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Topology in the 21st Century
Published on Jan 21, 20118859 Views
In recent years, classical methods of algebraic topology have found increasing use in applications. The key ingredient for these applications is the persistent homology algorithm of Edelsbrunner, Lets
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Plex14:02
Sensor networks - 114:33
Sensor networks - 214:53
The coverage problem - 116:49
The coverage problem - 217:04
The coverage problem - 317:14
The coverage problem - 417:23
The coverage problem - 517:25
The coverage problem - 617:42
The coverage problem - 717:57
Attacking the coverage problem - 118:10
Attacking the coverage problem - 218:16
Attacking the coverage problem - 318:25
Attacking the coverage problem - 418:44
Attacking the coverage problem - 518:53
Attacking the coverage problem - 619:32
Attacking the coverage problem - 719:41
Attacking the coverage problem - 819:43
Theorom - 121:39
Theorom - 221:42
Theorom - 321:59
Theorom - 422:16
Theorom - 522:31
The I - dimensional problem - 124:47
The I - dimensional problem - 225:05
The I - dimensional problem - 325:14
The I - dimensional problem - 425:24
The I - dimensional problem - 525:49
The I - dimensional problem - 625:59
The I - dimensional problem - 726:13
The I - dimensional problem - 826:15
The I - dimensional problem - 926:22
The I - dimensional problem: marked boundary - 228:04
The I - dimensional problem: marked boundary - 328:23
The I - dimensional problem: marked boundary - 428:42
The I - dimensional problem: marked boundary - 528:45
The I - dimensional problem: marked boundary - 628:48
The I - dimensional problem: marked boundary - 728:58
2 - dimensional coverage - 129:28
2 - dimensional coverage - 230:26
2 - dimensional coverage - 331:03
Discrete vs Continuos32:25
Point-cloud topology32:31
Standard Pipeline (first attempt)33:07
Betti numbers34:15
Reconstruction theorems34:20
One lump or two ? -134:46
One lump or two ? -234:53
One lump or two ? -334:54
One lump or two ? -434:54
One lump or two ? -534:55
One lump or two ? -634:55
Standard Pipeline (second attempt)36:07
Different scales, different features - 136:44
Different scales, different features - 236:59
Persistence pipeline37:11
Visual image patches45:27
The space of image patches46:58
High-density regions - 147:23
High-density regions - 250:31
Straining a data soup - 151:27
Varying the density parameter - 152:45
Varying the density parameter - 252:48
Varying the density parameter - 352:50
Varying the density parameter - 452:51
Varying the density parameter - 552:54
Varying the density parameter - 652:55
Varying the density parameter - 752:56
Varying the density parameter - 852:56
Varying the density parameter - 952:58
Varying the density parameter - 1052:58
Varying the density parameter - 1153:08
Varying the density parameter - 1253:11
Varying the density parameter - 1353:15
Varying the density parameter - 1453:15
Varying the density parameter - 1553:16
Straining a data soup - 253:17
A small platter of cuts - 254:31
(8-dimensional data) - 155:18
(8-dimensional data) - 255:20
3-circles model55:21
3-circles explaind56:12
The secondary circles57:06