$\varepsilon $-continuity and shape

Features of Derivative Continuity in Shape

tive continuity is a distributed invariant relationship between parts of flowing shapes. The l techniques presented here were developed for making the behavioral dynamics of x processes more recognizable, but are equally applicable to assisting in the recognition of in images. Regularizing a sequence using a constraint of derivative continuity is lent to using a bimodal smoothing kernel, produc...

Geometric Continuity and Shape Preservation Issues in Surface Modeler

A randomized online quantile summary in $O(\frac{1}{\varepsilon} \log \frac{1}{\varepsilon})$ words

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( 1 ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( 1 ε log 1 ε ) by Agarwal et. ...

Intergenerational continuity of cell shape dynamics in Caulobacter crescentus

We investigate the intergenerational shape dynamics of single Caulobacter crescentus cells using a novel combination of imaging techniques and theoretical modeling. We determine the dynamics of cell pole-to-pole lengths, cross-sectional widths, and medial curvatures from high accuracy measurements of cell contours. Moreover, these shape parameters are determined for over 250 cells across approx...

Biclique coverings, rectifier networks and the cost of $\varepsilon$-removal

We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rectifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G). As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with εtransitions, having n transitions total such that the smallest equivalent ...