scholarly journals Average Predictability Time. Part II: Seamless Diagnoses of Predictability on Multiple Time Scales

2009 ◽  
Vol 66 (5) ◽  
pp. 1188-1204 ◽  
Author(s):  
Timothy DelSole ◽  
Michael K. Tippett
Keyword(s):  
Time Scales ◽  
State Vector ◽  
Prediction Models ◽  
Decadal Variability ◽  
Linear Trend ◽  
New Method ◽  
Multiple Time Scales ◽  
Climate Change Signal ◽  
Time Averaging ◽  
Multiple Time

Abstract This paper proposes a new method for diagnosing predictability on multiple time scales without time averaging. The method finds components that maximize the average predictability time (APT) of a system, where APT is defined as the integral of the average predictability over all lead times. Basing the predictability measure on the Mahalanobis metric leads to a complete, uncorrelated set of components that can be ordered by their contribution to APT, analogous to the way principal components decompose variance. The components and associated APTs are invariant to nonsingular linear transformations, allowing variables with different units and natural variability to be considered in a single state vector without normalization. For prediction models derived from linear regression, maximizing APT is equivalent to maximizing the sum of squared multiple correlations between the component and the time-lagged state vector. The new method is used to diagnose predictability of 1000-hPa zonal velocity on time scales from 6 h to decades. The leading predictable component is dominated by a linear trend and presumably identifies a climate change signal. The next component is strongly correlated with ENSO indices and hence is identified with seasonal-to-interannual predictability. The third component is related to annular modes and presents decadal variability as well as a trend. The next few components have APTs exceeding 10 days. A reconstruction of the tropical zonal wind field based on the leading seven components reveals eastward propagation of anomalies with time scales consistent with the Madden–Julian oscillation. The remaining components have time scales less than a week and hence are identified with weather predictability. The detection of predictability on these time scales without time averaging is possible by virtue of the fact that predictability on different time scales is characterized by different spatial structures, which can be optimally extracted by suitable projections.

scholarly journals A NOISY SYSTEM WITH A FLATTENED HAMILTONIAN AND MULTIPLE TIME SCALES

2003 ◽  
Vol 03 (01) ◽  
pp. 1-54 ◽  
Author(s):  
NATELLA V. O'BRYANT
Keyword(s):  
Time Scales ◽  
Martingale Problem ◽  
Stochastic Averaging ◽  
Multiple Time Scales ◽  
Time Averaging ◽  
Multiple Time ◽  
Skew Brownian Motion ◽  
Stratified Space ◽  
Reduced Space ◽  
And Diffusion

We consider a two-dimensional weakly dissipative dynamical system with time-periodic drift and diffusion coefficients. The average of the drift is governed by a degenerate Hamiltonian whose set of critical points has an interior. The dynamics of the system is studied in the presence of three time scales. Using the martingale problem approach and separating the time scales, we average the system to show convergence to a Markov process on a stratified space. The averaging combines the deterministic time averaging of periodic coefficients, and the stochastic averaging of the resulting system. The corresponding strata of the reduced space are a two-sphere, a point and a line segment. Special attention is given to the description of the domain of the limiting generator, including the analysis of the gluing conditions at the point where the strata meet. These gluing conditions, resulting from the effects of the hierarchy of time scales, are similar to the conditions on the domain of skew Brownian motion and are related to the description of spider martingales.

One fossil record, multiple time resolutions: Disparate time-averaging of echinoids and mollusks on a Holocene carbonate platform

Geology ◽  
2017 ◽  
Vol 46 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Michał Kowalewski ◽  
Sahale Casebolt ◽  
Quan Hua ◽  
Katherine E. Whitacre ◽  
Darrell S. Kaufman ◽  
...  
Keyword(s):  
Fossil Record ◽  
Carbonate Platform ◽  
Time Averaging ◽  
Multiple Time

Bereavement or Breakup: A Network Approach to Modeling Differential Pathways into Depression

2019 ◽  
Author(s):  
Julian Burger ◽  
Margaret S. Stroebe ◽  
Pasqualina Perrig-Chiello ◽  
Henk A.W. Schut ◽  
Stefanie Spahni ◽  
...  
Keyword(s):  
Depressive Symptoms ◽  
Graphical Models ◽  
Contextual Factors ◽  
Marital Disruption ◽  
Depression Symptoms ◽  
Depression Symptom ◽  
Multiple Time ◽  
Cross Sectional ◽  
Network Analyses ◽  
Within Subjects

Background: Prior network analyses demonstrated that the death of a loved one potentially precedes specific depression symptoms, primarily loneliness, which in turn links to other depressive symptoms. In this study, we extend prior research by comparing depression symptom network structures following two types of marital disruption: bereavement versus separation. Methods: We fitted two Gaussian Graphical Models to cross-sectional data from a Swiss survey of older persons (145 bereaved, 217 separated, and 362 married controls), and compared symptom levels across bereaved and separated individuals. Results: Separated compared to widowed individuals were more likely to perceive an unfriendly environment and oneself as a failure. Both types of marital disruption were linked primarily to loneliness, from where different relations emerged to other depressive symptoms. Amongst others, loneliness had a stronger connection to perceiving oneself as a failure in separated compared to widowed individuals. Conversely, loneliness had a stronger connection to getting going in widowed individuals. Limitations: Analyses are based on cross-sectional between-subjects data, and conclusions regarding dynamic processes on the within-subjects level remain putative. Further, some of the estimated parameters in the network exhibited overlapping confidence intervals and their order needs to be interpreted with care. Replications should thus aim for studies with multiple time points and larger samples. Conclusions: The findings of this study add to a growing body of literature indicating that depressive symptom patterns depend on contextual factors. If replicated on the within-subjects level, such findings have implications for setting up patient-tailored treatment approaches in dependence of contextual factors.

Oscillatory Dynamics of P53 Network With Time Delays

2018 ◽  
Vol 21 (6) ◽  
pp. 411-419 ◽  
Author(s):  
Conghua Wang ◽  
Fang Yan ◽  
Yuan Zhang ◽  
Haihong Liu ◽  
Linghai Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Cell Fate ◽  
Time Delays ◽  
Sustained Oscillation ◽  
Multiple Time ◽  
Cell Fate Decisions ◽  
Oscillatory Dynamics ◽  
Main Components ◽  
Parameter Values ◽  
P53 Network

Aims and Objective: A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known. Method: Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays. Result and Conclusion: The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.

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