Special Issue – Mathematical Imaging

The multidisciplinary subject of Imaging Science concerning the generation, collection, duplication, analysis, modification, restoration, enhancement, comparison, feature extraction, and visualisation of images is developing in a rapid speed. It is increasingly used in more and more application areas, especially in cutting edge technologies. Mathematical Imaging firmly establishes mathematics as a rigorous basis for imaging science, complementing the image processing methodologies, in the discrete setting, of computer science and information science

A fourth-order PDE denoising model with an adaptive relaxation method

In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of PSNR

Development of temporal logic-based fuzzy decision support system for diagnosis of acute rheumatic fever/rheumatic heart disease

In this paper we describe our research work in developing a Clinical Decision Support System (CDSS) for the diagnosis of Acute Rheumatic Fever (ARF)/Rheumatic Heart Diseases (RHD) in Nepal. This paper expressively emphasizes the three problems which have previously not been addressed, which are: (a) ARF in Nepal has created a lot of confusion in the diagnosis and treatment, due to the lack of standard unique procedures, (b) the adoption of foreign guideline is not effective and does not meet the Nepali environment and lifestyle, (c) using (our proposed method) of hybrid methodologies (knowledge-based, temporal theory and Fuzzy logic) together to design and develop a system to diagnose of ARF case an early stage in the English and Nepali version. The three tier architecture is constructed by integrating the MS Access for backend and C#.net for fronted to deployment of the system

Comparison of analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations

Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. In this paper, different linearization techniques such as Newton’s method and the analytic asymptotic approximation formula are adopted and compared for a wide class of nonlinear Black–Scholes equations including, in particular, the market illiquidity model and the risk-adjusted pricing model. Accuracy and time complexity of both numerical methods are compared. Furthermore, market quotes data was used to calibrate model parameters

Two-step numerical simulation of the heat transfer from a flat plate to a swirling jet flow from rotating pipe

Purpose: Impinging jets have been widely studied and the addition of swirl has been found to be beneficial to heat transfer. Since there is no literature on RANS nor experimental data of swirling jet flows generated by a rotating pipe, this paper attempts to fill such gap by providing results on the performance of this type of design. Design/methodology/approach: Since the flow has a different behaviour at different parts of the design, the same turbulent model cannot be used for the full domain. To over-come this complexity, the simulation is split into two coupled stages. This is an alternative to use the costly Reynold Stress Model (RSM) for the rotating pipe simulation and the SST k-ω model for the impingement. Findings: To induce swirl by rotating pipes with swirl intensity ranging from 0 to 0.5 affects the velocity profiles but not noticeably the spreading angle. The heat transfer is increased with respect to a non-swirling flow only at short nozzle-to-plate distances H/D < 6, where H is the distance and D is the diameter of the pipe. For the impinging zone, the highest average heat transfer is achieved at H/D = 5 with swirl intensity S = 0.5. This is the highest swirl studied in this work. Research limitations/implications: High-fidelity simulations or experimental analysis may provide reliable data for higher swirl intensities, which is not covered in this work with RANS. Practical implications: This two-step approach and the data provided is of interest to other related investigations (e.g. using arrays of jets or other surfaces than flat plates). Originality/value: This paper is the first of its kind RANS simulation of the heat transfer from a flat plate to a swirling impinging jet flow issuing from a rotating pipe. An extensive study of these CFD simulations has been carried out with the emphasis of splitting the large domain into two parts to facilitate the use of different turbulent models and periodic boundary conditions for the flow confined in the pipe

A modification term for Black-Scholes model based on discrepancy calibrated with real market data. Data science in finance and economics

The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data

A supervised machine learning approach to generate the auto rule for clinical decision support system

This paper illustrates a prototype for a Clinical Decision Support System (CDSS), using Supervised Machine Learning (SML) to derive rules from pre-constructed cases or to automatically generate rules. We propose an integrated architecture invoking two main components - Rule Pattern Matching Process (RPMP) and Auto Rule Generation Process (ARGP). The RPMP searches for and matches rules from a clinically derived reference set, successful discovery resulting in continued processing through the system. If no rule is found, the AGRP is automatically activated. The AGRP has been designed based on the SML approach. A Decision Tree Algorithm has been used and nested If-else statements applied to transform the decision tree algorithm to generate rules. For experimental purposes, we have developed a prototype and implemented a learning algorithm for generating auto rules for the diagnosis of Acute Rheumatic Fever (ARF). Based on results, the prototype can successfully generate the auto rules for ARF diagnosis. The prototype was designed to classify the ARF stages into “Detected”, “Suspected” and “Not detected”, in addition, it has classifiers capable of classifying the severity levels of detected stage into Severe, Moderate or Mild case. We simulated a set of 104 cases of ARF and observed the rules. The prototype successfully generated the new rule and classified it with the appropriate category (stage). In summary, the applied approach performed extremely well and the developed prototype provided reliable rules for ARF diagnosis. This prototype therefore reduces the task of manually creating ARF diagnosis rules. This approach could be applied in other clinical diagnosis processes

Estimation of stochastic behaviour in cardiac myocytes: I. Calcium Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains

Background: Since the discovery of Ca2+ sparks and their stochastic behaviour in cardiac myocytes, models have focused on the inclusion of stochasticity in their studies. While most models pay more attention to the stochastic modelling of cytosolic Ca2+ concentration the coupling of Ca2+ sparks and blinks in a stochastic model has not been explored fully. The cell morphology in past in silico studies is assumed to be Cartesian, spherical or cylindrical. The application on curvilinear grids can easily address this restriction and provide more realistic cell morphology. This paper presents a stochastic reaction-diffusion model that couples Ca2+ sparks and blinks applied to curvilinear domains. Methodology: Transformation of the model was performed to the curvilinear coordinate system. A set of differential equations is used to produce Ca2+ waves initiated from sparks and blinks. A non-buffered and non-dyed version as well as a buffered and dyed version of these equations were studied in light of observing the effects of reactions on the Ca2+ wave properties. For comparison, results for both the Cartesian and curvilinear grids are provided. Results and Conclusions: A successful demonstration of the application of curvilinear grids serving as basis for future developments

Simultaneous estimation of tracer kinetic model parameters using analytical and inverse approaches with a hybrid method

The inverse problem approach to Tracer Kinetic Modelling (TKM) using dynamic positron-emission tomography (PET) images is important in identifying the kinetic parameters and then quantifying the tracer concentrations in the region of interest. In parameter estimation, knowledge of good initial approximations to the parameters is essential. The aim of this paper is to extend existing work on an inverse method for tracer kinetics by proposing an improved hybrid method integrated with an analytic solution in a multi-objective formulation of the inverse method. The analytical solution is derived through the use of the Laplace transformation technique. This integrated approach will be compared against other parameter estimation techniques in terms of computational efficiency and accuracy

Estimation of heat flux in inverse heat conduction problems using quantum-behaved particle swarm optimization

An inverse optimization algorithm based on Quantum-Behaved Particle Swarm Optimization (QPSO) is examined and applied to estimate the unknown transient heat flux applied to certain boundaries in transient heat conduction problems. Results demonstrate the accuracy, stability and validity of the QPSO method in inverse estimation of the heat flux without prior knowledge of the functional form of the unknown quantities. This paper also addresses the high computational costs of QPSO and proposes a hybrid method to reduce the computational costs by combining the advantages of a gradient method and a stochastic method. Finally comparison of the proposed hybrid method and Conjugate Gradient Method (CGM) is also included