Positive definite kernels on probability measures have been recently applied to classification problems involving text, images, and other types of structured data. Some of these kernels are related to classic information theoretic quantities, such as (Shannon's) mutual information and the Jensen-Shannon (JS) divergence. Meanwhile, there have been recent advances in nonextensive generalizations of Shannon's information theory. This paper bridges these two trends by introducing nonextensive information theoretic kernels on probability measures, based on new JS-type divergences. These new divergences result from extending the the two building blocks of the classical JS divergence: convexity and Shannon's entropy. The notion of convexity is extended to the wider concept of q-convexity, for which we prove a Jensen q-inequality. Based on this inequality, we introduce Jensen-Tsallis (JT) q-differences, a nonextensive generalization of the JS divergence, and define a k-th order JT q-difference between stochastic processes. We then define a new family of nonextensive mutual information kernels, which allow weights to be assigned to their arguments, and which includes the Boolean, JS, and linear kernels as particular cases. Nonextensive string kernels are also defined that generalize the p-spectrum kernel. We illustrate the performance of these kernels on text categorization tasks, in which documents are modeled both as bags of words and as sequences of characters.

https://jmlr.csail.mit.edu/papers/volume10/martins09a/martins09a.pdf

Nonextensive Information Theoretic Kernels on Measures

Over the past decade, boosting the electrical conductivity of nickel molybdate materials has been established to improve their supercapacitive performance. Nevertheless, it is significant to investigate a different approach from economic efficiency and operation time perspectives. Herein, we first prepare NiMoO4 nanoparticles using a simple ball-milling technique and then serve them in two different multi-walled carbon nanotubes (MWCNTs)/NiMoO4 composites fabricated using simple blending and ball-milling. The ball-milled nanocomposite delivers outstanding supercapacitive properties because of its good surface area, outstanding conductivity, fast kinetics, and many active sites. Its specific capacitance reached 727.2 F g−1 at 1 A g−1 and 709.8 at 10 mV sec−1, and cycling stability was measured to be 86.8 % after 2000 cycles at a current density of 20 A g−1, surpassing the other two samples. An asymmetric device based on ball-milled composite nanostructure resulted in a high specific energy of 40.9 Wh kg−1, a remarkable specific power of 918.5 W kg−1, an appealing rate performance of 73.6 % at 50 A g−1 current density, and a superb cycling durability of 85.4 %. As a result, combining storage attributes of NiMoO4 and MWCNTs with the ball-milling route provides a new strategy to enhance the electrochemical properties of nickel molybdate. 

A new strategy for the preparation of multi-walled carbon nanotubes/NiMoO4 nanostructures for high-performance asymmetric supercapacitors

Purpose
Architectural distortion is an important sign of early breast cancer. We present methods for computer-aided detection of architectural distortion in mammograms acquired prior to the diagnosis of breast cancer in the interval between scheduled screening sessions.

Measures of angular spread and entropy for the detection of architectural distortion in prior mammograms.

Computer-aided Detection of Architectural Distortion in Prior Mammograms of Interval Cancer

Positive definite kernels on probability measures have been recently applied in structured data classification problems. Some of these kernels are related to classic information theoretic quantities, such as mutual information and the Jensen-Shannon divergence. Meanwhile, driven by recent advances in Tsallis statistics, nonextensive generalizations of Shannon's information theory have been proposed. This paper bridges these two trends. We introduce the Jensen-Tsallis q-difference, a generalization of the Jensen-Shannon divergence. We then define a new family of nonextensive mutual information kernels, which allow weights to be assigned to their arguments, and which includes the Boolean, Jensen-Shannon, and linear kernels as particular cases. We illustrate the performance of these kernels on text categorization tasks.

/pdf/nonextensive-entropic-kernels-45ecpgqi2e.pdf

Nonextensive entropic kernels

Morphological matching plays a significant role in improving electrochemical properties of core-shell nanostructured as supercapacitor electrode. In this work, a hierarchical, vertically aligned funnel-shaped NiMoO4@Co3S4 core-shell nanostructure was designed by morphological matching for enhanced supercapacitor performance. The core electrode made of densely interconnected NiMoO4 nanosheets were prepared on nickel foam by hydrothermal synthesis, and the shell electrode made of loosely interconnected Co3S4 nanosheets with good conductivity were grown by electrochemical deposition to form a nanosheet-on-nanosheet core-shell nanostructure for improving the electrolyte penetration and storage, facilitating the charge transfer and diffusion. Consequently, the ultrathin nanosheets NiMoO4@Co3S4 core-shell electrode exhibits a remarkable specific capacitance as high as 359.31 mAh g−1 at current density 0.5 A g−1 (2589.6 F g−1 at current density 0.5 A g−1), and capacitance retention of 82.9% after 10,000 charge-discharge cycles. As positive electrode of NiMoO4@Co3S4 and negative electrode of activated carbon, a hybrid supercapacitor with an energy density of 33.37 W h kg−1 and a power density of 387.50 W kg−1 at current density 0.5 A g−1 was assembled. The excellent performance demonstrates that morphological matching is significant to construct core-shell nanostructure of supercapacitor electrode. 

Funnel-shaped hierarchical NiMoO4@Co3S4 core-shell nanostructure for enhanced supercapacitor performance

Preparation of ZnO p-n homojunction nanorod via nitrogen ion injection coupled with Au induced SPR effect for enhanced photoelectrochemical water splitting

Image segmentation is one of the most critical tasks in image processing. Entropy-based threshold value is one of the most efficient techniques for image segmentation. The non-extensive (or non-additive) entropy is a recent development in statistical mechanics. In this paper, a two-dimensional Tsallis entropy (TE) with non-additive information content based on co-occurrence matrix constructed by the pairs of pixel gray value and the average gray value for the neighborhood of each pixel is applied as a general entropy formalism for information theory in image segmentation. The method based on the minimum difference of two-dimensional TE is proposed. The advantage of using average gray value for the neighborhood of each pixel as threshold value instead of gray value is discussed. It is the first time that image threshold by two-dimensional non-additive entropy is proposed to segment images. Some typical results are presented to illustrate the effect of the proposed method in the threshold segmentation.

The Thresholding Methods Based on Two-Dimensional Non-extensive Entropy

Medical image registration methods based on the maximization of mutual information have shown promising results. But it needs much computing time. This paper presents a new method to rigid registration based on the combination of scale images and mutual information. Firstly, the concept of area morphology is introduced. And then, the scale images are constructed with the area morphological operators. Not only the noise in the image is removed, but also the intensity levels are decreased in the scale image by area morphological operators. Moreover, the images do not be blurred. As a result, the matching process is accelerated while the accuracy and the robustness of the method is hold. For magnetic resonance and computed tomography images, behavior of mutual information matching is examined in a scale scheme. The normalized mutual information and the area scale space are combined in registration for the first time. Experimental results show that the scale approach to mutual information matching works well.

Mutual Information of High Area Scale Space Images

25 Objective: Intrauterine adhesion (IUA) is one of the major causes of refractory 26 secondary infertility, especially in regions and countries with high abortion rates. In 27 this study, we used the mouse IUA model to evaluate the feasibility of the organoids, 28 a 3D cell structure derived from endometrial tissue, as grafts for the treatment of 29 post-traumatic endometrial regeneration disorders. Methods: The isolated and 30 cultured endometrial organoid was transplanted into the model IUA uterus by the 31 hydrogel scaffold method. Results: The cultured endometrial organoids were 32 transplanted into the basal layer of the damaged endometrium for 28 days. They were 33 completely implanted and grew normally. They not only reconstructed the structural 34 integrity of the endometrial epithelium but also realized the functional repair of the 35 endometrium through differentiation cultures and secretory functions. Conclusion: 36 For severe IUA, this method may be better than stem cell transplantation. These 37 findings provide useful insights into the use of endometrial organoid regeneration in 38 the treatment of injury repair. 39 40

Organoid Transplantation Can Improve Reproductive Prognosis By

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