179:. These conditions are often indicative of percolating clusters and their involvement in propagating the excess firing of neurons. Seizures occur when neurons in the brain fire simultaneously, and often these seizures can occur in one part of the brain which may then transfer to other parts. Researchers are able to facilitate a better understanding of these conditions because "the neurons involved in a seizure are analogous to the sites in a percolating cluster". Disorganized schizophrenia is more complex as the activity is indicative activity in a percolating cluster; however, some researchers have suggested that the percolation of information does not occur in a small cluster but on a global functional scale. Attention as well as percolation also plays a key role in disorganized and divergent thinking; however, it is more likely that directed percolation, that is a directionally controlled percolation, is more useful to study divergent thinking and creativity.
154:
long time, will the water reach the center of the stone?". Since its founding, percolation theory has been used in both applied fields and mathematical modeling, areas such as engineering, physics, chemistry, communications, economics, mathematics, medicine and geography. From a mathematical perspective, percolation is uniquely able to exhibit both algebraic and probabilistic relationships graphically. In network and cognitive sciences, percolation theory is often used as a computational model that has the benefit of testing theories on neural activity before any physical testing is necessary. It can also be used as a model to explain experimental observations of neural activity to a certain extent.
145:, which are single large groups of neurons that are all connected by open bonds and take up the majority of the network. Any signals that originate at any point within the percolating cluster will have a greater impact and diffusion across the network than signals that originate outside of the cluster. This is similar to a teacher spreading an infection to a whole community through contact with the students and subsequently with the families than an isolated businessman that works from home.
27:
445:
Percolation theory is widely used and impacts many different fields; however, the research in network science can still be developed further. As a computational model, percolation has its limitations in that it cannot always account for the variability of real-life neural networks. Its limitations do
124:
between people, then one can determine how easily messages between neurons will spread. When a neuron fires, the message is transmitted along all synaptic connections to other neurons until it can no longer continue. Synaptic connections are considered either open or closed (like a social or unsocial
301:
Percolation theory has been applied to a wide variety of fields of study, including medicine, economics, physics, as well as other areas of psychology, such as social sciences and industrial and organizational psychology. Below is a table of other areas of study that apply percolation theory as well
153:
Percolation theory was originally purposed by
Broadbent and Hammersley as a mathematical theory for determining the flow of fluids through porous material. An example of this is the question originally purposed by Broadbent and Hammersley: "suppose a large porous rock is submerged under water for a
162:
Percolation has been developed outside of the cognitive sciences; however, its application in the field has proven it to be a useful tool for understanding neural processes. Researchers have focused their attention not only studying how neural activity is diffused across networks, but also how
106:. Those who are more social and come into contact with more people will help to propagate the disease quicker than those who are less social. Factors such as occupation and sociability influence the rate of infection. Now, if one were to think of
450:
better, a closer objective look at percolation in neural networks is needed. The best possible way for this to occur would be to combine the applications of percolation modelling and experimental stimulation of artificial neural networks.
1187:
Winzeler, H. E.; Owens, P. R.; Waltman, S. W.; Waltman, W. J.; Libohova, Z.; Beaudette, D. (2013). "A Methodology for
Examining Changes in Soil Climate Geography through Time: U.S. Soil Moisture Regimes for the Period 1971–2000".
187:
Below is a table of some of the studies and experiments that have involved percolation. The majority of these studies focus on the application of percolation theory to neural network processing from a computational approach.
125:
person) and messages will flow along any and all open connections until they can go no further. Just like occupation and sociability play a key role in the spread of disease, so too do the number of neurons,
290:
Researchers purpose that disorganized schizophrenia is not due to small-world organization but in fact a breakdown in local organization that leads to global modularity of functioning
275:
Researchers use a modified percolation theory to attempt show a new way of thinking about the modularity of the brain as opposed to the widely accepted view of small world networks
167:
can affect decision making and thought processes. Percolation theory has enabled researchers to better understand many psychological conditions, such as
37:
48:
66:
404:
A Methodology for
Examining Changes in Soil Climate Geography through Time: U.S. Soil Moisture Regimes for the Period 1971–2000
1133:
Rebello, I.; Grana, M.; Cases, B. (2012). "Effect of spatial percolation on the convergence of a graph colouring boid swarm".
94:. Percolation is a model used to explain how neural activity is transmitted across the various connections within the brain.
1229:
862:"A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks"
962:
Duffie, Darrell; Malamud, Semyon; Manso, Gustavo (September 2014). "Information percolation in segmented markets".
762:"Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions"
271:
A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks
172:
256:
Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions
260:
Researchers aim to model phase transitions within the brain using percolation to understand neurphil properties
215:
Researchers use quorum percolation to describe the impacts of neural activity initiation in neural networks
230:
This paper discusses the contributions that percolation theory has made to the acquisition of human skills
130:
102:. Individuals who are infected with a disease can spread the disease through contact with others in their
1064:
1022:
944:
533:
41:
that states a
Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.
711:"Fragmentation: Loss of global coherence or breakdown of modularity in functional brain architecture?"
1197:
883:
826:
663:
569:
521:
286:
Fragmentation: Loss of global coherence or breakdown of modularity in functional brain architecture?
86:, meaning filtration) is a theoretical model used to understand the way activation and diffusion of
447:
126:
1014:
979:
873:
842:
816:
789:
653:
585:
511:
176:
95:
1115:
911:
781:
760:
Kozma, Robert; Puljic, Marko; Balister, Paul; Bollobás, Bela; Freeman, Walter J. (June 2005).
742:
691:
1205:
1169:
1160:
Wybo, J.L. (2012). "Percolation, temporal coherence of information, and crisis prevention".
1142:
1105:
1095:
1056:
1006:
971:
934:
901:
891:
834:
773:
732:
722:
681:
671:
619:
577:
164:
807:
Haggstrom, O.; Jonasson, J. (2006). "Uniqueness and non-uniqueness in percolation theory".
1084:"Far from Equilibrium Percolation, Stochastic and Shape Resonances in the Physics of Life"
546:
446:
not hinder its functionality in total, just in some cases. In order for one to understand
87:
400:
H. E. Winzeler, P. R. Owens, S. W. Waltman, W. J. Waltman, Z. Libohova & D. Beaudette
389:
Far from
Equilibrium Percolation, Stochastic and Shape Resonances in the Physics of Life
1201:
887:
830:
667:
573:
525:
1110:
1083:
906:
861:
737:
710:
686:
641:
245:
Researchers use neuropercolation models to outline the implications to decision making
103:
91:
1223:
1018:
589:
474:
EISTA 2004. Volume II: Education and
Training Systems, Technologies and Applications
983:
846:
99:
793:
1068:
1060:
1026:
469:
419:
Effect of spatial percolation on the convergence of a graph colouring boid swarm
1040:
Flores, Ramón; Koster, Maurice; Lindner, Ines; Molina, Elisenda (October 2012).
948:
1173:
838:
761:
607:
1146:
1010:
975:
777:
623:
581:
510:
Beffara, Vincent; Sidoravicius, Vladas (July 11, 2005). "Percolation theory".
727:
676:
560:
Broadbent, S.R.; Hammersley, J.M. (1957). "Percolation processes, I and II".
896:
608:"Modeling goal-oriented decision making through cognitive phase transitions"
329:
Ecology of infectious diseases with contact networks and percolation theory
1209:
1119:
931:
Ecology of infectious diseases with contact networks and percolation theory
915:
785:
746:
695:
470:"On the relevance of percolation theory to the acquisition of human skills"
241:
Modeling goal-oriented decision making through cognitive phase transitions
1100:
226:
On the relevance of percolation theory to the acquisition of human skills
168:
1041:
640:
Eckmann, J.P.; Moses, E.; Stetter, O.; Tlusty, T.; Zbinden, C. (2010).
434:
Percolation, temporal coherence of information, and crisis prevention
939:
821:
516:
108:
997:
Grebel, Thomas (July 2012). "Network evolution in basic science".
878:
658:
251:
R. Kozma, M. Puljic, P. Balister, B. Bollobas & W. J. Freeman
206:
J.P. Eckmann, E. Moses, O. Stetter, T. Tlusty, & C. Zbinden
709:
Van, D. B.; Gong, P.; Breakspear, M.; van
Leeuwen, C. (2012).
606:
Kozma, Robert; Puljic, Marko; Perlovsky, Leonid (March 2009).
20:
642:"Leaders of neuronal cultures in a quorum percolation model"
38:
personal reflection, personal essay, or argumentative essay
211:
Leaders of neuronal cultures in a quorum percolation model
495:
Cognitive
Science: An Introduction to the Study of Mind
44:
1135:
International
Journal on Artificial Intelligence Tools
281:
D. B. Van, P. Gong, M. Breakspear & C. Van
Leeuwen
562:Proceedings of the Cambridge Philosophical Society
98:can be easily understood by explaining its use in
489:
487:
485:
483:
370:R. Flores, M. Koster, I. Lindner, & E. Molina
860:Gallos, L. K.; Makse, H. A.; Sigman, M. (2012).
497:(2nd Ed.). Thousand Oaks, CA: SAGE Publications.
1082:Poccia, N.; Ansuini, A.; Bianconi, A. (2011).
141:A key aspect of percolation is the concept of
635:
633:
505:
503:
344:Information Percolation in Segmented Markets
8:
1088:International Journal of Molecular Sciences
601:
599:
425:Emergency management and crisis prevention
1109:
1099:
938:
905:
895:
877:
820:
736:
726:
685:
675:
657:
515:
266:L. K. Gallos, H. A. Makes & M. Sigman
67:Learn how and when to remove this message
304:
190:
1190:Soil Science Society of America Journal
646:Frontiers in Computational Neuroscience
612:New Mathematics and Natural Computation
493:Friedenbreg, J., Silverman, G. (2012).
460:
385:N. Poccia, A. Ansuini & A. Bianconi
133:when talking about neural percolation.
929:Bansal Khandelwal, Shweta (May 2008).
542:
531:
236:R. Kozma, M. Puljic & L. Perlovsky
7:
415:I. Rebollo, M. Grana, & B. Cases
340:D. Duffie, G. Manso & S. Malamud
359:Network evolution in basic science
14:
999:Journal of Evolutionary Economics
715:Frontiers in Systems Neuroscience
1042:"Networks and collective action"
476:. IIIS Editor. pp. 391–395.
302:as recent research information.
25:
374:Networks and collective action
350:Industrial/Organizational Psych
468:Leleu-Merviel, Sylvie (2004).
163:percolation and its aspect of
1:
1061:10.1016/j.socnet.2012.06.003
1246:
1174:10.1016/j.ssci.2013.01.021
964:Journal of Economic Theory
839:10.1214/154957806000000096
173:disorganized schizophrenia
1147:10.1142/S0218213012500157
1011:10.1007/s00191-012-0266-4
976:10.1016/j.jet.2014.05.006
778:10.1007/s00422-005-0565-z
624:10.1142/S1793005709001246
582:10.1017/s0305004100032680
728:10.3389/fnsys.2012.00020
677:10.3389/fncom.2010.00132
183:Table of recent research
897:10.1073/pnas.1106612109
410:Artificial intelligence
1210:10.2136/sssaj2012.0123
766:Biological Cybernetics
541:Cite journal requires
149:History and background
131:long-term potentiation
47:by rewriting it in an
320:Medicine/Epidemiology
82:(from the Latin word
1230:Cognitive psychology
1101:10.3390/ijms12106810
448:small-world networks
143:percolating clusters
118:synaptic connections
1202:2013SSASJ..77..213W
888:2012PNAS..109.2825G
831:2006math.....12812H
809:Probability Surveys
668:2010arXiv1009.5355E
574:1957PCPS...53..629B
526:2005math......7220B
137:Percolating cluster
127:synaptic plasticity
297:Other applications
177:divergent thinking
96:Percolation theory
49:encyclopedic style
36:is written like a
1094:(10): 6810–6833.
438:
437:
294:
293:
77:
76:
69:
16:Theoretical model
1237:
1214:
1213:
1184:
1178:
1177:
1157:
1151:
1150:
1130:
1124:
1123:
1113:
1103:
1079:
1073:
1072:
1046:
1037:
1031:
1030:
994:
988:
987:
959:
953:
952:
942:
926:
920:
919:
909:
899:
881:
872:(8): 2825–2830.
857:
851:
850:
824:
804:
798:
797:
757:
751:
750:
740:
730:
706:
700:
699:
689:
679:
661:
637:
628:
627:
603:
594:
593:
557:
551:
550:
544:
539:
537:
529:
519:
507:
498:
491:
478:
477:
465:
325:S. B. Khandelwal
305:
221:S. Leleu-Merviel
191:
165:phase transition
158:Current research
72:
65:
61:
58:
52:
29:
28:
21:
1245:
1244:
1240:
1239:
1238:
1236:
1235:
1234:
1220:
1219:
1218:
1217:
1186:
1185:
1181:
1159:
1158:
1154:
1132:
1131:
1127:
1081:
1080:
1076:
1049:Social Networks
1044:
1039:
1038:
1034:
996:
995:
991:
961:
960:
956:
928:
927:
923:
859:
858:
854:
806:
805:
801:
759:
758:
754:
708:
707:
703:
639:
638:
631:
605:
604:
597:
559:
558:
554:
540:
530:
509:
508:
501:
492:
481:
467:
466:
462:
457:
443:
441:Future research
299:
185:
160:
151:
139:
92:neural networks
88:neural activity
73:
62:
56:
53:
45:help improve it
42:
30:
26:
17:
12:
11:
5:
1243:
1241:
1233:
1232:
1222:
1221:
1216:
1215:
1196:(1): 213–225.
1179:
1162:Safety Science
1152:
1141:(6): 1250015.
1125:
1074:
1055:(4): 570–584.
1032:
1005:(3): 443–457.
989:
954:
921:
852:
799:
772:(6): 367–379.
752:
701:
629:
618:(1): 143–157.
595:
568:(3): 629–641.
552:
543:|journal=
499:
479:
459:
458:
456:
453:
442:
439:
436:
435:
432:
427:
421:
420:
417:
412:
406:
405:
402:
397:
391:
390:
387:
382:
376:
375:
372:
367:
361:
360:
357:
352:
346:
345:
342:
337:
331:
330:
327:
322:
316:
315:
312:
309:
298:
295:
292:
291:
288:
283:
277:
276:
273:
268:
262:
261:
258:
253:
247:
246:
243:
238:
232:
231:
228:
223:
217:
216:
213:
208:
202:
201:
198:
195:
184:
181:
159:
156:
150:
147:
138:
135:
104:social network
90:occurs within
75:
74:
33:
31:
24:
15:
13:
10:
9:
6:
4:
3:
2:
1242:
1231:
1228:
1227:
1225:
1211:
1207:
1203:
1199:
1195:
1191:
1183:
1180:
1175:
1171:
1167:
1163:
1156:
1153:
1148:
1144:
1140:
1136:
1129:
1126:
1121:
1117:
1112:
1107:
1102:
1097:
1093:
1089:
1085:
1078:
1075:
1070:
1066:
1062:
1058:
1054:
1050:
1043:
1036:
1033:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1000:
993:
990:
985:
981:
977:
973:
969:
965:
958:
955:
950:
946:
941:
936:
932:
925:
922:
917:
913:
908:
903:
898:
893:
889:
885:
880:
875:
871:
867:
863:
856:
853:
848:
844:
840:
836:
832:
828:
823:
818:
814:
810:
803:
800:
795:
791:
787:
783:
779:
775:
771:
767:
763:
756:
753:
748:
744:
739:
734:
729:
724:
720:
716:
712:
705:
702:
697:
693:
688:
683:
678:
673:
669:
665:
660:
655:
651:
647:
643:
636:
634:
630:
625:
621:
617:
613:
609:
602:
600:
596:
591:
587:
583:
579:
575:
571:
567:
563:
556:
553:
548:
535:
527:
523:
518:
513:
506:
504:
500:
496:
490:
488:
486:
484:
480:
475:
471:
464:
461:
454:
452:
449:
440:
433:
431:
428:
426:
423:
422:
418:
416:
413:
411:
408:
407:
403:
401:
398:
396:
393:
392:
388:
386:
383:
381:
378:
377:
373:
371:
368:
366:
363:
362:
358:
356:
353:
351:
348:
347:
343:
341:
338:
336:
333:
332:
328:
326:
323:
321:
318:
317:
313:
310:
308:Area of study
307:
306:
303:
296:
289:
287:
284:
282:
279:
278:
274:
272:
269:
267:
264:
263:
259:
257:
254:
252:
249:
248:
244:
242:
239:
237:
234:
233:
229:
227:
224:
222:
219:
218:
214:
212:
209:
207:
204:
203:
199:
196:
194:Researcher(s)
193:
192:
189:
182:
180:
178:
174:
170:
166:
157:
155:
148:
146:
144:
136:
134:
132:
128:
123:
119:
115:
111:
110:
105:
101:
97:
93:
89:
85:
81:
71:
68:
60:
50:
46:
40:
39:
34:This article
32:
23:
22:
19:
1193:
1189:
1182:
1165:
1161:
1155:
1138:
1134:
1128:
1091:
1087:
1077:
1052:
1048:
1035:
1002:
998:
992:
967:
963:
957:
930:
924:
869:
865:
855:
822:math/0612812
812:
808:
802:
769:
765:
755:
718:
714:
704:
649:
645:
615:
611:
565:
561:
555:
534:cite journal
517:math/0507220
494:
473:
463:
444:
429:
424:
414:
409:
399:
394:
384:
379:
369:
365:Social Psych
364:
354:
349:
339:
334:
324:
319:
300:
285:
280:
270:
265:
255:
250:
240:
235:
225:
220:
210:
205:
186:
161:
152:
142:
140:
122:social bonds
121:
117:
113:
107:
100:epidemiology
83:
79:
78:
63:
57:October 2021
54:
35:
18:
815:: 289–344.
311:Researchers
114:individuals
80:Percolation
1069:1027510949
1027:1282239642
933:(Thesis).
455:References
84:percolatio
1168:: 60–68.
1019:154217698
949:622038307
940:2152/3910
879:1102.0604
659:1009.5355
430:J.L. Wybo
395:Geography
355:T. Grebel
335:Economics
200:Overview
1224:Category
1120:22072921
1065:ProQuest
1023:ProQuest
970:: 1–32.
945:ProQuest
916:22308319
786:15920663
747:22479239
696:20953239
590:84176793
314:Article
169:epilepsy
1198:Bibcode
1111:3211012
984:6162521
907:3286928
884:Bibcode
847:7444277
827:Bibcode
738:3316147
687:2955434
664:Bibcode
652:: 132.
570:Bibcode
522:Bibcode
380:Physics
197:Article
120:as the
109:neurons
43:Please
1118:
1108:
1067:
1025:
1017:
982:
947:
914:
904:
845:
794:912262
792:
784:
745:
735:
721:: 20.
694:
684:
588:
1045:(PDF)
1015:S2CID
980:S2CID
874:arXiv
843:S2CID
817:arXiv
790:S2CID
654:arXiv
586:S2CID
512:arXiv
1116:PMID
912:PMID
866:PNAS
782:PMID
743:PMID
692:PMID
547:help
175:and
129:and
116:and
112:as
1206:doi
1170:doi
1143:doi
1106:PMC
1096:doi
1057:doi
1007:doi
972:doi
968:153
935:hdl
902:PMC
892:doi
870:109
835:doi
774:doi
733:PMC
723:doi
682:PMC
672:doi
620:doi
578:doi
1226::
1204:.
1194:77
1192:.
1166:57
1164:.
1139:21
1137:.
1114:.
1104:.
1092:12
1090:.
1086:.
1063:.
1053:34
1051:.
1047:.
1021:.
1013:.
1003:22
1001:.
978:.
966:.
943:.
910:.
900:.
890:.
882:.
868:.
864:.
841:.
833:.
825:.
811:.
788:.
780:.
770:92
768:.
764:.
741:.
731:.
717:.
713:.
690:.
680:.
670:.
662:.
648:.
644:.
632:^
616:05
614:.
610:.
598:^
584:.
576:.
566:53
564:.
538::
536:}}
532:{{
520:.
502:^
482:^
472:.
171:,
1212:.
1208::
1200::
1176:.
1172::
1149:.
1145::
1122:.
1098::
1071:.
1059::
1029:.
1009::
986:.
974::
951:.
937::
918:.
894::
886::
876::
849:.
837::
829::
819::
813:3
796:.
776::
749:.
725::
719:6
698:.
674::
666::
656::
650:4
626:.
622::
592:.
580::
572::
549:)
545:(
528:.
524::
514::
70:)
64:(
59:)
55:(
51:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.