Participants 2018

Jillian Greene

Name  

Jillian Greene

University

University of North Texas

Supervisor

Prof. Dr. Anna Marciniak-Czochra

Workgroup  

Applied Analysis and Modelling in Biosciences

Project

Neurogenesis Modelling in Adult Hippocampal Cells

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There has been a large amount of research done recently regarding the age-related changes happening in the neurogenesis of hippocampal cells using various mathematical models. Looking at the previous data that has been gathered from teams of mathematicians and biologists, we can see that there is some relationship between the total neural stem cells recorded in any one cycling of the pool of neural stem cells (NSCs) in an animal and the rate of quiescence of this pool of NSCs. The goal is to adjust the parameters in the original models of total NSC growth and declination in order to closely fit the trend lines created by the original model of the rate of quiescence. The trickiest part of creating accurate parameters is ensuring the biological reasoning behind every adjustment made to any piece of our model along the way. These models consisted of systems of ordinary differential equations that were calculated and adjusted using MATLAB. As this research moves further in the teams at IWR, it will open up a new understanding about the reproduction and quiescence in mammalian stem cells. I had a fantastic time in the MathComp Post-Bachelor program, and would like to thank my team, Prof. Marciniak, and HGS for welcoming me so graciously.

Judith Nneamaka

Name  

Judith Nneamaka

University

PAU Institute for Basic Sciences, Technology and Innovation

Supervisor

Dr. Michael Winckler

Workgroup  

Queuing theory

Project

Transient Analysis of an M/M/1 Queuing System with Working Breakdowns and Recovery Policies

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Queuing system with working breakdowns has a wide variety of applications such as in computer network,  manufacturing industries and transportation systems. It is obvious that server unreliability makes negative impact on performance of any queuing system, and undoubtedly, a reliable server with smooth services has a  positive impact on the economic activities of such systems. Therefore, in order to maintain a desired level of service in any queuing system, performance modeling is a first step to providing a solution. Using a set of differential equations, we modeled a single server Markovian queuing system  with working breakdowns and recovery policies.  The time-dependent solution was obtained using a numerical scheme which was implemented in Matlab. Further, the performance measures were analyzed to understand the sensitivity of the parameters on the model solution. The experience I had during the post-bachelor program was indeed awesome as I was exposed to learn many new things which have added to my academic skills.  My special thanks goes to Dr. Michael Winckler for his thorough supervision, and to the HGS MathComp, for providing the Post-bachelor learning platform.