Intuitive modeling of vaporish objects

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν=-N/(N+1) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.

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“…In the non-Markovian case, the dynamics of the probabilities P i,j (t) obey a generalized master equation [59][60][61][62][63]…”

Section: The Generalized Master Equation and Its Laplace Transformmentioning

confidence: 99%

The stretch to stray on time: Resonant length of random walks in a transient

Falcke

Friedhoff

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…IFS attractors have been used to model a variety of phenomena. Models of objects have included: horns, seashells and other natural forms (Stępień 2009); tree crowns (Collin et al 2011); and vaporish objects (Sokol and Gentil 2015). The data stream from the IFS has been used to model: sequences over an arbitrary finite number of symbols (Tiňo 1999) such as DNA (Jeffrey 1990); economies (La Torre et al 2011); and the formation of episodic memory in the hippocampus (Yamaguti 2011).…”

Section: Iterated Function Systemsmentioning

confidence: 99%

Advances in technology commercialization models

Marinakis¹

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The Richards model has a shape parameter m that allows it to fit any sigmoidal curve. This article demonstrates the ability of a modified Richards model to fit a variety of technology diffusion curvilinear data that would otherwise be fit by Bass, Gompertz, Logistic, and other models. The performance of the Richards model in forecasting was examined by analyzing fragments of data computed from the model itself, where the fragments simulated either an entire diffusion curve but with sparse data points, or only the initial trajectory of a diffusion curve but with dense data points. It was determined that accurate parameter estimates could be obtained when the data was sparse but traced out the curve at least up to the third inflection point (concave down), and when the data was dense and traced out the curve up to the first inflection point (concave up). Rogers' Innovation I, II and III are discussed in the context of the Richards model. Since m is scale independent, the model allows for a typology of diffusion curves and may provide an alternative to Rogers' typology.

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Intuitive modeling of vaporish objects

Cited by 2 publications

References 11 publications

The stretch to stray on time: Resonant length of random walks in a transient

The stretch to stray on time: Resonant length of random walks in a transient

Advances in technology commercialization models

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