The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> III. RÉNYI ENTROPY A. DESCRIPTION OF RÉNYI ENTROPY <s> The notion of smooth entropy allows a unifying, generalized formulation of privacy amplification and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the Renyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other hand, an assumption about Shannon entropy (which is Renyi entropy of order 1) is too weak to guarantee any non-trivial amount of smooth entropy. In this work we close the gap between Renyi entropy of order 1 and 2. In particular, we show that Renyi entropy of order o for any 1 < α < 2 is a lower bound for smooth entropy, up to a small parameter depending on α, the alphabet size and the failure probability. The results have applications in cryptography for unconditionally secure protocols such as quantum key agreement, key agreement from correlated information, oblivious transfer, and bit commitment. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> III. RÉNYI ENTROPY A. DESCRIPTION OF RÉNYI ENTROPY <s> Epilepsy can be detected using EEG signals.The entropy indicates the complexity of the EEG signal.Various entropies are used to diagnose epilepsy.Unique ranges for various entropies are proposed. Epilepsy is the neurological disorder of the brain which is difficult to diagnose visually using Electroencephalogram (EEG) signals. Hence, an automated detection of epilepsy using EEG signals will be a useful tool in medical field. The automation of epilepsy detection using signal processing techniques such as wavelet transform and entropies may optimise the performance of the system. Many algorithms have been developed to diagnose the presence of seizure in the EEG signals. The entropy is a nonlinear parameter that reflects the complexity of the EEG signal. Many entropies have been used to differentiate normal, interictal and ictal EEG signals. This paper discusses various entropies used for an automated diagnosis of epilepsy using EEG signals. We have presented unique ranges for various entropies used to differentiate normal, interictal, and ictal EEG signals and also ranked them depending on the ability to discrimination ability of three classes. These entropies can be used to classify the different stages of epilepsy and can also be used for other biomedical applications. <s> BIB002
Rényi entropy is a generalized form of Shannon entropy, which can quantify the irregularity, uncertainty, or randomness of time series  . The definition of REN with order is expressed as follows. where p i represents the probability of a time series {x 1 , x 2 , . . . , x n } and the order α = 1. For α ≥ 2, REN provides a lower bound for its smooth entropy BIB001 . For α = 1, REN equals to Shannon entropy. REN has two main advantages. Frist, REN changes by an additive constant at the rescaling of the variables; Second, REN remains unchanged for the different density functions. In other words, REN does not vary irrespective of the density functions used. Also, REN has its own shortcoming. REN is not a sub-additive, recursive, nor it possess the branching and sum properties BIB002 .