scholarly journals Relative entropy and the Pinsker product formula for sofic groups

2021 ◽  
Author(s):  
Ben Hayes
Keyword(s):  
Relative Entropy ◽  
Product Formula ◽  
Sofic Groups

scholarly journals Geometry from divergence functions and complex structures

2020 ◽  
Vol 18 (01) ◽  
pp. 1941020
Author(s):  
Florio Maria Ciaglia ◽  
Fabio Di Cosmo ◽  
Armando Figueroa ◽  
Giuseppe Marmo ◽  
Luca Schiavone
Keyword(s):  
Relative Entropy ◽  
Complex Structure ◽  
Product Formula ◽  
Complex Structures ◽  
Statistical Manifold ◽  
Geometrical Structures ◽  
Von Neumann ◽  
Density Operators ◽  
Almost Complex ◽  
Structure Formula

Motivated by the geometrical structures of quantum mechanics, we introduce an almost complex structure [Formula: see text] on the product [Formula: see text] of any parallelizable statistical manifold [Formula: see text]. Then, we use [Formula: see text] to extract a pre-symplectic form and a metric-like tensor on [Formula: see text] from a divergence function. These tensors may be pulled back to [Formula: see text], and we compute them in the case of an N-dimensional symplex with respect to the Kullback–Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann–Umegaki relative entropy.

Efficient Steganography Algorithm Based On DCT And Entropy Thresholding Technique

2018 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Satvir Singh
Keyword(s):  
Relative Entropy ◽  
Experimental Work ◽  
Random Function ◽  
Signal To Noise Ratio ◽  
Binary Sequence ◽  
Threshold Value ◽  
Absolute Difference ◽  
Secret Message ◽  
Signal To Noise ◽  
Confidential Information

Steganography is the special art of hidding important and confidential information in appropriate multimedia carrier. It also restrict the detection of  hidden messages. In this paper we proposes steganographic method based on dct and entropy thresholding technique. The steganographic algorithm uses random function in order to select block of the image where the elements of the binary sequence of a secret message will be inserted. Insertion takes place at the lower frequency  AC coefficients of the  block. Before we insert the secret  message. Image under goes dc transformations after insertion of the secret message we apply inverse dc transformations. Secret message will only be inserted into a particular block if  entropy value of that particular block is greater then threshold value of the entropy and if block is selected by the random function. In  Experimental work we calculated the peak signal to noise ratio(PSNR), Absolute difference , Relative entropy. Proposed algorithm give high value of PSNR  and low value of Absolute difference which clearly indicate level of distortion in image due to insertion of secret message is reduced. Also value of  relative entropy is close to zero which clearly indicate proposed algorithm is sufficiently secure. 

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

scholarly journals Maximum relative entropy of coherence for quantum channels

2021 ◽  
Vol 64 (8) ◽  
Author(s):  
Zhi-Xiang Jin ◽  
Long-Mei Yang ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost ◽  
Zhi-Xi Wang ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Quantum Channels ◽  
Relative Entropy Of Coherence

scholarly journals Relative Entropy Regularised TDLAS Tomography for Robust Temperature Imaging

2020 ◽  
pp. 1-1
Author(s):  
Yong Bao ◽  
Rui Zhang ◽  
Godwin Enemali ◽  
Zhang Cao ◽  
Bin Zhou ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Temperature Imaging

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

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