scholarly journals Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150324 ◽  
Author(s):  
Dmitry S. Shalymov ◽  
Alexander L. Fradkov
Keyword(s):  
Limit Distribution ◽  
Mass Conservation ◽  
Random Variable ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Stationary Processes ◽  
Entropy Principle ◽  
Gradient Principle ◽  
Probability Density Function Pdf ◽  
Speed Gradient

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

scholarly journals Evolution of non-stationary processes and some maximum entropy principles

2018 ◽  
Vol 56 (2) ◽  
pp. 43-70
Author(s):  
Vasile Preda ◽  
Irina Băncescu
Keyword(s):  
Maximum Entropy ◽  
Stationary Processes ◽  
Gradient Principle ◽  
Speed Gradient

AbstractThis paper studies, by using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rényi-Tsallis of order α entropies.

scholarly journals Study of Quantile-Based Cumulative Renyi Information Measure

2020 ◽  
Vol 9 (4) ◽  
pp. 886-909
Author(s):  
Rekha ◽  
Vikas Kumar
Keyword(s):  
Order Statistic ◽  
Random Variable ◽  
Information Measure ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Reliability Measure ◽  
Extreme Order Statistic ◽  
The Relationship

In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.

Speed-gradient principle for description of transient dynamics in systems obeying maximum entropy principle

2011 ◽  
Author(s):  
Alexander Fradkov ◽  
Anton Krivtsov ◽  
Ali Mohammad-Djafari ◽  
Jean-François Bercher ◽  
Pierre Bessiére
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Transient Dynamics ◽  
Entropy Principle ◽  
Gradient Principle ◽  
Speed Gradient

scholarly journals Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 896 ◽  
Author(s):  
Igal Sason
Keyword(s):  
Lower Bound ◽  
Finite Number ◽  
Random Variable ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Finite Support ◽  
Discrete Random Variable ◽  
Asymptotic Bounds ◽  
Lossless Data Compression ◽  
Published Paper

This paper provides tight bounds on the Rényi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one to one. To that end, a tight lower bound on the Rényi entropy of a discrete random variable with a finite support is derived as a function of the size of the support, and the ratio of the maximal to minimal probability masses. This work was inspired by the recently published paper by Cicalese et al., which is focused on the Shannon entropy, and it strengthens and generalizes the results of that paper to Rényi entropies of arbitrary positive orders. In view of these generalized bounds and the works by Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and lossless data compression of discrete memoryless sources.

Infrared Electric Image Enhancement Based On Fuzzy Renyi Entropy and Quantum Genetic Algorithm

2011 ◽  
Vol 66-68 ◽  
pp. 1774-1780
Author(s):  
Song Hai Fan ◽  
Shu Hong Yang ◽  
Pu He ◽  
Hong Yu Nie
Keyword(s):  
Genetic Algorithm ◽  
Infrared Image ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Maximal Entropy ◽  
Infrared Images ◽  
Low Contrast ◽  
Quantum Genetic Algorithm ◽  
Entropy Principle ◽  
Electric Equipment

Infrared thermograph has been applied in electric equipment inspection widely, but the visual effects of infrared images are always undesirable. Considering the limitation of low luminance，low contrast in infrared images，an enhancement method based on fuzzy Renyi entropy and quantum genetic algorithm is presented in this paper．Firstly，the contrast-sketching function presented in [1] is improved based on the idea of segmentation. Then, in order to segment the infrared image, Renyi entropy is extend to fuzzy domain considering the fuzzy nature of infrared image, and is employed to threshold the infrared image following maximal entropy principle. In order to meet the real-time demand of online monitoring, quantum genetic algorithm is employed to search the optimal parameters of the transform function. The experimental results indicate that the method can well improve the visual effect of infrared electric images．

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

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