We present a framework for mining frequent trajectories, which are translated and/or rotated with respect to one another. We then discuss a multiresolution methodology, based on the wavelet transformation, for speeding up the discovery of frequent trajectories. We present experimental results using noisy protein unfolding trajectories and synthetic datasets. Our results demonstrate the effectiv...

We introduce and investigate a new way of generating mildly context-sensitive languages. The main idea is that the contexts are adjoined by shu ing them on certain trajectories. In this way we obtain also a very general class of contextual grammars such that most of the fundamental classes of contextual grammars, for instance, internal contextual grammars, external contextual grammars, n-contex...

We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize non-metric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive not...

Steepest descent drives both theory and practice of nonsmooth optimization. We study slight relaxations of two influential notions of steepest descent curves — curves of maximal slope and solutions to evolution equations. In particular, we provide a simple proof showing that lower-semicontinuous functions that are locally Lipschitz continuous on their domains — functions playing a central role ...

A fundamental question in aging research concerns the demographic trajectories at the highest ages, especially for supercentenarians (persons aged 110 or more). We wish to demonstrate that the Weon model enables scientists to describe the demographic trajectories for supercentenarians. We evaluate the average survival data from the modern eight countries and the valid and complete data for supe...

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker’s map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

This study examines how the movement patterns of individuals may reveal their intent. Subjects were asked to deceive an imaginary observer using a paper-and-pencil test. Geographical and qualitative methods were used to analyze the data. The results showed that deceptive intent can be detected in the subjects' trajectories. Additionally, conformity of trajectories was observed.

This paper investigates the institutional reason underlying the change in the trajectory of economic growth in post-reform China, and argues that the trajectory of growth was much more normal during the period of 1978-89 than in the post-1989 era. In the former period, growth was largely induced by equality-generating institutional change in agriculture and the emergence of non-state industrial...