-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcomputations_final.nb
5638 lines (5516 loc) · 267 KB
/
computations_final.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 11.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 273223, 5630]
NotebookOptionsPosition[ 264104, 5474]
NotebookOutlinePosition[ 264512, 5492]
CellTagsIndexPosition[ 264469, 5489]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"(*",
RowBox[{"Chemotactic", " ", "response", " ", "function", " ", "K",
RowBox[{"(", "t", ")"}]}], "*)"}]], "Input",
CellChangeTimes->{{3.758808729230567*^9, 3.758808744135152*^9}},
Background->RGBColor[
1, 0.85, 0.85],ExpressionUUID->"6be90174-fabc-4699-ab3e-f260a33b81c7"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"K", "[", "t_", "]"}], " ", "=",
RowBox[{"Piecewise", "[", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
FractionBox["1", "\[Gamma]"],
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox["t", "\[Gamma]"]}]], " ", "\[Beta]", " ",
RowBox[{"(",
RowBox[{
FractionBox["t", "\[Gamma]"], "-",
FractionBox[
SuperscriptBox["t", "2"],
RowBox[{"2", " ",
SuperscriptBox["\[Gamma]", "2"]}]]}], ")"}]}], ",",
RowBox[{"t", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"t", "<", "0"}]}], "}"}]}], "}"}], "]"}]}]], "Input",
CellChangeTimes->{{3.736235042417225*^9, 3.7362350994762363`*^9}, {
3.736235212356587*^9, 3.736235234619841*^9}, {3.758806609481101*^9,
3.7588066131430473`*^9}, {3.758806672967634*^9, 3.758806714412796*^9}, {
3.758806785612549*^9, 3.758806818307024*^9}, {3.758806962092731*^9,
3.758806988743326*^9}, {3.75880761427846*^9, 3.758807635951316*^9}, {
3.758807718407082*^9, 3.758807726132083*^9}, 3.758808598964279*^9, {
3.7588087105081167`*^9, 3.758808722366989*^9}, {3.759058408656547*^9,
3.75905841999681*^9}, {3.761626768150836*^9, 3.761626768264573*^9}, {
3.762519585373658*^9, 3.762519591299541*^9}, 3.762519764380076*^9, {
3.762604507603455*^9, 3.76260453867838*^9}, {3.7639739802719593`*^9,
3.763974021251401*^9}},
Background->RGBColor[0.87, 0.94, 1],
CellLabel->"In[1]:=",ExpressionUUID->"f158abd7-e77e-41cc-9414-c5a8d289b965"],
Cell[BoxData[
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{
FractionBox[
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox["t", "\[Gamma]"]}]], " ", "\[Beta]", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
FractionBox[
SuperscriptBox["t", "2"],
RowBox[{"2", " ",
SuperscriptBox["\[Gamma]", "2"]}]]}], "+",
FractionBox["t", "\[Gamma]"]}], ")"}]}], "\[Gamma]"],
RowBox[{"t", ">", "0"}]},
{"0",
TagBox["True",
"PiecewiseDefault",
AutoDelete->True]}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}},
Selectable->True]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False]], "Output",
CellChangeTimes->{3.763974021937204*^9, 3.764044800453848*^9,
3.7645616690049973`*^9, 3.764598600785101*^9},
CellLabel->"Out[1]=",ExpressionUUID->"74e0577d-fd47-4200-97f9-84a7f653f184"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"\[Gamma]", "^", "2"}], "*",
RowBox[{"K", "[", "t", "]"}]}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "a"}], "}"}], ",", " ",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"\[Gamma]", ">", "0"}], ",",
RowBox[{"a", ">", "0"}]}], "}"}]}]}], "]"}]], "Input",
CellChangeTimes->{{3.76459860357161*^9, 3.7645986589095984`*^9}, {
3.76459871094976*^9, 3.76459872243184*^9}, {3.76459877521704*^9,
3.764598782195294*^9}, {3.764599288247126*^9, 3.764599291679956*^9}},
CellLabel->"In[9]:=",ExpressionUUID->"248edf10-286f-45b7-a5a0-19788d06f8b3"],
Cell[BoxData[
RowBox[{
FractionBox["1", "2"], " ",
SuperscriptBox["a", "2"], " ",
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox["a", "\[Gamma]"]}]], " ", "\[Beta]"}]], "Output",
CellChangeTimes->{{3.764598617023641*^9, 3.764598660128364*^9}, {
3.764598713763405*^9, 3.7645987230213737`*^9}, {3.764598777527749*^9,
3.764598783249259*^9}, 3.76459929315565*^9},
CellLabel->"Out[9]=",ExpressionUUID->"ca999b54-e4d3-4509-982d-285dba865b53"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"p1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
SuperscriptBox["\[ExponentialE]", "t"], " ",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "t"}], "-",
FractionBox[
SuperscriptBox["t", "2"], "2"]}], ")"}], "/",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Sqrt", "[", "2", "]"}], "-", "1"}], ")"}], "*",
RowBox[{"E", "^",
RowBox[{"(",
RowBox[{
RowBox[{"Sqrt", "[", "2", "]"}], "-", "2"}], ")"}]}]}],
")"}]}]}], " ", ",",
RowBox[{"t", "<", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"t", "\[GreaterEqual]", "0"}]}], "}"}]}], "}"}], "]"}], ",",
RowBox[{"{",
RowBox[{"t", ",",
RowBox[{"-", "5"}], ",", "2"}], "}"}], ",",
RowBox[{"PlotStyle", "\[Rule]", "Red"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.7639630265352583`*^9, 3.763963037935429*^9}, {
3.7639631342482967`*^9, 3.763963228483387*^9}, {3.7639632633940277`*^9,
3.763963322002563*^9}, {3.763963818185637*^9, 3.7639638237513313`*^9}},
CellLabel->"In[2]:=",ExpressionUUID->"a039f546-c55b-4cb4-bce1-5c6811ed1dee"],
Cell[BoxData[
GraphicsBox[{{{{}, {},
TagBox[
{RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.],
LineBox[CompressedData["
1:eJwV1wk0VV8XAHCZvWceohIqyVCIDBUORREKJeovJJKhkooGSRmizEnJkFKp
yDxH+xDKlOldU+Z5voUkUd/91nprvfVb67x97j377H3O2+Rw0cKJmYmJ6e0a
Jqb/f7/84LL4758QFr418V8YTz1IlUUoNKwK4altDtEgXA+JH/Ptn/4Rwr8U
7lvPbaiH2PI1dbt+CeE112UjT8jXQ/DnuGcus0K48LlStOLBenBvrTFs7RbC
drCRPudXD7um5OJfFwvh+WKZ7+0L9VC5fhKZXhbCK3zNkSM9DSC+w6mtsksQ
ryTOp4Z2NQL38HcxaxNBPG9v7GvT1QQSZGB0ARbAUhF7HZWgGVzei5xAcgKY
dlRL4E9GCxjzF9QNxfPjO5Fxo3/vtIKTjPmDHGZ+nFA0mWFswQDeIoV5ayZ+
HP1j7qyRJQMuPOQu+PuHDzsWidkaWDNAsMvL8skcH9bsvLFG05YBJ52NY+r6
+PCN5qBBDlcGTNxZEFAp4cNFz+V2m91hAGfhAZ5/F/jwg7WPjl7JoMZ3/ek2
duXDul9VO9SyGZC+mpX+xIkP71oKtvqZywAz/Q0mKjZ8WCjFS/tCMQMeN5P3
nYz4cPrKkvPBSgbITD/hrN/Ch+Xt9HUfdTLAYNMUS1wHL24wL2GKYCagtIYp
W53Bi51fxH/qZyVAxXOtLaORF0stpAYocxAg9UmviO8zL35TFPK7hk7AsuMT
96B8XnywSPXasDABWW8MiMvRvLhSaEmoQIaA9crJrw+b8GInHZnxMkMCIjvy
j04f5MXMJ0uT6w4RwHGnjun+fl4sMNot2m5CwELz4smqPbz4W0LQ7jEzAhov
m/JpyfFit+tV/NPWBAQULnvLsfPip27T2kHnCCB1LI1YMQ8W6q0kZgIJYCpr
Mdz/gQcfSi2SJO4RwL/XzPBuAQ+emyU9i0MIUNYwPsj0ngefEKTJXw8jwFNJ
z2AljgeL6FSFMmIIWJTcobdwmQeftvPOWHpBAHvSO13VizyY7fxarcyXBIiK
y+p6uvLgdSqdrxxeE6AptgV9t+fBUQfNmPFbAq7zr9OeNuXBYe9Phx/LImCF
iW338DYenJVp4jJYSgD37buaW7bw4OXZ+VNOHwnYuPpPw0GCB/NIqDKNAAE6
v5fV+4V58L3/Xup1VRBw+8f3Xd1rqN/HKjklfCGAebBbmfGNGweekYzyaSVA
0P6kslA7N46WPfn7C4OALb3tShYt3PjCN5U+gTYC9LtaFJu+cGOPw2GicR0E
BLV82V6fz419qnVHfHoI4PqUJ1sZwY03d5buezxKzV8dzXbsATfutG+efTxG
wJUaj8GhIG58NJrn9KNxAnobtyew+HLjktufw4ImCcjpfsm3350b35IMx3qz
BIz13Z1ucebGJzR3HZclCRAfsq9xOMON7728kUj/TsC9CXH/uye5cR5zpPqX
HwTYLMYslhtyY5mzuw6t+0lA1G/PVnN9bvzLXEt6hHL1ilnWAOLGcRqi8e8X
qfyx8Liu0eDGWjdrj+1aIoCNP7BHdys3Pns5JEPsDwF7hM6UNElxY2Onh1tr
KHus1XtsL86N/y7ZSHutENAlvmrmJ8SN22MiM6pWCciQu1oJa7gx/cTYuz1M
bTC0/ejzI6t03FByRqSRspjyTt++JTruvnpgzm5NG9xVn9H4R9Ix06NbS17M
bVC4u044YoqOrcIuiK9SntZ6+0NijI5fcvxLvc3SBlb7ndJ0euk4OE1h6jpr
G4Qe2B/8tZOOlbP+S/xBucJok5MtQccbZizSndjaYLtZj4RvPR0zanKIfext
wHTKMrqshI6vKZZxNXO0gZq96kXTAjq+kZ9rqcDZBq5nBEx6sun4RGLo+B3K
DJcGttU3dMx7s7d9C1cbcJ1PGwx9SccRSs2KFynreISAeDIde1fElRdQfutl
cF3rMR1/5o+J2ENrg97rW47XR9PxZLd6lRdl4VtrVG3C6VjsbZRCJmUjvz6+
6RA61jDsgiHKvv5l0zcD6ZjjmsFtYXob5AbF19Dv0PHeAXZnPcrjIddfx/vQ
cZKo+RVXyhvDrPwVrtGx+lPLlxGULSLV7D9cpuOTrfoLWZRle+tiT1+k47W2
xW0NlP8qODRwuNHxMQOH5VHKjOtLLBln6RhFxdqsUE77HL7nmAMdMxunL/Nw
U/kR2Xpp+RQdL/gsNW+gbH3mQ2ryCTpOUWns20pZMdu894AlHYtc99+0nTLr
vzHhGTM6brN1jlGk3GXia/zQhI5lF+rUdlDOeip8d7chHW81XsMiSzlo/F1R
335qfbyP/5agfEpdjwxEdJwXuW6tIOVdAe1bt++lY8GMx8fXUKa1nLdpUadj
rinxomnqefslWR9eU6FjXacFDQblgvNPayQU6Vha+1xrIeXQD8pMVXJ0LB5b
fu8xZQeuz+puW+n4XayhxWXKmlanzgtsouOEc/rKxpT5Xs2nFIrTsfbuPxKS
lEfnQrpOiVH7Y3fOBpLKT6mulACrMB0LJb3f8oHyuW4TXzM6HRfcvHXoIGUd
+aG8RXY6Fr5MnOH4f76vXZ9KYKbjvrprtz5R+wMLvbae+E3DSc2Jr5Uox57W
ioj4ScPSW+Kz+qj95p7ZUqX2g4ZTJL9lPqC8zvifyt1xGn6XxOffTu3X708e
ucgO07DPnLe5N+XqUYXkr300rBVDowlR9rxrzbOhnYa93z5Q1KH2u2HT7P7y
Fhqu3TQa00DVg4RE4A3nrzSsMLevy5pybXH2WG4VDbMtNC06UPWTzGEocbKc
hrc4nf0yQNWbl2XvMaYyGhbOqD5vQ3nLD1qFSR4Nuye/kjWg6tNH1jFh5AUN
2wy28w3/I8DCa7nlQRINO+ZXKetRlq2M5FJ5SsOpf/t5n/4lgLAr8/KNomHz
VZ1fOlS/UHy81lzUj4a7jpTKWi4TwDqSfq/sJg0rquoORfym+ovK/o9nvGm4
9NNa/WqqP937elEh6wINW7lrzWz9RUA/Ww2b0SkaFkRFoVnzBJjJfQ6PtKZh
U/5U1bw5ArBJlWjHURrefYg7OYfqj8kPy+WcD1HP1+dQ8ozqp/abSkwDNWi4
R3ht2J4pApr0i9rqVWi4k4j9JUT1Y91zBXbCijQcy/+Ra5zq11KZOZdSpGnY
+MI/ET+qv/drpT0qF6DhrQeYnS4OUPPbv5Xg4qHhM9ZXUjb2U/P7p6aacVL5
eODqVt1LzV+bUtz3lwubzxQHc3RT81sn9KxOceHs2ZvhB6nzpf9y2NY91Vz4
xUOZix9qqHiPH2TcKefC3hOOPvzUeYVLQjRqSrlwOet3wq6aircmyMg6lwtH
q1y2naHON/sI3/NeyVzY1fax9acPVLx3F/NzbnBhs+E3wVbpVLyv53WWr3Lh
ZPuf9468o+L9cPusd4kLIzvxR3pvqHia5zqbnLnwkVOqNULU+Wxfbb86e4wL
d5YQch7xBPQNmBsoKHHh6g1Pj7JR5/+V+1lpn+S5cPfEq8aqIAI4VfkEbWS4
cGHpgTG/AOq+E1DfG7qRC1/6vqd79DZ135A5eG2WzoVtLc/eueRFgLybVlr2
OCf29ajt9HUgAITiBQ4Nc+JX2mTgmB0Bx0p/ew/2ceKj9iJxh04RcIunUF+o
nRMf/LRl7J8Vla/Mnb1XqjixbeDhKhlTArwWZAQ0X3DiWLrLMwd1AuiJgd5N
iZz416Ledg9V6v0MhnvOxXHiJM2iSW9lAmpin7+Li+TE2u6c5FV56nzdLa7/
x5cTOzT1FihIEFBxS8D743+cODdT9vBN6v7Gw7HSrS/CiZtyt9dF1zNAK7Di
kS8/J74vIbUz8gsDXFlCDhfROfHnBHn9IOp+WP1PBCswc+Kn6rN2NqUM8FtS
ShEkOfC61b65zDQGLEyccen/woEPh4i+/R7MgO76up83fTjwckqVbrE2A2jG
0Rn53hw4QCYn75MmA3bXWDuTnhzY/ej5g9WqDIitGulwcOHA7RzHCnPlqPvq
x38fjI5zYIHZb/uURBhQmal6V1SZA0vb31n7arIV0qPjeXOH2LFRvf5ft4hW
8Plv/SaWPnbs+k7laVhIKxhLx6ke7WLHkzRbwVT/VpjMj7Web2LHBZLbgsq9
W0G2M+qF6kd2HGx6lznGrhVeSQar5z1hxwdmNQLTdrRCUvoV23xTdvzBSfFk
0KcWuHB13oPNiB3fS/i6Lr60BbR1PP0t9dlx4p8p+dT8FuhuvPjm5x52fER8
t/Kr1BZYP+86pybLjjN/HjPVfNACj3efDipgZsdvmRRZCs1aILLaNKOwkA2/
Pm459YvRDAHCO5Ksc9lwanCH3fWGZrjmwB3+O4MNP0+L+DpX1Qyn/9ae3/ua
Gr8QGNpQ0Awq6oY7IIYN1wQKyW5+0gzEq33p1ZfY8Lv227X6J5phfaDGO0KB
Db9l11OxIpqAt3XtU69tbHhQMFWqub4JmDcthohuYcPtV5Xi9lU2wVRpnsuJ
9WzYdO7jeu7cJihd2CnXw8mGrRqf/tWMbAJbx+1vhkdYceSsqN4vwyZI2b/p
9fwzVnyFy1rim3MjqDifG1eLZ8XTd+q2sBxtBHw/U/5aLCvm5/isvVanEbqb
tTNXQlmxn3B26KpQIwjbnyxiu8GKN4ubv2z8+BUCfB7Wih5jxdYbO1Ru8H8F
x3w2ci8nKz4dTt/wPqUeZLZNagR4sGDzqmNTBfdqoLMxykrUnQVfSGwO2nKx
BkKv7fZ+58yCV+WObfA5XgM/aoILmmxZsJGc5Nof0jVQ6r5NbaMpC5aNjHox
gb+ARY6jSoEcC15iqn/O9/Mz3Nbu2z4+yIzVHEhn1sPV0HGUscnEkhnrel3w
MiqvAOmWoYd+1FVe6iuTM8fzCrhkNs+Wb8yMlXhPbUr3qwCaqeDkxn3MePze
/c63qAK0DpjlkIrM+MwP3ZdXS8vhuWb9voeczDip8oq0UTYG142VZ7o+rMGt
QkxBbnxl8Gc099W5zWtwMC8fz0x9LlTrmyhpTP4D+/oqh74UF7RgevkTvWgV
3rNZmzv8KEAs0oEPQo7/gdcOtjlj7DXII7STxWvjb1gej1vHf7cVORsctY4g
F+FUUv2Ha/1dSLeusN88egFuSgyazyUOIK8h23X+p+ZgqDI8DUJGkHjUAP3D
HAnix5t0oqImUM2hbQfm+0g4NLXQdSd5AnmxnvdTaCChSHXltkvmBGryXlqI
TyVBLFrNZ2PDBAqw5ev1sSEh5tidkyKck2hGQTtLp3oWbs/EbNvhM4k+Vj85
VhE3A7/VbZ7utplCbn694ctBM9BDLsi0uUwhsT3SNSpXZiDzVKbaWe8p5Pk+
Uzvl8Aysd5S0s4+eQjIx1TIBLDMQt5riV/x5CkWcXlgyOD8NZVtfXRlSmkb2
K0cSa3SngLaikb7z5zRKrhU1NVCagkTHyitqTDOo/0nfCt44BYMVN+vk6TPI
Xu2iTdHyJNjVpmdOSFG+EL4hNW8S/ovK25RvTLm/Pi5AdhJqIq3zziXNoOSM
GCMm0UlwdS667/2Giudj8/sm2yTcEFIX8Mqhxq+btr48OAEbvjnm6FVTtqCL
OSRMQPWW6Q6+GcqVRrGIfwJefVTpddOYRcnRAgc+/B0HlotuA2d1Z1G/fedP
9Zlx2LeiGnPEaBbZr56zVKwdhzo45z9xkrJ6sPDGgHGwWVrTs/cW5TfV0cu/
xkBoejZV6yMVzyt8n9foGDzOngPmaiqe/vG5H4wxyBb0dMhroMYPjJhPZI9B
Spd7UWc35fVsAh1uY8AdF1EiuzyL7EL3R+T3jULaa1PZImUSsWe/Cy6oH4Ui
J8P2TA0SZRACdwuLR6HTqRpCdUi0ItF/pfjhKGzLrb7x05hET7J9TpYdHIVN
EyV7bjmRCLUNHf24axTmPbVOxLmRaHT5kClsGoVl4bMycZdItEt/nW75nxF4
a/Gbef8tEjW15W+tyhwBp6q9u/Y8JJH3H3HJ6oQR2Po2S/PCExJJSAWIfQ4Z
AecpW4uARBK5u1jQa86MQEvS/gXLVBIJhRez1pqNgCm/uZBAOolKcqT+1mqP
QIGbwdX3WSTiXJn9Xi86Aran5reHFJMoU+r4ZAPrCPz6Fi/6pYxExw3Khr7+
GIYLSZwXx8pJ9DL8QVtT3TDwcjs9qK4hke4m2VLG7WFY57Xqy9RBojGDiHzC
fRiiRo3btL6RKNx1MaPtxDDwSJ4ftOolUXdu5fMO1WFYFPXRlBsmkX+HQnyn
1DD03L0s0DdKIvnV6JgunmFYCjcr85wg0bUDp+91jw3BagXHW5VZEkm6ffHr
YQzBB4WRq7bfSVQdoXSjt3wIunZnKDnPkeh8XuzlvowhqHusm2CyQCLhzlX3
/vghKB/XuMO7SKIPq45nB4KHYEfITEr6LxI5bK63G7w6BPQj12pkfpOI66Dq
iSGHIfhjlF7gs0yiLLenFsNHhkDcf71yxh8SWUWuMRnRGoL0Uv7lkhUS/c07
ZzAqNwTeO+M6XqyS6FVno87Y2iHgOXYjwukviUz+qmuOs1Dzh6kPMv8j0fzm
pJ0T3wfhxCo95gblpwfZFCZ7BiFPbcG5nrKeu7v0VO0gVa8pUkuUxyNbN04X
DsJftgd+q5Qj8veIzrwchPDCVqNuyupdz/lnowbhTb+DTgzlnr+cNNJ3EJ7f
aJfcSjlgiwfLd7dB+M/pfmY49TwKhu0r360HQV86PKOJet4Wd53FHwaDIBif
0TNJvc/1qFfknMog7Kn1WO2m3leqgHtiXnIQTB4Ifn1NrcdJ8qeVJu8gfOTx
TbWn1itGtq/aZ2UA6hTKFxap9fx6+ota+eQAMNda3nGh1pszPvslW+cAGK36
ihVR+djHeCp06PMAcHUZBg5S+fLhCbgbnj8A+vuDo8epfH6/fdxeNHoADsq9
LgqapvZDMWr8z28ANErEzkpMkshxTlYn+cIALCXI9kSOkajD8c8GOWMqvkT/
YbZBEgkmDd8/v3sA1oSe7Gbvo9a/veF39rYBiAgUPTFI7UdslNy+h3UArkHY
fhmCRMt3Qw7cnuuHGQOLfeHNVP2VeuZ/6u+HWd+LFo0NJHqjaPDQpKwfiobN
qr9VkWjQWZE5Kq0fdnpZFL+m6kH8ueglIq4fKsS3dRtR9RIpNHnY1qsftv7Q
axDNI1GtSWvZC0dqvNoP2X2ZJGINKt0+ZtEPBRYGjfvfUft7KZzmodQPSu2b
heufkehjiXMoS3MfLN2N2DAZTCKVHXtcQ9/3gSBfv+uXuyR6/YzbUOR+H1hN
HFLy8aHqKyCbZdv+Psh5oSB75iKJTh3+c+NQfi/Qqxr0ZI9S/QM3WLdG9cIl
8nBKGtWP9FWT1W0u9IIEr+QjZn0SbRczmDu/rRfuV6WqyO+i+tdAuEtUXA+k
+roHnRAkkcex0wfXe/VA2vrtiZ5cJBquVt2aYtEDc9nlR04xkag+raM/j94D
ssWeIa9nZlHC1c3WHbe6IdGMOLiG6rd7uQoOSDp8gyC3hP6k87OoqOnQ3En0
DVj90AB5ehbtetKXGCv+DS7P2J/iPz6LFLdx/eRp74IqXZMvH7VnkZSBTcqK
cReca5e3qaXNItY7zExdap1QudvS4Ez8DPIzfJwmItQJkT/FboeFzqBVvu1W
5t87YHGYVcz/1gxaTLLM+PKuA76NHrVqtJ1B46VvbAolO+CLknzYsMQMql86
XBzD1Q7GTBosVTHTyBAPOTaNtoFNyb9PAXenUdW9a/zclW2wXckwkO4xjT6u
feHs79sGCrcMxt0PTaOsXT9FPKn/pQ9MOXd7r0yhGI94zyM9DLhjt+joYjmF
+DWVJR6UMGD8QWKJF5pCYf8qa6ofM0AzTMH9gNwUCgqfldKxYECO/GSmwsok
upau17j9cyv4NWvqsz2bRKfGxxRo2S0gaKm9ktkxgd7YfHA1o+7Nu/hZ1IJK
J9BcU/jbWKcWMOuSYuGl7iPBxWrbtqxvgez7Tz4qn51AOff9N2v5N4Pq7Fa1
wtlxxLFDct0Fyyb4OjDd4Pp9DFk8n7PKU2qC++lJz2Ubx1CCSHXsMlcTlPkn
WEa9H0NnVjpleW81wl+94eenXcZQUdJVSd0jX0E768T9H92jyGEonfvlfB2I
desKueWOoF91R+8rv6mDqX/zA89DR1Bo3jJHmU0dJLXXu/g4jaDCQEOWtqpa
6Guaql2/dgRxyw7/5nhSA4/DFCpIz2FU4L5hzE3rM5Db490i1w8h+mJIuWpg
Bfx8cn39Pol+NK28W+SrTgXsy5rnH+vuQw1u4+fOLZXDmMveiTCfPhQxcIA/
0a0cFtUWpV8W9yKhBhY7dgsMBRtsirrke5C64Z+lbO1SMKxI2/h+vBMdfzl4
YcUjF1oCP1c8r2tBYuv11u4czgFziTKPBosW1BXxrMzJKgd4aJWaUp3NyPam
DXejdja89lTW0xhqQvUv04/uF8kAGcdD5lJdDWiGKaYmzPAVNCme45J+X4Uu
TZuJ/VJ8CQ/N+r9eeVaJfrbzONuLpMBpptmDCxGf0GrGPVbVwWRIrtLY5e1W
jtaXLPpm/XoCeU77zFLFStDmKA9x/8pYsLny7WF5XyGSPzdZbBkVA6NLG06K
peSjPWt7F5blI2G2ZDzXVSIbBXRlSseTD+DywBL+kP4exQSn2OmG3IM9ln7+
v4XfIpcakTSR67dA2mvsdU7CM8R34s13VvIy5NZPnoi88gi5Nl91H69xhEda
bvs0rwShaGkj6uMA8buKRy5V+KP/AexQKfA=
"]], LineBox[CompressedData["
1:eJxTTMoPSmViYGCwBmIQPUnFE4iS7BmgICKD96etZRGcv+lG1Wa/w9Vw/uY7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"]]},
Annotation[#,
"Charting`Private`Tag$2217#1"]& ], {}}, {{}, {}, {}}}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{-5, 2}, {-0.34449352734143923`, 0.9999988089186329}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.763962938415165*^9, {3.763963027120199*^9, 3.763963038427253*^9}, {
3.7639631628132467`*^9, 3.763963181584343*^9}, {3.763963212887355*^9,
3.763963229092948*^9}, 3.7639633228705606`*^9, 3.763963824412386*^9,
3.7640448055168*^9},
CellLabel->"Out[2]=",ExpressionUUID->"80bc77a1-1d40-438f-924a-093d8ab5cf03"]
}, Open ]],
Cell[BoxData[""], "Input",
CellChangeTimes->{3.761547820419183*^9,
3.7626019409687033`*^9},ExpressionUUID->"9f68ffc4-2327-4aa8-a7c2-\
180ed7d7d124"],
Cell[BoxData[
RowBox[{"(*",
RowBox[{
"Autocorrelation", " ", "function", " ", "of", " ", "landscape", " ", "S",
RowBox[{"(", "x", ")"}]}], "*)"}]], "Input",
CellChangeTimes->{{3.7588086674233923`*^9, 3.7588086967435827`*^9}, {
3.7588087464903517`*^9, 3.758808747260695*^9}},
Background->RGBColor[1, 0.85, 0.85],
CellLabel->"In[2]:=",ExpressionUUID->"1e78bca3-cd11-485e-abc1-adae18f7849c"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"R", "[",
RowBox[{"t_", ",", "\[Tau]_"}], "]"}], " ", "=",
RowBox[{
SuperscriptBox["\[Sigma]", "2"], " ",
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox[
RowBox[{"RealAbs", "[",
RowBox[{"t", "-", "\[Tau]"}], "]"}], "\[Mu]"]}]]}]}]], "Input",
CellChangeTimes->{{3.7588070130677547`*^9, 3.758807014167885*^9}, {
3.7588070979471416`*^9, 3.758807139479947*^9}, {3.7590584423858967`*^9,
3.7590584535073013`*^9}, {3.7590585547467318`*^9, 3.759058563997566*^9}, {
3.759058668359453*^9, 3.759058669709127*^9}, {3.759484789072097*^9,
3.759484790092545*^9}, 3.7615489660538797`*^9, 3.761557845111711*^9, {
3.761558598485821*^9, 3.761558598875678*^9}, {3.762519604309206*^9,
3.762519608040803*^9}, {3.7633775242051373`*^9, 3.763377524678279*^9}, {
3.763377732240451*^9, 3.763377733582656*^9}, {3.7638837337083*^9,
3.763883742292844*^9}},
Background->RGBColor[0.87, 0.94, 1],
CellLabel->"In[3]:=",ExpressionUUID->"7283c407-a7e5-494d-a1a8-100f0a2074b6"],
Cell[BoxData[
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox[
RowBox[{"RealAbs", "[",
RowBox[{"t", "-", "\[Tau]"}], "]"}], "\[Mu]"]}]], " ",
SuperscriptBox["\[Sigma]", "2"]}]], "Output",
CellChangeTimes->{{3.75905844666329*^9, 3.759058454225544*^9}, {
3.759058566128186*^9, 3.75905858555217*^9}, {3.759058665553195*^9,
3.759058685364448*^9}, 3.759058729040155*^9, 3.759481631654183*^9,
3.759484791606964*^9, 3.761545324509094*^9, 3.7615478472436047`*^9,
3.761547947380535*^9, 3.761548992250098*^9, 3.761556549627582*^9,
3.7615578830424347`*^9, 3.761557915075225*^9, 3.7615585997363787`*^9,
3.761558804783197*^9, 3.761560597894598*^9, 3.761564987268189*^9,
3.761569373254591*^9, 3.76162677817025*^9, 3.76251576363342*^9,
3.762516946504575*^9, 3.762519609582656*^9, 3.7626019270689898`*^9,
3.7626045450934343`*^9, 3.7626900981366367`*^9, 3.7627692119337797`*^9, {
3.7633775263857813`*^9, 3.7633775316870193`*^9}, 3.7633777341404257`*^9,
3.7638837159352293`*^9, 3.763883749986579*^9, 3.763885729140033*^9,
3.763886490506021*^9, 3.763888624808138*^9, 3.7639593636058207`*^9,
3.76397395844838*^9, 3.76397402800451*^9, 3.7640448138889103`*^9},
CellLabel->"Out[3]=",ExpressionUUID->"be086fe2-0a03-464e-8cf5-d73461012745"]
}, Open ]],
Cell[BoxData[""], "Input",
CellChangeTimes->{
3.758808652182513*^9, {3.7588121867951403`*^9, 3.7588121959020653`*^9},
3.75905835485426*^9, 3.761556417841506*^9,
3.76156943337283*^9},ExpressionUUID->"814c27de-8b9e-491d-89ab-\
a61152045112"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"p2", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"Table", "[", " ",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
RowBox[{"RealAbs", "[",
RowBox[{"t", "-", "\[Tau]"}], "]"}]}]], ",",
RowBox[{"{",
RowBox[{"\[Tau]", ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "2"}], ",", "1"}], "}"}]}], "}"}]}], "]"}], "]"}],
",",
RowBox[{"{",
RowBox[{"t", ",",
RowBox[{"-", "5"}], ",", "2"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.763962961418271*^9, 3.763963022030917*^9}, {
3.763963231675683*^9, 3.7639632326030483`*^9}, {3.763963373031145*^9,
3.7639633817355833`*^9}},
CellLabel->"In[4]:=",ExpressionUUID->"2b0611fd-ca0a-4888-aff6-9c0037d933fb"],
Cell[BoxData[
GraphicsBox[{{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwBUQOu/CFib1JlAgAAADQAAAACAAAApLtp9v//E8DOG+cJsX2pPyC9jyvN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"]], LineBox[CompressedData["
1:eJwBoQNe/CFib1JlAgAAADkAAAACAAAAbtu2bdv2/796Q+cTvO3vP8ZETC83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"]]},
Annotation[#, "Charting`Private`Tag$2332#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwVy2s0m3ccwHGEWUINma02K7GsdGrOaJB1pz8dWtf20KRDXcJkqrSoSmuK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"]], LineBox[CompressedData["
1:eJwBIQLe/SFib1JlAgAAACEAAAACAAAAkiRJkiQJ8D96Q+cTvO3vP6bPt11U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"]]},
Annotation[#,
"Charting`Private`Tag$2332#2"]& ], {}}, {{}, {}, {}, {}}}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{-5, 2}, {0., 0.997770346521164}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.763962980100914*^9, 3.763963022534708*^9},
3.763963233130123*^9, {3.763963373514597*^9, 3.7639633821808977`*^9},
3.764044817163803*^9},
CellLabel->"Out[4]=",ExpressionUUID->"ab5263f4-249b-4287-91ea-4844116f8c94"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Show", "[",
RowBox[{"p1", ",", "p2"}], "]"}]], "Input",
CellChangeTimes->{{3.763963240980245*^9, 3.7639632456815033`*^9}},
CellLabel->"In[5]:=",ExpressionUUID->"93218f6e-f756-4dfd-9a3c-a89bca0d9b3d"],
Cell[BoxData[
GraphicsBox[{{{{{}, {},
TagBox[
{RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.],
LineBox[CompressedData["
1:eJwV1wk0VV8XAHCZvWceohIqyVCIDBUORREKJeovJJKhkooGSRmizEnJkFKp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"]], LineBox[CompressedData["
1:eJxTTMoPSmViYGCwBmIQPUnFE4iS7BmgICKD96etZRGcv+lG1Wa/w9Vw/uY7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"]]},
Annotation[#,
"Charting`Private`Tag$2217#1"]& ], {}}, {{}, {}, {}}}, {}, {}}, \
{{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwBUQOu/CFib1JlAgAAADQAAAACAAAApLtp9v//E8DOG+cJsX2pPyC9jyvN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"]], LineBox[CompressedData["
1:eJwBoQNe/CFib1JlAgAAADkAAAACAAAAbtu2bdv2/796Q+cTvO3vP8ZETC83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"]]},
Annotation[#, "Charting`Private`Tag$2332#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwVy2s0m3ccwHGEWUINma02K7GsdGrOaJB1pz8dWtf20KRDXcJkqrSoSmuK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"]], LineBox[CompressedData["
1:eJwBIQLe/SFib1JlAgAAACEAAAACAAAAkiRJkiQJ8D96Q+cTvO3vP6bPt11U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"]]},
Annotation[#,
"Charting`Private`Tag$2332#2"]& ], {}}, {{}, {}, {}, {}}}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{-5, 2}, {-0.34449352734143923`, 0.9999988089186329}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{3.7639632461109133`*^9, 3.763963333893241*^9,
3.7639633859803047`*^9, 3.763963829972486*^9, 3.764044822084735*^9},
CellLabel->"Out[5]=",ExpressionUUID->"b283f6ca-74d3-449a-b85c-97ff1dd0de38"]
}, Open ]],
Cell[BoxData[
RowBox[{"(*",
RowBox[{"Input", "-",
RowBox[{"output", " ", "covariance", " ",
RowBox[{"C_", "\\", "eta", "\\", "Lambda"}],
RowBox[{"(",
RowBox[{
RowBox[{"t", "'"}], "-", "v", "-", "t"}], ")"}]}]}], "*)"}]], "Input",
CellChangeTimes->{{3.7588120286644487`*^9, 3.758812049232781*^9},
3.759058360791103*^9, {3.763883807457386*^9, 3.763883811726856*^9}},
Background->RGBColor[
1, 0.85, 0.85],ExpressionUUID->"655f3745-68d5-4c09-a463-a7f4fd6babcf"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
SubscriptBox["C", "\[Eta]\[Lambda]"], " ", "=", " ",
RowBox[{
RowBox[{"Integrate", "[", " ",
RowBox[{
RowBox[{
RowBox[{"R", "[",
RowBox[{"u", ",", "\[Tau]"}], "]"}], "*",
RowBox[{"K", "[", "u", "]"}]}], ",",
RowBox[{"{",
RowBox[{"u", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"\[Sigma]", ">", "0"}], ",",
RowBox[{"\[Beta]", ">", "0"}], ",",
RowBox[{"\[Gamma]", ">", "0"}], ",",
RowBox[{"\[Mu]", ">", "0"}]}], "}"}]}]}], "]"}], "//",
"FullSimplify"}]}]], "Input",
CellChangeTimes->{{3.7588108212208757`*^9, 3.7588108614116163`*^9}, {
3.758810919124207*^9, 3.758810920629794*^9}, {3.758810976533802*^9,
3.758810992224696*^9}, 3.758811242447968*^9, 3.758811280174861*^9, {
3.759056882990885*^9, 3.7590569243003674`*^9}, {3.759056965945754*^9,
3.7590570101266108`*^9}, {3.759057129678933*^9, 3.759057133466504*^9}, {
3.759058790720463*^9, 3.75905879884062*^9}, {3.761545343444633*^9,
3.761545348241384*^9}, {3.761547360605204*^9, 3.7615473635857153`*^9}, {
3.761548074231719*^9, 3.761548083675735*^9}, {3.761548320236281*^9,
3.761548327527223*^9}, {3.761548378040991*^9, 3.7615483826408157`*^9},