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We study the evolution of Tsallis entropy along the heat flow and establish its concavity in arbitrary dimensions. Extending prior results that were restricted to the one-dimensional setting, we prove that the Tsallis entropy is concave in…
Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis…
Medical image registration plays an important role in determining topographic and morphological changes for functional diagnostic and therapeutic purposes. Manual alignment and semi-automated software still have been used; however they are…
The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that…
We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis…
One of the most straightforward, direct and efficient approaches to Image Segmentation is Image Thresholding. Multi-level Image Thresholding is an essential viewpoint in many image processing and Pattern Recognition based real-time…
In the field of image analysis, segmentation is one of the most important preprocessing steps. One way to achieve segmentation is by mean of threshold selection, where each pixel that belongs to a determined class islabeled according to the…
A new thresholding strategy for the estimation of a deterministic image immersed in noise is introduced. The threshold is combined with a wavelet decomposition, where the wavelet coefficient of the image at any fixed value of the…
The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based…
We present a sampling-based trajectory optimization method derived from the maximum entropy formulation of Differential Dynamic Programming with Tsallis entropy. This method is a generalization of the legacy work with Shannon entropy, which…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure.…
The structure entropy is one of the most important parameters to describe the structure property of the complex networks. Most of the existing struc- ture entropies are based on the degree or the betweenness centrality. In order to describe…
In recent years, learning for neural networks can be viewed as optimization in the space of probability measures. To obtain the exponential convergence to the optimizer, the regularizing term based on Shannon entropy plays an important…
We present Generalized Histogram Thresholding (GHT), a simple, fast, and effective technique for histogram-based image thresholding. GHT works by performing approximate maximum a posteriori estimation of a mixture of Gaussians with…
This study derived the vertical distribution of streamwise velocity in wide open channels by maximizing Tsallis entropy, in accordance with the maximum entropy principle, subject to the total probability rule and the conservation of mass,…
Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
Following the work on Shannon entropy together with the principle of maximum entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo (J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive Tsallis…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…