scholarly journals Anytime Lane-Level Intersection Estimation Based on Trajectories of Other Traffic Participants

2019 ◽  
Author(s):  
Annika Meyer ◽  
Jonas Walter ◽  
Martin Lauer ◽  
Christoph Stiller
Keyword(s):  
Level Intersection

scholarly journals Detailed analysis and comparison of different activity metrics

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0261718
Author(s):  
Bálint Maczák ◽  
Gergely Vadai ◽  
András Dér ◽  
István Szendi ◽  
Zoltán Gingl
Keyword(s):  
Threshold Level ◽  
Data Series ◽  
Acceleration Signal ◽  
Acceleration Data ◽  
Different Types ◽  
Comprehensive Comparison ◽  
General Guide ◽  
Level Intersection ◽  
Acceleration Signals

Actigraphic measurements are an important part of research in different disciplines, yet the procedure of determining activity values is unexpectedly not standardized in the literature. Although the measured raw acceleration signal can be diversely processed, and then the activity values can be calculated by different activity calculation methods, the documentations of them are generally incomplete or vary by manufacturer. These numerous activity metrics may require different types of preprocessing of the acceleration signal. For example, digital filtering of the acceleration signals can have various parameters; moreover, both the filter and the activity metrics can also be applied per axis or on the magnitudes of the acceleration vector. Level crossing-based activity metrics also depend on threshold level values, yet the determination of their exact values is unclear as well. Due to the serious inconsistency of determining activity values, we created a detailed and comprehensive comparison of the different available activity calculation procedures because, up to the present, it was lacking in the literature. We assessed the different methods by analysing the triaxial acceleration signals measured during a 10-day movement of 42 subjects. We calculated 148 different activity signals for each subject’s movement using the combinations of various types of preprocessing and 7 different activity metrics applied on both axial and magnitude data. We determined the strength of the linear relationship between the metrics by correlation analysis, while we also examined the effects of the preprocessing steps. Moreover, we established that the standard deviation of the data series can be used as an appropriate, adaptive and generalized threshold level for the level intersection-based metrics. On the basis of these results, our work also serves as a general guide on how to proceed if one wants to determine activity from the raw acceleration data. All of the analysed raw acceleration signals are also publicly available.

scholarly journals Cycle-Level Intersection Theory for Toric Varieties

2004 ◽  
Vol 56 (5) ◽  
pp. 1094-1120
Author(s):  
Hugh Thomas
Keyword(s):  
Toric Variety ◽  
Linear Subspace ◽  
Toric Varieties ◽  
Cartier Divisor ◽  
Ring Structure ◽  
Intersection Theory ◽  
Inner Product ◽  
Characteristic Classes ◽  
Level Intersection ◽  
Complete Flag

AbstractThis paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor with an invariant cycle on a toric variety. For a toric variety defined by a fan inN, the choice consists of giving an inner product or a complete flag forMQ= ℚ ⊗ Hom(N, ℤ), or more generally giving for each cone σ in the fan a linear subspace ofMQcomplementary to σ⊥, satisfying certain compatibility conditions. We show that these intersection cycles have properties analogous to the usual intersections modulo rational equivalence. IfXis simplicial (for instance, ifXis non-singular), we obtain a commutative ring structure to the invariant cycles ofXwith rational coefficients. This ring structure determines cycles representing certain characteristic classes of the toric variety. We also discuss how to define intersection cycles that require no choices, at the expense of increasing the size of the coefficient field.

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