Suppose / is a single-valued transformation of the metric space M onto the metric space fM. Many of the theorems of topology assert that if / is continuous, then it must have various other properties also. We deal here with the problem of determining under what circumstances certain of these properties are actually equivalent to continuity. The properties considered are: (1) fX is compact for e...

The Kohonen Self Organizing Map (SOM), is a topology preserving map that maps data from higher dimensions onto a (typically) two dimensional grid of lattice points[3]. The aim of Self-Organization is to generate a topology preserving mapping, where the neighborhood relations in the input space are preserved as well as possible, in the neighborhood relations of the units of the map[2]. One of th...

Abstract—Diabetes is considered a lifestyle disease and a well managed self-care plays an important role in the treatment. Clinicians often conduct surveys to understand the self-care behaviours in their patients. In this context, we propose to use Self-Organising Maps (SOM) to explore the survey data for assessing the self-care behaviours in Type-1 diabetic patients. Specifically, SOM is used ...

Currently, there exist many research areas that produce large multivariable datasets that are difficult to visualize in order to extract useful information. Kohonen selforganizing maps have been used successfully in the visualization and analysis of multidimensional data. In this work, a projection technique that compresses multidimensional datasets into two dimensional space using growing self...

We consider the standard model of i.i.d. first passage percolation on Zd given a distribution G [0,+∞] ( +∞ is allowed). When G([0,+∞))>pc(d), it known that time constant μG exists. are interested in regularity properties map G↦μG. study specific case distributions form Gp=pδ1+(1−p)δ∞ for p>pc(d). In this case, travel between two points equal to length shortest path bond parameter p. show funct...