scholarly journals Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles

2021 ◽  
Vol 383 (2) ◽  
pp. 1243-1289
Author(s):  
Julien Sedro ◽  
Hans Henrik Rugh
Keyword(s):  
Linear Response ◽  
Transfer Operator ◽  
Characteristic Exponents

scholarly journals Response and Sensitivity Using Markov Chains

2020 ◽  
Author(s):  
Manuel Santos Gutiérrez ◽  
Valerio Lucarini
Keyword(s):  
Dynamical Systems ◽  
Linear Response ◽  
Transfer Operator ◽  
Real Life ◽  
Planck Equation ◽  
Matrix Representations ◽  
Operator Formalism ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Linear And Nonlinear

<p>Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study</p><p>how this affects their statistical properties. A prominent real-life example of this class of problems is the investigation</p><p>of climate response to perturbations. In this respect, it is crucial to determine what the linear response of a system is</p><p>as a quantification of sensitivity. Alongside previous work, here we use the transfer operator formalism to study the</p><p>response and sensitivity of a dynamical system undergoing perturbations. By projecting the transfer operator onto a</p><p>suitable finite dimensional vector space, one is able to obtain matrix representations which determine finite Markov</p><p>processes. Further, using perturbation theory for Markov matrices, it is possible to determine the linear and nonlinear</p><p>response of the system given a prescribed forcing. Here, we suggest a methodology which puts the scope on the</p><p>evolution law of densities (the Liouville/Fokker-Planck equation), allowing to effectively calculate the sensitivity and</p><p>response of two representative dynamical systems.</p>

scholarly journals Statistical stability and linear response for random hyperbolic dynamics

2021 ◽  
pp. 1-30
Author(s):  
DAVOR DRAGIČEVIĆ ◽  
JULIEN SEDRO
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Linear Response ◽  
Ad Hoc ◽  
Transfer Operator ◽  
Statistical Stability ◽  
Hyperbolic Dynamics ◽  
Quenched Central Limit Theorem ◽  
Random Products

Abstract We consider families of random products of close-by Anosov diffeomorphisms, and show that statistical stability and linear response hold for the associated families of equivariant and stationary measures. Our analysis relies on the study of the top Oseledets space of a parametrized transfer operator cocycle, as well as ad-hoc abstract perturbation statements. As an application, we show that, when the quenched central limit theorem (CLT) holds, under the conditions that ensure linear response for our cocycle, the variance in the CLT depends differentiably on the parameter.

scholarly journals Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Stefano Galatolo ◽  
Alfonso Sorrentino
Keyword(s):  
Rotation Number ◽  
Linear Response ◽  
Transfer Operator ◽  
Kam Theory ◽  
Hölder Exponent ◽  
Statistical Stability ◽  
Rotation Numbers ◽  
Circle Diffeomorphisms ◽  
Stability Results ◽  
Spaces Of Measures

<p style='text-indent:20px;'>We prove quantitative statistical stability results for a large class of small <inline-formula><tex-math id="M1">\begin{document}$ C^{0} $\end{document}</tex-math></inline-formula> perturbations of circle diffeomorphisms with irrational rotation numbers. We show that if the rotation number is Diophantine the invariant measure varies in a Hölder way under perturbation of the map and the Hölder exponent depends on the Diophantine type of the rotation number. The set of admissible perturbations includes the ones coming from spatial discretization and hence numerical truncation. We also show linear response for smooth perturbations that preserve the rotation number, as well as for more general ones. This is done by means of classical tools from KAM theory, while the quantitative stability results are obtained by transfer operator techniques applied to suitable spaces of measures with a weak topology.</p>

Photographic Equidensitometry of High Voltage Electron Images of Thick Noncrystalline Materials

1972 ◽  
Vol 30 ◽  
pp. 594-595
Author(s):  
Keinosuke Kobayashi
Keyword(s):  
High Voltage ◽  
Linear Response ◽  
Thickness Distribution ◽  
Contour Map ◽  
Mass Thickness ◽  
Voltage Electron ◽  
High Voltage Electron ◽  
Homogeneous Particle ◽  
Photographic Emulsions ◽  
Logarithmic Relation

Equidensitometry as developed by E. Lau and W. Krug has been little used in the analysis of ordinary electron photomicrographs, yet its application to the high voltage electron images proves merits of this procedure. Proper sets (families) of equidensities as shown in the next page are able to reveal the contour map of mass thickness distribution in thick noncrystalline specimens. The change in density of the electron micrograph is directly related to the mass thickness of corresponding area in the specimen, because of the linear response of photographic emulsions to electrons and the logarithmic relation between electron opacity and mass thickness of amorphous object.This linearity is verified by equidensitometry of a spherical solid object as shown in Fig. 1a. The object is a large (1 μ) homogeneous particle of polystyrene. Fig. 1b is a composite print of three equidensities of the 1st order prepared from Fig. 1a.

Flow velocity and light level drive non-linear response of seagrass Zostera noltei to ammonium enrichment

2016 ◽  
Vol 545 ◽  
pp. 109-121 ◽  
Author(s):  
B Villazán ◽  
FG Brun ◽  
V González‑Ortiz ◽  
F Moreno‑Marín ◽  
TJ Bouma ◽  
...  
Keyword(s):  
Flow Velocity ◽  
Linear Response ◽  
Light Level ◽  
Zostera Noltei ◽  
Non Linear

An Over 120dB Dynamic Range Linear Response Single Exposure CMOS Image Sensor with Two-stage Lateral Overflow Integration Trench Capacitors

2020 ◽  
Vol 2020 (7) ◽  
pp. 143-1-143-6 ◽  
Author(s):  
Yasuyuki Fujihara ◽  
Maasa Murata ◽  
Shota Nakayama ◽  
Rihito Kuroda ◽  
Shigetoshi Sugawa
Keyword(s):  
Linear Response ◽  
Dynamic Range ◽  
Signal To Noise Ratio ◽  
Cmos Image Sensor ◽  
Image Sensor ◽  
Signal To Noise ◽  
Single Exposure ◽  
Two Stage ◽  
Noise Ratio ◽  
Maximum Signal

This paper presents a prototype linear response single exposure CMOS image sensor with two-stage lateral overflow integration trench capacitors (LOFITreCs) exhibiting over 120dB dynamic range with 11.4Me- full well capacity (FWC) and maximum signal-to-noise ratio (SNR) of 70dB. The measured SNR at all switching points were over 35dB thanks to the proposed two-stage LOFITreCs.

A First Principles Approach for Partitioning Linear Response Properties into Additive and Cooperative Contributions

2018 ◽  
Author(s):  
Daniel Lambrecht ◽  
Eric Berquist
Keyword(s):  
First Principles ◽  
Linear Response ◽  
Building Blocks ◽  
Field Method ◽  
Response Property ◽  
Response Properties ◽  
Consistent Field ◽  
Molecular Building Blocks ◽  
Self Consistent ◽  
Self Consistent Field

We present a first principles approach for decomposing molecular linear response properties into orthogonal (additive) plus non-orthogonal/cooperative contributions. This approach enables one to 1) identify the contributions of molecular building blocks like functional groups or monomer units to a given response property and 2) quantify cooperativity between these contributions. In analogy to the self consistent field method for molecular interactions, SCF(MI), we term our approach LR(MI). The theory, implementation and pilot data are described in detail in the manuscript and supporting information.

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