Permutation Conditional Mutual Information and Its Application to Epileptic EEG

2013 ◽  
Author(s):  
Jing Li ◽  
Xianzeng Liu ◽  
Gaoxiang Ouyang
Keyword(s):  
Mutual Information ◽  
Conditional Mutual Information

scholarly journals Bulk private curves require large conditional mutual information

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Alex May
Keyword(s):  
Mutual Information ◽  
Boundary Region ◽  
Theoretic Approach ◽  
Strong Correlations ◽  
Conditional Mutual Information ◽  
Information Theoretic ◽  
Causal Curve ◽  
Resource Requirements ◽  
Theoretic Argument ◽  
Information Theoretic Approach

Abstract We prove a theorem showing that the existence of “private” curves in the bulk of AdS implies two regions of the dual CFT share strong correlations. A private curve is a causal curve which avoids the entanglement wedge of a specified boundary region $$ \mathcal{U} $$ U . The implied correlation is measured by the conditional mutual information $$ I\left({\mathcal{V}}_1:\left.{\mathcal{V}}_2\right|\mathcal{U}\right) $$ I V 1 : V 2 U , which is O(1/GN) when a private causal curve exists. The regions $$ {\mathcal{V}}_1 $$ V 1 and $$ {\mathcal{V}}_2 $$ V 2 are specified by the endpoints of the causal curve and the placement of the region $$ \mathcal{U} $$ U . This gives a causal perspective on the conditional mutual information in AdS/CFT, analogous to the causal perspective on the mutual information given by earlier work on the connected wedge theorem. We give an information theoretic argument for our theorem, along with a bulk geometric proof. In the geometric perspective, the theorem follows from the maximin formula and entanglement wedge nesting. In the information theoretic approach, the theorem follows from resource requirements for sending private messages over a public quantum channel.

Calculating Quantitative Integrity and Secrecy for Imperative Programs

2015 ◽  
Vol 6 (2) ◽  
pp. 23-46
Author(s):  
Tom Chothia ◽  
Chris Novakovic ◽  
Rajiv Ranjan Singh
Keyword(s):  
Mutual Information ◽  
Information Flow ◽  
Quantitative Information ◽  
Error Correcting Codes ◽  
Conditional Mutual Information ◽  
Program Integrity ◽  
Data Contamination ◽  
Definition Of ◽  
Quantitative Information Flow ◽  
Libor Rate

This paper presents a framework for calculating measures of data integrity for programs in a small imperative language. The authors develop a Markov chain semantics for their language which calculates Clarkson and Schneider's definitions of data contamination, data suppression, program suppression and program transmission. The authors then propose their own definition of program integrity for probabilistic specifications. These definitions are based on conditional mutual information and entropy; they present a result relating them to mutual information, which can be calculated by a number of existing tools. The authors extend a quantitative information flow tool (CH-IMP) to calculate these measures of integrity and demonstrate this tool with examples including error correcting codes, the Dining Cryptographers protocol and the attempts by a number of banks to influence the Libor rate.

scholarly journals Individual Resting-State Brain Networks Enabled by Massive Multivariate Conditional Mutual Information

2020 ◽  
Vol 39 (6) ◽  
pp. 1957-1966
Author(s):  
Padmavathi Sundaram ◽  
Martin Luessi ◽  
Marta Bianciardi ◽  
Steven Stufflebeam ◽  
Matti Hamalainen ◽  
...  
Keyword(s):  
Mutual Information ◽  
Resting State ◽  
Brain Networks ◽  
Conditional Mutual Information
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