...

One of the fundamental problems in accurate indoor place recognition is the presence of similar scene images in different places in the environmental space of the mobile robot, such as the presence of computer or office table in many rooms. This problem causes bewilderment and confusion among different places. To overcome this, the local features of these image scenes should be represented in m...

In the last years the use of the so-called bag-of-features approach, often referred to also as the codebook approach, has extensively gained large popularity among researchers in the image classification field, as it exhibited high levels of performance. A large variety of image classification, scene recognition, and more in general computer vision problems have been addressed according to this...

We construct counterexamples to the rationality conjecture regarding the new version of the Makar-Limanov invariant introduced in [Li2]. Let k be an algebraically closed field. Below variety means algebraic variety over k in the sense of Serre (so algebraic group means algebraic group over k). We use standard notation and conventions of [Bo] and [Sp]. In particular, given a variety X, we denote...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.