Mining periodic patterns in spatio-temporal sequences at different time granularities1

2009 ◽  
Vol 13 (2) ◽  
pp. 301-335 ◽  
Author(s):  
Sezin Karli ◽  
Yucel Saygin
Keyword(s):  
Periodic Patterns ◽  
Spatio Temporal ◽  
Temporal Sequences

Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations

1995 ◽  
Vol 352 (1698) ◽  
pp. 125-168 ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Pattern ◽  
Invariant Equilibrium ◽  
Periodic Patterns ◽  
Planar Lattice ◽  
Diffusive Convection ◽  
Spatially Periodic ◽  
Spatio Temporal ◽  
Boussinesq Fluid ◽  
Time Periodic

In Rayleigh-Bénard convection, the spatially uniform motionless state of a fluid loses stability as the Rayleigh number is increased beyond a critical value. In the simplest case of convection in a pure Boussinesq fluid, the instability is a symmetry-breaking steady-state bifurcation that leads to the formation of spatially periodic patterns. However, in many double-diffusive convection systems the heat-conduction solution actually loses stability via Hopf bifurcation. These hydrodynamic systems provide motivation for the present study of spatiotemporally periodic pattern formation in Euclidean equivariant systems. We call such patterns planforms . We classify, according to spatio-temporal symmetries and spatial periodicity, many of the time-periodic solutions that may be obtained through equivariant Hopf bifurcation from a group-invariant equilibrium. Instead of focusing on plan- forms periodic with respect to a specified planar lattice, as has been done in previous investigations, we consider all planforms that are spatially periodic with respect to some planar lattice. Our classification results rely only on the existence of Hopf bifurcation and planar Euclidean symmetry and not on the particular dif­ferential equation.

scholarly journals Periodic-CRN: A Convolutional Recurrent Model for Crowd Density Prediction with Recurring Periodic Patterns

2018 ◽  
Author(s):  
Ali Zonoozi ◽  
Jung-jae Kim ◽  
Xiao-Li Li ◽  
Gao Cong
Keyword(s):  
Traffic Management ◽  
State Of The Art ◽  
Recurrent Network ◽  
Temporal Data ◽  
Periodic Patterns ◽  
Temporal Correlations ◽  
Density Prediction ◽  
Crowd Density ◽  
Spatial Domains ◽  
Spatio Temporal

Time-series forecasting in geo-spatial domains has important applications, including urban planning, traffic management and behavioral analysis. We observed recurring periodic patterns in some spatio-temporal data, which were not considered explicitly by previous non-linear works. To address this lack, we propose novel `Periodic-CRN' (PCRN) method, which adapts convolutional recurrent network (CRN) to accurately capture spatial and temporal correlations, learns and incorporates explicit periodic representations, and can be optimized with multi-step ahead prediction. We show that PCRN consistently outperforms the state-of-the-art methods for crowd density prediction across two taxi datasets from Beijing and Singapore.

Dynamics of Two-Phase Flow through a Minichannel: Fourier and Multiscale Entropy Analyses

2015 ◽  
Vol 791 ◽  
pp. 217-223 ◽  
Author(s):  
Grzegorz Górski ◽  
Grzegorz Litak ◽  
Romuald Mosdorf ◽  
Andrzej Rysak
Keyword(s):  
Light Transmission ◽  
Digital Camera ◽  
Multiscale Entropy ◽  
Air Bubbles ◽  
Periodic Patterns ◽  
Two Phase ◽  
Temporal Behaviour ◽  
Air Bubble ◽  
Flow Through ◽  
Spatio Temporal

By changing a air flow rate of the two-phase (air-water) flow through a minichannel weidentified aggregation and partitioning of air bubbles and slugs of different sizes and air bubble arrangement into periodic patterns. The identification of these spatio-temporal behaviour was doneby digital camera. Simultaneously, we provide the detailed studies of these phenomena by using thecorresponding sequences of light transmission time series recorded by a laser-phototransistor sensor.To distinguish the instabilities in air slags and their breakups and aggregations we used the Fourierand multiscale entropy analysis.

scholarly journals Dynamic Proximity of Spatio-Temporal Sequences

2004 ◽  
Vol 15 (5) ◽  
pp. 1002-1008 ◽  
Author(s):  
D. Horn ◽  
G. Dror ◽  
B. Quenet
Keyword(s):  
Spatio Temporal ◽  
Temporal Sequences
Sign in / Sign up

Export Citation Format

Share Document