Special Colloquium: UMBC Undergraduate Research Students

Speaker: Nathan Michael Tamiru

Title: Computational Analysis and Conditioning of Navigational Systems using Nonlinear Least Squares

Abstract: We will explore computational analysis and conditioning of the Global Positioning System (GPS). GPS has become an integral part of our daily lives, enabling us to navigate and locate ourselves accurately. However, achieving a high-level precision requires the use of suitable mathematical models and numerical methods. We will begin by discussing the GPS function and how it determines accurate location. The GPS system relies on a network of satellites that orbit the earth and transmit signals to GPS receivers on the ground. These signals are used to determine the receiver's distance from the satellites, which is then used to calculate its precise location. However, errors that affect the accuracy of the data can still occur. We will discuss the sources of error and how it can be mitigated while using numerical methods such as nonlinear least squares and multivariate Newton's method. An essential component of GPS systems is the atomic clock, which provides precise timing information to synchronize the signals from the satellites. We will discuss the function and importance of atomic clocks in maintaining accurate GPS data and how they are used in conjunction with the GPS system.

Speakers: Alex Flitter and Nathan Michael Tamiru

Title: Epidemic Modeling using the SIR Model and Graph Networks

Abstract: The study focuses on a SIR model that uses a graph network to simulate a spread of an epidemic through a region divided into smaller geographical units. The models were implemented using Python and Matlab to simulate the percentage of a susceptible, infected, or recovered population in the region during a given time interval. Simulating the model requires parameters that describe the disease and an adjacency matrix that describes the graph network as the inputs. The adjacency matrix is converted into a graph-Laplacian matrix to simulate mobility in the network. The code produces a SIR graph for each region using the Laplacian and disease parameters. Finally, we also compare the error from an explicit and implicit solvers in a sequence of numerical experiments.