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Relevant bibliographies by topics / Mathematical and computational ophthalmology

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Academic literature on the topic 'Mathematical and computational ophthalmology'

Author: Grafiati

Published: 8 March 2025

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Journal articles on the topic "Mathematical and computational ophthalmology"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Mathematical and computational ophthalmology"

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Andrews, Brian. "Computational Solutions for Medical Issues in Ophthalmology." Case Western Reserve University School of Graduate Studies / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=case15275972120621.

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Macdougall, Lindsey C. "Mathematical modelling of retinal metabolism." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/30615/.

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Age-related macular degeneration and diabetic retinopathy, in which the cells at the back of the eye degrade due to age and diabetes respectively, are prevalent causes of vision loss in adults. We formulate mathematical models of retinal metabolic regulation to investigate defects that may be responsible for pathology. Continuum PDE models are developed to test whether rod photoreceptors, light detecting cells in the eye, may regulate their energy demand by adapting their length under light and dark conditions. These models assume photoreceptor length depends on the availability of nutrients, such as oxygen, which diffuse and are consumed within the photoreceptor. Our results suggest that the length is limited by oxygen and phosphocreatine shuttle-derived ATP under dark and light conditions respectively. Parameter sensitivity analysis indicates that lowered mitochondrial efficiency due to ageing may be responsible for the damage to and death of photoreceptors that are characteristic of age-related macular degeneration. In the latter part of this thesis we shift our focus to the inner retina and examine how metabolite levels in the tissue surrounding the neurons (highly sensitive, excitable cells that transmit electrical signals) are regulated by glial cells. For instance, stimulated neurons activate their neighbours via the release of the neurotransmitter glutamate, while glial cells regulate neuronal activity via glutamate uptake. Diabetes produces large fluctuations in blood glucose levels, and eventually results in neuronal cell death, causing vision loss. We generate an ODE model for the exchange of key metabolites between neurons and surrounding cells. Using numerical and analytical techniques, we use the model to show that the fluctuations in blood glucose and metabolic changes associated with diabetes may result in abnormally high glutamate levels in the inner retina, which could lead to neuronal damage via excitotoxicity (unregulated neuronal stimulation).

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Casarin, Stefano. "Mathematical models in computational surgery." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS008/document.

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La chirurgie informatisée est une science nouvelle dont le but est de croiser la chirurgie avec les sciences de l’informatique afin d’aboutir à des améliorations significatives dans les deux domaines. Avec l’évolution des nouvelles techniques chirurgicales, une collaboration étroite entre chirurgiens et chercheurs est devenue à la fois inévitable et essentielle à l’optimisation des soins chirurgicaux. L’utilisation de modèles mathématiques est la pierre angulaire de ce nouveau domaine. Cette thèse démontre comment une approche systématique d’un problème clinique nous a amenés à répondre à des questions ouvertes dans le domaine chirurgical en utilisant des modèles mathématiques à grande échelle. De manière générale, notre approche inclut (i) une vision générale du problème, (ii) le ciblage du/des système(s) physiologique(s) à étudier pour y répondre, et (iii) un effort de modélisation mathématique, qui a toujours été poussé par la recherche d’un compromis entre complexité du système étudié et réalité physiologique. Nous avons consacré la première partie de cette thèse à l’optimisation des conditions limites à appliquer à un bio-réacteur utilisé pour démultiplier le tissu pulmonaire provenant d’un donneur. Un modèle géométrique de l’arbre trachéo-bronchique couplé à un modèle de dépôt de soluté nous a permis de déterminer l’ensemble des pressions à appliquer aux pompes servant le bio-réacteur afin d’obtenir une distribution optimale des nutriments à travers les cultures de tissus. Nous avons consacré la seconde partie de cette thèse au problème de resténose des greffes de veines utilisées pour contourner une occlusion artérielle. Nous avons reproduit l’apparition de resténose grâce à plusieurs modèles mathématiques qui permettent d’étudier les preuves cliniques et de tester des hypothèses cliniques avec un niveau croissant de complexité et de précision. Pour finir, nous avons développé un cadre de travail robuste pour tester les effets des thérapies géniques afin de limiter la resténose. Une découverte intéressante a été de constater qu’en contrôlant un groupe de gènes spécifique, la perméabilité à la lumière double après un mois de suivi. Grace aux résultats obtenus, nous avons démontré que la modélisation mathématique peut servir de puissant outil pour l’innovation chirurgicale
Computational surgery is a new science that aims to intersect surgery and computational sciences in order to bring significant improvements in both fields. With the evolution of new surgical techniques, a close collaboration between surgeons and computational scientists became unavoidable and also essential to optimize surgical care. A large usage of mathematical models is the cornerstone in this new field. The present thesis shows how a systematic approach to a clinical problem brought us to answer open questions in the field of surgery by using mathematical models on a large scale. In general, our approach includes (i) an overview of the problem, (ii) the individuation of which physiological system/s is/are to be studied to address the question, and (iii) a mathematical modeling effort, which has been always driven by the pursue of a compromise between system complexity and closeness to the physiological reality. In the first part, we focused on the optimization of the boundary conditions to be applied to a bioreactor used to re-populate lung tissue from donor. A geometrical model of tracheobronchial tree combined with a solute deposition model allowed us to retrieve the set of pressures to be applied to the pumps serving the bioreactor in order to reach an optimal distribution of nourishment across the lung scaffold. In the second part, we focused on the issue of post-surgical restenosis of vein grafts used to bypass arterial occlusions. We replicated the event of restenosis with several mathematical models that allow us to study the clinical evidences and to test hypothesis with an escalating level of complexity and accuracy. Finally, we developed a solid framework to test the effect of gene therapies aimed to limit the restenosis. Interestingly, we found that by controlling a specific group of genes, the lumen patency is double after a month of follow-up. With the results achieved, we proved how mathematical modeling can be used as a powerful tool for surgical innovation

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He, Xiaoyin. "CHARACTERIZATION OF CORNEAL BIOMECHANICAL PROPERTIES USING EXPERIMENTAL AND COMPUTATIONAL METHODS." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1280178567.

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Baker, Nathan Andrew. "Mathematical and computational modeling of biomolecular systems /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2001. http://wwwlib.umi.com/cr/ucsd/fullcit?p3007138.

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Remias, Michael George. "Computational studies of some fuzzy mathematical problems." Thesis, Curtin University, 2012. http://hdl.handle.net/20.500.11937/1147.

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In modelling and optimizing real world systems and processes, one usually ends up with a linear or nonlinear programming problem, namely maximizing one or more objective functions subject to a set of constraint equations or inequalities. For many cases, the constraints do not need to be satisfied exactly, and the coefficients involved in the model are imprecise in nature and have to be described by fuzzy numbers to reflect the real world nature. The resulting mathematical programming problem is referred to as a fuzzy mathematical programming problem.Over the past decades, a great deal of work has been conducted to study fuzzy mathematical programming problems and a large volume of results have been obtained. However, many issues have not been resolved. This research is thus undertaken to study two types of fuzzy mathematical programming problems. The first type of problems is fuzzy linear programming in which the objective function contains fuzzy numbers. To solve this type of problems, we firstly introduce the concept of fuzzy max order and non-dominated optimal solution to fuzzy mathematical programming problems within the framework of fuzzy mathematics. Then, based on the new concept introduced, various theorems are developed, which involve converting the fuzzy linear programming problem to a four objective linear programming problem of non-fuzzy members. The theoretical results and methods developed are then validated and their applications for solving fuzzy linear problems are demonstrated through examples.The second type of problems which we tackle in this research is fuzzy linear programming in which the constraint equations or inequalities contain fuzzy numbers. For this work, we first introduce a new concept, the α-fuzzy max order. Based on this concept, the general framework of an α-fuzzy max order method is developed for solving fuzzy linear programming problems with fuzzy parameters in the constraints. For the special cases in which the constraints consist of inequalities containing fuzzy numbers with isosceles triangle or trapezoidal membership functions, we prove that the feasible solution space can be determined by the respective 3n or 4n non-fuzzy inequalities. For the general cases in which the constraints contain fuzzy numbers with any other form of membership functions, robust numerical algorithms have been developed for the determination of the feasible solution space and the optimal solution to the fuzzy linear programming problem in which the constraints contain fuzzy parameters. Further, by using the results for both the first and second types of problems, general algorithms have also been developed for the general fuzzy linear programming problems in which both the objective function and the constraint inequalities contain fuzzy numbers with any forms of membership functions. Some examples are then presented to validate the theoretical results and the algorithms developed, and to demonstrate their applications.

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Thorn, Graeme John. "Mathematical and computational modelling of friction stir welding." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426545.

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Southern, James Alastair. "Mathematical and computational modelling of ultrasound elasticity imaging." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:242fddf0-ef9c-4a90-88f5-c7b41f4bda5a.

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In this thesis a parameter recovery method for use in ultrasound elasticity imaging is developed. Elasticity imaging is a method for using a series of ultrasound images (and the displacement field between them) to estimate the spatial variation of the stiffness of the tissue being imaged. Currently iterative methods are used to do this: a model of tissue mechanics is assumed and a large number of simulations using varying parameters are compared to the actual displacement field. The aim of this work is to develop a solution method that works back from the known displacement field to determine the tissue properties, reducing the number of simulations that must be performed to one. The parameter recovery method is based on the formulation and direct solution of the 2-d linear elasticity inverse problem using finite element methods. The inverse problem is analyzed mathematically and the existence and uniqueness of solutions is described for varying numbers of displacement fields and appropriate boundary conditions. It is shown to be hyperbolic (and so difficult to solve numerically) and then reformulated as a minimization problem with hyperbolic Euler-Lagrange equations. A finite element solution of the minimization problem is developed and implemented. The results of the finite element implementation are shown to work well in recovering the parameters used in numerical simulations of the linear elasticity forward problem so long as these are continuous. The method is shown to be robust in dealing with small errors in displacement estimation and larger errors in the boundary values of the parameters. The method is also tested on displacement fields calculated from series of real ultrasound images. The validity of modelling the ultrasound elasticity imaging process as a 2-d problem is discussed. The assumption of plane strain is shown not to be valid and methods for extending the parameter recovery method to 3 dimensions once 3-d ultrasound becomes more widely used are described (but not implemented).

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GIRIBONE, PIER GIUSEPPE. "Mathematical modeling in Quantitative Finance and Computational Economics." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1046108.

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The first part of my PhD Thesis deals with different Machine Learning techniques mainly applied to solve financial engineering and risk management issues. After a short literary review, every chapter analyzes a particular topic linked to the implementation of these models, showing the most suitable methodologies able to solve it efficiently. The following topics are therefore covered: *) Data Fitting and Regression *) Forecasting *) Classification *) Outlier Detection and Data Quality *) Pricing Every chapter provides the theoretical explanation of the model, the description of the implementation in a numerical computing environment and the solution for real case-studies. Among others, the main technologies discussed in this work are the following: *) Shallow Multi-Layers networks *) Feed-forward and static networks *) Radial Basis Functions (RBF) networks *) Recurrent and Dynamic Neural Networks *) Nonlinear Autoregressive (NAR) networks and Nonlinear Autoregressive networks with exogenous variables (NARX) *) Deep Neural networks *) Convolutional Networks (Conv Net) *) Fuzzy C-Means (FCM) clustering *) Self-Organizing Maps (SOM) and Kohonen networks *) Neural Networks with Circular Neurons *) Auto-Associative Neural Networks (AANN) and Auto-encoders for Nonlinear Principal Component Analysis (NLPCA) The second part of my PhD Thesis deals with the problem of Optimal Control in Quantitative Finance and Labour Economics. Even if the fields of application are hugely different, they share the same mathematical instrument for their solution: the Bellman principle of optimality. After a short literary review that introduces the financial and economic problems solved in this part, the following four chapters show the most popular pricing techniques used to evaluate an option: closed formulas, Partial Differential Equations (PDE), Lattice methods and Stochastic Differential Equations (SDE). Chapter 6 faces the problem of early-exercise in option pricing and shows how to apply the principle of optimality in the models presented in the previous chapters. The following pricing methodologies are covered: *) Stochastic Trees and Lattice models (Cox-Ross-Rubinstein, Tian, Jarrow-Rudd, Drifted CRR, Leisen-Reimer, CRR Trinomial, Adaptive Mesh Method (AMM), Pentanomial and Heptanomial Trees) *) PDE numerical schemes (Finite Difference Method - FDM, Finite Elements Method - FEM and Radial Basis Function - RBF) *) SDE numerical solution (Longstaff-Schwartz Monte Carlo) *) Quasi-closed formulas (Roll-Geske-Whaley, Barone-Adesi-Whaley, Bjerksund- Stensland model) The last two chapters examine two important Labour Economics dynamic problems in the field of Optimal Control Theory: Implicit Contracts and Wage Bargaining. They share the same procedure for the solution which can be synthesized in these steps: *) Infinite-horizon deterministic optimal control problem formulation. The solution for this kind of problem can be found applying the Hamilton – Jacobi – Bellman (HJB) Equation. *) Design of a Markov Decision Chain for the numerical solution of the previous problem. *) Infinite-horizon stochastic optimal control problem formulation. After the validation of the discretization scheme in the deterministic context, the Markov Decision Chain can be extended in order to solve the stochastic version of the problem. In particular, an Ornstein-Uhlenbeck process has been introduced in the model. The third part of my PhD Thesis deals with Forecasting and Risk Management in Energy Markets. The first chapter introduces the two studies presented in this field through a short literary review and the Regulatory framework. The second chapter suggests some quantitative methods with the aim of managing the main risks of Guarantees of Origin (Gos). Given that Gos trading is rather recent, it implements an innovative integrated control system in order to handle market and counterparty risks. The following techniques are covered: *) Market Risk: Historical, parametric and Monte Carlo VaR with a special focus on volatility modeling (historical, implied, GARCH, SABR). *) Liquidity Risk: Bid-Ask spread analysis. *) Counterparty Risk: Probability of Default estimation starting from: listed CDS premium, traded bond prices and statement analysis (KMV model). The third chapter deals with the energy spot prices forecasting problem. The aim of the study is to establish a time-horizon within which it is reasonable to predict prices. The state-of-the-art architectures based on Deep Learning methods are implemented in order to solve this econometric issue. The analyzed techniques are: *) A multi-layered Nonlinear Autoregressive (NAR) network (Endogenous variable: prices). *) A multi-layered Nonlinear Autoregressive with an exogenous variable (NARX) network (Endogenous variable: prices - Exogenous variable: demand). *) A Long Short-Term Memory (LSTM) network with one feature (prices). *) A Long Short-Term Memory (LSTM) network with two features (prices and demand).

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Dutta, Jayanta. "Computational aspects of some mathematical and numerical problems." Thesis, University of North Bengal, 2015. http://ir.nbu.ac.in/handle/123456789/1850.

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Books on the topic "Mathematical and computational ophthalmology"

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Schittkowski, Klaus, ed. Computational Mathematical Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82450-0.

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1946-, Schittkowski Klaus, and North Atlantic Treaty Organization. Scientific Affairs Division., eds. Computational mathematical programming. Berlin: Springer-Verlag, 1985.

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L, Hoffman K., Jackson Richard Henry Frymuth, Telgen J, Mathematical Programming Society (U.S.). Committee on Algorithms., and NATO Advanced Study Institute on Computational Mathematical Programming (1984 : Bad Windsheim, Germany), eds. Computational mathematical programming. Amsterdam: North-Holland, 1987.

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Hubey, H. M. Mathematical and computational linguistics. Múnchen: LINCOM Europa, 1999.

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Bebis, George, Terry Gaasterland, Mamoru Kato, Mohammad Kohandel, and Kathleen Wilkie, eds. Mathematical and Computational Oncology. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91241-3.

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Brebbia, C. A., W. L. Wendland, and G. Kuhn, eds. Mathematical and Computational Aspects. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-21908-9.

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Bebis, George, Takis Benos, Ken Chen, Katharina Jahn, and Ernesto Lima, eds. Mathematical and Computational Oncology. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35210-3.

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Bebis, George, Max Alekseyev, Heyrim Cho, Jana Gevertz, and Maria Rodriguez Martinez, eds. Mathematical and Computational Oncology. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64511-3.

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Melnik, Roderick, ed. Mathematical and Computational Modeling. Hoboken, NJ: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118853887.

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Hubey, H. Mark. Mathematical and computational linguistics. Munich: Lincom Europa, 1999.

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Book chapters on the topic "Mathematical and computational ophthalmology"

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Wallace, Rodrick. "Mathematical Appendix." In Computational Psychiatry, 221–33. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53910-2_12.

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Prasad, Ram Yatan, and Pranita. "Mathematical Techniques." In Computational Quantum Chemistry, 49–90. 2nd ed. Second edition. | Boca Raton : CRC Press, 2021.: CRC Press, 2021. http://dx.doi.org/10.1201/9781003133605-3.

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Kuhl, Ellen. "Introduction to mathematical epidemiology." In Computational Epidemiology, 3–31. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-82890-5_1.

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Eberly, David. "Mathematical Preliminaries." In Computational Imaging and Vision, 9–38. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8765-5_2.

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Wang, Paul Keng-Chieh. "Mathematical Preliminaries." In Studies in Computational Intelligence, 7–34. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09779-4_2.

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Mazzola, Guerino, Maria Mannone, Yan Pang, Margaret O’Brien, and Nathan Torunsky. "Mathematical Gesture Theory." In Computational Music Science, 163–71. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47334-5_19.

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Grunsky, Eric. "Computational Geoscience." In Encyclopedia of Mathematical Geosciences, 143–64. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-85040-1_6.

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Schwartz, Richard. "Computational methods." In Mathematical Surveys and Monographs, 185–91. Providence, Rhode Island: American Mathematical Society, 2014. http://dx.doi.org/10.1090/surv/197/26.

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Das, Tapan Kumar. "Computational Techniques." In Theoretical and Mathematical Physics, 141–56. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2361-0_10.

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Beale, E. M. L. "Integer Programming." In Computational Mathematical Programming, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82450-0_1.

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Conference papers on the topic "Mathematical and computational ophthalmology"

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Pustovalov, Victor K. "Mathematical modeling of laser applications in ophthalmology." In Europto Biomedical Optics '93, edited by Shlomo T. Melamed. SPIE, 1994. http://dx.doi.org/10.1117/12.168734.

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Zheltov, Georgi I., V. N. Glazkov, A. I. Kirkovsky, and Alexander S. Podol'tsev. "Mathematical models of laser/tissue interactions for treatment and diagnosis in ophthalmology." In Moscow - DL tentative, edited by Sergei A. Akhmanov and Marina Y. Poroshina. SPIE, 1991. http://dx.doi.org/10.1117/12.57371.

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Gaffar, Ashraf, Dharmendra R. Patel, Peter J. Pallagi, Rouan Gaffar, and Mansooreh Karami. "Identifying and Mitigating Design Challenges of Ophthalmology Tele-medicine at Mayo Clinic." In 2017 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2017. http://dx.doi.org/10.1109/csci.2017.301.

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Olivo-Marin, Jean-Christophe. "Mathematical Microscopy." In Computational Optical Sensing and Imaging. Washington, D.C.: OSA, 2016. http://dx.doi.org/10.1364/cosi.2016.cm3d.1.

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Watt, Stephen M. "Computational Tools for Mathematical Collaboration." In 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2011. http://dx.doi.org/10.1109/synasc.2011.64.

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Handley, John C. "Architecture for computational mathematical morphology." In Photonics West 2001 - Electronic Imaging, edited by Edward R. Dougherty and Jaakko T. Astola. SPIE, 2001. http://dx.doi.org/10.1117/12.424963.

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Roy, Somnath. "Prominence Detection in Hindi: A Mathematical Perspective." In 2014 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2014. http://dx.doi.org/10.1109/csci.2014.105.

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Guo, Wei, Wei Su, Lian Li, Ning An, and Linwei Cui. "MQL: A Mathematical Formula Query Language for Mathematical Search." In 2011 IEEE 14th International Conference on Computational Science and Engineering (CSE). IEEE, 2011. http://dx.doi.org/10.1109/cse.2011.52.

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Orzen, S. N. "Mathematical expressiveness for computational network interaction." In 2013 IEEE 8th International Symposium on Applied Computational Intelligence and Informatics (SACI). IEEE, 2013. http://dx.doi.org/10.1109/saci.2013.6608943.

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"Topic 7 Mathematical and computational methods." In 2008 International Conference on Signals and Electronic Systems. IEEE, 2008. http://dx.doi.org/10.1109/icses.2008.4673441.

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Reports on the topic "Mathematical and computational ophthalmology"

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Boisvert, Ronald F. Mathematical and Computational Sciences Division :. Gaithersburg, MD: National Institute of Standards and Technology, 2010. http://dx.doi.org/10.6028/nist.ir.7671.

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Karniadakis, George E. Mathematical and Computational Issues in Plasma Microthrusters. Fort Belvoir, VA: Defense Technical Information Center, January 2000. http://dx.doi.org/10.21236/ada415042.

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Dupuis, Paul, David Gottlieb, and Jan Hesthaven. Novel Mathematical and Computational Techniques for Robust Uncertainty Quantification. Fort Belvoir, VA: Defense Technical Information Center, June 2011. http://dx.doi.org/10.21236/ada567849.

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Szabo, Barna A. Mathematical and Computational Framework for Virtual Fabrication Environment for Aircraft Components. Fort Belvoir, VA: Defense Technical Information Center, March 2008. http://dx.doi.org/10.21236/ada483777.

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Basak, Subhash C. Use of Biodescriptors and Chemodescriptors in Predictive Toxicology: A Mathematical/Computational Approach. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada434129.

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Van Dongen, Hans P. Homeostatic and Circadian Modulation of Cognition: Integrating Mathematical and Computational Modeling Approaches. Fort Belvoir, VA: Defense Technical Information Center, August 2012. http://dx.doi.org/10.21236/ada579501.

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Ghanem, Roger. Mathematical and Computational Tools for Predictive Simulation of Complex Coupled Systems under Uncertainty. Office of Scientific and Technical Information (OSTI), March 2013. http://dx.doi.org/10.2172/1070028.

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Schunn, C. D. A Review of Human Spatial Representations Computational, Neuroscience, Mathematical, Developmental, and Cognitive Psychology Considerations. Fort Belvoir, VA: Defense Technical Information Center, December 2000. http://dx.doi.org/10.21236/ada440864.

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Surana, Karan S., J. N. Reddy, and Peter W. TenPas. kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP. Fort Belvoir, VA: Defense Technical Information Center, January 2007. http://dx.doi.org/10.21236/ada465662.

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Willenbring, James M., Roscoe Ainsworth Bartlett, and Michael Allen Heroux. TriBITS lifecycle model. Version 1.0, a lean/agile software lifecycle model for research-based computational science and engineering and applied mathematical software. Office of Scientific and Technical Information (OSTI), January 2012. http://dx.doi.org/10.2172/1038225.

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