Evolution and Optimum Seeking

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256 References Beyer, H.-G. (1994b), Towards a theory of `evolution strategies'|results from the Ndependent ( ) and the multi-recombinant ( = )theory, technical report SYS- 5/94, Systems Analysis Research Group, University of Dortmund, Department of Computer Science, Oct. 1994 Biggs, M.C. (1971), Minimization algorithms making use of non-quadratic properties of the objective function, JIMA 8, 315-327 (errata in 9 (1972)) Biggs, M.C. (1973), A note on minimization algorithms which make use of non-quadratic properties of the objective function, JIMA 12, 337-338 Birkho , G., S. MacLane (1965), A survey of modern algebra, 3rd ed., Macmillan, New York Blakemore, J.W., S.H. Davis, Jr. (Eds.) (1964), Optimization techniques, AIChE Chemical Engineering Progress Symposium Series 60, no.50 Bledsoe, W.W. (1961), A basic limitation on the speed of digital computers, IRE Trans. EC-10, 530 Blum, J.R. (1954a), Approximation methods which converge with probability one, Ann. Math. Stat. 25, 382-386 Blum, J.R. (1954b), Multidimensional stochastic approximation methods, Ann. Math. Stat. 25, 737-744 Boas, A.H. (1962), What optimization is all about, Chem. Engng. 69(25), 147-152 Boas, A.H. (1963a), How to use Lagrange multipliers, Chem. Engng. 70(1), 95-98 Boas, A.H. (1963b), How search methods locate optimum in univariable problems, Chem. Engng. 70(3), 105-108 Boas, A.H. (1963c), Optimizing multivariable functions, Chem. Engng. 70(5), 97-104 Boas, A.H. (1963d), Optimization via linear and dynamic programming, Chem. Engng. 70(7), 85-88 Bocharov, I.N., A.A. Feldbaum (1962), An automatic optimizer for the search for the smallest of several minima|a global optimizer, ARC 23, 260-270 Bohling, K.H., P.P. Spies (Eds.) (1979), 9th GI-Jahrestagung, Bonn, Oct. 1979, Springer, Berlin Boltjanski, W.G. (1972), Mathematische Methoden der optimalen Steuerung, Hanser, Munich Booth, A.D. (1949), An application of the method of steepest descents to the solution of systems of non-linear simultaneous equations, Quart. J. Mech. Appl. Math. 2, 460-468
References 257 Booth, A.D. (1955), Numerical methods, Butterworths, London Booth, R.S. (1967), Location of zeros of derivatives, SIAM J. Appl. Math. 15, 1496-1501 Boothroyd, J. (1965), Certi cation of algorithm 2|Fibonacci search, Comp. Bull. 9, 105, 108 Born, J. (1978), Evolutionsstrategien zur numerischen Losung von Adaptationsaufgaben, Dr. rer. nat. Diss., Humboldt University at Berlin Box, G.E.P. (1957), Evolutionary operation|a method for increasing industrial productivity, Appl. Stat. 6, 81-101 Box, G.E.P., D.W. Behnken (1960), Simplex-sum designs|a class of second order rotatable designs derivable from those of rst order, Ann. Math. Stat. 31, 838-864 Box, G.E.P., N.R. Draper (1969), Evolutionary operation|a statistical method for process improvement, Wiley, New York Box, G.E.P., N.R. Draper (1987), Empirical model-building and response surfaces, Wiley, New York Box, G.E.P., J.S. Hunter (1957), Multi-factor experimental designs for exploring response surfaces, Ann. Math. Stat. 28, 195-241 Box, G.E.P., M.E. Muller (1958), A note on the generation of random normal deviates, Ann. Math. Stat. 29, 610-611 Box, G.E.P., K.B. Wilson (1951), On the experimental attainment ofoptimum conditions, J. of the Royal Statistical Society B, Methodological 8, 1-45 Box, M.J. (1965), A new method of constrained optimization and a comparison with other methods, Comp. J. 8, 42-52 Box, M.J. (1966), A comparison of several current optimization methods and the use of transformations in constrained problems, Comp. J. 9, 67-77 Box, M.J., D. Davies, W.H. Swann (1969), Nonlinear optimization techniques, ICI Monograph 5, Oliver Boyd, Edinburgh Bracken, J., G.P. McCormick (1970), Ausgewahlte Anwendungen nicht-linearer Programmierung, Berliner Union und Kohlhammer, Stuttgart Brajnes, S.N., V.B. Svecinskij (1971), Probleme der Neurokybernetik und Neurobionik, 2nd ed., G. Fischer, Stuttgart Brandl, V. (1969), Ein wirksames Monte-Carlo-Schatzverfahren zur simultanen Behandlung hinreichend eng verwandter Probleme angewandt auf Fragen der Neutronenphysik, Tagungsbericht der Reaktortagung des Deutschen Atomforums, Frankfort/ Main, April 1969, Sektion 1, pp. 6-7
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Evolution and Optimum Seeking Hans-
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vi Multiple Data) machines with man
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viii 3.2.1.6 Complex Strategy of Bo
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Chapter 1 Introduction There is sca
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Introduction 3 simple matter to col
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Chapter 2 Problems and Methods of O
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Particular Problems and Methods of
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Other Special Cases 19 with expecta
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Other Special Cases 21 parts of the
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Chapter 3 Hill climbing Strategies
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One Dimensional Strategies 25 then
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One Dimensional Strategies 27 Even
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One Dimensional Strategies 29 The b
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One Dimensional Strategies 31 F(x)
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One Dimensional Strategies 33 For t
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One Dimensional Strategies 35 It is
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One Dimensional Strategies 37 F P F
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Multidimensional Strategies 39 the
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Multidimensional Strategies 41 asch
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Multidimensional Strategies 43 e 2
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Multidimensional Strategies 45 Step
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Multidimensional Strategies 47 Numb
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Multidimensional Strategies 49 wher
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Multidimensional Strategies 53 Numb
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Multidimensional Strategies 55 The
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Multidimensional Strategies 57 Anum
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Multidimensional Strategies 61 Iter
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Multidimensional Strategies 63 (If
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Multidimensional Strategies 65 eval
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Multidimensional Strategies 67 The
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Multidimensional Strategies 69 devi
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Multidimensional Strategies 71 spec
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Multidimensional Strategies 73 othe
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Multidimensional Strategies 75 anot
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Multidimensional Strategies 77 3.2.
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Multidimensional Strategies 81 Brow
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Multidimensional Strategies 83 (197
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Multidimensional Strategies 85 meth
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Chapter 4 Random Strategies One gro
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Random Strategies 89 parts is taken
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Random Strategies 91 Pardalos and R
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Random Strategies 93 to write the n
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Random Strategies 95 the expectatio
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Random Strategies 97 maintained at
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Random Strategies 99 works entirely
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Random Strategies 101 the principle
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Random Strategies 103 out, a limite
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Chapter 5 Evolution Strategies for
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The Two Membered Evolution Strategy
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A Multimembered Evolution Strategy
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Genetic Algorithms 151 too is the c
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Genetic Algorithms 153 mean objecti
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Genetic Algorithms 155 p( ∆x) 1 1
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Genetic Algorithms 157 out any chan
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Genetic Algorithms 159 Average Numb
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Simulated Annealing 161 There are t
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Tabu Search and Other Hybrid Concep
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Chapter 6 Comparison of Direct Sear
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Theoretical Results 167 Oettli, 196
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Theoretical Results 169 where 0
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Theoretical Results 171 tions. Simi
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Numerical Comparison of Strategies
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Page 257 and 258: Chapter 8 References Glossary of ab
Page 259 and 260: References 251 Anscombe, F.J. (1959
Page 261 and 262: References 253 Bandler, J.W. (1969b
Page 263: References 255 Bendin, F. (1992), E
Page 267 and 268: References 259 Brent, R.P. (1971),
Page 269 and 270: References 261 Carroll, C.W. (1961)
Page 271 and 272: References 263 Courant, R., D. Hilb
Page 273 and 274: References 265 Davies, M., I.J. Whi
Page 275 and 276: References 267 Dvoretzky, A. (1956)
Page 277 and 278: References 269 Fiacco, A.V. (1974),
Page 279 and 280: References 271 Fogel, L.J., A.J. Ow
Page 281 and 282: References 273 Gill, P.E., W. Murra
Page 283 and 284: References 275 Graves, R.L., P. Wol
Page 285 and 286: References 277 Heckler, R., H.-P. S
Page 287 and 288: References 279 Ho meister, F., H.-P
Page 289 and 290: References 281 Idelsohn, J.M. (1964
Page 291 and 292: References 283 Karnopp, D.C. (1966)
Page 293 and 294: References 285 Kochen, M., H.M. Has
Page 295 and 296: References 287 Kunzi, H.P., H.G. Tz
Page 297 and 298: References 289 LeCam, L.M., J. Neym
Page 299 and 300: References 291 Mamen, R., D.Q. Mayn
Page 301 and 302: 294 References Miele, A., H.Y. Huan
Page 303 and 304: 296 References Murray, W. (Ed.) (19
Page 305 and 306: 298 References Oldenburger, R. (Ed.
Page 307 and 308: 300 References Peschel, M. (1980),
Page 309 and 310: 302 References Powell, M.J.D. (1970
Page 311 and 312: 304 References Rechenberg, I. (1989
Page 313 and 314: 306 References Rybashov, M.V. (1969
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308 References Schmidt, J.W., K. Ve
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310 References Shedler, G.S. (1967)
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312 References Steinbuch, K. (1971)
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314 References Tabak, D. (1970), Ap
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316 References Varela, F.J., P. Bou
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318 References White, L.J., R.G. Da
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320 References Youden, W.J., O. Kem
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322 References Glossary of Abbrevia
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324 References
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326 Appendix A Problem 1.2 Objectiv
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328 Appendix A Minimum: x =(3 0:5)
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330 Appendix A Figure A.3: Graphica
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332 Appendix A Several of the searc
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338 Appendix A Minimum: Start: Prob
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340 Appendix A Problem 2.20 Objecti
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342 Appendix A Problem 2.23 Objecti
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344 Appendix A Start: x (0) i =10 f
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346 Appendix A on the interval 0 y
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348 Appendix A Problem 2.32 after B
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350 Appendix A Constraints: Gj(x) =
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352 Appendix A The constraints form
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354 Appendix A Start: x (0) =(250 2
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356 Appendix A Problem 2.44 As Prob
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358 Appendix A Figure A.29: Graphic
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360 Appendix A Start: Figure A.31:
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362 Appendix A Problem 3.2 (analogo
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364 Appendix A Problem 3.6 (analogo
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366 Appendix A Minimum: x i =0 for
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368 Appendix B LF (integer) Return
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370 Appendix B 4. Convergence crite
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372 Appendix B 8. Function Z(S,R) T
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374 Appendix B 25 L(K)=L(K+1) L(10)
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376 Appendix B LF=2 (continued) No
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378 Appendix B man), vol. 15 of Pro
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380 Appendix B instead of T, as a p
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382 Appendix B 15 CONTINUE 16 FF=F(
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384 Appendix B SK(KS)=AMAX1(SM(I),A
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386 Appendix B B.3 ( + ) Evolution
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388 Appendix B EPSILO (one dimensio
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390 Appendix B GLEICH (real functio
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392 Appendix B GLEICH, and TKONTR d
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394 Appendix B 1 NL=1+N-NS NM=N-1 N
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396 Appendix B ZSTERN=ZBEST K=LBEST
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398 Appendix B C NEGATIVE (LETHAL M
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400 Appendix B C C PREPARE FINAL DA
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402 Appendix B 2 IF(.NOT.BKOMMA.OR.
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404 Appendix B 32 WRITE(KANAL,126)
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406 Appendix B DO 4 I=1,NX KI=KI1 I
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408 Appendix B Subroutine MINMAX MI
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410 Appendix B 2 IF(U.LT..965487131
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412 Appendix B parameters by multip
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414 Appendix B
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416 Appendix C - SIMP Simplex strat
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418 Appendix C C.3.2 How to Install
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420 Appendix C { } return(0.26*(x[0
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422 Appendix C 1 No recombination 2
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424 Appendix C 8e-07 8e-07 Initial
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426 Index Banach, S., 10 Bandler, J
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428 Index Coordinate strategy, 41{4
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430 Index Evolution strategy, 3, 6,
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432 Index Graves, R.L., 23 Great de
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434 Index Khurgin, Ya.I., 89 Kiefer
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436 Index Michie, D., 102 Mickey, M
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438 Index Parkinson, J.M., 61 Parta
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440 Index Rotating coordinates meth
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442 Index Storey, C., 23, 50, 54 St
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444 Index Wilson, S.W., 103 Witt, U
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