Discipline: Technology and Engineering
Subcategory: Mathematics and Statistics
Raji Dinka - Rutgers University
Co-Author(s): 1.Benedetto Piccoli, Associate Provost for Research Rutgers University, Camden, Associate Provost for Research 2.Sean McQuade, Ph. D. candidate at RU, New Jersey
The existing conventional definition of entrainment only describes the role of period. And the purpose of our research was to investigate other factors that affect entrainment. We have worked on a mathematical model that describes the circadian rhythm and diurnal rhythms. The experimental data have been used in optimizing the mathematical model. Three separate in silico experiments were done to analyze the phase of entrainment by using Mat lab- ODE45. First, analysis of phase of entrainment by taking 100 randomly generated clocks with τ = 24, and random θ ∼ Gaussian (µ = 0, σ= pi/12 ). Second, analysis of phase of entrainment by taking 100 randomly generated clocks with τ ∼ Gaussian ( µ = 24, σ = 4), and θ = 0. Third, analysis of phase of entrainment by taking 100 randomly generated clocks with τ ∼ Gaussian ( µ = 24 σ = 4), and random θ ∼ Gaussian ( µ = 0, σ = pi /2 ). And finally, in order to analyze the phase of entrainment we have plotted random parameters of initial angle of (N) on the x-axis vs phase of entrainment on the y-axis. We have reason to think that these dynamics may be the correct way to approach the problem. This is because our Psi function changes the shape of the wave plotted by r*sine(θ + φ), just as in the collected from previous research. In the data, the shape changes as well. The outcome of the project will impact in our ability to understand the human clock disorders such as Familial advanced sleep phase syndrome.
Not SubmittedFunder Acknowledgement(s): I would like to acknowledge and thank REU. I am so grateful for the experience I have gotten from this research. And also I want to thank you, Rutgers University for giving me where I live during this research.
Faculty Advisor: Sean McQuade, sn.mcquade@gmail.com
Role: I have done pretty much all the mathematical modeling part. I have done three separate in silico experiments to analyze the phase of entrainment by using Mat lab- ODE45. First, the analysis of phase of entrainment by taking 100 randomly generated clocks with τ = 24, and random θ ∼ Gaussian (µ = 0, σ= pi/12 ). Second, the analysis of phase of entrainment by taking 100 randomly generated clocks with τ ∼ Gaussian ( µ = 24, σ = 4), and θ = 0. Third, the analysis of phase of entrainment by taking 100 randomly generated clocks with τ ∼ Gaussian ( µ = 24 σ = 4), and random θ ∼ Gaussian ( µ = 0, σ = pi /2 ). And finally, to analyze the phase of entrainment, I have plotted random parameters of initial angle of (N) on the x-axis vs phase of entrainment on the y-axis.