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Abstract: The compressible Murnaghan’s materials composed in the hyperelastic rod describing the far-field equation as the KdV equation for the weak nonliear waves traversing inside the rod is studied with the F expansion method and solved to get the exact elliptic function solutions. The necessary condition for the each Jacobi solutions are reported. The 2D and 3D graphicals are simulated for certain periodic waves. The necessary condition of selection of material and geometric constants for distraction free wave travelling are suggested. PubDate: 2023-01-14
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Abstract: This paper aims to explore the transmission dynamics of COVID-19 with dengue co-infection using mathematical modeling. In this study, SIR model is developed that explains the trajectory of the epidemic to boost a plan for an effective control strategy for COVID-19 in Bangladesh. The model is extended to optimal control strategies. Pontryagin’s Principle is used to establish the appropriate conditions for the existence of optimal control and the optimality system for the co-infection model. Coinfected cases were reduced with control greater than without control. Using Omicron incidence cases from 1st January – 13th April 2022, the maximum likelihood estimate of R0 with a 95% confidence interval is1.89 [ 95% CI: 1.88, 1.91]. The R0 estimated from the exponential growth method is 2.08 [95% CI: 2.07,2.09]and time-dependent estimate is 2.10[95% CI: 1.72,2.58]. The generalized logistic growth model predicted 19, 52,131 cumulative cases on day 103 (April 13, 2022), and a relatively flat curve of cumulative growth of COVID-19 cases implies a declining trend of new cases. The study also found from sensitivity analysis that, R0 is proportional to the mean generation time. This paper attempted to focus on suppressing the COVID-19 co-infections by preventing dengue and COVID-19. The results of the study show that by implementing optimal control spread of dengue and COVID-19 could be minimized. The logistic growth model suggests that the infection rate of COVID-19 is decreasing. PubDate: 2023-01-14
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Abstract: Early detection of cancer tumors significantly increases the chances of recovery and usually results in improved quality of life and patient lifespan. In this context, computer systems can help and accelerate health care decision making regarding brain diagnoses, based, for example, on machine learning (ML) algorithms applied to neurological magnetic resonance images (MRIs). In the last decade, several ML approaches have been tested for this purpose, with varied levels of accuracy, precision, and sensitivity. It is already clear that this performance depends on the type of tumor, the quality of the image, the number of training images, and, in the case of supervised training, the quality of previously diagnosed images used for training. An important question remains regarding how the performance of these diagnostic tools is affected by image quality, as it is influenced by several factors common to MRIs, such as artifact like ringing effects, Gaussian noise, reconstruction artifacts associated with lower numbers of measurements, movement artifacts, and so forth. In this paper, we conduct a systematic analysis of this relationship, based on a state-of-art ML diagnosis system, but under different levels of image degradation. Our experiments suggest that severe degradations, leading to reduced mean squared error (MSE) values, can systematically reduce the values of all performance evaluated metrics, but whether such reduction occurs for a specified MSE depends on the type of effect. In addition, for all artifacts tested, we evaluated the range of MSE for which the performance reduction is below a specified threshold. These results can be used in the future to indicate the level of confidence in a certain automatic diagnostic result for different image qualities. PubDate: 2023-01-13
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: We investigate the parameter structure of artificial neural networks with ReLU activation functions by methods of tropical geometry. The main result is a fundamentally new formulation of the problem to detect the onset of neutral network overtraining by using only tropical parameter structures on the training sample. A hypothesis is proposed that detects overtraining from geometrical characteristics; its applicability on prototype datasets is demonstrated. We also investigate on prototype data the dependence of the data structures on starting initialization. The results make it possible to analyze also more complex effects observed in artificial neural network training from the point of view of theoretical parameter structure. PubDate: 2023-01-12
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Abstract: We consider the automatic hardness determination of a chest X-ray image and the effect of pre-filtering of the training and validation samples on the performance of the classification algorithm of tuberculosis diagnosis from chest X-rays. Convolutional neural networks are used in automatic hardness determination and tuberculosis diagnosis. The results of the present study are compared with those from different datasets, including datasets pruned by image hardness criteria. PubDate: 2023-01-12
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Abstract: A new method if proposed for content-based image retrieval in whole-slide histological images. Given a fragment isolated on the query image, the method finds structurally similar fragments in a large set of images. Such methods are needed in medicine and may help diagnosticians in medical image analysis. The application of such methods to whole-slide histological images has its specifics due to the extremely high resolution of the images and their multiscale structure. These features have been taken into consideration during the development of the method. PubDate: 2023-01-12
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Abstract: We use the continuous model to study the formation of a portfolio of securities with prices described by Ornstein–Uhlenbeck processes. A zero-sum game is solved in which the investor chooses a vector of portfolio weights with the objective of maximizing the quantile estimator of the portfolio value, while Nature strives to minimize the value by choosing the time. A method is proposed for the construction of the saddle point in this game. PubDate: 2023-01-11
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Abstract: We consider a mathematical model for electrodynamic analysis of antennas. The problem is reduced to solving an integral equation over an antenna section. The dependence of the main lobe and the first lobe of the directional pattern on the body shape is investigated. Comparison with experimental results is carried out. PubDate: 2023-01-11
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Abstract: We show that the equations of mathematical physics that describe real processes and include the equations of the conservation laws for energy, momentum, moment of momentum, and mass have a peculiar feature. The conservation law equations turn out to be inconsistent. This produces the integrability of the mathematical physics equations and the specific features of their solutions, namely the presence of double solutions: on a nonintegrable coordinate space and on integrable structures. As a consequence, we can describe evolutionary processes, such as the emergence of discrete structures and observable formations (waves, vortices, turbulent pulsations). Since double solutions are defined on different spatial objects, they can be obtained only in two coordinate systems and using simultaneously two methods of equation solving: numerical and analytical. Appropriate results have been derived in the framework of skew-symmetric forms. PubDate: 2023-01-11
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Abstract: A numerical algorithm is developed for the diffraction of an electromagnetic wave on an infinite dielectric cylinder of arbitrary cross section immersed in a free space. The boundary-value problem for the Maxwell equations in a nonhomogeneous space is reduced to solving a system of singular integral equations by the approximation and collocation method. The matrix elements are evaluated by a special numerical algorithm. The evaluation of the singular integrals is reduced to the evaluation of integrals with a logarithmic singularity. PubDate: 2023-01-11
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Abstract: We consider the transfer to a given orbit of a controlled spacecraft whose dynamics is described by the mathematical model of motion in a gravitational field with one attractive center. We propose a class of engine-thrust positional controls dependent on the problem parameters that solve the controllability problem for a given target orbit. The trajectory of motion of a phase point under such control is determined on an infinite time axis. On the initial time interval, the trajectory reaches a neighborhood of the target set, and thereafter it moves in this neighborhood asymptotically approaching the target. The positional control is derived in analytical form. Calculation results are reported for the positional control and the trajectories of motion using different test parameters and different types of spacecraft target trajectories. PubDate: 2022-08-06 DOI: 10.1007/s10598-022-09555-0
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Abstract: We consider the synthesis of three and four abstract polymer chains classified into two sexes, where the synthesis quality is determined by the pairing of different-sex chains. The use of some types of entangled biphotons in one-sided control produces a difference in the degree of superimposition between good and bad pairs that is unattainable with classical control. This example demonstrates the quantum superiority in distributed computations following from the violation of Bell’s inequality. This may be relevant for elucidating quantum mechanisms in the synthesis of real biopolymers with various properties. PubDate: 2022-08-06 DOI: 10.1007/s10598-022-09553-2
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Abstract: In this paper, we are concerned with a nonmatching grid mixed finite-elements–finite-differences approximation (FEM-FD) method of overlapping nonlinear multiplicative Schwarz iterations for nonlinear elliptic PDEs. By means of a geometric convergence result in L∞ for the nonlinear Schwarz iterations and a Lipschitz property with respect to the data of both the FEM and FD solutions of the corresponding linear PDE problems, we derive an L∞ error estimate on each subdomain between the discrete nth Schwarz iterate and the true solution of the nonlinear PDE. PubDate: 2022-08-06 DOI: 10.1007/s10598-022-09558-x
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Abstract: We consider the inverse problem of simultaneous determination of two coefficients in a model of small transverse oscillations in a homogeneous semi-bounded rod with an elastic force applied to one end. The oscillations are modeled by a nonhomogeneous equation of a hyperbolic type on a half-line. A boundary condition of the third kind is specified at the end of the rod. Supplementary information for the solution of the inverse problem includes given values of the forward solution at a fixed point of the rod. The inverse problem requires the reconstruction of a function in the boundary condition and a functional multiplier in the nonhomogeneity term on a part of the multiplier’s definition domain. We establish the solvability conditions of the inverse problem, some properties of its solution, and propose an algorithm for numerical approximation of the solution. PubDate: 2022-08-06 DOI: 10.1007/s10598-022-09552-3
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Abstract: A wireless sensor network (WSN) is an important modern technology supporting the internet of things. These networks are created as needed. There is no leading protocol, and many competing protocols exist. When a new protocol is developed, it must be tested on hardware. However, a simpler approach is to debug the protocol logic on a PC, not directly on hardware. Yet existing simulators do not allow easy transfer of the simulation code to WSN nodes. The present article describes a simulator that allows easy code transfer from PC to Arduino. PubDate: 2022-08-05 DOI: 10.1007/s10598-022-09557-y
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Abstract: We investigate the inverse problem for the heat equation with an unknown source represented as the sum of several spatially localized sources with unknown time-dependent intensities. Supplementary information required for the determination of the unknown intensities includes the temperatures at some points as a function of time. Unique solvability of the inverse problem is proved. A numerical method for its solution is proposed. Results of computational experiments are reported demonstrating the efficiency of the proposed numerical method. PubDate: 2022-08-05 DOI: 10.1007/s10598-022-09551-4
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Abstract: We consider the application of neural-network approaches to time-series analysis for the investigation of modern production processes. As an application of the proposed techniques, we study the optimization problem for a fixed set of process outputs. We examine and experimentally evaluate the most appropriate algorithms for industrial process modeling. Methods are proposed for choosing the algorithm architecture and parameters. An optimization method is advanced that allows for the technological constraints in the objective functions. PubDate: 2022-08-05 DOI: 10.1007/s10598-022-09556-z
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Abstract: The discrete sources method is used in the framework of the generalized nonlocal optical response theory (GNOR) to construct a mathematical model of a layered magnetite-Au nanoparticle allowing for the spatial dispersion in the gold shell. We analyze the additional boundary conditions on the magnetite-Au interface that ensure unique solvability of the boundary-value diffraction problem. We investigate the effect of spatial dispersion on the field enhancement factor at the exterior boundary of the layered particle, allowing also for possible asymmetry in the position of the core relative to the shell. PubDate: 2022-08-05 DOI: 10.1007/s10598-022-09554-1
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Abstract: We consider a mathematical model of the deionization of aqueous solutions described by a mixed initial–boundary-value problem for a partial-differential system. Uniqueness of the solution if proved. The inverse problem is posed for the ion absorption kinetics given the integral ion concentration observed at the output. Unique solvability of the inverse problem is proved. A numerical method is proposed for the inverse problem. Results of computational experiments demonstrate the efficiency of the proposed numerical method. PubDate: 2022-05-05 DOI: 10.1007/s10598-022-09541-6
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