Math

The Abu Dhabi and Dubai stock exchanges are among the most important ones in the region. Combined, they comprise a market capitalization of over 230,000 trillion USD. The size and complexity of such financial markets require the development of new mathematical and statistical tools.

This apparatus, when conjoined with the speed of modern computers and the availability of multiple sources of data, can be extremely powerful in dealing with the main challenges addressed in this project:

1. 1. Assessing, quantifying, and managing risk and volatility in financial markets employing large data sets and multiple information sources.
   2. Understanding and quantitatively describing complex phenomena such as trade agreements, social interactions, contagious dynamics, and biological phenomena.
   3. Solving relevant statistical inverse (calibration) problems that arise in medical and biological contexts such as in impedance and optical diffusion tomography.

This project aims at exploring the benefits of recent developments in Machine Learning (ML) in designing better models and solution methods for discrete optimization problems, in particular in the field of Supply Chain and Logistics. Our research will be focused on two directions. First, we will try to use ML techniques to incorporate demand learning into optimization problems. This will lead to increased responsiveness of the supply chain processes modeled. The joint optimization of demand learning and of the supply chain process will increase the scale of the problem, while maintaining its linearity. One of our goals is to design efficient algorithms for the joint problem.

Second, we will investigate methods to learn the structure of optimal solutions of computationally tractable problems and use this structure to solve efficiently large-scale supply chain optimization problems, such as vehicle routing or delivery problems.

This project will focus on supply chain, an essential part of any large company. Hopefully, the techniques developed in this project will lead to a higher efficiency and responsiveness of supply chains.

We consider a biologically based mathematical model (system of ODEs) that describe a disease prevalence in a logistically growing population. Some vaccine parameters in both childhood and adult stages are considered in the model to control the disease. Then we introduce some optimization problems constrained by this system of ODEs. We use optimal problems to find vaccine optimal parameters that imply the most cost-effective method for introducing vaccine for this population. The optimal problem is implemented and solved using MATLAB coding. This work will help in improving the way of delivering vaccine at schools and health units in the UAE, and will also help policy making in controlling any possible future health problems. This research project target a worldwide health problem and will support the research activity in both the Mathematics Department and the College of Medicine and Health Sciences at Khalifa University.