We introduce the following general question: Let V be a complex n-dimensional space and for m k consider the GL V -module V n m k V m defined by V n m k f v vm V m dimSpanfv vmg k g We would like to determine dimV n m k for any choice of n m k. This question appears in various disguises in computer vision problems where the constraints of a multi-linear problem occupy a lowdimensional subspace....

A study on properties of data sets representing public domain audio and visual content and their relation to their indexability is presented. Data analysis considers the pairwise distance distributions and various techniques to estimate the true intrinsic dimensionality of the studied data. One own alternative to dimensionality estimation is also presented. These results are contrasted with the...

  Since late 1960's, the emergency location problems, fire stations and medical emergency services have attracted the attention of researchers. Mathematical models, both deterministic and probabilistic, have been proposed and applied to find suitable locations for such facilities in many urban and rural areas. Here, we review some models proposed for finding the location of such facilities, wit...

This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy theory. Reformulating M. Mandell's result in terms of an adjunction between p-complete, nilp...