A variational principle for the topological conditional entropy

1979 ◽  
pp. 78-88 ◽  
Author(s):  
F. Ledrappier
Keyword(s):  
Variational Principle ◽  
Conditional Entropy

Variational Principle for Conditional Pressure with Subadditive Potential

2011 ◽  
Vol 18 (04) ◽  
pp. 389-404 ◽  
Author(s):  
Yun Zhao ◽  
Wen-Chiao Cheng
Keyword(s):  
Variational Principle ◽  
Main Idea ◽  
Conditional Entropy

The purpose of this paper is to define and study conditional pressure for subadditive potentials which is an extension of conditional entropy. This study reveals a variational principle of topological conditional pressure for subadditive potentials. Besides, we discuss the topological conditional pressure for asymptotically subadditive potentials. The main idea of the proof is quite similar to that of Cao, Feng and Huang's approximations.

A local variational principle for conditional entropy

2006 ◽  
Vol 26 (01) ◽  
pp. 219 ◽  
Author(s):  
WEN HUANG ◽  
XIANGDONG YE ◽  
GUOHUA ZHANG
Keyword(s):  
Variational Principle ◽  
Conditional Entropy

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Conditional Entropy: A Potential Digital Marker for Stress

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 286
Author(s):  
Soheil Keshmiri
Keyword(s):  
Resting State ◽  
Nearest Neighbor ◽  
Brain Activity ◽  
Solution Concept ◽  
Conditional Entropy ◽  
K Nearest Neighbor ◽  
Brain Response ◽  
Substantial Progress ◽  
Eeg Recordings ◽  
The Brain

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

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