Renyi Entropy Research Articles

Энтропийная космология на основе модифицированной энтропии Шарма-Миттала на космологическом горизонте Вселенной

In the framework of entropic cosmology, several scenarios of the evolution of the Friedman-Robertson-Walker (FRW) Universe are considered, based on a new modification of the non-additive Sharma-Mittal and Renyi entropy measures on the cosmological horizon. This is done by replacing in the original logarithmic formulas for these entropies, the Tsallis entropy by the Barrow entropy associated with the modification of the horizon surface due to quantum gravitational effects. Several versions of the generalised multi-parametric FRW equations have been constructed, which can serve as an effective theoretical basis for describing the accelerating phase of the expansion of the late Universe. In the considered model there is no mutual interaction between the black components of the cosmos. The proposed approach, based on the use of non-additive extensive entropic measures on the cosmological horizon, meets the well-known requirements for thermodynamic modelling of the dynamical evolution of the Universe without involving the concept of hypothetical dark energy, but using the antigravity effect of entropic forces. The obtained results show that the generalised entropic formalism can open new possibilities for a deeper insight into the nature of spacetime and its fractal properties.

Characterization of the null energy condition via displacement convexity of entropy

AbstractWe characterize the null energy condition for an ‐dimensional, time‐oriented Lorentzian manifold in terms of convexity of the relative ‐Renyi entropy along displacement interpolations on null hypersurfaces. More generally, we also consider Lorentzian manifolds with a smooth weight function and introduce the Bakry–Emery ‐null energy condition that we characterize in terms of null displacement convexity of the relative ‐Renyi entropy. As application we then revisit Hawking's area monotonicity theorem for a black hole horizon and the Penrose Singularity Theorem from the viewpoint of this characterization and in the context of weighted Lorentzian manifolds.

A note on interval cumulative past Renyi entropy

In analogy with cumulative residual entropy, Di Crescenzo and Longobardi (2009) proposed cumulative past entropy which served as the basis for many following works. To this end, we define cumulative past Renyi entropy for double truncated random variable which we call as interval cumulative past Renyi entropy (ICPRE). Some properties, such as effect of monotone transformation and bounds of ICPRE, are studied. Furthermore, it is shown that the proposed measure uniquely determines the distribution function and characterizes certain lifetime distributions. Finally, non-parametric estimators of ICPRE are obtained and the best proposed estimator is investigated with the help of simulated data set and real-life data set.

Deep learning based Non-Local k-best renyi entropy for classification of white blood cell subtypes

The major issue in classifying blood cells from the microscopic image is overlapping cells and overfitting data. Therefore, to solve these problems in microscopic imaging, a thresholding scheme based on a non-local average filter approach is used to segment cells that separate the overlap of cells and thus perform the segmentation procedure. Basic convolutional neural networks (CNN) such as AlexNet, ResNet, and DenseNet have proven to be more powerful in image classification in various fields. However, the problem is that the number of parameters used in the network increased, which tends to separate the optimization procedure; otherwise, it leads to complexity in processing (increased simulation time). The SqueezeNet architecture is used to reduce these problems and overcome the problems in blood cell classification, like the overfitting of data and gradient vanishing problems. That will extract and classify the features based on the ground truth with 5 times fewer parameters than the traditional CNN architectures. The proposed method has improved the accuracy to 99.83%, 99.67%, 99.56% and 99.02% for the test datasets of kaggle-blood cell image, LISC dataset, Raabin-WBC and BCCD dataset, respectively.

Chirp Rate Estimation of LFM Signals Based on Second-Order Synchrosqueezing Transform

For the problem of low time-frequency aggregation of the short-time Fourier transform (STFT), which causes the parameter estimation performance degradation of linear frequency modulation (LFM) signals at low signal-to-noise ratio (SNR), second-order synchrosqueezing transform (SSST) is proposed based on the square of STFT amplitude. The time-frequency resolution and energy aggregation are improved by means of squeezing and reassigning the time-frequency spectrum. Meanwhile, in order to decrease the calculation of classical parameter estimation methods, the Hough transform is used for rough estimation, and then the fractional Fourier transform (FRFT) is used for accuracy estimation based on the Renyi entropy. The simulation result shows that higher estimation accuracy is obtained at low SNR, and it has better robustness.

Study on the sentimental influence on Indian stock price

The rapidly increasing scientific research on the stock market and the visible impact of media on equity prices are nowadays in limelight. To a greater extent, causal analysis can reckon the sentimental effect of the broadcasted content on stock valuation. We propose a four stage model to detect the direction of information flow between the news sentiment and stock price. Whilst web scraping explores and extracts the news datasets, the modified VADER algorithm finds the sentiments of the aired media. The associational causal analysis determines the cause effect between the news and stock price. The results suggest that the non parametric Shannon and Renyi's entropy approach supersedes the Granger test, a parametric study which is constrained to Gaussian time series with linear causation. Since Renyi's Entropy can perfectly identify the deluge of information during quick leaps, it is regarded as a beneficial formulation for investors when evaluating stocks with a fewer number of news mentions. The impact of news during the COVID-19 pandemic over the pharmaceutical sector was also done. The study infers an explicit information flow and direction of causality between news sentiment and stock price movement, which can be used to devise future investment and consumption strategies.

Long-Range Order for Critical Book-Ising and Book-Percolation

In this paper, we investigate the behaviour of statistical physics models on a book with pages that are isomorphic to half-planes. We show that even for models undergoing a continuous phase transition on Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^2$$\\end{document}, the phase transition becomes discontinuous as soon as the number of pages is sufficiently large. In particular, we prove that the Ising model on a three pages book has a discontinuous phase transition (if one allows oneself to consider large coupling constants along the line on which pages are glued). Our work confirms predictions in theoretical physics which relied on renormalization group, conformal field theory and numerics (Cardy in J Phys A Math Gen 24(22):L131, 1991; Iglói et al. in J Phys A Math Gen 24(17):L1031, 1991; Stéphan et al. in Phys Rev B 82(12):125455, 2010) some of which were motivated by the analysis of the Renyi entropy of certain quantum spin systems.

Statistical Analysis of Covid-19 Data using the Odd Log Logistic Kumaraswamy Distribution

This paper presents a statistical analysis of Covid-19 data using the Odd log logistic kumaraswamy Kumaraswamy (OLLK) distribution. Some mathematical properties of the proposed OLLK distribution such as the survival and hazard functions, quantile function, ordinary and incomplete moments, moment generating function, probability weighted moment, distribution of order statistic and Renyi entropy were derived. Five estimators are examined for unknown model parameters. The performance of the estimators is compared using an extensive simulation study based on the bias and mean square error criteria. Two Covid-19 data sets representing the percentage of daily recoveries of Covid-19 patients are used to illustrate the applicability of the proposed OLLK distribution. Results revealed that the OLLK distribution is a better alternative to some existing models with bounded support.

The Type II Topp-Leone Inverse Power Lomax distribution with Simulation and Applications

In this work, we present a four-parameter lifetime model that can be used to model reliability issues, fatigue life studies, and survival data called the Type II Topp-Leone Inverse Power Lomax distribution. It has the Type II inverse Lomax, Inverse Power Lomax, and Inverse Lomax distributions as sub-models. Some of its statistical properties, including complete and incomplete moments, generating functions, characteristics functions, mean residual life, mean inactivity time, Renyi entropy, Tsallis entropy, order statistics, stress-strength reliability, and weighted probability moment, have formal formulas that we have developed. The model's parameters are estimated using the maximum likelihood estimation technique. The effectiveness of maximum likelihood estimators is evaluated in terms of absolute bias and simulation study standard error. Two lifetime data sets are used to demonstrate how the new model can be applied. Using the same comparative criteria, the proposed distribution offers a better fit than a few well-known distributions.

Renyi entropy analysis of a deep convolutional representation for texture recognition

Despite the recent success of convolutional neural networks in computer vision in general, texture images still pose an important challenge to those models, especially when dealing with textures “in the wild”. In this context, deep learning models can benefit from the introduction of features long known to be useful for texture modeling. And that is the case of entropy, a measure of texture regularity that has played an important role in classical computer vision. Based on this observation, here we propose an alternative analysis over deep convolutional neural features based on entropy for texture representation and, particularly, texture classification. More precisely, we couple a module to the convolutional backbone that locally computes the Renyi entropy of the latent representation at multiple levels. The rationale for using Renyi entropy is essentially two-fold: (1) It connects the concept of entropy with multifractal theory, another well explored measure especially in domains of application where we seek some physical interpretation of the descriptors, e.g., in medicine, biology, and others; (2) It has an extra degree of freedom (α parameter) that can be fine-tuned. The main contribution of this study is the development of a strategy that can improve the performance of convolutional neural networks in texture recognition tasks, adding low computational cost. The effectiveness of our method is verified in texture classification of benchmark datasets, as well as in a practical task of plant species identification. Our method achieves a competitive accuracy of 84.5% in the classification of KTH-TIPS-2b and 80.9% in FMD, which are two challenging benchmark databases. Besides, an accuracy of 91.6% is obtained in the plant identification application, to our knowledge outperforming all the results previously published on this task. In both scenarios, the proposed descriptors outperform several approaches from the state-of-the-art, confirming the method potential as a rich and robust solution for texture analysis in general. The results also suggest that information-theoretical measures like entropy can be a reliable source of information to compose a precise and robust latent representation of texture images.

Exponentiated generalized Ramos-Louzada distribution with properties and applications

In this paper, we propose a new generalization of Ramos-Louzada (RL) distribution based on two additional shape parameters. Along with the genesis of its distributional form, the derivation of cumulative density function (cdf), survival and hazard rate functions, the quantile function (qf), moments, moment generating function (mgf), Shannon and Renyi entropies, order statistics and a linear representation of the proposed distribution are inspected. Several estimation methods of the model parameters are discussed throughout two comprehensive simulation studies conducted to compare its performance against some lifetime distributions. Application of a real dataset is presented to illustrate the potentiality of this distribution in line with the simulation studies.

PRMxAI: protein arginine methylation sites prediction based on amino acid spatial distribution using explainable artificial intelligence

BackgroundProtein methylation, a post-translational modification, is crucial in regulating various cellular functions. Arginine methylation is required to understand crucial biochemical activities and biological functions, like gene regulation, signal transduction, etc. However, some experimental methods, including Chip–Chip, mass spectrometry, and methylation-specific antibodies, exist for the prediction of methylated proteins. These experimental methods are expensive and tedious. As a result, computational methods based on machine learning play an efficient role in predicting arginine methylation sites.ResultsIn this research, a novel method called PRMxAI has been proposed to predict arginine methylation sites. The proposed PRMxAI extract sequence-based features, such as dipeptide composition, physicochemical properties, amino acid composition, and information theory-based features (Arimoto, Havrda-Charvat, Renyi, and Shannon entropy), to represent the protein sequences into numerical format. Various machine learning algorithms are implemented to select the better classifier, such as Decision trees, Naive Bayes, Random Forest, Support vector machines, and K-nearest neighbors. The random forest algorithm is selected as the underlying classifier for the PRMxAI model. The performance of PRMxAI is evaluated by employing 10-fold cross-validation, and it yields 87.17% and 90.40% accuracy on mono-methylarginine and di-methylarginine data sets, respectively. This research also examines the impact of various features on both data sets using explainable artificial intelligence.ConclusionsThe proposed PRMxAI shows the effectiveness of the features for predicting arginine methylation sites. Additionally, the SHapley Additive exPlanation method is used to interpret the predictive mechanism of the proposed model. The results indicate that the proposed PRMxAI model outperforms other state-of-the-art predictors.

Generalizations of Levinson type inequalities via new Green functions with applications to information theory

In this paper, four new Green functions are used to generalize Levinson-type inequalities for the class of 3-convex functions. The f-divergence, Renyi entropy, Renyi divergence, Shannon entropy, and the Zipf–Mandelbrot law are also used to apply the main results to information theory.

A New Member in the Lindley Class of Distributions with Flexible Applications

In this paper, a new lifetime distribution in the class of Lindley is developed and it is called "Doje Distribution". It is flexible in modeling lifetime data. The mathematical properties which include moments, the shape of the distribution, Quantile function, hazard function, survival function, stochastic ordering, mean deviation, Bonferroni and Lorenz curve, order statistic, and Renyi entropy have been studied. The maximum likelihood estimation has also been discussed. Two-lifetime data sets were utilized to demonstrate its usefulness. The results show that the proposed Doje distribution is better than Lindley, Ishita, Pareto, Chris-Jerry, Sushila, and Rama’s distribution in the instances of the data used.

The Odd Ramos-Louzada Generator of distributions with applications to failure and waiting times

In this study, we have proposed a new generator called the Odd Ramos-Louzada Generator (ORL-G), which can extend many well-known distributions by applying the T-X method. Some of its basic statistical properties such as the quantile function, the rthnon-central moments and Renyi entropy are also investigated. The ORL-G has the ability to model symmetric and asymmetric data as well as non-monotonic and monotonic failure rate datasets. Three new distributions of the ORL-G family are the ORL-Burr XII (ORLBXII), ORL-Log Logistic (ORLLoL), and ORL-Weibull (ORLWei) which are respectively obtained using the Burr XII, the Log-Logistic, and Weibull as baseline models. The RL and Generalized RL distributions are sub-models of the ORLBXII and ORLLoL distributions. The ORL-G model parameters have been estimated using the maximum likelihood (ML) method. Simulation analysis carried out indicates that the ML estimation method and its asymptotic properties performed quite well. The flexibility of the ORL-G family is demonstrated through the application of three real, complete datasets, including failure and waiting times and it is evident that ORLBXII outperformed its sub-models and other competing models.

Simplified expression and recursive algorithm of multi-threshold Tsallis entropy

Image segmentation is an important step in obtaining image information, and it has always been an extremely critical link in the fields of computer vision and pattern recognition. Because of its simplicity and effectiveness, threshold-based image segmentation technology has received significant attention and research by researchers. Tsallis entropy and Renyi entropy are two important global threshold selection methods in image thresholding. They not only have a special correspondence in mathematical expression, but also have a certain relationship in the field of image segmentation. Considering the number of thresholds increases, the complexity of the expression of Tsallis entropy criterion function also increases sharply, which is difficult to apply in multiple thresholds. Given this, this paper proposes a simplified expression of Tsallis entropy with multiple thresholds, which is proved by mathematical induction. Simultaneously, it is concluded that the multiple-threshold segmentation of Tsallis entropy and Renyi entropy with the same parameters is equivalent. To overcome the inconvenience of high calculation cost under multi-threshold and to improve calculation efficiency, recursive algorithms based on simplified Tsallis entropy and Renyi entropy under multi-threshold are given. The calculation costs of the traditional Tsallis entropy and Renyi entropy threshold, simplified Tsallis entropy and Renyi entropy threshold, and the recursive simplified Tsallis entropy and Renyi entropy are compared through experiments. The results have revealed that the calculation time of simplified Tsallis entropy and Renyi entropy is shorter than the traditional methods, and the calculation time of the recursive simplified Tsallis entropy and Renyi entropy is much lower than that of the simplified expression. Finally, we use the three optimization algorithms including particle swarm, differential evolution and Harris hawks algorithm to solve the optimal solutions of the six expressions in the case of multilevel thresholds. Experiments also show that recursive simplified Tsallis entropy and Renyi entropy have the lowest calculation time cost under the same parameters.

Influence of the channel bed slope on Shannon, Tsallis, and Renyi entropy parameters

Abstract Velocity distribution plays a fundamental role in understanding the hydrodynamics of open-channel flow. Among a multitude of approaches, the entropy-based approach holds great promise in achieving a reasonable characterisation of the velocity distribution. In entropy-based methods, the distribution depends on a key parameter, known as the entropy parameter (a function of the time-averaged mean velocity and maximum velocity), that relates to channel characteristics, such as channel roughness and channel bed slopes. The entropy parameter was regarded as constant for lack of experimental evidence, which would otherwise demonstrate if it had any correlation with channel properties. A series of experiments were conducted to collect velocity data in the laboratory flume for seven different values of the channel bed slope. The experimental data analysis revealed dissimilar fluctuations in entropy parameter values with varying bed slopes, with the lowest coefficient of variation in Renyi's (∼0.5%) and the highest in Shannon's case (∼10%). Performance evaluation of the predicted results substantiated good accuracy for all three entropies with the best results of Renyi entropy and lent strong support for using a constant (overall average) value of the entropy parameter for a specific channel cross-section rather than separate values for each channel bed slope.

Characterizing the uncertainty relation via a class of measurements

The connection between uncertainty and entanglement is a prevalent topic in quantum information processing. Based on a broad class of informationally complete symmetric measurements, which can be viewed as a common generalization of symmetric, informationally complete positive operator-valued measures and mutually unbiased bases, a conical 2-design is calculated. This design plays a crucial role in quantum measurement theory. Subsequently, the relation between the uncertainty and the entanglement for a set of measurements is portrayed using conditional collision entropy. Furthermore, a tighter lower bound of the uncertainty relation is discussed according to the characterization of the entropic bound. Finally, the relation is applied to entanglement witnesses. It is demonstrated that the present results are unified and comprehensive.

A Generalized Approach to Model One-Dimensional Nonmonotonous Distributions Using Renyi Entropy Theory with Applications to Open-Channel Turbulent Flows

A Generalized Approach to Model One-Dimensional Nonmonotonous Distributions Using Renyi Entropy Theory with Applications to Open-Channel Turbulent Flows

The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications

In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.