Fast Frechet Distance Between Curves With Long Edges

Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves in $\mathbb{R}^d$ with $n$ and $m$ vertices, respectively. We prove four results for the case when all edges of both curves are long compared to the Fr\'echet distance between them: (1) a linear-time algorithm for deciding the Fr\'echet distance between two curves, (2) an algorithm that computes the Fr\'echet distance in $O((n+m)\log (n+m))$ time, (3) a linear-time $\sqrt{d}$-approximation algorithm, and (4) a data structure that supports $O(m\log^2 n)$-time decision queries, where $m$ is the number of vertices of the query curve and $n$ the number of vertices of the preprocessed curve

Pattern of initiation of monomorphic ventricular tachycardia in recorded intracardiac electrograms

Background: By analyzing stored intracardiac electrograms during spontaneous monomorphic ventricular tachycardia (VT), we examined the patterns of the VT initiation in a group of patients with implantable cardioverter defibrillators (ICDs). Methods: Stored electrograms (EGMs) were monomorphic VTs and at least 5 beats before the initiation and after the termination of VT were analyzed. Cycle length, sinus rate, and the prematurity index for each episode were noted. Results: We studied 182 episodes of VT among 50 patients with ICDs. VPC-induced (extrasystolic initiation) episode was the most frequent pattern (106; 58%) followed by 76 episodes (42%) in sudden-onset group. Among the VPC-induced group, VPCs in 85 episodes (80%) were different in morphology from subsequent VT. Sudden-onset episodes had longer cycle lengths (377±30ms) in comparison with the VPC-induced ones (349±29ms; P= 0.001). Sinus rate before VT was faster in the sudden-onset compared to that in VPC-induced one (599±227ms versus 664±213ms; P=0.005). Both of these episodes responded similarly to ICD tiered therapy. There was no statistically significant difference in coupling interval, prematurity index, underlying heart disease, ejection fraction, and antiarrhythmic drug usage between two groups (P=NS). Conclusions: Dissimilarities between VT initiation patterns could not be explained by differences in electrical (coupling interval, and prematurity index) or clinical (heart disease, ejection fraction, and antiarrhythmic drug) variables among the patients. There is no association between pattern of VT initiation and the success rate of electrical therapy

Pattern Generation for Walking on Slippery Terrains

In this paper, we extend state of the art Model Predictive Control (MPC) approaches to generate safe bipedal walking on slippery surfaces. In this setting, we formulate walking as a trade off between realizing a desired walking velocity and preserving robust foot-ground contact. Exploiting this formulation inside MPC, we show that safe walking on various flat terrains can be achieved by compromising three main attributes, i. e. walking velocity tracking, the Zero Moment Point (ZMP) modulation, and the Required Coefficient of Friction (RCoF) regulation. Simulation results show that increasing the walking velocity increases the possibility of slippage, while reducing the slippage possibility conflicts with reducing the tip-over possibility of the contact and vice versa.Comment: 6 pages, 7 figure