System for Neural Network Determination of Atrial Fibrillation on ECG Signals with Wavelet-Based Preprocessing

Today, cardiovascular disease is the leading cause of death in developed countries. The most common arrhythmia is atrial fibrillation, which increases the risk of ischemic stroke. An electrocardiogram is one of the best methods for diagnosing cardiac arrhythmias. Often, the signals of the electrocardiogram are distorted by noises of varying nature. In this paper, we propose a neural network classification system for electrocardiogram signals based on the Long Short-Term Memory neural network architecture with a preprocessing stage. Signal preprocessing was carried out using a symlet wavelet filter with further application of the instantaneous frequency and spectral entropy functions. For the experimental part of the article, electrocardiogram signals were selected from the open database PhysioNet Computing in Cardiology Challenge 2017 (CinC Challenge). The simulation was carried out using the MatLab 2020b software package for solving technical calculations. The best simulation result was obtained using a symlet with five coefficients and made it possible to achieve an accuracy of 87.5% in recognizing electrocardiogram signals.

Is the EMI model a QFT? An inquiry on the space of allowed entropy functions

The mutual information I(A, B) of pairs of spatially separated regions satisfies, for any d-dimensional CFT, a set of structural physical properties such as positivity, monotonicity, clustering, or Poincaré invariance, among others. If one imposes the extra requirement that I(A, B) is extensive as a function of its arguments (so that the tripartite information vanishes for any set of regions, I3(A, B, C ) ≡ 0), a closed geometric formula involving integrals over ∂A and ∂B can be obtained. We explore whether this “Extensive Mutual Information” model (EMI), which in fact describes a free fermion in d = 2, may similarly correspond to an actual CFT in general dimensions. Using the long-distance behavior of IEMI(A, B) we show that, if it did, it would necessarily include a free fermion, but also that additional operators would have to be present in the model. Remarkably, we find that IEMI(A, B) for two arbitrarily boosted spheres in general d exactly matches the result for the free fermion current conformal block $$ {G}_{\Delta =\left(d-1\right),J=1}^d $$ G ∆ = d − 1 , J = 1 d . On the other hand, a detailed analysis of the subleading contribution in the long-distance regime rules out the possibility that the EMI formula represents the mutual information of any actual CFT or even any limit of CFTs. These results make manifest the incompleteness of the set of known constraints required to describe the space of allowed entropy functions in QFT.

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.

Interactive Decision Tree Learning and Decision Rule Extraction Based on the ImbTreeEntropy and ImbTreeAUC Packages

This paper presents two new R packages ImbTreeEntropy and ImbTreeAUC for building decision trees, including their interactive construction and analysis, which is a highly regarded feature for field experts who want to be involved in the learning process. ImbTreeEntropy functionality includes the application of generalized entropy functions, such as Renyi, Tsallis, Sharma-Mittal, Sharma-Taneja and Kapur, to measure the impurity of a node. ImbTreeAUC provides non-standard measures to choose an optimal split point for an attribute (as well the optimal attribute for splitting) by employing local, semi-global and global AUC measures. The contribution of both packages is that thanks to interactive learning, the user is able to construct a new tree from scratch or, if required, the learning phase enables making a decision regarding the optimal split in ambiguous situations, taking into account each attribute and its cut-off. The main difference with existing solutions is that our packages provide mechanisms that allow for analyzing the trees’ structures (several trees simultaneously) that are built after growing and/or pruning. Both packages support cost-sensitive learning by defining a misclassification cost matrix, as well as weight-sensitive learning. Additionally, the tree structure of the model can be represented as a rule-based model, along with the various quality measures, such as support, confidence, lift, conviction, addedValue, cosine, Jaccard and Laplace.

DERIVATIVES BY RATIO PRINCIPLE FOR q-SETS ON THE TIME SCALE CALCULUS

The definitions of derivatives as delta and nabla in time scale theory are kept to follow the notion of the classical derivative. The jump operators are used to transfer the notion from the classical derivative to the derivatives in the time scale theory. The jump operators can be determined by analyst to model phenomena. In this study, the definitions of derivatives in the time scale theory are transferred to ratio of function which has jump operators from [Formula: see text]-deformation. If we use [Formula: see text]-deformation as a subset of real line [Formula: see text], we can have a chance to define a derivative via consulting ratio of two expressions on [Formula: see text]-sets. The applications are performed to produce the new entropy functions by use of the partition function and the derivatives proposed. The concavity and convexity of the proposed entropy functions are examined by use of Taylor expansion with first-order derivative. The entropy functions can catch the rare events in an image. It can be observed that rare events or minor changes in regular pattern of an image can be detected efficiently for different values of [Formula: see text] when compared with the proposed entropies based on [Formula: see text]-sense.

Generalized Lindley Family with application on Wind Speed Data

In this study we introduce a new extended class of continuous distributions named generalized Lindley family of distributions. Some properties of the new generator, including ordinary moments, quantile, generating and entropy functions, which hold for any baseline model, are presented. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new family of distributions is shown via an application on the wind speed data set. The results shows that the proposed family is better than well-known distributions including log-logistic, Burr, Dagum, Frechet, Pearson, Dagum, Lindley, Weibull and exponential distributions.

Different Faces of Generalized Holographic Dark Energy

In the formalism of generalized holographic dark energy (HDE), the holographic cut-off is generalized to depend upon LIR=LIRLp,L˙p,L¨p,⋯,Lf,L˙f,⋯,a with Lp and Lf being the particle horizon and the future horizon, respectively (moreover, a is the scale factor of the Universe). Based on such formalism, in the present paper, we show that a wide class of dark energy (DE) models can be regarded as different candidates for the generalized HDE family, with respective cut-offs. This can be thought as a symmetry between the generalized HDE and different DE models. In this regard, we considered several entropic dark energy models—such as the Tsallis entropic DE, the Rényi entropic DE, and the Sharma–Mittal entropic DE—and found that they are indeed equivalent with the generalized HDE. Such equivalence between the entropic DE and the generalized HDE is extended to the scenario where the respective exponents of the entropy functions are allowed to vary with the expansion of the Universe. Besides the entropic DE models, the correspondence with the generalized HDE was also established for the quintessence and for the Ricci DE model. In all the above cases, the effective equation of state (EoS) parameter corresponding to the holographic energy density was determined, by which the equivalence of various DE models with the respective generalized HDE models was further confirmed. The equivalent holographic cut-offs were determined by two ways: (1) in terms of the particle horizon and its derivatives, (2) in terms of the future horizon horizon and its derivatives.