Physical Sciences and Mathematics Commons^™

Modeling Trajectories With Recurrent Neural Networks, Hao Wu, Ziyang Chen, Weiwei Sun, Baihua Zheng, Wei Wang

Research Collection School Of Computing and Information Systems

Modeling trajectory data is a building block for many smart-mobility initiatives. Existing approaches apply shallow models such as Markov chain and inverse reinforcement learning to model trajectories, which cannot capture the long-term dependencies. On the other hand, deep models such as Recurrent Neura lNetwork (RNN) have demonstrated their strength of modeling variable length sequences. However, directly adopting RNN to model trajectories is not appropriate because of the unique topological constraints faced by trajectories. Motivated by these findings, we design two RNN-based models which can make full advantage of the strength of RNN to capture variable length sequence and meanwhile to …

Joint Inversion Of Compact Operators, James Ford

Boise State University Theses and Dissertations

The first mention of joint inversion came in [22], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.

The operators are …

Optical Tomography On Graphs, Francis J. Chung, Anna C. Gilbert, Jeremy G. Hoskins, John C. Schotland

Mathematics Faculty Publications

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.

Dynamical Systems Modeling To Identify A Cohort Of Problem Drinkers With Similar Mechanisms Of Behavior Change, Kidist Maxwell, Rebecca Everett, Sijing Shao, Alexis Kuerbis, Lyric Stephenson, H. T. Banks, Jon Morgenstern

Publications and Research

One challenge to understanding mechanisms of behavior change (MOBC) completely among individuals with alcohol use disorder is that processes of change are theorized to be complex, dynamic (time varying), and at times non-linear, and they interact with each other to influence alcohol consumption. We used dynamical systems modeling to better understand MOBC within a cohort of problem drinkers undergoing treatment. We fit a mathematical model to ecological momentary assessment data from individual patients who successfully reduced their drinking by the end of the treatment. The model solutions agreed with the trend of the data reasonably well, suggesting the cohort patients …