Choice of Metric Divergence in Genome Sequence Comparison.

The paper introduces a novel probability descriptor for genome sequence comparison, employing a generalized form of Jensen-Shannon divergence. This divergence metric stems from a one-parameter family, comprising fractions up to a maximum value of half. Utilizing this metric as a distance measure, a distance matrix is computed for the new probability descriptor, shaping Phylogenetic trees via the neighbor-joining method. Initial exploration involves setting the parameter at half for various species. Assessing the impact of parameter variation, trees drawn at different parameter values (half, one-fourth, one-eighth). However, measurement scales decrease with parameter value increments, with higher similarity accuracy corresponding to lower scale values. Ultimately, the highest accuracy aligns with the maximum parameter value of half. Comparative analyses against previous methods, evaluating via Symmetric Distance (SD) values and rationalized perception, consistently favor the present approach's results. Notably, outcomes at the maximum parameter value exhibit the most accuracy, validating the method's efficacy against earlier approaches.

Impact of general incidence function on three-strain SEIAR model.

We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and recovered compartments. The model is well-posed and verified through existence, positivity and boundedness. Eight equilibria comprise a disease-free equilibria and seven endemic equilibrium points following the existence of three strains. The basic reproduction numbers $ \mathfrak{R}_{01} $, $ \mathfrak{R}_{02} $ and $ \mathfrak{R}_{03} $ represent the dominance of strain 1, strain 2 and strain 3 in the environment for new strain emergence. The model establishes local stability at a disease-free equilibrium point. Numerical simulations endorse the impact of general incidence rates, including bi-linear, saturated, Beddington DeAngelis, non-monotone and Crowley Martin incidence rates.

Protein sequence comparison based on representation on a finite dimensional unit hypercube.

Numerous techniques are used to compare protein sequences based on the values of the physiochemical properties of amino acids. In this work, a single physical/chemical property value based non-binary representation of protein sequences is obtained on a 20 × 20-dimensional unit hypercube. The represented vector expressed in the matrix form is taken as the descriptor. The generalized NTV metric, which is an extension of the NTV metric used for polynucleotide space is taken as a distance measure. Based on this distance measure, a distance matrix is obtained for protein sequence comparison. Using this distance matrix, phylogenetic trees are drawn by using Molecular Evolutionary Genetics Analysis 11 (MEGA11) software applying the neighbor-joining method. Data sets used in this current work are 9-ND4, 9-ND5, 9-ND6, 24 TF-LF proteins, 27 different viruses and 127 proteins from the protein kinase C (PKC) family. Two sets of phylogenetic trees are obtained - one based on property value of polarity and the other based on property value of molecular weight. They are found to be exactly the same. Similar results also hold for other single property value based representation. The present trees are individually tested for efficiency based on the criterion of rationalized perception and computational time. The results of the present method are compared with those obtained earlier by other methods on the same protein sequences using assessment criteria of Symmetric distance (SD), Correlation coefficient, and Rationalized perception. In all the cases, the present results are found to be better than the results of other methods under comparison.Communicated by Ramaswamy H. Sarma.

Under nonlinear prey-harvesting, effect of strong Allee effect on the dynamics of a modified Leslie-Gower predator-prey model.

In the present study, the effects of the strong Allee effect on the dynamics of the modified Leslie-Gower predator-prey model, in the presence of nonlinear prey-harvesting, have been investigated. In our findings, it is seen that the behaviors of the described mathematical model are positive and bounded for all future times. The conditions for the local stability and existence for various distinct equilibrium points have been determined. The present research concludes that system dynamics are vulnerable to initial conditions. In addition, the presence of several types of bifurcations (e.g., saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation, homoclinic bifurcation) has been investigated. The first Lyapunov coefficient has been evaluated to study the stability of the limit cycle that results from Hopf bifurcation. The presence of a homoclinic loop has been demonstrated by numerical simulation. Finally, possible phase drawings and parametric figures have been depicted to validate the outcomes.

Multi-Fractal Weibull Adaptive Model for the Remaining Useful Life Prediction of Electric Vehicle Lithium Batteries.

In this paper, an adaptive remaining useful life prediction model is proposed for electric vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the multi-fractal Weibull motion. The varying degree of long-range dependence and the 1/f characteristics in the frequency domain are also analyzed. The age and state-dependent degradation model is derived, with the associated adaptive drift and diffusion coefficients. The adaptive mechanism considers the quantitative relations between the drift and diffusion coefficients. The unit-to-unit variability is considered a random variable. To facilitate the application, the convergence of the RUL prediction model is proved. Replacement of the lithium battery in the electric car is recommended according to the remaining useful life prediction results. The effectiveness of the proposed model is shown in the case study.

A New X-ray Medical-Image-Enhancement Method Based on Multiscale Shannon-Cosine Wavelet.

Because of noise interference, improper exposure, and the over thickness of human tissues, the detailed information of DR (digital radiography) images can be masked, including unclear edges and reduced contrast. An image-enhancement algorithm based on wavelet multiscale decomposition is proposed to address the shortcomings of existing single-scale image-enhancement algorithms. The proposed algorithm is based on Shannon-Cosine wavelets by taking advantage of the interpolation, smoothness, tight support, and normalization properties. Next a multiscale interpolation wavelet operator is constructed to divide the image into several sub-images from high frequency to low frequency, and to perform different multi-scale wavelet transforms on the detailed image of each channel. So that the most subtle and diagnostically useful information in the image can be effectively enhanced. Moreover, the image will not be over-enhanced and combined with the high contrast sensitivity of the human eye's visual system in smooth regions, different attenuation coefficients are used for different regions to achieve the purpose of suppressing noise while enhancing details. The results obtained by some simulations show that this method can effectively eliminate the noise in the DR image, and the enhanced DR image detail information is clearer than before while having high effectiveness and robustness.

Clifford Wavelet Entropy for Fetal ECG Extraction.

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73-97, and Arfaoui, et al.Acta Appl. Math.2020, 170, 1-35.. Additionally, classical Haar-Faber-Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se=100%, PPV=100% for FECG extraction and peak detection.

The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation.

The well-known novel virus (COVID-19) is a new strain of coronavirus family, declared by the World Health Organization (WHO) as a dangerous epidemic. More than 3.5 million positive cases and 250 thousand deaths (up to May 5, 2020) caused by COVID-19 and has affected more than 280 countries over the world. Therefore studying the prediction of this virus spreading in further attracts a major public attention. In the Arab Emirates (UAE), up to the same date, there are 14,730 positive cases and 137 deaths according to national authorities. In this work, we study a dynamical model based on the fractional derivatives of nonlinear equations that describe the outbreak of COVID-19 according to the available infection data announced and approved by the national committee in the press. We simulate the available total cases reported based on Riesz wavelets generated by some refinable functions, namely the smoothed pseudosplines of types I and II with high vanishing moments. Based on these data, we also consider the formulation of the pandemic model using the Caputo fractional derivative. Then we numerically solve the nonlinear system that describes the dynamics of COVID-19 with given resources based on the collocation Riesz wavelet system constructed. We present graphical illustrations of the numerical solutions with parameters of the model handled under different situations. We anticipate that these results will contribute to the ongoing research to reduce the spreading of the virus and infection cases.

An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations.

This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions; taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a collocation discretization technique. We present many important examples of FVIEs for which accurate and efficient numerical solutions have been accomplished and the numerical results converge very rapidly to the exact ones.

WITHDRAWN: Bearing fault diagnosis using sparse Daubechies-wavelet impulse isolation and horizontal-vertical synchrosqueezing transform approach.

This article has been withdrawn at the request of the author(s). The authors apologize for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at https://www.elsevier.com/about/our-business/policies/article-withdrawal.

The Differential Diagnosis of Multiple Sclerosis Using Convex Combination of Infinite Kernels.

Our purpose is to develop a clinical decision support system to classify the patients' diagnostics based on features gathered from Magnetic Resonance Imaging (MRI) and Expanded Disability Status Scale (EDSS). We studied 120 patients and 19 healthy individuals (not afflicted with MS) have been studied for this study. Healthy individuals in the control group do not have any complaint or drug use history. For the kernel trick, efficient performance in non-linear classification, the Convex Combination of Infinite Kernels model was developed to measure the health status of patients based on features gathered from MRI and EDSS. Our calculations show that our proposed model classifies the multiple sclerosis (MS) diagnosis level with better accuracy than single kernel, artificial neural network and other machine learning methods, and it can also be used as a decision support system for identifying MS health status of patients.

Detection of Dendritic Spines Using Wavelet Packet Entropy and Fuzzy Support Vector Machine.

The morphology of dendritic spines is highly correlated with the neuron function. Therefore, it is of positive influence for the research of the dendritic spines. However, it is tried to manually label the spine types for statistical analysis. In this work, we proposed an approach based on the combination of wavelet contour analysis for the backbone detection, wavelet packet entropy, and fuzzy support vector machine for the spine classification. The experiments show that this approach is promising. The average detection accuracy of "MushRoom" achieves 97.3%, "Stubby" achieves 94.6%, and "Thin" achieves 97.2%.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

Dimensionality reduction by supervised neighbor embedding using laplacian search.

Dimensionality reduction is an important issue for numerous applications including biomedical images analysis and living system analysis. Neighbor embedding, those representing the global and local structure as well as dealing with multiple manifolds, such as the elastic embedding techniques, can go beyond traditional dimensionality reduction methods and find better optima. Nevertheless, existing neighbor embedding algorithms can not be directly applied in classification as suffering from several problems: (1) high computational complexity, (2) nonparametric mappings, and (3) lack of class labels information. We propose a supervised neighbor embedding called discriminative elastic embedding (DEE) which integrates linear projection matrix and class labels into the final objective function. In addition, we present the Laplacian search direction for fast convergence. DEE is evaluated in three aspects: embedding visualization, training efficiency, and classification performance. Experimental results on several benchmark databases present that the proposed DEE exhibits a supervised dimensionality reduction approach which not only has strong pattern revealing capability, but also brings computational advantages over standard gradient based methods.

Fractal analysis of elastographic images for automatic detection of diffuse diseases of salivary glands: preliminary results.

The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD). It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of "real-time" elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology.

On the fractal geometry of DNA by the binary image analysis.

The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.

A rate-distortion-based merging algorithm for compressed image segmentation.

Original images are often compressed for the communication applications. In order to avoid the burden of decompressing computations, it is thus desirable to segment images in the compressed domain directly. This paper presents a simple rate-distortion-based scheme to segment images in the JPEG2000 domain. It is based on a binary arithmetic code table used in the JPEG2000 standard, which is available at both encoder and decoder; thus, there is no need to transmit the segmentation result. Experimental results on the Berkeley image database show that the proposed algorithm is preferable in terms of the running time and the quantitative measures: probabilistic Rand index (PRI) and boundary displacement error (BDE).