Stabilization of Systems Under Stochastic Clock Offsets

2018 ◽  
Author(s):  
Haoyuan Sun ◽  
Jie Chen ◽  
Jian Sun
Keyword(s):  
Stochastic Clock

scholarly journals Time without time: A stochastic clock model

2002 ◽  
Vol 66 (4) ◽  
Author(s):  
Hans-Thomas Elze ◽  
Otavio Schipper
Keyword(s):  
Clock Model ◽  
Stochastic Clock

scholarly journals Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
C. Caranica ◽  
A. Al-Omari ◽  
H.-B. Schüttler ◽  
J. Arnold
Keyword(s):  
Genetic Algorithms ◽  
Single Cell ◽  
Stochastic Resonance ◽  
Rate Constants ◽  
Single Cells ◽  
Ensemble Methods ◽  
Parallel Tempering ◽  
Model Parameters ◽  
Clock Network ◽  
Stochastic Clock

Abstract Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurosporacrassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit $${x}^{2}$$ x 2 was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting $${x}^{2}$$ x 2 per data point was only $${\chi }^{2}/n$$ χ 2 / n = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for “cell size”. The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 107 cells.

The Stochastic Mode of Molecular Evolution: What Consequences for Systematic Investigations?

The Auk ◽  
1988 ◽  
Vol 105 (3) ◽  
pp. 565-573 ◽  
Author(s):  
Scott M. Lanyon
Keyword(s):  
Evolutionary Rate ◽  
Phylogeny Reconstruction ◽  
Case Scenario ◽  
Phylogenetic Information ◽  
Branching Patterns ◽  
Shared Ancestry ◽  
Stochastic Mode ◽  
Homologous Characters ◽  
Stochastic Clock ◽  
Shared Character

Abstract Biochemical characters have been proposed as ideal sources of phylogenetic information. The homologous characters are easily identified, the relationships between such characters and the underlying genetic code is well understood, and, most importantly, biochemical characters are thought to evolve in a stochastic, clock-like manner. I present a modified version of the Zuckerkandl and Pauling (1965) model of stochastic evolution which is used to explore the consequences of a stochastic mode of evolution. The probability of observing shared character states is determined as a function of the evolutionary rate of a character, the time of independent ancestry for two sister taxa, the time of shared ancestry for the sister taxa independent of their next closest relative, and the number of functionally equivalent, equally probable character states. I found that, while many branching patterns can be reliably reconstructed using stochastically evolving characters, a large subset of theoretically possible phylogenies (as defined by the duration of shared and independent ancestry) would not be derived correctly. The model simulates a "best-case scenario" in which the rate of character evolution is constant over time. Violation of this assumption complicates phylogeny reconstruction and further limits the types of phylogenies that can be addressed with stochastically evolving characters. I discuss the implications of these findings for data analysis and experimental design.

scholarly journals An Actuarial Approach for Modeling Pandemic Risk

Risks ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 3
Author(s):  
Donatien Hainaut
Keyword(s):  
Deterministic Model ◽  
Jump Process ◽  
The Core ◽  
Brownian Noise ◽  
Pure Premium ◽  
Actuarial Approach ◽  
Premium Calculation ◽  
Efficient Alternative ◽  
Stochastic Clock

In this article, a model for pandemic risk and two stochastic extensions is proposed. It is designed for actuarial valuation of insurance plans providing healthcare and death benefits. The core of our approach relies on a deterministic model that is an efficient alternative to the susceptible-infected-recovered (SIR) method. This model explains the evolution of the first waves of COVID-19 in Belgium, Germany, Italy and Spain. Furthermore, it is analytically tractable for fair pure premium calculation. In a first extension, we replace the time by a gamma stochastic clock. This approach randomizes the timing of the epidemic peak. A second extension consists of adding a Brownian noise and a jump process to explain the erratic evolution of the population of confirmed cases. The jump component allows for local resurgences of the epidemic.

scholarly journals The Benefits of Receiver Clock Modelling in Satellite Timing

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 466
Author(s):  
Weijin Qin ◽  
Xiao Wang ◽  
Hang Su ◽  
Zhe Zhang ◽  
Xiao Li ◽  
...  
Keyword(s):  
White Noise ◽  
Noise Model ◽  
Kinematic Scheme ◽  
Clock Model ◽  
Average Improvement ◽  
Receiver Clock ◽  
Averaging Time ◽  
Stochastic Clock ◽  
Clock Offset ◽  
Sampling Times

Satellite timing is an effective and convenient method that has been widely accepted in the time community. The key to satellite timing is obtaining a clean receiver clock offset. In this paper, instead of regarding the receiver clock offset as white noise, a two-state stochastic clock model involving three kinds of noise was conceived and used in PPP filter estimation. The influence of clock type and sampling time on satellite timing performance was first analysed. In addition, the kinematic scheme and static scheme were both investigated for meeting the demands of multi-occasional users. The values show that the model works well for both the kinematic scheme and static scheme; in contrast to that of the white noise model, the timing stability is enhanced at all the sampling times. For the six stations, especially when the averaging time is less than 1000 s, the average stability improvement values of the kinematic scheme are 75.53, 43.24, 75.00, 69.05, 40.57, and 25.45%, and the average improvement values of the static scheme are 65.49, 77.94, 56.71, 60.78, 64.41, and 39.41%. Furthermore, the enhancement magnitude is related to clock type. For a high-stability clock, the improvement of the kinematic scheme is greater than that of the static scheme, whereas for a low-stability clock, the improvement of the kinematic scheme is less than that of the static scheme.

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