Development of Linnik’s Work in His Investigation of the Probabilities of Large Deviation

Self-organization describes a dynamic in a system whereby local interactions between individuals collectively yield global order, i.e. spatial patterns unobservable in their entirety to the individuals. By this working definition, self-organization is intimately related to chaos, i.e. global order in the dynamics of deterministic systems that are locally unpredictable. A useful distinction is that a small perturbation to a chaotic system causes a large deviation in its trajectory, i.e. the butterfly effect, whereas self-organizing patterns are robust to noise and perturbation. For many, self-organization is as important to the understanding of biological processes as natural selection. For some, self-organization explains where the complex forms that compete for survival in the natural world originate from. This chapter outlines some fundamental ideas from the study of simulated self-organizing systems, before suggesting how self-organizing principles could be applied through biohybrid societies to establish new theories of living systems.

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Large Deviation Principles for Random Walk Trajectories. II

Theory of Probability and Its Applications ◽

10.1137/s0040585x97985765 ◽

2013 ◽

Vol 57 (1) ◽

pp. 1-27 ◽

Cited By ~ 1

Author(s):

A. A. Borovkov ◽

A. A. Mogulskii

Keyword(s):

Random Walk ◽

Large Deviation ◽

Large Deviation Principles

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Reasons analysis of the large deviation in the NOx emission data of the coal-fired power plant

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/675/1/012030 ◽

2021 ◽

Vol 675 (1) ◽

pp. 012030

Author(s):

Ruifeng Dong ◽

Kai Zhang ◽

Yang Guo

Keyword(s):

Power Plant ◽

Large Deviation ◽

Nox Emission ◽

Emission Data

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Vicarious Radiometric Calibration of Ocean Color Bands for FY-3D/MERSI-II at Lake Qinghai, China

Sensors ◽

10.3390/s21010139 ◽

2020 ◽

Vol 21 (1) ◽

pp. 139

Author(s):

Shengli Chen ◽

Xiaobing Zheng ◽

Xin Li ◽

Wei Wei ◽

Shenda Du ◽

...

Keyword(s):

Infrared Imaging ◽

Large Deviation ◽

Ocean Color ◽

Calibration Method ◽

Surface Measurement ◽

Radiometric Calibration ◽

Lake Qinghai ◽

Vicarious Calibration ◽

Calibration Methods ◽

Spectral Imager

To calibrate the low signal response of the ocean color (OC) bands and test the stability of the Fengyun-3D (FY-3D)/Medium Resolution Spectral Imager II (MERSI-II), an absolute radiometric calibration field test of FY-3D/MERSI-II at the Lake Qinghai Radiometric Calibration Site (RCS) was carried out in August 2018. The lake surface and atmospheric parameters were mainly measured by advanced observation instruments, and the MODerate spectral resolution atmospheric TRANsmittance algorithm and computer model (MODTRAN4.0) was used to simulate the multiple scattering radiance value at the altitude of the sensor. The results showed that the relative deviations between bands 9 and 12 are within 5.0%, while the relative deviations of bands 8, and 13 are 17.1%, and 12.0%, respectively. The precision of the calibration method was verified by calibrating the Aqua/Moderate-resolution Imaging Spectroradiometer (MODIS) and National Polar-orbiting Partnership (NPP)/Visible Infrared Imaging Radiometer (VIIRS), and the deviation of the calibration results was evaluated with the results of the Dunhuang RCS calibration and lunar calibration. The results showed that the relative deviations of NPP/VIIRS were within 7.0%, and the relative deviations of Aqua/MODIS were within 4.1% from 400 nm to 600 nm. The comparisons of three on-orbit calibration methods indicated that band 8 exhibited a large attenuation after launch and the calibration results had good consistency at the other bands except for band 13. The uncertainty value of the whole calibration system was approximately 6.3%, and the uncertainty brought by the field surface measurement reached 5.4%, which might be the main reason for the relatively large deviation of band 13. This study verifies the feasibility of the vicarious calibration method at the Lake Qinghai RCS and provides the basis and reference for the subsequent on-orbit calibration of FY-3D/MERSI-II.

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Large deviation principle for the field in prequantum classical statistical field theory

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025717500254 ◽

2017 ◽

Vol 20 (04) ◽

pp. 1750025

Author(s):

Andrei Khrennikov ◽

Achref Majid

Keyword(s):

Field Theory ◽

Random Field ◽

Field Model ◽

Large Deviation Principle ◽

Large Deviation ◽

Background Field ◽

Deviation Principle ◽

Statistical Field ◽

Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

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An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

Journal of Applied Probability ◽

10.2307/3214649 ◽

1990 ◽

Vol 27 (2) ◽

pp. 303-313 ◽

Cited By ~ 13

Author(s):

Claudine Robert

Keyword(s):

Artificial Intelligence ◽

Maximum Entropy ◽

Large Deviation ◽

Maximum Entropy Principle ◽

Statistical Modelling ◽

Linear Constraints ◽

Descriptive Statistics ◽

Entropy Principle ◽

Maximum Entropy Distribution ◽

Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

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