Knowledge (XXG)

Euler calculus

Source đź“ť

287: 328: 258: 237: 166: 174: 352: 136:
Schapira, P. "Cycles Lagrangiens, fonctions constructibles et applications", Seminaire EDP, Publ. Ecole Polytechnique (1988/89)
55: 211: 347: 321: 357: 79: 51: 367: 362: 314: 63: 35: 39: 43: 117: 27: 163: 146: 254: 247: 233: 31: 17: 298: 178: 243: 170: 116:
McTague, Carl (1 Nov 2015). "A New Approach to Euler Calculus for Continuous Integrands".
67: 47: 341: 50:. In the presence of a metric, it can be extended to continuous integrands via the 271: 227: 99: 182: 286: 59: 294: 194: 173:, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 122: 16:
For numerical analysis of ordinary differential equations, see
302: 274:
video presentation, June 2009. published 30 July 2009.
212:
Target enumeration via Euler characteristic integrals
195:
Some integral calculus based on Euler characteristic
62:in 1988, and is useful for enumeration problems in 322: 8: 201:, vol. 1346, Springer-Verlag, 1988, 127–138. 329: 315: 121: 100:Euler integration for definable functions 91: 229:Tame Topology and O-minimal Structures 164:Tomography of constructible functions 147:Operations on constructible functions 54:. It was introduced independently by 7: 283: 281: 232:, Cambridge University Press, 1998. 42:by integrating with respect to the 301:. You can help Knowledge (XXG) by 177:, 1995, Volume 948/1995, 427–435, 106:, 107(21), 9525–9530, 25 May 2010. 14: 175:Lecture Notes in Computer Science 285: 253:, Springer, 1998, p. 219. 26:is a methodology from applied 1: 210:Baryshnikov, Y.; Ghrist, R. 98:Baryshnikov, Y.; Ghrist, R. 384: 280: 15: 104:Proc. National Acad. Sci. 80:Topological data analysis 183:10.1007/3-540-60114-7_33 218:, 70(3), 825–844, 2009. 46:as a finitely-additive 36:constructible functions 353:Computational topology 199:Lecture Notes in Math. 64:computational geometry 151:J. Pure Appl. Algebra 226:Van den Dries, Lou. 52:Gauss–Bonnet theorem 44:Euler characteristic 40:definable functions 348:Algebraic topology 249:Singularity Theory 169:2011-10-05 at the 162:Schapira, Pierre. 38:and more recently 28:algebraic topology 358:Integral geometry 310: 309: 259:978-3-540-63711-0 246:; Lyashko, O. V. 238:978-0-521-59838-5 32:integral geometry 375: 331: 324: 317: 295:topology-related 289: 282: 270:Ghrist, Robert. 219: 208: 202: 191: 185: 160: 154: 153:72, 1991, 83–93. 143: 137: 134: 128: 127: 125: 113: 107: 96: 34:that integrates 383: 382: 378: 377: 376: 374: 373: 372: 338: 337: 336: 335: 278: 267: 244:Goryunov, V. V. 242:Arnold, V. I.; 223: 222: 209: 205: 192: 188: 171:Wayback Machine 161: 157: 144: 140: 135: 131: 115: 114: 110: 97: 93: 88: 76: 68:sensor networks 56:Pierre Schapira 21: 12: 11: 5: 381: 379: 371: 370: 368:Topology stubs 365: 363:Measure theory 360: 355: 350: 340: 339: 334: 333: 326: 319: 311: 308: 307: 290: 276: 275: 272:Euler Calculus 266: 265:External links 263: 262: 261: 240: 221: 220: 216:J. Appl. Math. 203: 186: 155: 138: 129: 108: 90: 89: 87: 84: 83: 82: 75: 72: 24:Euler calculus 18:Euler's method 13: 10: 9: 6: 4: 3: 2: 380: 369: 366: 364: 361: 359: 356: 354: 351: 349: 346: 345: 343: 332: 327: 325: 320: 318: 313: 312: 306: 304: 300: 297:article is a 296: 291: 288: 284: 279: 273: 269: 268: 264: 260: 256: 252: 250: 245: 241: 239: 235: 231: 230: 225: 224: 217: 213: 207: 204: 200: 196: 190: 187: 184: 180: 176: 172: 168: 165: 159: 156: 152: 148: 145:Schapira, P. 142: 139: 133: 130: 124: 119: 112: 109: 105: 101: 95: 92: 85: 81: 78: 77: 73: 71: 69: 65: 61: 57: 53: 49: 45: 41: 37: 33: 29: 25: 19: 303:expanding it 292: 277: 248: 228: 215: 206: 198: 189: 158: 150: 141: 132: 111: 103: 94: 23: 22: 342:Categories 251:, Volume 1 123:1511.00257 86:References 193:Viro, O. 60:Oleg Viro 167:Archived 74:See also 214:, SIAM 48:measure 257:  236:  293:This 118:arXiv 299:stub 255:ISBN 234:ISBN 66:and 58:and 30:and 179:doi 344:: 197:, 149:, 102:, 70:. 330:e 323:t 316:v 305:. 181:: 126:. 120:: 20:.

Index

Euler's method
algebraic topology
integral geometry
constructible functions
definable functions
Euler characteristic
measure
Gauss–Bonnet theorem
Pierre Schapira
Oleg Viro
computational geometry
sensor networks
Topological data analysis
Euler integration for definable functions
arXiv
1511.00257
Operations on constructible functions
Tomography of constructible functions
Archived
Wayback Machine
Lecture Notes in Computer Science
doi
10.1007/3-540-60114-7_33
Some integral calculus based on Euler characteristic
Target enumeration via Euler characteristic integrals
Tame Topology and O-minimal Structures
ISBN
978-0-521-59838-5
Goryunov, V. V.
Singularity Theory, Volume 1

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑