It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...

We present a consistent, geometric notion of homogeneity, for vector elds (diierential equations and control systems), functions, diierential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinate-free characterization is given, and shown to yield the desired/expected results. This also addresses: \When do there ex...

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontinuous setting: the equivalence of the global asymptotic stability and the existence o...

Sufficient as well as necessary conditions are studied for a dendrite or a dendroid to be homogeneous with respect to monotone mappings. The obtained results extend ones due to H. Kato and the first named author. A number of open problems are asked.

Jarik Nešetřil suggested to the first author the investigation of notions of homogeneity for relational structures, where “isomorphism” is replaced by “homomorphism” in the definition. Here we look in detail at what happens for posets. For the strict order, all five generalisations of homogeneity coincide, and we give a characterisation of the countable structures that arise. For the non-strict...

Many medical studies are carried out to investigate the size of some effect, for example the treatment effect in a controlled clinical trial or the risk of exposure to some substance in an observational study. To this end it is usual to compare groups of subjects, such as those receiving active treatment with those getting placebo or those exposed with those not exposed. The comparison is often...

V. Parpura and P.G. Haydon (eds.), Astrocytes in (Patho)Physiology of the Nervous System, 1 DOI: 10.1007/978-0-387-79492-1_1, © Springer Science + Business Media, LLC 2009 The history of the morphology and electrophysiology of the neuroglia , which was the historical term used for what are now termed astroglia or astrocytes, is briefly reviewed. The interpretation of these data around 1970 was ...

The statistical NLP and IR literatures tend to make a “homogeneity assumption” about the distribution of terms, either by adopting a “bag of words” model, or in their treatment of function words. In this paper we develop a notion of homogeneity detection to a level of statistical significance, and conduct a series of experiments on different datasets, to show that the homogeneity assumption doe...