Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Development of motor speed and associated movements from 5 to 18 years.

AIM: To study the development of motor speed and associated movements in participants aged 5 to 18 years for age, sex, and laterality. METHOD: Ten motor tasks of the Zurich Neuromotor Assessment (repetitive and alternating movements of hands and feet, repetitive and sequential finger movements, the pegboard, static and dynamic balance, diadochokinesis) were administered to 593 right-handed participants (286 males, 307 females). RESULTS: A strong improvement with age was observed in motor speed from age 5 to 10, followed by a levelling-off between 12 and 18 years. Simple tasks and the pegboard matured early and complex tasks later. Simple tasks showed no associated movements beyond early childhood; in complex tasks associated movements persisted until early adulthood. The two sexes differed only marginally in speed, but markedly in associated movements. A significant laterality (p<0.001) in speed was found for all tasks except for static balance; the pegboard was most lateralized, and sequential finger movements least. Associated movements were lateralized only for a few complex tasks. We also noted a substantial interindividual variability. INTERPRETATION: Motor speed and associated movements improve strongly in childhood, weakly in adolescence, and are both of developmental relevance. Because they correlate weakly, they provide complementary information.