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Vascular-related diseases pose significant public health challenges and are a leading cause of mortality and disability. Understanding the complex structure of the vascular system and its processes is crucial for addressing these issues. Recent advancements in medical imaging technology have enabled the generation of high-resolution 3D images of vascular structures, leading to a diverse array of methods for vascular extraction. While previous research has often assumed a normal distribution of image data, this paper introduces a novel vessel extraction method that utilizes the skew normal distribution for more accurate probability distribution modeling. The proposed method begins with a preprocessing step to enhance vessel structures and reduce noise in Magnetic Resonance Angiography (MRA) images. The skew normal distribution, known for its ability to model skewed data, is then employed to characterize the intensity distribution of vessels. By estimating the parameters of the skew normal distribution using the Expectation-Maximization (EM) algorithm, the method effectively separates vessel pixels from the background and non-vessel regions. To extract vessels, a thresholding technique is applied based on the estimated skew normal distribution parameters. This segmentation process enables accurate vessel extraction, particularly in detecting thin vessels and enhancing the delineation of vascular edges with low contrast. Experimental evaluations on a diverse set of MRA images demonstrate the superior performance of the proposed method compared to previous approaches in terms of accuracy and computational efficiency. The presented vessel extraction method holds promise for improving the diagnosis and treatment of vascular-related diseases. By leveraging the skew normal distribution, it provides accurate and efficient vessel segmentation, contributing to the advancement of vascular imaging in the field of medical image analysis. [ABSTRACT FROM AUTHOR]

In this paper, the time-varying system control is resolved with the aid of forward Riccati formulation and hybrid functions. The applied Riccati equations need neither advanced knowledge of the system dynamics nor the assumption of the future information of system matrices. Herein, the state space equation of LTV system is rewritten in the Hybrid functions (HF) domain where results a set of linear discrete equations instead of having a complex Forward-in-time Propagating Riccati Equation (FPRE). The HF evolve from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) that can estimate any functions based on the summation of two series. The feasibility of the proposed method is investigated by various numerical control cases. Numerical results demonstrated that the proposed method is usable in both periodic and non-periodic systems with less control effort and significant damping time. [ABSTRACT FROM AUTHOR]

In this work, we design, analyze, and test the multiwavelets Galerkin method to solve the two‐dimensional Burgers equation. Using Crank–Nicolson scheme, time is discretized and a PDE is obtained for each time step. We use the multiwavelets Galerkin method for solving these PDEs. Multiwavelets Galerkin method reduces these PDEs to sparse systems of algebraic equations. The cost of this method is proportional to the number of nonzero coefficients at each time step. The results illustrate, by selecting the appropriate threshold while the number of nonzero coefficients reduces, the error will not be less than a certain amount. The L2 stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The paper reports a spectral method for generating an approximate solution for the space-time fractional PDEs with variable coefficients based on the spectral shifted Jacobi collocation method in conjunction with the shifted Jacobi operational matrix of fractional derivatives. The spectral collocation method investigates both temporal and spatial discretizations. By applying the shifted Jacobi collocation method, the problem reduces to a system of algebraic equations, which greatly simplifies the problem. Numerical results are given to establish the validity and accuracy of the presented procedure for space-time fractional PDE. [ABSTRACT FROM AUTHOR]

An efficient algorithm based on the wavelet collocation method is introduced in order to solve nonlinear fractional optimal control problems (FOCPs) with inequality constraints. By using the interpolation properties of Hermite cubic spline functions, we construct an operational matrix of the Caputo fractional derivative for the first time. Using this matrix, we reduce the nonlinear fractional optimal control problem to a nonlinear programming problem that can be solved with some suitable optimization algorithms. Illustrative examples are examined to demonstrate the important features of the new method. [ABSTRACT FROM AUTHOR]

In this work, we established some exact solutions for the (1 + 1)-dimensional and (2 + 1)-dimensional fifth-order integrable equations ((1 + 1)D and (2 + 1)D FOIEs) which is considered based on the improved tanh(ϕ(ξ)/2)- expansion method (IThEM), by utilizing Maple software. We obtained new periodic solitary wave solutions. The obtained solutions include soliton, periodic, kink, kink-singular wave solutions. Comparing our new results with Wazwaz results, namely, the Hereman-Nuseri method shows that our results give further solutions. Many other such types of nonlinear equations arise in fluid dynamics, plasma physics, and nonlinear physics. [ABSTRACT FROM AUTHOR]

This paper aims to compute solitary wave solutions and soliton wave solutions based on the ansatz methods to the perturbed nonlinear Schrödinger equation (NLSE) arising in nano-fibers. The improved tan (/ 2) -expansion method and the rational extended sinh–Gordon equation expansion method are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accuracy interpretation of the propagation of solitons. We held a comparison between our results and those are in the previous work. The outcome indicates that perturbed NLSE arising nano-fibers is used in optical problems. Finally, via symbolic computation, their dynamic structure and physical properties were vividly shown by three-dimensional, density, and t -curves plots. These solutions have greatly enriched the exact solutions of (2+1)-dimensional perturbed nonlinear Schrödinger equation in the existing literatures. [ABSTRACT FROM AUTHOR]

In this article, a class of fractional optimal control problems (FOCPs) are solved using a direct method. We present a new operational matrix of the fractional derivative in the sense of Caputo based on the B-spline functions. Then we reduce the solution of fractional optimal control problem to a nonlinear programming (NLP) one, where some existing well-developed algorithms may be applied. Numerical results demonstrate the efficiency of the presented technique. [ABSTRACT FROM AUTHOR]

In this paper, a novel image enhancement model based on shock filter for image deblurring is proposed in three cases. For the weight of shock filter, the fractional‐order derivative of initial blurry image is used. This fractional‐order weight can be adjusted adaptively according to the gradient of blurred image. Compared with the traditional integer‐order shock filter, the proposed model creates less staircase effect, whereas the enhancement and deblurring of the resulted images are efficiently good. Stability properties of the proposed method are studied theoretically, and also to show the validity of stability studies results, some numerical experiments are presented. The three cases of proposed method are compared with together and with other methods. Different test images are used to show the validity of these cases. Numerical experiments confirm the efficiency of these cases. [ABSTRACT FROM AUTHOR]

The Hirota bilinear method is prepared for searching the diverse soliton solutions for the fractional generalized Calogero‐Bogoyavlenskii‐Schiff‐Bogoyavlensky‐Konopelchenko (CBS‐BK) equation. Also, the Hirota bilinear method is used to finding the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and multi‐kink soliton solutions will be investigated. Also, the solitary wave, periodic wave, and cross‐kink wave solutions will be examined for the fractional gCBS‐BK equation. The graphs for various fractional order α are plotted to contain 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types solutions, by solving the under‐determined nonlinear system of algebraic equations for the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed. The existence conditions are employed to discuss the available got solutions. [ABSTRACT FROM AUTHOR]

The vessel extraction is very important for the vascular disease diagnosis and grading of the stenoses and aneurysms in vessels. This aids in brain surgery and making angioplasty. The presence of noise in the MRA image, etc., turns the vessel extraction into a difficult problem. In this paper, we derive a vessel extraction algorithm based on TFA and EMS algorithms. We prove the convergence of the proposed method within a few iterations. Results of applying the presented method on real 2D MRA images demonstrate that our method is very efficient. [ABSTRACT FROM AUTHOR]

In this paper, we solve a class of fractional optimal control problems in the sense of Caputo derivative using Genocchi polynomials. At first we present some properties of these polynomials and we make the Genocchi operational matrix for Caputo fractional derivatives. Then using them, we solve the problem by converting it to a system of algebraic equations. Some examples are presented to show the effciency and accuracy of the method. [ABSTRACT FROM AUTHOR]

Summary: This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann‐Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well‐developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results. [ABSTRACT FROM AUTHOR]