publication . Preprint . 2016

Continuous Sensitivity and Reversibility

İlhan, Aslı Güçlükan; Ünlü, Özgün;
Open Access English
  • Published: 22 Jan 2016
Abstract
Let $n$ be a positive integer and $f$ a differentiable function from a convex subset $C$ of the Euclidean space $\mathbb{R}^n$ to a smooth manifold. We define an invariant of $f$ via counting certain threshold functions associated to $f$. We call this invariant the continuous sensitivity of $f$ and denote it by $\mathrm{cs}_{C}(f)$. This invariant is a real number between $0$ and $n$ and measures how sensitive $f$ is to change in its input variables. For example, if $f$ is a constant function then $\mathrm{cs}_{C}(f)=0$. On the other extreme, if $\mathrm{cs}_{C}(f)=n$ then $f$ is one-to-one on $C$. This last statement is important for reversibility problems. To ...
Subjects
free text keywords: Mathematics - Combinatorics, Computer Science - Discrete Mathematics
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