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Статті в журналах з теми "Mathematical and computational ophthalmology"

Автор: Grafiati

Опубліковано: 8 березня 2025

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1

Roberts, Paul A., Eamonn A. Gaffney, Philip J. Luthert, Alexander J. E. Foss, and Helen M. Byrne. "Mathematical and computational models of the retina in health, development and disease." Progress in Retinal and Eye Research 53 (July 2016): 48–69. http://dx.doi.org/10.1016/j.preteyeres.2016.04.001.

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2

ELSAYED, ASSMA F., and O. ANWAR BÉG. "NEW COMPUTATIONAL APPROACHES FOR BIOPHYSICAL HEAT TRANSFER IN TISSUE UNDER ULTRASONIC WAVES: THE VARIATIONAL ITERATION AND CHEBYSCHEV SPECTRAL SIMULATIONS." Journal of Mechanics in Medicine and Biology 14, no. 03 (March 13, 2014): 1450043. http://dx.doi.org/10.1142/s0219519414500432.

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A mathematical and numerical study is presented for simulating temperature distribution in a two-dimensional tissue medium using Pennes bioheat transfer equation, when the tissue is subjected to ultrasonic waves. Following nondimensionalization of the governing partial differential equation, a novel variational iteration method (VIM) solution is developed. This excellent technique introduced by He [Variational iteration method — a kind of non-linear analytical technique: Some examples, Int J Non-Linear Mech.34:699–708, 1999] employs Lagrange multipliers which can be identified optimally via variational theory. The space and time distributions of temperature are studied and solutions visualized via Mathematica. The influence of thermal conductivity and relaxation time are also examined. Excellent stability and convergence characteristics of VIM are demonstrated. Validation is achieved with a Chebyschev spectral collocation method (CSCM). The present work demonstrates the excellent potential of this powerful semi-numerical method in nonlinear biological heat transfer and furthermore provides an alternative strategy to conventional finite element and finite difference computational simulations. The model finds applications in minimally-invasive spinal laser treatments, glaucoma therapy in ophthalmology and thermoradiotherapy for malignant tumors.

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3

Wang, Xiaoliang, and Xiaogang Wang. "Simulation of fluid dynamics and turbulence during phacoemulsification using the new propeller turbo tip." BMJ Open Ophthalmology 8, no. 1 (September 2023): e001391. http://dx.doi.org/10.1136/bmjophth-2023-001391.

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PurposeTo investigate the fluid dynamics and turbulence in the anterior chamber during phacoemulsification with a new propeller turbo tip using computational fluid dynamics methods.MethodsA theoretical study, three-dimensional model with the corresponding mathematical equations for the propeller turbo phaco tip, anterior chamber and lens capsular bag was developed. A simulation was performed for the new propeller turbo tip with various parameter settings (vacuum, irrigation bottle height and phaco power). Fluid dynamics and turbulence in the anterior chamber, lens capsular bag and phaco tip were evaluated. The linear relationship between the different setting parameters and a stable anterior chamber pressure was assessed.ResultsThe fluid dynamic turbulence was mainly symmetrically distributed in the anterior chamber. Propeller turbo phaco tip vibration caused increased fluid velocity and asymmetrical fluid turbulence in the metal lumen but had little influence on dynamic intraocular pressure. Reasonable phaco machine parameter settings can maintain a stable intraocular pressure during phacoemulsification.ConclusionsEvaluation of phacoemulsification fluid dynamics using computational simulation methods could provide detailed information about the influence of the propeller on dynamic intraocular pressure during phacoemulsification, which is useful for a better understanding of this procedure.

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4

CAVAS MARTINEZ, FRANCISCO, FRANCISCO LUIS SAEZ GUTIERREZ, JOSÉ SEBASTIÁN VELÁZQUEZ BLÁZQUEZ, JORGE LUCIANO ALIO, and JORGE ALIO DEL BARRIO. "RECONSTRUCTION OF THE CORNEAL SURFACE OF THE HUMAN EYE USING A COMPUTATIONAL EVOLUTIONARY ALGORITHM. PRACTICAL APPLICATION IN NON-PATHOLOGICAL CASES." DYNA 99, no. 1 (January 1, 2024): 85–92. http://dx.doi.org/10.6036/10998.

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Increasingly, the use of geometric modelling techniques in Applied Ophthalmology is significant in the characterization of important pathologies of the cornea, such as Keratoconus. This article presents a novel method for the geometric reconstruction of the corneal surface from optical topography using a genetic algorithm. Traditionally, mathematical programming methods such as the least squares method have been used to obtain the coefficients of the corneal surface function, such as Navarro model or Zernike polynomials. This new method uses non-dominated multivariable genetic algorithm optimization to obtain the surface function coefficients from the point cloud obtained with corneal topographer device. Once the reconstruction is performed, the surface is represented using CAD software, and morphogeometric parameters are obtained. The experimental sample consisted in 33 healthy patients eyes, aged from 11 to 63, and without previous ocular surgeries or pathologies. Topographic data were obtained using a Scheimpflug Sirius tomographer (CSO, Italy). The computational optimization was executed under Matlab software environment (Mathworks, USA). The new method provides a lower mean squared error (MSE) than those obtained by the least squares or the nonlinear programming algorithms. Thus, the morphogeometric parameters obtained from the patient's corneas fit better, allowing for a better analysis of real clinical conditions.

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5

Et. al., Aditya Singh,. "Development of GUI for Detetection of Eye Disorders in Infants." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 11 (May 10, 2021): 1980–85. http://dx.doi.org/10.17762/turcomat.v12i11.6154.

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Strabismus is one of the most common vision diseases in which the eyes do not properly align with each other when looking at an object. The condition may be present occasionally or constantly and if it is present during a large part of childhood, it may result in amblyopia or loss of depth perception. In contrast to manual diagnosis, automatic recognition can significantly reduce labor cost and increase diagnosis efficiency. In this paper, we propose to detect ICD-10-CM Code H50.9 unspecified strabismus using CNN and Image Processing techniques. There are four types of strabismus namely exotropia, esotropia, hypertropia and hypotropia which we aim to detect. We furthermore aim to introduce a GUI particularly into pediatric ophthalmology where obtaining relevant diagnostic information is taxing.

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6

Erkelens, Casper J. "Geometric Constraints of Visual Space." i-Perception 12, no. 6 (November 2021): 204166952110552. http://dx.doi.org/10.1177/20416695211055212.

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Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to straight lines in visual space. A second requirement is that parallel lines oriented in depth in physical space, converge to a finite vanishing point in visual space. A rational function for perceived distance, compatible with the perspective-space model of visual space, satisfies the requirements. The function is unique. Analysis of alternative functions shows there is little tolerance for deviations. Conservation of the straightness of lines constrains visual space to having a single geometry. Visual space is described by an analytical function having one free parameter, that is, the distance of the vanishing point.

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7

Fan, Wenjuan, Yi Wang, Tongzhu Liu, and Guixian Tong. "A patient flow scheduling problem in ophthalmology clinic solved by the hybrid EDA–VNS algorithm." Journal of Combinatorial Optimization 39, no. 2 (December 7, 2019): 547–80. http://dx.doi.org/10.1007/s10878-019-00497-9.

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8

Nandhagopal, N., S. Navaneethan, V. Nivedita, A. Parimala, and Dinesh Valluru. "Human Eye Pupil Detection System for Different IRIS Database Images." Journal of Computational and Theoretical Nanoscience 18, no. 4 (April 1, 2021): 1239–42. http://dx.doi.org/10.1166/jctn.2021.9390.

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The pupil detection system plays a vital role in ophthalmology diagnosis equipments because pupil has a center place of human eye to locate the exact position. To identify the exact human eye pupil region in near infrared (NIR) images, this work proposes the Center of gravity method and its real time FPGA hardware implementation. The proposed work involves global threshold method to segment the pupil region from human eye and the bright spot suppression process removes the light reflections on the pupil due to the IR (Infra red) rays then the morphology dilation process removes unnecessary black pixels other than pupil region on the image. Finally, center of gravity (COG) method provides the exact pupil center coordinate and radius of the human eye. CASIA IRIS V4 and UBIRIS iris database images used in this work and achieved 90-95% of recognition rate.

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9

Friedmann, Elfriede, Simon Dörsam, and Gerd U. Auffarth. "Models and Algorithms for the Refinement of Therapeutic Approaches for Retinal Diseases." Diagnostics 13, no. 5 (March 3, 2023): 975. http://dx.doi.org/10.3390/diagnostics13050975.

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We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatment for age-related macular degeneration is anti-vascular endothelial growth factor (VEGF) drugs administered by repeated injections. The treatment is risky, unpopular with patients, and some of them are unresponsive with no alternative treatment. Much attention is paid to the efficacy of these drugs, and many efforts are being made to improve them. We are designing a mathematical model and performing long-term three-dimensional Finite Element simulations for drug distribution in the human eye to gain new insights in the underlying processes using computational experiments. The underlying model consists of a time-dependent convection-diffusion equation for the drug coupled with a steady-state Darcy equation describing the flow of aqueous humor through the vitreous medium. The influence of collagen fibers in the vitreous on drug distribution is included by anisotropic diffusion and the gravity via an additional transport term. The resulting coupled model was solved in a decoupled way: first the Darcy equation with mixed finite elements, then the convection-diffusion equation with trilinear Lagrange elements. Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. Using this strategy, we compute a good approximation to the solution that converges quadratically in both time and space. The developed simulations were used for the therapy optimization, for which specific output functionals are evaluated. We show that the effect of gravity on drug distribution is negligible, that the optimal pair of injection angles is (50∘,50∘), that larger angles can result in 38% less drug at the macula, and that in the best case only 40% of the drug reaches the macula while the rest escapes, e.g., through the retina, that by using heavier drug molecules, more of the drug concentration reaches the macula in an average of 30 days. As a refined therapy, we have found that for longer-acting drugs, the injection should be made in the center of the vitreous, and for more intensive initial treatment, the drug should be injected even closer to the macula. In this way, we can perform accurate and efficient treatment testing, calculate the optimal injection position, perform drug comparison, and quantify the effectiveness of the therapy using the developed functionals. We describe the first steps towards virtual exploration and improvement of therapy for retinal diseases such as age-related macular degeneration.

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10

Yue, Chen, Mingquan Ye, Peipei Wang, Daobin Huang, and Xiaojie Lu. "SRV-GAN: A generative adversarial network for segmenting retinal vessels." Mathematical Biosciences and Engineering 19, no. 10 (2022): 9948–65. http://dx.doi.org/10.3934/mbe.2022464.

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<abstract> <p>In the field of ophthalmology, retinal diseases are often accompanied by complications, and effective segmentation of retinal blood vessels is an important condition for judging retinal diseases. Therefore, this paper proposes a segmentation model for retinal blood vessel segmentation. Generative adversarial networks (GANs) have been used for image semantic segmentation and show good performance. So, this paper proposes an improved GAN. Based on R2U-Net, the generator adds an attention mechanism, channel and spatial attention, which can reduce the loss of information and extract more effective features. We use dense connection modules in the discriminator. The dense connection module has the characteristics of alleviating gradient disappearance and realizing feature reuse. After a certain amount of iterative training, the generated prediction map and label map can be distinguished. Based on the loss function in the traditional GAN, we introduce the mean squared error. By using this loss, we ensure that the synthetic images contain more realistic blood vessel structures. The values of area under the curve (AUC) in the retinal blood vessel pixel segmentation of the three public data sets DRIVE, CHASE-DB1 and STARE of the proposed method are 0.9869, 0.9894 and 0.9885, respectively. The indicators of this experiment have improved compared to previous methods.</p> </abstract>

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11

Wilson, J. M., K. L. Hoffman, R. H. F. Jackson, and J. Telgen. "Computational Mathematical Programming." Journal of the Operational Research Society 39, no. 8 (August 1988): 792. http://dx.doi.org/10.2307/2583777.

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12

Wilson, J. M. "Computational Mathematical Programming." Journal of the Operational Research Society 39, no. 8 (August 1988): 792. http://dx.doi.org/10.1057/jors.1988.137.

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13

Dougherty, Edward R., and Divyendu Sinha. "Computational mathematical morphology." Signal Processing 38, no. 1 (July 1994): 21–29. http://dx.doi.org/10.1016/0165-1684(94)90054-x.

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14

Sachs, E. "Computational mathematical programming." European Journal of Operational Research 39, no. 2 (March 1989): 227–28. http://dx.doi.org/10.1016/0377-2217(89)90199-9.

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15

Lee, Seong-Ran. "A New Development of the Medical lnformation Management for the Treatment of Retinal Vascular Occlusions." Journal of Computational and Theoretical Nanoscience 18, no. 5 (May 1, 2021): 1557–60. http://dx.doi.org/10.1166/jctn.2021.9575.

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Retinal vascular occlusions are an emergency disease of ophthalmology that causes blood vessels in the eye to block or burst, causing vision loss or blindness. Therefore, this study attempts to develop new medical information management to treat retinal vascular occlusion. The data were surveyed on 122 people who visited the ophthalmologist from May 6 to July 10, 2019. The survey was conducted by classifying 61 test respondents who mediated the information management and 61 comparative respondents who did not mediated. The basic information of participants was provided using the X2 test. The approach for preventing retinal vascular occlusion before and after information management application was analyzed as t-test. A comparative analysis of overall eye conditions was performed with t-test. The participants’ practice of eye health was analyzed with t-test. Findings: The derived data present the following. (1) The blinking eyes inner canthus were significantly higher after the attempt than before management (t = −5.83, p = .000). (2) The acupressure around the eyes was significantly higher 43.62% after the management attempt, compared to the 14.93% before the attempt (t = −3.47, p = .000). (3) The eye movement was significantly higher after the attempt than before the attempt (t = −1.08, p = .000). (4) Renal vessel has been confirmed that the retinal vessel is also improving significantly after care than before (p < .05). (5) In particular, retinal blood vessels have improved significantly since the 18th. However, since the 22nd, retinal blood vessels have shown a slight decrease. The above findings pointed out that retinal vascular occlusion requires routine eye care. Therefore, this study found that medical information management applied to the experiment was effective in preventing retinal vascular occlusion.

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16

Sanford, John F., and Jaideep T. Naidu. "Mathematical Modeling And Computational Thinking." Contemporary Issues in Education Research (CIER) 10, no. 2 (March 31, 2017): 158–68. http://dx.doi.org/10.19030/cier.v10i2.9925.

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The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced level such as high school or early college.

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17

SUZUKI, M. "MATHEMATICAL BASIS OF COMPUTATIONAL PHYSICS." International Journal of Modern Physics C 07, no. 03 (June 1996): 355–59. http://dx.doi.org/10.1142/s0129183196000296.

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The present paper explains some general basic formulas concerning quantum Monte Carlo simulations, symplectic integration and other numerical calculations. A generalization of the BCH formula is given with an application to the decomposition of exponential operators in the presence of small parameters.

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18

Leydesdorff, L. "Mathematical, biological, and computational explanations." Heredity 94, no. 4 (March 29, 2005): 458. http://dx.doi.org/10.1038/sj.hdy.6800630.

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19

Torregrosa, Juan R., Lucas Jódar, Juan C. Cortés, and Regino Criado. "Mathematical modeling and computational methods." Journal of Computational and Applied Mathematics 291 (January 2016): 1–4. http://dx.doi.org/10.1016/j.cam.2015.04.023.

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20

Torregrosa, Juan R., Lucas Jodar, Juan C. Cortés, and Regino Criado. "Mathematical Modeling and Computational Methods." Journal of Computational and Applied Mathematics 309 (January 2017): 320–24. http://dx.doi.org/10.1016/j.cam.2016.08.001.

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21

Jodar, Lucas, Juan R. Torregrosa, Juan C. Cortés, and Regino Criado. "Mathematical modeling and computational methods." Journal of Computational and Applied Mathematics 330 (March 2018): 661–65. http://dx.doi.org/10.1016/j.cam.2017.10.015.

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22

Spälti, S., and M. Liebling. "Computational mathematical programming — Proceedings of the NATO advanced study institute on computational mathematical programming." Signal Processing 13, no. 3 (October 1987): 334–35. http://dx.doi.org/10.1016/0165-1684(87)90135-6.

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23

Turner, Raymond. "Computational Abstraction." Entropy 23, no. 2 (February 10, 2021): 213. http://dx.doi.org/10.3390/e23020213.

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Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.

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24

Ram, Mangey, Vijay Kumar, and G. S. Ladde. "Computational and mathematical approach for recent problems in mathematical sciences." International Journal for Computational Methods in Engineering Science and Mechanics 22, no. 3 (May 4, 2021): 169. http://dx.doi.org/10.1080/15502287.2021.1916172.

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25

Codony, D., A. Mocci, J. Barceló-Mercader, and I. Arias. "Mathematical and computational modeling of flexoelectricity." Journal of Applied Physics 130, no. 23 (December 21, 2021): 231102. http://dx.doi.org/10.1063/5.0067852.

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26

Rubenstein, Rheta N. "Computational Estimation and Related Mathematical Skills." Journal for Research in Mathematics Education 16, no. 2 (March 1985): 106. http://dx.doi.org/10.2307/748368.

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27

Rubenstein, Rheta N. "Computational Estimation and Related Mathematical Skills." Journal for Research in Mathematics Education 16, no. 2 (March 1985): 106–19. http://dx.doi.org/10.5951/jresematheduc.16.2.0106.

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Varieties of computational estimation were explored in relation to other mathematical skills and sex differences. The subjects were eighth graders (144 girls and 165 boys) from seven schools. Open-ended estimation was the most difficult, followed by estimation relative to a reference number and estimation within an order of magnitude. Verbal tasks were not more difficult than numerical tasks, but decimals were more difficult than whole numbers, and quotients were more difficult than products, which in turn were more difficult than sums and differences. Boys scored higher than girls on the total estimation test and on the order of magnitude scale. Stepwise regression analyses indicated that estimation performance was best predicted by skill in operating with tens.

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28

Hunt, C. Anthony, Glen E. P. Ropella, Sunwoo Park, and Jesse Engelberg. "Dichotomies between computational and mathematical models." Nature Biotechnology 26, no. 7 (July 2008): 737–38. http://dx.doi.org/10.1038/nbt0708-737.

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29

Kass, Robert E., Shun-Ichi Amari, Kensuke Arai, Emery N. Brown, Casey O. Diekman, Markus Diesmann, Brent Doiron, et al. "Computational Neuroscience: Mathematical and Statistical Perspectives." Annual Review of Statistics and Its Application 5, no. 1 (March 7, 2018): 183–214. http://dx.doi.org/10.1146/annurev-statistics-041715-033733.

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30

Jones, Pamela, and Sivabal Sivaloganathan. "Computational and Mathematical Methods in Medicine." Computational and Mathematical Methods in Medicine 2011 (2011): 1. http://dx.doi.org/10.1155/2011/303089.

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31

Varshney, L. R. "Mathematical limit theorems for computational creativity." IBM Journal of Research and Development 63, no. 1 (January 2019): 2:1–2:12. http://dx.doi.org/10.1147/jrd.2019.2893907.

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32

Peirce, Shayn M. "Computational and Mathematical Modeling of Angiogenesis." Microcirculation 15, no. 8 (January 2008): 739–51. http://dx.doi.org/10.1080/10739680802220331.

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33

Gascuel, Olivier, and Tanja Stadler. "Mathematical and Computational Evolutionary Biology (2013)." Systematic Biology 64, no. 1 (December 12, 2014): 1–2. http://dx.doi.org/10.1093/sysbio/syu086.

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34

Wickramasinghe, W. A. P., A. T. Dharmarathne, and N. D. Kodikara. "A mathematical model for computational aesthetics." International Journal of Computational Vision and Robotics 1, no. 3 (2010): 311. http://dx.doi.org/10.1504/ijcvr.2010.038077.

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35

Vigo-Aguiar, Jesús, and Juan L. G. Guirao. "Advances in computational and mathematical chemistry." Journal of Mathematical Chemistry 50, no. 2 (March 18, 2011): 311–12. http://dx.doi.org/10.1007/s10910-011-9805-8.

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36

Hilinski, EdwinF. "Mathematical and computational concepts in chemistry." Computers & Chemistry 11, no. 4 (January 1987): 305–6. http://dx.doi.org/10.1016/0097-8485(87)85009-x.

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37

Nguyen, Hung T. "Some mathematical structures for computational information." Information Sciences 128, no. 1-2 (September 2000): 67–89. http://dx.doi.org/10.1016/s0020-0255(00)00039-6.

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38

Sleeman, Brian, and Pamela Jones. "Computational and Mathematical Methods in Medicine." Computational and Mathematical Methods in Medicine 7, no. 1 (2006): 1–2. http://dx.doi.org/10.1080/10273660600818264.

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39

Ariati, Chelsi, and Aswin Aswin. "Mathematical Computational Thinking : Systematic Literature Review." Eduma : Mathematics Education Learning and Teaching 12, no. 2 (December 1, 2023): 213. http://dx.doi.org/10.24235/eduma.v12i2.13796.

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40

Pisarchik, Alexander N. "Computational and Mathematical Methods for Neuroscience." Applied Sciences 14, no. 23 (December 4, 2024): 11296. https://doi.org/10.3390/app142311296.

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As our understanding of the brain continues to advance, so too does the demand for sophisticated tools that can model, simulate, and interpret the intricate data generated by contemporary neuroimaging and electrophysiological techniques [...]

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41

Waring, George O. "Computational Methods Advantageous for Ophthalmology." Journal of Refractive Surgery 8, no. 2 (March 1992): 126. http://dx.doi.org/10.3928/1081-597x-19920301-06.

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42

Ali, M. Syed. "Computational Mathematics and Modeling." Journal of Interdisciplinary Mathematics 27, no. 5 (2024): i—vi. http://dx.doi.org/10.47974/jim-27-5-foreword.

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Анотація:

This Special Issue on Computational Mathematics and Modeling mainly focuses on applications and methodological research in all fields of computational mathematics and modeling. Computational Mathematics and modelling are two related fields that play a crucial and important role in the development and advancement of various scientific and technological domains. This issue comprises investigations involving the theory, and applications of mathematical analytic tools and techniques which are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

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43

Yamaguchi, Tatsuo. "Mathematical Analysis for Rotating Autokeratoplasty." Cornea 11, no. 5 (September 1992): 489. http://dx.doi.org/10.1097/00003226-199209000-00023.

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44

Azizia, Ananda Jullailatul, Masrukan Masrukan, and Bambang Eko Susilo. "Systematic Literature Review: Trends Computational Thinking and Mathematical Disposition in Mathematics Learning." Kontinu: Jurnal Penelitian Didaktik Matematika 8, no. 2 (December 28, 2024): 152. https://doi.org/10.30659/kontinu.8.2.152-169.

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Abstract. This research aims to provide comprehensive information on the trend of computational thinking ability and mathematical disposition in mathematics learning. The method used was a Systematic Literature Review (SLR). Data was collected by reviewing articles on computational thinking skills and mathematical disposition published in 2019-2024. There were 15 articles, nine related to computational thinking ability and six related to mathematical disposition, obtained from Google Scholar and Scopus. The results of this study indicate that the methods and research designs that tend to be used for research on computational thinking ability and mathematical disposition tend to use quantitative research with quasi-experimental design, and PBL learning models are widely used. Research on thinking ability is predominantly carried out on elementary school students but for mathematical disposition at the junior and senior high school levels with geometry, algebra, and statistics mathematics materials. Computational thinking skills and mathematical disposition are two important aspects of mathematics education that are interrelated and influence each other.Keywords: computational thinking ability, mathematical disposition, mathematics learning

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45

Agustiani, Nur. "IDENTIFICATION OF HIGH SCHOOL STUDENTS' COMPUTATIONAL THINKING SKILLS IN SOLVING BINOMIAL PROBABILITY PROBLEMS." AKSIOMA: Jurnal Program Studi Pendidikan Matematika 11, no. 3 (September 28, 2022): 2096. http://dx.doi.org/10.24127/ajpm.v11i3.5026.

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This study aims to identify the computational thinking skills of high school students in solving binomial probability problems. This research uses a case study method with a descriptive qualitative approach. The subjects of this study were three students of class XI, where each student represented each category of mathematical ability in general, namely: low, medium, and high. Data collection using test and interview methods. Based on the results of data analysis using computational thinking stages, that found: 1) Students with high mathematical abilities can fulfill the stages of computational thinking skills in each given problem. 2) Students with medium mathematical abilities can’t always fulfill the stages of computational thinking. When unable to solve problems, students with medium mathematical abilities have problem formulation and abstraction skills. 3) Students with low mathematical abilities are not as good as students with medium or high mathematical abilities. Students with low mathematical ability cannot fulfill all stages of computational thinking when they cannot solve problems.

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46

Mezhoud, Salim. "Language Mathematics and Mathematics Language, Reading from Computational Linguistics." Mathematical Linguistics 1, no. 1 (December 31, 2021): 7–24. http://dx.doi.org/10.58205/ml.v1i1.140.

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The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language using technical terms and grammatical conventions that are peculiar to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas. mathematical characterizations of various notions of linguistic complexity include also computational linguistics, philosophical logic, knowledge representation as a branch of artificial intelligence, theoretical computer science, and computational psychology. Mathematical linguistics has initially served as a foundation for computational linguistics, though its research agenda of designing machines to simulate natural language understanding is clearly more applied. Inductive methods have gained the upper hand in applied computational linguistics The question is whether mathematics is a language, or that language is mathematical, and how computational linguistics employs language as mathematics.

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47

Yu, Haoyang, Jingzhe Hu, Lingyun Zhao, Bowen Yuan, Hongyi Tian, and Shituo Ma. "Computational Thinking: The Third Paradigm for Mathematical Modeling Teaching." Advances in Education, Humanities and Social Science Research 9, no. 1 (January 9, 2024): 53. http://dx.doi.org/10.56028/aehssr.9.1.53.2024.

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Mathematical modeling provides a good platform for guiding students to flexibly apply mathematical knowledge to solve practical problems, and universities have also launched rich mathematical modeling teaching activities. However, in the process of university mathematical modeling teaching, the drawbacks of two traditional teaching methods that focus on cases and models have gradually emerged. Therefore, this article suggests using computational thinking as a third paradigm for mathematical modeling teaching. This paper shows the computational thinking in the new teaching. This article also gives some suggestions to nowadays teaching module. The proposal of this concept has a certain reference value for the reform of mathematical modeling teaching.

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48

Alsulami, M. D. "Computational mathematical techniques model for investment strategies." Applied Mathematical Sciences 15, no. 1 (2021): 47–55. http://dx.doi.org/10.12988/ams.2021.914378.

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Laviola, Marianna, Declan G. Bates, and Jonathan G. Hardman. "Mathematical and Computational Modelling in Critical Illness." European Respiratory & Pulmonary Diseases 5, no. 1 (2019): 12. http://dx.doi.org/10.17925/erpd.2019.5.1.12.

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50

Cortez, Ricardo. "Mathematical and Computational Modeling of Microorganism Swimming." Notices of the American Mathematical Society 63, no. 10 (November 1, 2016): 1156–57. http://dx.doi.org/10.1090/noti1436.

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