| LDR | | 02210nmm uu200409 4500 |
| 001 | | 000000331290 |
| 005 | | 20240805164105 |
| 008 | | 181129s2018 |||||||||||||||||c||eng d |
| 020 | |
▼a 9780438371040 |
| 035 | |
▼a (MiAaPQ)AAI10841159 |
| 035 | |
▼a (MiAaPQ)uchicago:14501 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 248032 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Chai, Wei. |
| 245 | 10 |
▼a Random Topological Structures. |
| 260 | |
▼a [S.l.] :
▼b The University of Chicago.,
▼c 2018 |
| 260 | 1 |
▼a Ann Arbor :
▼b ProQuest Dissertations & Theses,
▼c 2018 |
| 300 | |
▼a 105 p. |
| 500 | |
▼a Source: Dissertation Abstracts International, Volume: 80-01(E), Section: B. |
| 500 | |
▼a Adviser: Shmuel Weinberger. |
| 502 | 1 |
▼a Thesis (Ph.D.)--The University of Chicago, 2018. |
| 520 | |
▼a Data science is a recent focus across many fields such as mathematics, statistics and computer sciences aiming at discovering and understand patterns from data. Topological data analysis (TDA) is a solution to discover the underlying topological |
| 520 | |
▼a The first part of this thesis is on the random coverage. We estimate the number of data points to cover an underlying manifold with possibly boundaries or singularities and with possibly non-uniform probability distribution. In general, the expe |
| 520 | |
▼a The second part is about the thresholds of correct Cech homology on a flat torus Td. The thresholds are estimated by the critical points of distance function and Morse theory. This thesis examines a special type of critical points and makes an i |
| 520 | |
▼a The last part proposes a method to detect topological periodicity in a time series. Topological periodicity allows distortion of the function's domain. The proposed method is about encoding the topological information of a function by a tree. Co |
| 590 | |
▼a School code: 0330. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a The University of Chicago.
▼b Mathematics. |
| 773 | 0 |
▼t Dissertation Abstracts International
▼g 80-01B(E). |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0330 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2018 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T14999771
▼n KERIS |
| 980 | |
▼a 201812
▼f 2019 |
| 990 | |
▼a 관리자 |