Data-Driven Dynamics: Estimation in the Presence of Noise
| dc.contributor.author | Javeed, Aurya | |
| dc.contributor.chair | Guckenheimer, John Mark | |
| dc.contributor.committeeMember | Hooker, Giles J. | |
| dc.contributor.committeeMember | Levine, Lionel | |
| dc.date.accessioned | 2019-04-02T14:00:47Z | |
| dc.date.available | 2021-01-02T07:01:16Z | |
| dc.date.issued | 2018-12-30 | |
| dc.description.abstract | Dynamical systems theory is routinely applied to a mathematical model of a process rather than the process itself. In contrast, this dissertation advances a data-driven approach to dynamics in which conclusions are drawn directly from observations of the process of interest. The focus here is on laying mathematical foundations for this perspective; thus the data has been idealized as paths of stochastic differential equations (SDEs). An example that makes this summary concrete is the study of locomotion: A "routine'' approach is to analyze a model; for instance, is the runner's gait stable or unstable per the model? Instead, this dissertation is motivated by motion capture data---a time series reminiscent of a periodic process perturbed by noise. A prevailing theory is that organisms remain upright by using sensory information (akin to motion capture data) to subconsciously estimate the stability of their gait. Chapter 2 studies this estimation problem mathematically. It derives an inequality that quantifies the uncertainty intrinsic to Floquet multiplier estimates constructed from SDE paths. This inequality governs a sufficiently broad class of estimation strategies that the bound it establishes sheds light on the feasibility of the theory about how animals remain upright. The "data-first" perspective pursued in Chapter 2 is so underdeveloped in the context of dynamics that the other chapters of this dissertation arise naturally: Do certain types of noise yield better multiplier estimates? (Chapter 3.) And what should be done when observations of the process are costly? (Chapter 4.) | |
| dc.identifier.doi | https://doi.org/10.7298/0vg0-0y95 | |
| dc.identifier.other | Javeed_cornellgrad_0058F_11188 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:11188 | |
| dc.identifier.other | bibid: 10758079 | |
| dc.identifier.uri | https://hdl.handle.net/1813/64939 | |
| dc.language.iso | en_US | |
| dc.subject | Statistics | |
| dc.subject | Applied mathematics | |
| dc.title | Data-Driven Dynamics: Estimation in the Presence of Noise | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| thesis.degree.discipline | Applied Mathematics | |
| thesis.degree.grantor | Cornell University | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Applied Mathematics |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Javeed_cornellgrad_0058F_11188.pdf
- Size:
- 2.74 MB
- Format:
- Adobe Portable Document Format