We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least ...

In this paper, we study connected components of strata of the space of quadratic differentials lying over Tg. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on the number of such components. For strata with sufficiently many zeroes of the sam...

Subtle structural differences can be observed in the islets of Langerhans region of microscopic image of pancreas cell of the rats having normal glucose tolerance and the rats having pre-diabetic (glucose intolerant) situations. This paper proposes a way to automatically segment the islets of Langerhans region from the histological image of rat's pancreas cell and on the basis of some morpholog...