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The proposed framework keeps computation traces of collapsing the complex using persistence algorithm proposed in [42].
Using persistence in streamflow, existing indices of climate, and sea surface temperature (SST) expansion coefficient time-series from singular value decomposition (SVD) analysis, this work developed probability of exceedance streamflow forecasts for multiple stations, seasons, and lead-times.
Fig. 2 Plot of the predicted values for 1 day ahead using persistence model Fig. 3 Plot of the predicted values for 1 day ahead using ARIMA model Fig. 4 Plot of the predicted values for 1 day ahead using BPNN model Fig. 5 Plot of the predicted values for 1 day ahead using TES model Fig. 6 Plot of the predicted values for 1 day ahead using decomposition model.
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We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series.
(d) An alternative graphical way to represent barcodes (which gives exactly the same information) is to use persistence diagrams, in which an interval ([i,j)) is represented by the point ((i,j)) in the extended plane (overline{mathbb{R}}^{2}), where (overline{mathbb{R}}=mathbb{R}cup{infty}). Therefore, a persistence diagram is a finite multiset of points in (overline {mathbb{R}}^{2}).
The short range variation which uses persistence is the Tropical Rainfall Potential technique (TRaP) technique, which uses satellite-derived rainfall amounts from microwave imaging satellites and extrapolates the current rainfall configuration forward for 24 hours along the current forecast track.
In natural waves, Dictyostelium cells circumvent the trade-off by extending a de novo pseudopod to immediately move in the correct direction of the new gradient and only then use persistence by pseudopod splitting to stay on-track.
We have also used persistence rates for studies in AD patients treated with cholinesterase inhibitors.
Adherence ranged from 92% (self-report) to 94.7% (physician report), depending on the measure used; persistence was 74.7% at 5 years of follow-up.
For the older cohort, we can use persistence in wealth index over the Young Lives follow-up period as a proxy for continuity in living standards before the study's inception.
This is consistent with a previous cohort study, which also used persistence as an outcome variable in conjunction with a 4.5-year follow-up period (Hershman et al, 2010a).
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