Molecular dynamics in systems with multiple time scales: Systems with stiff and soft degrees of freedom and with short and long range forces

1991 ◽  
Vol 95 (11) ◽  
pp. 8362-8364 ◽  
Author(s):  
Mark E. Tuckerman ◽  
Bruce J. Berne
Keyword(s):  
Molecular Dynamics ◽  
Long Range ◽  
Time Scales ◽  
Degrees Of Freedom ◽  
Multiple Time Scales ◽  
Multiple Time

Molecular dynamics algorithm for multiple time scales: Systems with long range forces

1991 ◽  
Vol 94 (10) ◽  
pp. 6811-6815 ◽  
Author(s):  
Mark E. Tuckerman ◽  
Bruce J. Berne ◽  
Glenn J. Martyna
Keyword(s):  
Molecular Dynamics ◽  
Long Range ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Molecular Dynamics with Multiple Time Scales: How to Avoid Pitfalls

2010 ◽  
Vol 6 (6) ◽  
pp. 1798-1804 ◽  
Author(s):  
Joseph A. Morrone ◽  
Ruhong Zhou ◽  
B. J. Berne
Keyword(s):  
Molecular Dynamics ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 315 ◽  
Author(s):  
Aurora Martins ◽  
Riccardo Pernice ◽  
Celestino Amado ◽  
Ana Paula Rocha ◽  
Maria Eduarda Silva ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Scales ◽  
Multivariate Time Series ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Control Mechanisms ◽  
Long Range Correlations ◽  
Dynamical Complexity

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

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