Department of Mathematics

Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21

Browse

Author: search.filters.author.Dr. Ayesha SohailSubject: search.filters.subject.Dr. Ayesha Sohail

Search Results

Now showing 1 - 10 of 10
  • No Thumbnail Available
    Item
    Comparative Study of Different Fractional Operators on the Stochastic Diffusion Equation
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Rana Talha Ahmad; CIIT/FA19-RMT-021/LHR; Dr. Ayesha Sohail; LHR TP 7436
    In this work, we studied ecological model of fractional order prey-predator with Holling type II functional response and harvesting effect. Fractional Order Operators along with existence and uniqueness properties are defined. Finally, numerical simulations are performed to see the convergence of solutions with the help of Backward Euler’s method.
  • No Thumbnail Available
    Item
    Hybrid Modeling Approach for the Forecasting of the Fibrilization Process and the Resulting AD
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mudassar Fiaz; CIIT/FA19-RMT-112/LHR; Dr. Ayesha Sohail; LHR TP 7429
    Imaging has played a variety of roles in the study of Alzheimer disease (AD) over the past four decades. Initially, computed tomography (CT) and then magnetic resonance imaging (MRI) were used diagnostically to rule out other causes of dementia. More recently, a variety of imaging modalities including structural and functional MRI and positron emission tomography (PET) studies of cerebral metabolism with fluoro- deoxy-D-glucose (FDG) and amyloid tracers such as Pittsburgh Compound-B (PiB) have shown characteristic changes in the brains of patients with AD. These modalities and their particular utilities are discussed in this thesis. Machine learning and deep learning have demonstrated a wonderful performance in the classification task. Important progress has been made in image recognition, mainly due to the availability of large-scale annotated datasets and the revival of convolutional neural networks (CNNs). The aim of this study is to help the neurologists in selection of appropriate classification method based on several parameters like accuracy, computer complexity, and low training data availability. The challenge for the future will be to combine imaging biomarkers to most efficiently facilitate diagnosis, disease staging, and, most importantly, development of effective disease-modifying therapies.
  • No Thumbnail Available
    Item
    A Composite Modeling Approach for the 3D Simulations and Medical Imaging of Cardiac ATTR Amyloidosis
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Usman Ashiq; CIIT/FA19-RMT-031/LHR; Dr. Ayesha Sohail; LHR TP 7441
    Mathematical Modeling and Machine Learning is playing a key role in applied mathematics. Machine learning has witnessed a tremendous amount of attention over the last few years. Deep neural networks are now the state-of-the-art machine learning models across a variety of areas, from image analysis to natural language processing. These developments have a huge potential for medical imaging technology, medical data analysis, medical diagnostics and healthcare in general, slowly being realized. Imaging has played a variety of roles in the study of Cardiac Amyloid (CA) over the past four decades. We provide a short overview of Cardiac Amyloid and Medical imaging techniques used for diagnosis of amyloids in our heart as well as recent advances in techniques. We also working on different neural networks especially on CNN for diagnosis of cardiac amyloid with the aid of Resnet-50 network on MATLAB and tensor-flow on Python. This study aims to assist doctors in choosing an acceptable classification method for each patient's condition. The challenge for the future will be to availability to most efficient imaging data for this disease.
  • No Thumbnail Available
    Item
    Space Spectral Time Fractional Finite Difference Method along with Stability Analysis for Fractional Order Nonlinear Wave Equations
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Sarmad Arshad; SP13-PMATH-004; Dr. Ayesha Sohail; LHR TP 5299
    In this work, nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM) is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated. Afterwards, dynamical analysis of fractional order Schr dinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the Fractional Homotopy Analysis Transform Method and the Optimal Homotopy Analysis Method is performed to select the most accurate technique for the stated problem. Space spectral analysis with integrating factor technique and time fraction finite difference method have been implemented to study the pressure waves propagating in bubbly fluids as well as nonlinear phenomena of plasma waves. Dynamical analysis of acoustic/pressure waves propagating in bubbly fluids is of great significance. Such flows arise in many engineering problems including sonochemistry, sonochemical reactors, cavitation around hydrofoils and ultrasonic propagation in medicine and biology. Fractional approach for modeling the propagation of the pressure waves in liquids containing a large number of tiny gas bubbles is proposed. Moreover, numerical solution of the fractional order Modified Korteweg-de Vries equation governing the dynamics is approximated using a novel space spectral time fractional finite difference tool. A spectral technique for space and a multi-step finite difference scheme for time are designed and implemented. The spatial spectral discretization error and the stability bounds are discussed. The nonlinear phenomena of plasma waves are well demonstrated with the aid of graphical analysis. Stability analysis of integer and fractional order KdV equations have been discussed quantitatively with the help of Evans function approximation.
  • No Thumbnail Available
    Item
    Hybrid Deep Learning for the Classification of Oncological-Imaging-Data Sets
    (Library Information Services, CUI Lahore, 2023) Usama Ahmad Khan; FA20-RMT-004; Dr. Ayesha Sohail
    Medical imaging is the process of visualizing the diseased part, with the aid of images, inside the patient's body. The field of medical imaging depends on several disciplines of science and technology, including physics, biological sciences, engineering, artificial intelligence and mathematics. These disciplines contribute in designing the imaging devices, installation of the devices and the collection and analysis of the images for better understanding and future forecasting of the disease prognosis and prevention. In this manuscript, medical images are analyzed with the aid of a new hybrid machine learning approach, where the breast cancer images are studied in a novel manner with the help of a newly devised algorithm that is conceptually sounder as compared to already existing algorithms. Step by step stages are followed by the algorithm to process, filter, segment, statistically analyze and to classify the medical images. The results from different classification tools are compared in a novel manner, inspired from the explainable artificial intelligence tools for classification.
  • No Thumbnail Available
    Item
    Numerical Solution of Coupled Delay Differential Equations in the Field of Oncology
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Robia Arif; SP19-RMT-037; LHR TP 6484; Dr. Ayesha Sohail
    In the dissertation, the models of delay differential equations from the math- ematical biology are considered, focusing on the oncology. For the study of these kinds of models, one should be capable to establish linear stability of the steady states. In Chapter 2, I have apply the method on models. Adoptive im- munotherapy against cancer has received remarkable consideration. The cyto- toxic CD8+ T cells have been studied for a long time and experimented with re- ceptor engineering techniques through the creation of chimeric receptors called CAR (Chimeric Antigen Receptor). This fact puts a cell line in the background which, on the other hand, is fundamental for the organization of the antitumor response: “CD4+” T cells. In this article, a model is constructed in which the ability of “CD4+” T cells to induce control of the tumor cell population is ana- lyzed, using a mediator such as the cytokine IFN- , and to quantify the action of the same which, although indirect, also carry out a control of the persistence of the antitumor action itself. The model focuses on the modalities of cellular interaction where it is possible to imagine a future development on the basis of recent data and idealize a therapeutic scheme where “CD4+” T cells play a leading role. The linear stability analysis is analyzed and analysis of Hopf bifur- cation is established. Finally, the numerical simulations are executed to validate analytical results.
  • No Thumbnail Available
    Item
    Analysis of Plasma Modified KdV Waves using Discrete Periodic Inverse Scattering Transformation
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Noaman Akbar; SP15-RMT-005; LHR TP 6989; Dr. Ayesha Sohail
    Discrete Periodic Inverse Scattering Transformation (DPIST) are presented in this paper for solution of the well-known Korteweg-de Vries equations that has been hypothesized hypothetically such that non-linear dispersive waves spreading on interface of length only a joined of products fluid profundity fulfill a development condition with more extreme non-linearity than ordinary Korteweg-de Vries (KdV) equations for shallow water hypothesis. In this paper non-linear Fourier investigation is processed on time and space arrangement of surface relocation create at two areas downstream of a wavering film. Comes about because of a DPIST in view of the KdV equation, that decays a flag into soliton, sinusoidal and cnoidal parts, demonstrate while the amplitude of direct modes are preserved as unsettling influence spreads among two sensors, amplitudes of nonlinear modes increment. This recommends non-linearity of such surface waves is without a doubt more grounded than that anticipated by the KdV equations.
  • No Thumbnail Available
    Item
    Algorithm Development for the Bayesian Optimization of Complex Data Sets
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Javed Zahoor; FA18-RMT-057; LHR TP 6461; Dr. Ayesha Sohail
    Optimization is a subfield of applied mathematics and is used in the fields of nano-medicine, applied sciences and computational biology extensively. The recent trends of optimizations are focused on the algorithm development of nonlinear programs for complex data sets. During this research, an algorithm is developed for the application of “Bayesian Optimization”, for the selection of the most accurate hyper-parameter, using the Python framework as well as the MatlabTM 2020 packages. The developed model is then implemented on the experimental data sets, extracted from the online repositories. To ensure the optimalilty of the forecasting, the algorithms are exploited in detailed manner during this research.
  • No Thumbnail Available
    Item
    Fractional Order Model of Tumor-Induced Angiogenesis
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Sufian Asgher; SP15-RMT-001; LHR TP 6936; Dr. Ayesha Sohail
    Methods of blood vessel formation is termed angiogenesis. Two distinguishing features of cancer, uncontrollable cell growth and metastasis, cannot be sustained in the absence of neovascularisation. Angiogenesis enhances the arrangement of solid tumors and their metastasis. During this research, present progress in understanding the procedure of angiogenesis in dynamic tumor development is talked about. The development of strong tumors, including neck and head squamous cell carcinomas, relies on upon the foundation of a blood supply inside the tumor (neovascularization or angiogenesis). For this procedure to occur, tumors create development components which stimulate the expansion, movement, and separation of endothelial cells. Nonlinear pde model of tumour induced angiogenesis is discussed during this research. The semi-analytic solution of this model is presented.
  • No Thumbnail Available
    Item
    Explainable Machine Learning for Medical Imaging
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Shahid; FA18-RMT-043; LHR TP 6023; Dr. Ayesha Sohail
    In the recent literature, artificial intelligence tools have been used very suc cessfully to investigate the history of medical images, where incomplete data is available. In this thesis, data obtained from a clinical study is analyzed using medical imaging algorithms. We have used a Bayesian machine learning clas sifier i.e. Naïve Bayes to obtain the results. We have considered the medical images from 20 patients having gastric cancer. Futhermore, we have compared the accuracy of Naïve Bayes classifier to the other medical imaging techniques such as CNN.