Talk Details

Synchronization of Complex Dynamical Networks: An Application to Real World Problems

Complex dynamical networks are important research topic in today modern world. Most of the real-world systems, can naturally arise in the form of complex networks like cluster of honeybees, Prey-predator systems, Human brain, Nervous systems, Economic networks, social networks etc. while these types of interconnected systems arise, there is some possibilities to affect the system stability, due to some internal or external disturbances or perturbations. This type of disturbances is unavoidable in most real-world systems, causing significant performance degradation and even instability. For that reason, controllers must be built to ensure external disturbances while ensuring system stability. Synchronization plays a key role in the interconnected networks, we may be able to better understand the collective behaviour of complex systems, like the human body, heart cells beating in unison, or schools of fish moving together, with the aid of advanced synchronization concepts. Many real-world applications can be perfectly modelled by complex networks and its prediction can be done accurately from the numerical simulations.

The Evolution of Fractional-Order Derivative:

Opportunities and Challenges in Mathematical Biology

The famous way of understanding biological phenomena using mathematical modeling is proposed by the deterministic approach with a differential equation. That being the case, two crucial points are amplified to reach something that is considered glorious in research known as a scientific novelty. First, the biological conditions with unique, specific, or exclusive cases, and the second is the novelty of the mathematical operator which contemplated more effective and precise in describing those given phenomena. Particularly, the use of fractional-order derivative for the operator has become the preference of several researchers for doing better biological modeling in recent decades. The evolution of the fractional-order derivative has indisputably been the critical pathway for scientific amelioration to approach the natural circumstances involving the memory effect. As researchers, these glad tidings can be an opportunity as well as a challenge to contribute to mathematical biology in several ways for instance: proposing new fractional operators, establishing the dynamical analysis tools due to the limitation of new operators, comparing the dynamical behaviors for different operators, and developing a novel numerical scheme.

Mathematical Modelling of Wave Energy Converter Devices

Renewable Energy harvesting technologies have been modelled and developed by researchers for more than two decades as an alternative to conventional energy sources such as fossil fuel, nuclear power, natural gases, coal, etc. The limited availability of conventional energy sources and their negative impact on the environment demands the necessity of exploring the technologies for harvesting energy from renewable energy resources. Out of various sources of renewable energy; solar energy, wind energy, and hydraulic energy are the three major sources of renewable energy. Among these renewable energy sources, ocean wave energy, a form of hydraulic energy, is one of the most promising and untapped renewable energy that can fulfil the current energy crisis. In this lecture, the mathematical modelling of wave energy converter devices, its advantages, limitations and future scope will be discussed.

Two Stages Hybrid Model of Fuzzy Linear Regression with Support Vector Machines for Colorectal Cancer

Fuzzy linear regression analysis has become popular among researchers and standard model in analyzing data in vagueness phenomena. However, the factor and symptoms to predict tumor size of colorectal cancer still ambiguous and not clear. The problem in using a linear regression will arise when uncertain data and not precise data were presented. Since the fuzzy set theorys concept can deal with data not to a precise point value (uncertainty data), fuzzy linear regression was applied. In this study, two new models for hybrid model namely the multiple linear regression clustering with support vector machine model (MLRCSVM) and fuzzy linear regression with symmetric parameter with support vector machine (FLRWSPCSVM) were proposed to analyze colorectal cancer data. Other than that, the parameter, error and explanation of the five procedures to both new models were included. These models applying five statistical models such as multiple linear regression, fuzzy linear regression, fuzzy linear regression with symmetric parameter, fuzzy linear regression with asymmetric parameter and support vector machine model. At first, the proposed models were applied to the 1000 simulated data. Furthermore, secondary data of 180 colorectal cancer patients who received treatment in general hospital with twenty five independent variables with different combination of variable types were considered to find the best models to predict the tumor size of CRC. The main objective of this study is to determine the best model to predicting the tumor size of CRC and to identify the factors and symptoms that contribute to the size of CRC. The comparisons among all the models were carried out to find the best model by using statistical measurements of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The results showed that the FLRWSPCSVM was found to be the best model, having the lowest MSE, RMSE, MAE and MAPE value by 100.605, 10.030, 7.556 and 14.769. Hence, the size of colorectal cancer could be predicted by managing twenty-five independent variables.

A Sustainable Circular Economic Supply Chain System with Waste Minimization Using 3D Printing and Emissions Reduction in Plastic Reforming Industry

A sustainable development model is vital to repair the environmental damage caused by the industrial revolution. The circular economy is presented as an alternative model capable of resolving the problems caused by the linear model of the economy. A circular supply chain consists of emission and waste minimization technologies with a remarkable gain in profit, which is the aim of any industry that is concerned about environmental conservation. One of the most critical hurdles to the transition to sustainability is waste management. A circular sustainable integrated model for the plastic reforming industry with an investment in 3D printing techniques to minimize waste, emission reduction, and ordering cost reduction will have a positive impact on profit as well as the environment. The customer's demand and the unit profit depends on the circularity index of the product. The profit of the plastic reforming industry is optimized with optimal values ​​of ordering quantity, circularity index, and investment in waste minimization, emission reduction, and ordering cost under carbon cap policy through an algorithm. The model establishes that the plastic reforming industry will get more profit and an optimal level of circularity index when it works with high efficiency of emission and waste minimization technologies under low investment, a rise in the carbon tax, and less opportunity cost. and ordering cost under carbon cap policy through an algorithm. The model establishes that the plastic reforming industry will get more profit and an optimal level of circularity index when it works with high efficiency of emission and waste minimization technologies under low investment, a rise in the carbon tax, and less opportunity cost. and ordering cost under carbon cap policy through an algorithm. The model establishes that the plastic reforming industry will get more profit and an optimal level of circularity index when it works with high efficiency of emission and waste minimization technologies under low investment, a rise in the carbon tax, and less opportunity cost.

Fractal Geometry: The Geometry of Nature

The Fractal Geometry is considered to be the geometry that can give the best approximation of nature and natural objects. We discuss the difference of the classical geometry and fractal geometry in terms of objects and space. The different properties and applications of fractals are explained. The fractal dimension is derived and the construction of Mandelbrot set is demonstrated through iterative steps.

An Overview of Data Science and its Application to Real-World Scenarios

Data Science which is the study of data is a blend of various tools, algorithms, and machine learning principles with the goal to discover hidden patterns from the raw data. It involves developing methods of recording, storing, and analyzing data to effectively extract useful information. The goal of data science is to gain insights and knowledge from any type of data — both structured and unstructured. It employs techniques and theories from a variety of disciplines, including mathematics, statistics, computer science, information science, and domain knowledge. Data Science is one of the most widely used technologies in the modern era. Data Science is expanding its applications in a variety of industries, including healthcare, media and entertainment, banking and finance, education, retail, and e-commerce, among others. Furthermore, Data Science applications aid in the analysis, manipulation, and visualisation of business data in order to better understand it and change business strategies accordingly.

Modelling The Transmission Dynamics of Anthrax with Optimal Control and Cost Effectiveness Analysis.

Anthrax is an infectious disease caused by bacteria called Bacillus anthracis. It affects both human and animal populations. Anthrax is a zoonotic diseases and humans can contract infection through contact with infected animals, ingest contaminated dairy and animal products. In this research, a mathematical model for transmission dynamics of anthrax in both human and animal populations with optimal control was developed. The anthrax deterministic model was analysed qualitatively and quantitatively. A vaccination compartment with waning immunity was incorporated into the model. The local and global stability analysis and the existence of equilibria were determined. The basic reproductive number was computed and it is the threshold parameter that governs the spread of a disease. It plays a key role in the transmission dynamics of the Anthrax disease. Sensitivity analysis of the basic reproduction number was performed. It was established that increasing animal (livestock) recovery rate would cause a decrease in the basic reproduction number. The Anthrax model exhibited the phenomenon of backward bifurcation. Biologically, the implication is that the idea of a model been locally asymptotically stable whenever the reproduction number is less than unity and unstable otherwise is not a sufficient condition for disease eradication. Moreover, an extension of the Anthrax model to optimal control theory which seeks to minimise the objective functional subject to some controls variables was incorporated. The resulting control problem was solved numerically in order to determine the most effective control measure in combating the Anthrax infections. Cost-benefit analysis was conducted to determine the costs associated with prevention of susceptible humans, treatment of infectious humans, vaccination of susceptible animals and treatment of infectious animals. The Infection Averted Ratio (IAR) approach was considered. Analysis of optimal control and cost effectiveness of the Anthrax model showed that the best and most effective strategy is vaccination of animals and prevention of susceptible humans in the system. Prevention control on humans and vaccination of animals should be considered as priority when fighting anthrax infections. There should be proper campaign on anthrax prevention and more animals should be vaccinated against the disease.

Computational Multiscale Model of Cancer Cell Migration and Invasion Phenotypes

The spread of cancer cells from a localized tumor mass in one part of the body to another is known as metastasis. It plays a crucial role in cancer-related death in cancer patients and reducing the efficacy of cancer treatment. Cancer cells in a tumor mass interact with one another as well as their local tumor microenvironment, particularly the extracellular matrix (ECM), during metastasis. The ECM undergoes structural remodeling of biochemical, physical, and mechanical characteristics because of this interaction. Cancer cells exhibit different mode of migration and invasion properties which includes single and collective migration modes. Single and collective cancer cell migration from the tumor is influenced by this structural remodeling. The processes and techniques that produce these cancer cell migratory characteristics are still unknown. Our group used the free open-source software CompuCell3D to create a computer model that mimicked in vivo cancer cell movement across the ECM during structural remodeling. Here, we discuss how we used in vitro migration tests for varied ECM collagen fiber concentrations and pore diameters to evaluate phenotypic changes from single cell to collective cell migration to validate this model. We also investigate the impact of cell adhesion. Chemotaxis-induced cancer cell motility is also investigated and quantified. The cancer cells are represented as discrete agents in our model, and the ECM components, including collagen fibers and remodeling enzyme(s), are modeled using a system of partial differential equations. The goal is to be able to validate the in vitro model and then go on to in vivo investigations to provide cancer metastasis prediction capacity.

A Simulation Study of HIV/AIDS-Listeriosis Co-dynamics in the Human Population.

Epidemiologically, co-infection is the simultaneous infection of a host by multiple pathogen species such as viruses, bacteria, or fungi. In this work, we model Human Immunodeficiency virus/Acquired Immunodeficiency Syndrome (HIV/AIDS) and Listeriosis co-infection dynamics using a set of nine ordinary differential equations. HIV/AIDS only sub-model and Listeriosis only sub-model are presented and analyzed. The steady states for each sub-model were also determined and the basic reproduction numbers were computed using the next generation matrix approach. The HIV/AIDS only basic reproduction number (R0h) and the Listeriosis only infection threshold parameter, (R0l) are derived. It has been shown that both the HIV/AIDS-only sub-model and Listeriosis-only sub-model have unique endemic equilibrium. Analysis of the HIV/AIDS-Listeriosis co-infection model is presented and results indicate that the disease-free equilibrium for the HIV/AIDS-Listeriosis co-infection model is globally asymptotically stable. Uncertainty analysis was performed using the Latin Hypercube Sampling Technique and conclusions on the sensitive parameters were drawn. Results from the analysis indicate that to reduce HIV/Listeriosis co-infection there is a need to concentrate on reducing the parameters that bear positive high PRCCs values with P-values lower than 0.05. To achieve this there is a need to implement interventions or control measures that reduce the co-infection reproduction number and consequently reduce infection spread within the population. Numerical simulations on the dynamics of the HIV/AIDS-Listeriosis co-infection model are performed and the results support the theoretical findings in the paper. It is envisaged that results obtained from this study will be useful in the fight against HIV/AIDS and Listeriosis co-dynamics.

Aedes Aegypti vs Wolbachia-An Innovative Method to Control Mosquito-Borne Diseases

Mosquito-borne diseases are primarily spread by female mosquitoes while taking a blood meal from living organisms such as humans, animals and birds. A parasite, virus, or bacteria-infected female mosquito can transmit those foreign agents to humans. The Dengue virus, Zika virus, Yellow fever virus and Chikungunya are transmitted from infected human to uninfected human via primary vector Aedes aegypti mosquitoes. The secondary vector for the above-mentioned diseases is Aedes albopictus. Wolbachia is an endosymbiotic bacterium that is reported in nearly 60% of insect species found by Wolbach (1924). The World Mosquito Program (WMP) from Australia currently release Wolbachia infected mosquitoes over 10 countries, such as countries in Latin America, India, Sri Lanka, Vietnam, Indonesia and cities in Oceania. In that research, they found that Wolbachia is a self-sustaining bacterium and in the presence of Wolbachia infected mosquitoes there is zero possibility of having Dengue. This talk try to answer the following questions, What is the role of Wolbachia in population suppression and virus control, how the concepts of mathematics used to control Aedes aegypti mosquitoes via Wolbachia method, control measures, why have to study the mathematical models, the ideas derived through mathematics.

New Applications of Fractional Differential Equations with Different Kernels

In this work, we present the history of the reproducing kernel Hilbert space method in details. We give the applications of the method to the fractional differential equations with different kernels. We apply the reproducing kernel Hilbert space method to the fractal fractional differential equations. We use the integral transforms to get the exact solutions of the problems. We compare the exact solutions with the approximate solutions. We demonstrate our results by some tables and figures. We prove the efficiency of the proposed technique for fractal fractional differential equations.

Mathematical Modeling of Neural Networks and its Dynamical Analysis

The differential dynamical model is one of the basic tools in the characterization of natural and engineering process, and it is also a basic block of the complicated neural network. A simplified mathematical description of natural neural networks is known as the artificial neural networks model. Since 1940, the neural networks have been studied due to its application in the various area such as pattern recognition, signal and image processing, associative memory, system identification and control, sequence recognition, medical diagnosis, data mining, and visualization. Consequently, the dynamical analysis is essential for the design and execution of neural networks and hence the dynamical problem for neural networks has attracted considerable attention in recent years. On the whole we examine the dynamical analysis of neural networks with various perturbations.

Asymmetric Laplace Distribution and ARMA Time Series Modeling of Micro-array Gene Expression Data

In this talk we consider the asymmetric Laplace distribution and its generalizations like Normal-Laplace distribution. We review its properties and address the problem of simulation as well as estimation of parameters. Microarray gene expression data are asymmetric and exhibit high skewness and heavy tails. The usual method of fitting normal distribution to log-transformed data is found to be inadequate in most cases. An asymmetric Laplace distribution is fitted to a micro-array gene expression data on potato. Considering the temporal behavior of the data, we develop a first order auto-regressive model with asymmetric Laplace stationary distribution. Sample path properties of the new time series model are also studied. It is extended to the case of Normal-Laplace distribution and ARMA models are also developed. Simulation studies are conducted to establish that the model is suitable for such data which exhibits temporal behavior.

On Oncolytic Viro-therapy Models

I will revisit and carry out further works on tumor-virotherapy compartmental models of [Tian, 2011, Phan and Tian, 2017, Guo et al., 2019]. The results of these papers are only slightly pushed further. Here, I will present a contribution to what was missing in these papers. On the other hand, I will present all the scientific, and research opportunities offered within my university, in order to encourage the student to be part of it.

Cohen-Macaulayness of Certain Families of Graphs

The study of Cohen – Macaulay rings, which historically goes back to about a century, plays a special role in commutative algebra. Polynomial rings and formal power series rings are examples of Cohen-Macaulay rings. Due to their special properties Cohen-Macaulay rings have found many applications in algebraic geometry. A connection can be made between commutative algebra and graph theory via the edge rings constructed from graphs. By definition, a graph is Cohen-Macaulay when ever its edge ring is Cohen-Macaulay.

This talk revolves around my attempt to characterize the Cohen-Macaulay property of certain graphs with very strong algebraic properties namely the strongly regular graphs.

An Introduction to Control Theory

The main purpose of this presentation is to give a brief introduction to my university Cadi Ayyad, we will see some details about the different fields of research at the Faculty of Science Semlalia. In addition, we will see some possibilities of schooling and opportunities.

On the other hand, I will present my field of research, the control theory which is a branch of the systems theory that studies the behavior of dynamic systems that can be controlled. The goal is to bring the system from an initial state to a final state in a specified time.

Multi-Agent Systems and its Applications

Multi-Agent Systems (MASs) has been well documented over the years as it is widely implemented in a variety of areas, including sensor networks, satellite sensors, unmanned-air-vehicle formulation and multi-robotics technology. Synchronization analysis of multi-agent systems (MASs) with time-varying delay is studied in this research work. First, we need to discuss synchronization with time-varying delays for MASs. We have also developed a linear feedback controller to achieve an synchronization criterion for uncertain MASs with time-varying delays. Numerical simulations are also used to verify the performance of the suggested control design system.