• Non ci sono risultati.

Attractor-like dynamics in belief updating in schizophrenia

N/A
N/A
Info
Scarica
Protected

Academic year: 2021

Condividi "Attractor-like dynamics in belief updating in schizophrenia"

Copied!
63
0
0

Caricamento.... (Visualizza il testo completo ora)

Scarica adesso ( 63 pagine )

Testo completo

(1)This Accepted Manuscript has not been copyedited and formatted. The final version may differ from this version.. Research Articles: Behavioral/Cognitive. Attractor-like dynamics in belief updating in schizophrenia 1,2. Rick A Adams. 1. 1. 3,4,5. , Gary Napier , Jonathan P Roiser , Christoph Mathys. and James Gilleen. 1. Institute of Cognitive Neuroscience, UCL, 17 Queen Square, London, WC1N 3AZ, UK. 2. Division of Psychiatry, UCL, 6th floor, 149 Tottenham Court Road, London, W1T 7NF, UK. 3. Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy. 6,7. 4. Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering, University of Zurich and ETH Zurich, Wilfriedstrasse 6, 8032 Zurich, Switzerland 5. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, 10-12 Russell Square, London, WC1B 5EH, UK 6. Department of Psychology, University of Roehampton, London, SE15 4JD.. 7. Department of Psychosis Studies; Institute of Psychiatry, Psychology and Neuroscience, Kings College London, London, SE5 8AF. DOI: 10.1523/JNEUROSCI.3163-17.2018 Received: 2 November 2017 Revised: 3 May 2018 Accepted: 27 June 2018 Published: 5 September 2018. Author contributions: R.A.A., J.R., C.M., and J.G. designed research; R.A.A., G.N., and J.G. performed research; R.A.A. and G.N. analyzed data; R.A.A. wrote the first draft of the paper; R.A.A., G.N., J.R., C.M., and J.G. wrote the paper; C.M. contributed unpublished reagents/analytic tools. Conflict of Interest: The authors declare no competing financial interests. The authors are very grateful to Dr Emmanuelle Peters for providing them with dataset 1. Dr Rick Adams is funded by the Academy of Medical Sciences (AMS-SGCL13-Adams) and the National Institute of Health Research (CL-2013-18-003). JG was supported in his contribution to this project by the British Academy Correspondence should be addressed to corresponding author: rick.adams@ucl.ac.uk Cite as: J. Neurosci ; 10.1523/JNEUROSCI.3163-17.2018 Alerts: Sign up at www.jneurosci.org/cgi/alerts to receive customized email alerts when the fully formatted version of this article is published.. Accepted manuscripts are peer-reviewed but have not been through the copyediting, formatting, or proofreading process. Copyright © 2018 the authors.

(2) . ʹ. Attractor-like dynamics in belief updating in schizophrenia. ͵. . Ͷ. . ͷ. ‹ †ƒ•ͳǡʹȗȘǡ ƒ”›ƒ’‹‡”ͳȘǡ ‘ƒ–Šƒ‘‹•‡”ͳǡŠ”‹•–‘’Šƒ–Š›•͵ǡͶǡͷțǡ. ͸. ƒ‡• ‹ŽŽ‡‡͸ǡ͹ț. ͹. . ͺ. ͳ

(3) •–‹–—–‡‘ˆ‘‰‹–‹˜‡‡—”‘• ‹‡ ‡ǡǡͳ͹—‡‡“—ƒ”‡ǡ‘†‘ǡͳ͵ǡ. ͻ. . ͳ. ͳͲ. ʹ‹˜‹•‹‘‘ˆ•› Š‹ƒ–”›ǡǡ͸–ŠˆŽ‘‘”ǡͳͶͻ‘––‡Šƒ‘—”–‘ƒ†ǡ‘†‘ǡͳ. ͳͳ. ͹ ǡ. ͳʹ. ͵ —‘Žƒ

(4) –‡”ƒœ‹‘ƒŽ‡—’‡”‹‘”‡†‹–—†‹˜ƒœƒ–‹ȋ

(5) Ȍǡ‹ƒ‘‘‡ƒʹ͸ͷǡ. ͳ͵. ͵Ͷͳ͵͸”‹‡•–‡ǡ

(6) –ƒŽ›. ͳͶ. Ͷ”ƒ•Žƒ–‹‘ƒŽ‡—”‘‘†‡Ž‹‰‹–ȋȌǡ

(7) •–‹–—–‡ˆ‘”‹‘‡†‹ ƒŽ‰‹‡‡”‹‰ǡ. ͳͷ. ‹˜‡”•‹–›‘ˆ—”‹ Šƒ† —”‹ Šǡ‹Žˆ”‹‡†•–”ƒ••‡͸ǡͺͲ͵ʹ—”‹ Šǡ™‹–œ‡”Žƒ†. ͳ͸. ͷƒšŽƒ ‡–”‡ˆ‘”‘’—–ƒ–‹‘ƒŽ•› Š‹ƒ–”›ƒ†‰‡‹‰‡•‡ƒ” ŠǡͳͲǦ. ͳ͹. ͳʹ—••‡ŽŽ“—ƒ”‡ǡ‘†‘ǡͳͷ ǡ. ͳͺ. ͸‡’ƒ”–‡–‘ˆ•› Š‘Ž‘‰›ǡ‹˜‡”•‹–›‘ˆ‘‡Šƒ’–‘ǡ‘†‘ǡͳͷͶ Ǥ. ͳͻ. ͹‡’ƒ”–‡–‘ˆ•› Š‘•‹•–—†‹‡•Ǣ

(8) •–‹–—–‡‘ˆ•› Š‹ƒ–”›ǡ•› Š‘Ž‘‰›ƒ†. ʹͲ. ‡—”‘• ‹‡ ‡ǡ‹‰•‘ŽŽ‡‰‡‘†‘ǡ‘†‘ǡͷͺ Ǥ. ʹͳ. Ș‡“—ƒŽ ‘–”‹„—–‹‘. ʹʹ. țŒ‘‹–•‡‹‘”ƒ—–Š‘”•. ʹ͵. . ʹͶ. ȗ ‘””‡•’‘†‹‰ƒ—–Š‘”ǣ. ʹͷ. ”‹ Ǥƒ†ƒ•̷— ŽǤƒ Ǥ—. ʹ͸. . ʹ͹. ‡›™‘”†•ǣ• Š‹œ‘’Š”‡‹ƒǢ’•› Š‘•‹•Ǣƒ›‡•‹ƒǢ†‹• ‘ˆ‹”ƒ–‘”›„‹ƒ•Ǣ„‡ƒ†•–ƒ•Ǣ. ʹͺ. ƒ––”ƒ –‘”‘†‡Ž. ʹͻ. . ͵Ͳ. „•–”ƒ –™‘”† ‘—–ǣʹͶ͹™‘”†•. ͵ͳ.

(9) –”‘†— –‹‘™‘”† ‘—–ǣ͸ͳͲ™‘”†•. .

(10)  ͵ʹ. ‹• —••‹‘™‘”† ‘—–ǣͳͷͲͲ. ͵͵. ͵ƒ„Ž‡•ǡͳͲ ‹‰—”‡•. ͵Ͷ. Abstract. ͵ͷ. . ͵͸. —„Œ‡ –•™‹–Šƒ†‹ƒ‰‘•‹•‘ˆ• Š‹œ‘’Š”‡‹ƒȋ œȌ‘˜‡”™‡‹‰Š–—‡š’‡ –‡†. ͵͹. ‡˜‹†‡ ‡‹’”‘„ƒ„‹Ž‹•–‹ ‹ˆ‡”‡ ‡ǣ•— Š‡˜‹†‡ ‡„‡ ‘‡•Ǯƒ„‡””ƒ–Ž›•ƒŽ‹‡–ǯǤ. ͵ͺ. ‡—”‘„‹‘Ž‘‰‹ ƒŽ‡š’Žƒƒ–‹‘ˆ‘”–Š‹•‡ˆˆ‡ –‹•–Šƒ–†‹‹‹•Š‡†•›ƒ’–‹ ‰ƒ‹ȋ‡Ǥ‰Ǥ. ͵ͻ. Š›’‘ˆ— –‹‘‘ˆ ‘”–‹ ƒŽNǦ‡–Š›ŽǦǦƒ•’ƒ”–ƒ–‡”‡ ‡’–‘”•Ȍ‹ œ†‡•–ƒ„‹Ž‹œ‡•. ͶͲ. “—ƒ•‹Ǧ•–ƒ„Ž‡‡—”‘ƒŽ‡–™‘”•–ƒ–‡•ȋ‘”Ǯƒ––”ƒ –‘”•ǯȌǤŠ‹•ƒ––”ƒ –‘”‹•–ƒ„‹Ž‹–›. Ͷͳ. ƒ ‘—–’”‡†‹ –•–Šƒ–‹Ȍ œ™‘—Ž†‘˜‡”™‡‹‰Š–—‡š’‡ –‡†‡˜‹†‡ ‡„—–. Ͷʹ. —†‡”™‡‹‰Š– ‘•‹•–‡–‡˜‹†‡ ‡ǡ‹‹Ȍ„‡Ž‹‡ˆ—’†ƒ–‹‰™‘—Ž†„‡‘”‡˜—Ž‡”ƒ„Ž‡. Ͷ͵. –‘•–‘ Šƒ•–‹ ˆŽ— –—ƒ–‹‘•‹‡—”ƒŽƒ –‹˜‹–›ǡƒ†‹‹‹Ȍ–Š‡•‡‡ˆˆ‡ –•™‘—Ž† ‘””‡Žƒ–‡Ǥ. ͶͶ. . Ͷͷ. ‹‡”ƒ” Š‹ ƒŽƒ›‡•‹ƒ„‡Ž‹‡ˆ—’†ƒ–‹‰‘†‡Ž•™‡”‡–‡•–‡†‹–™‘‹†‡’‡†‡–. Ͷ͸. †ƒ–ƒ•‡–•ȋαͺͲƒ†αͳ͸͹ǡƒŽ‡ƒ†ˆ‡ƒŽ‡Ȍ ‘’”‹•‹‰Š—ƒ•—„Œ‡ –•™‹–Š. Ͷ͹. • Š‹œ‘’Š”‡‹ƒǡƒ†„‘–Š Ž‹‹ ƒŽƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ȋ•‘‡–‡•–‡†™Š‡. Ͷͺ. —™‡ŽŽƒ†‘”‡ ‘˜‡”›Ȍ’‡”ˆ‘”‹‰–Š‡Ǯ’”‘„ƒ„‹Ž‹–›‡•–‹ƒ–‡•ǯ˜‡”•‹‘‘ˆ–Š‡. Ͷͻ. „‡ƒ†•–ƒ•ȋƒ’”‘„ƒ„‹Ž‹•–‹ ‹ˆ‡”‡ ‡–ƒ•ȌǤ‘†‡Ž•™‹–Šƒ•–ƒ†ƒ”†Ž‡ƒ”‹‰”ƒ–‡ǡ. ͷͲ. ‘”‹ Ž—†‹‰ƒ’ƒ”ƒ‡–‡”‹ ”‡ƒ•‹‰—’†ƒ–‹‰–‘Ǯ†‹• ‘ˆ‹”ƒ–‘”›‡˜‹†‡ ‡ǯǡ‘”ƒ. ͷͳ. ’ƒ”ƒ‡–‡”‡ ‘†‹‰„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›™‡”‡ˆ‘”ƒŽŽ› ‘’ƒ”‡†Ǥ. ͷʹ. . ͷ͵. Š‡Ǯ„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›ǯ‘†‡Žȋ„ƒ•‡†‘–Š‡’”‹ ‹’Ž‡•‘ˆƒ––”ƒ –‘”†›ƒ‹ •ȌŠƒ†. ͷͶ. ‘•–‡˜‹†‡ ‡‹ƒŽŽ‰”‘—’•‹„‘–Š†ƒ–ƒ•‡–•Ǥ™‘‘ˆˆ‘—”’ƒ”ƒ‡–‡”•†‹ˆˆ‡”‡†. ͷͷ. „‡–™‡‡ œƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•‹‡ƒ Š†ƒ–ƒ•‡–ǣ„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›ƒ†. . ʹ.

(11)  ͷ͸. ”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›ǤŠ‡•‡’ƒ”ƒ‡–‡”• ‘””‡Žƒ–‡†‹„‘–Š†ƒ–ƒ•‡–•Ǥ. ͷ͹. —”–Š‡”‘”‡ǡ–Š‡ Ž‹‹ ƒŽ ‘–”‘Ž••Š‘™‡†•‹‹Žƒ”’ƒ”ƒ‡–‡”†‹•–”‹„—–‹‘•–‘ œ. ͷͺ. ™Š‡—™‡ŽŽǡ„—–™‡”‡‘†‹ˆˆ‡”‡––‘ ‘–”‘Ž•‘ ‡”‡ ‘˜‡”‡†Ǥ. ͷͻ. . ͸Ͳ. Š‡•‡ˆ‹†‹‰•ƒ”‡ ‘•‹•–‡–™‹–Š–Š‡Š›’‘–Š‡•‹•–Šƒ–ƒ––”ƒ –‘”‡–™‘”. ͸ͳ. ‹•–ƒ„‹Ž‹–› ‘–”‹„—–‡•–‘„‡Ž‹‡ˆ—’†ƒ–‹‰ƒ„‘”ƒŽ‹–‹‡•‹ œǡƒ†•—‰‰‡•––Šƒ–. ͸ʹ. •‹‹Žƒ” Šƒ‰‡•ƒ›‡š‹•–†—”‹‰ƒ —–‡‹ŽŽ‡••‹‘–Š‡”’•› Š‹ƒ–”‹  ‘†‹–‹‘•Ǥ. ͸͵. . ͸Ͷ ͸ͷ ͸͸. Significance Statement. ͸͹. —„Œ‡ –•™‹–Šƒ†‹ƒ‰‘•‹•‘ˆ• Š‹œ‘’Š”‡‹ƒȋ œȌƒ‡Žƒ”‰‡ƒ†Œ—•–‡–•–‘–Š‡‹”. ͸ͺ. „‡Ž‹‡ˆ•ˆ‘ŽŽ‘™‹‰—‡š’‡ –‡†‡˜‹†‡ ‡ǡ„—–ƒŽ•‘•ƒŽŽ‡”ƒ†Œ—•–‡–•–Šƒ. ͸ͻ. ‘–”‘Ž•ˆ‘ŽŽ‘™‹‰ ‘•‹•–‡–‡˜‹†‡ ‡ǤŠ‹•Šƒ•’”‡˜‹‘—•Ž›„‡‡ ‘•–”—‡†ƒ•ƒ. ͹Ͳ. „‹ƒ•–‘™ƒ”†•Ǯ†‹• ‘ˆ‹”ƒ–‘”›ǯ‹ˆ‘”ƒ–‹‘ǡ„—–ƒ‘”‡‡ Šƒ‹•–‹ ‡š’Žƒƒ–‹‘. ͹ͳ. ƒ›„‡–Šƒ–‹ œǡ‡—”ƒŽˆ‹”‹‰’ƒ––‡”•ȋǮƒ––”ƒ –‘”•–ƒ–‡•ǯȌƒ”‡Ž‡•••–ƒ„Ž‡ƒ†. ͹ʹ. Š‡ ‡‡ƒ•‹Ž›ƒŽ–‡”‡†‹”‡•’‘•‡–‘„‘–Š‡™‡˜‹†‡ ‡ƒ†•–‘ Šƒ•–‹ ‡—”ƒŽ. ͹͵. ˆ‹”‹‰Ǥ‡‘†‡Ž„‡Ž‹‡ˆ—’†ƒ–‹‰‹ œƒ† ‘–”‘Ž•‹–™‘‹†‡’‡†‡–†ƒ–ƒ•‡–•. ͹Ͷ. —•‹‰ƒŠ‹‡”ƒ” Š‹ ƒŽƒ›‡•‹ƒ‘†‡Žǡƒ†•Š‘™–Šƒ–ƒŽŽ•—„Œ‡ –•ƒ”‡„‡•–ˆ‹–„›ƒ. ͹ͷ. ‘†‡Ž ‘–ƒ‹‹‰ƒ„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›’ƒ”ƒ‡–‡”Ǥ‘–Š–Š‹•ƒ†ƒ”‡•’‘•‡. ͹͸. •–‘ Šƒ•–‹ ‹–›’ƒ”ƒ‡–‡”ƒ”‡ ‘•‹•–‡–Ž›ƒŽ–‡”‡†‹ œǡƒ•–Š‡—•–ƒ„Ž‡ƒ––”ƒ –‘”. ͹͹. Š›’‘–Š‡•‹•’”‡†‹ –•Ǥ.  . . ͵.

(12)  ͹ͺ. ͹ͻ ͺͲ ͺͳ. Introduction. ͺʹ. —„Œ‡ –•™‹–Šƒ†‹ƒ‰‘•‹•‘ˆ• Š‹œ‘’Š”‡‹ƒȋ œȌ–‡†–‘—•‡Ž‡••‡˜‹†‡ ‡–‘. ͺ͵. ƒ‡†‡ ‹•‹‘•‹’”‘„ƒ„‹Ž‹•–‹ –ƒ••–ŠƒŠ‡ƒŽ–Š› ‘–”‘Ž•ȋ ƒ”‡–›‡–ƒŽǤǡͳͻͻͳǢ. ͺͶ. —†Ž‡›‡–ƒŽǤǡʹͲͳ͸ȌǤŠ‡’ƒ”ƒ†‹‰‘•– ‘‘Ž›—•‡†–‘†‡‘•–”ƒ–‡–Š‹•. ͺͷ. ‡ˆˆ‡ –‹•–Š‡Ǯ„‡ƒ†•ǯ‘”Ǯ—”ǯ–ƒ•ǡ‹™Š‹ Š•—„Œ‡ –•ƒ”‡•Š‘™–™‘—”•ǡ‡ƒ Š. ͺ͸. ‘–ƒ‹‹‰‘’’‘•‹–‡”ƒ–‹‘•‘ˆ ‘Ž‘—”‡†„‡ƒ†•ȋ‡Ǥ‰ǤͺͷΨ„Ž—‡ƒ†ͳͷΨ”‡†ƒ†. ͺ͹. ˜‹ ‡˜‡”•ƒȌǡ™Š‹ Šƒ”‡–Š‡Š‹††‡Ǥ•‡“—‡ ‡‘ˆ„‡ƒ†•‹•–Š‡†”ƒ™ȋ™‹–Š. ͺͺ. ”‡’Žƒ ‡‡–Ȍˆ”‘‘‡—”ǡƒ†–Š‡•—„Œ‡ –‡‹–Š‡”Šƒ•–‘•–‘’–Š‡•‡“—‡ ‡™Š‡. ͺͻ. –Š‡›ƒ”‡•—”‡™Š‹ Š—”‹–‹• ‘‹‰ˆ”‘ȋ–Š‡Ǯ†”ƒ™•–‘†‡ ‹•‹‘ǯ–ƒ•Ȍ‘”–Š‡. ͻͲ. •—„Œ‡ –—•–”ƒ–‡–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡•‡“—‡ ‡ ‘‹‰ˆ”‘‡‹–Š‡”—”ƒˆ–‡”. ͻͳ. •‡‡‹‰‡ƒ Š„‡ƒ†ǡ™‹–Š‘—–Šƒ˜‹‰–‘ƒ‡ƒ›†‡ ‹•‹‘ȋ–Š‡Ǯ’”‘„ƒ„‹Ž‹–›. ͻʹ. ‡•–‹ƒ–‡•ǯ–ƒ•ȌǤƒ›‡•‹ƒƒƒŽ›•‹•‘ˆ–Š‡•‡–ƒ••Šƒ•‹†‹ ƒ–‡†–Šƒ– œƒ”‡‘”‡. ͻ͵. •–‘ Šƒ•–‹ ‹–Š‡‹””‡•’‘†‹‰ȋ‘—–‘—••‹•‡–ƒŽǤǡʹͲͳͳȌƒ†–Šƒ––Š‡›‘˜‡”™‡‹‰Š–. ͻͶ. ”‡ ‡–‡˜‹†‡ ‡ƒ†–Š—•—’†ƒ–‡–Š‡‹”„‡Ž‹‡ˆ•ȋ‹–Š‡’”‘„ƒ„‹Ž‹•–‹ •‡•‡Ȍ‘”‡. ͻͷ. ”ƒ’‹†Ž›ȋ ƒ”†”‹‡–ƒŽǤǡʹͲͳ͹ȌǤ.  . ͻ͸. ‡˜‡”ƒŽ„‡Ž‹‡ˆǦ—’†ƒ–‹‰ƒ„‘”ƒŽ‹–‹‡•Šƒ˜‡„‡‡ˆ‘—†‹ œ—•‹‰–Š‡. ͻ͹. Ǯ’”‘„ƒ„‹Ž‹–›‡•–‹ƒ–‡•ǯ–ƒ•ǤŠ‡‘•– ‘•‹•–‡–ˆ‹†‹‰‹•–Šƒ– œȋ‘”Œ—•– œ. ͻͺ. ™‹–Š†‡Ž—•‹‘•ȋ‘”‹–œƒ†‘‘†™ƒ”†ǡʹͲͲͷȌȌ Šƒ‰‡–Š‡‹”„‡Ž‹‡ˆ•more–Šƒ. ͻͻ. ‘Ǧ’•› Š‹ƒ–”‹  ‘–”‘Ž•‹”‡•’‘•‡–‘ Šƒ‰‡•‹‡˜‹†‡ ‡ȋƒ‰†‘‡–ƒŽǤǡ. ͳͲͲ. ʹͲͳͲȌȂ’ƒ”–‹ —Žƒ”Ž›Ǯ†‹• ‘ˆ‹”ƒ–‘”›ǯ‡˜‹†‡ ‡ǡ‹Ǥ‡Ǥ‡˜‹†‡ ‡ ‘–”ƒ†‹ –‹‰ƒ. ͳͲͳ. —””‡–„‡Ž‹‡ˆȋ ƒ”‡–›‡–ƒŽǤǡͳͻͻͳǢ ‡ƒ”ƒ† ‡ƒŽ›ǡͳͻͻ͹Ǣ‘—‰ƒ†‡–ƒŽŽǡ. . Ͷ.

(13)  ͳͲʹ. ͳͻͻ͹Ǣ‡–‡”•ƒ† ƒ”‡–›ǡʹͲͲ͸ȌǤ‘–Š‡”‹•–Šƒ–’”‘„ƒ„‹Ž‹–›”ƒ–‹‰•ƒ––Š‡•–ƒ”–‘ˆ. ͳͲ͵. –Š‡•‡“—‡ ‡ƒ”‡Š‹‰Š‡”‹ —””‡–Ž›’•› Š‘–‹ ȋ„—–‘–‹”‡ ‘˜‡”‡†Ȍ œ–Šƒ‹. ͳͲͶ. „‘–Š Ž‹‹ ƒŽƒ†Š‡ƒŽ–Š› ‘–”‘Ž•ȋ‡–‡”•ƒ† ƒ”‡–›ǡʹͲͲ͸Ȍǡ•‹‹Žƒ”–‘–Š‡. ͳͲͷ. ǮŒ—’‹‰–‘ ‘ Ž—•‹‘•ǯ„‹ƒ•‹–Š‡Ǯ†”ƒ™•–‘†‡ ‹•‹‘ǯ˜‡”•‹‘‘ˆ–Š‡–ƒ•Ǥ–Š‡”•. ͳͲ͸. Šƒ˜‡ƒŽ•‘ˆ‘—†–Šƒ– œ—’†ƒ–‡less–Šƒ ‘–”‘Ž•–‘‘”‡consistent‡˜‹†‡ ‡ǡ‹. ͳͲ͹. –Š‹•ȋ ‘”‰ƒǡ‹’”‡’ƒ”ƒ–‹‘Ȍƒ†‘–Š‡”’ƒ”ƒ†‹‰•ȋ˜‡”„‡ ‡–ƒŽǤǡʹͲͳͲȌǤ. ͳͲͺ. Š‡•‡ˆ‹†‹‰• ƒ’‘–‡–‹ƒŽŽ›„‡—†‡”•–‘‘†‹–Š‡Ž‹‰Š–‘ˆ–Š‡Ǯ—•–ƒ„Ž‡. ͳͲͻ. ƒ––”ƒ –‘”‡–™‘”ǯŠ›’‘–Š‡•‹•‘ˆ œǤƒ––”ƒ –‘”‡–™‘”‹•ƒ‡—”ƒŽ‡–™‘”. ͳͳͲ. –Šƒ– ƒ‘ —’›—‡”‘—••–ƒ„Ž‡•–ƒ–‡•–Šƒ–ƒ”‡Ž‡ƒ”‡†ˆ”‘‡š’‡”‹‡ ‡ǡ˜‹ƒ. ͳͳͳ. ƒ†Œ—•–‡–•–‘•›ƒ’–‹ ™‡‹‰Š–•Ǥ

(14) – ƒ”‡˜‹•‹––Š‡•‡•–ƒ–‡•‹ˆ’”‡•‡–‡†™‹–Š. ͳͳʹ. ‹’—–•–Šƒ–”‡•‡„Ž‡’”‡˜‹‘—•’ƒ––‡”•‘ˆ•›ƒ’–‹ ™‡‹‰Š–•ǡ‘”–Š”‘—‰Š. ͳͳ͵. •’‘–ƒ‡‘—•ˆŽ— –—ƒ–‹‘•‹‡—”ƒŽƒ –‹˜‹–›ǣ‡‹–Š‡”™ƒ›ǡ–Š‡ƒ –‹˜‹–›‘ˆƒŽŽ‘†‡•‹•. ͳͳͶ. Ǯƒ––”ƒ –‡†ǯ–‘ƒ“—ƒ•‹Ǧ•–ƒ„Ž‡•–ƒ–‡„‡ ƒ—•‡–Š‡‡–™‘”‡‡”‰›‹•Ž‘™‡”ƒ––Š‡•‡. ͳͳͷ. •–ƒ–‡•ǡƒ†‡–™‘”ˆ‹”‹‰’ƒ––‡”•‡˜‘Ž˜‡–‘‹‹‹•‡‡‡”‰›Ǥ––”ƒ –‘”. ͳͳ͸. ‡–™‘”•™‡”‡‘”‹‰‹ƒŽŽ›†‡˜‡Ž‘’‡†–‘‘†‡Ž–Š‡•–‘”ƒ‰‡ƒ†”‡ƒ –‹˜ƒ–‹‘‘ˆ. ͳͳ͹. ‡‘”‹‡•ȋ ‘’ˆ‹‡Ž†ǡͳͻͺʹȌǡ„—–”‡Žƒ–‡†‡–™‘”‘†‡Ž•ƒŽ•‘‘ˆˆ‡”‡ Šƒ‹•–‹ . ͳͳͺ. ‡š’Žƒƒ–‹‘•ˆ‘”™‘”‹‰‡‘”›•–‘”ƒ‰‡ȋ‡Ǥ‰Ǥ”—‡Žƒ†ƒ‰ǡʹͲͲͳȌǡ. ͳͳͻ. †‡ ‹•‹‘Ǧƒ‹‰ȋƒ‰ǡʹͲͳ͵Ȍƒ†‹–‡”˜ƒŽ–‹‹‰ȋ–ƒ†ƒ‰‡‡–ƒŽǤǡʹͲͳ͵Ȍǡƒ•. ͳʹͲ. ™‡ŽŽƒ•ƒ›‡•‹ƒ„‡Ž‹‡ˆ—’†ƒ–‹‰ȋ ‡’’‡”–Šƒ†‡ˆ‘”–ǡʹͲͳ͸ȌǤ. ͳʹͳ.

(15)  œǡƒ––”ƒ –‘”•–ƒ–‡•‹’”‡ˆ”‘–ƒŽ ‘”–‡šƒ”‡–Š‘—‰Š––‘„‡Ž‡•••–ƒ„Ž‡ǡ•‘. ͳʹʹ. ‹–‹•‡ƒ•‹‡”ˆ‘”–Š‡‡–™‘”–‘•™‹– Š„‡–™‡‡–Š‡ǡ„—–Šƒ”†‡”–‘„‡ ‘‡‘”‡. ͳʹ͵. ‘ˆ‹†‡–ƒ„‘—–ȋ‹Ǥ‡Ǥ‹ ”‡ƒ•‡–Š‡•–ƒ„‹Ž‹–›‘ˆȌƒ›’ƒ”–‹ —Žƒ”‘‡ȋ‘ŽŽ•‡–ƒŽǤǡ. ͳʹͶ. ʹͲͲͺȌǤŠ‹•Ž‘••‘ˆ•–ƒ„Ž‡‡—”‘ƒŽ•–ƒ–‡•Ȃ”‡ ‡–Ž›†‡‘•–”ƒ–‡†‹–™‘ƒ‹ƒŽ. ͳʹͷ. ‘†‡Ž•‘ˆ œȋ ƒ‡–ƒŽǤǡʹͲͳ͹ȌȂ‹•–Š‘—‰Š––‘„‡†—‡–‘Š›’‘ˆ— –‹‘‘ˆNǦ. ͳʹ͸. ‡–Š›ŽǦǦƒ•’ƒ”–ƒ–‡”‡ ‡’–‘”•ȋ•Ȍ‘” ‘”–‹ ƒŽ†‘’ƒ‹‡ͳ”‡ ‡’–‘”•‹ œ. . ͷ.

(16)  ͳʹ͹. ȋ ‹‰—”‡ͳȌǤ

(17) –‡”‡•–‹‰Ž›ǡŠ‡ƒŽ–Š›˜‘Ž—–‡‡”•‰‹˜‡‡–ƒ‹‡ȋƒ. ͳʹͺ. ƒ–ƒ‰‘‹•–Ȍ•Š‘™ƒ†‡ ”‡‡–‹—’†ƒ–‹‰–‘ ‘•‹•–‡–•–‹—Ž—•ƒ••‘ ‹ƒ–‹‘•. ͳʹͻ. ƒ†ƒ‹ ”‡ƒ•‡‹†‡ ‹•‹‘•–‘ Šƒ•–‹ ‹–›‹–Š‹• ‘–‡š–ȋ‹ ‹‡”‡–ƒŽǤǡʹͲͳ͸ȌǤ. ͳ͵Ͳ. ––”ƒ –‘”‡–™‘”’‡”–—”„ƒ–‹‘•Šƒ˜‡„‡‡Ž‹‡†–‘™‘”‹‰‡‘”›’”‘„Ž‡•. ͳ͵ͳ. ‹ œ—•‹‰ƒ„‹•–ƒ„Ž‡ȋ‹Ǥ‡Ǥƒ•–ƒ„Ž‡Ǯ—’ǯ•–ƒ–‡ ‘””‡•’‘†‹‰–‘’‡”•‹•–‡–. ͳ͵ʹ. ‡—”‘ƒŽƒ –‹˜‹–›ǡƒ†ƒǮ†‘™ǯ•–ƒ–‡ ‘””‡•’‘†‹‰–‘„ƒ ‰”‘—†ƒ –‹˜‹–›Ȍ. ͳ͵͵. ‘†‡Žȋ—””ƒ›‡–ƒŽǤǡʹͲͳͶȌǡ„—–‘–ƒ•›‡––‘ƒ ‘’—–ƒ–‹‘ƒŽ—†‡”•–ƒ†‹‰‘ˆ. ͳ͵Ͷ. „‡Ž‹‡ˆ—’†ƒ–‹‰Ǥ. ͳ͵ͷ. . ͳ͵͸. ȋ Ǣƒ–Š›•‡–ƒŽǤǡʹͲͳͳȌǡƒ˜ƒ”‹ƒ–‹‘ƒŽƒ›‡•‹ƒ‘†‡Ž™‹–Š‹†‹˜‹†—ƒŽ’”‹‘”•ǡ. ͳ͵͹. ‹–™‘‹†‡’‡†‡–Ǯ’”‘„ƒ„‹Ž‹–›‡•–‹ƒ–‡•ǯ„‡ƒ†•–ƒ•†ƒ–ƒ•‡–•Ǥ‡ƒ•‡†ǣ‰‹˜‡. ͳ͵ͺ. –Š‡Žƒ”‰‡”„‡Ž‹‡ˆ—’†ƒ–‡•‹ œ ‘’ƒ”‡†™‹–Š ‘–”‘Ž•ǡ ƒ–Š‡•‡„‡‡š’Žƒ‹‡†. ͳ͵ͻ. „›‰”‘—’†‹ˆˆ‡”‡ ‡•‹‹Ȍ‰‡‡”ƒŽŽ‡ƒ”‹‰”ƒ–‡ƒ†Ȁ‘”‹‹Ȍ”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›ǡ. ͳͶͲ. ‘”„›ƒ††‹‰’ƒ”ƒ‡–‡”•‡ ‘†‹‰‹‹‹Ȍ–Š‡˜ƒ”‹ƒ ‡ȋ‹Ǥ‡Ǥ— ‡”–ƒ‹–›Ȍ‘ˆ„‡Ž‹‡ˆ•ƒ–. ͳͶͳ. –Š‡•–ƒ”–‘ˆ–Š‡•‡“—‡ ‡ǡ‹˜Ȍƒ’”‘’‡•‹–›–‘‘˜‡”™‡‹‰Š–†‹• ‘ˆ‹”ƒ–‘”›. ͳͶʹ. ‡˜‹†‡ ‡•’‡ ‹ˆ‹ ƒŽŽ›ǡ‘”˜Ȍ’ƒ––‡”•‘ˆ„‡Ž‹‡ˆ—’†ƒ–‹‰–›’‹ ƒŽ‘ˆ—•–ƒ„Ž‡. ͳͶ͵. ƒ––”ƒ –‘”•–ƒ–‡•‹ƒ ‘’ˆ‹‡Ž†Ǧ–›’‡‡–™‘”ǡ‹Ǥ‡Ǥ‰”‡ƒ–‡”‹•–ƒ„‹Ž‹–›ƒ†. ͳͶͶ. •–‘ Šƒ•–‹ ‹–›ǡ™Š‹ Š ‘””‡Žƒ–‡™‹–Š‡ƒ Š‘–Š‡”ǫȋ‘–‡–Šƒ––Š‡ †‘‡•‘–. ͳͶͷ. ‘–ƒ‹ƒ––”ƒ –‘”•–ƒ–‡•ǣ–Š‡‘†‡Ž‹ȋ˜Ȍ‹•†‡•‹‰‡†–‘•‹—Žƒ–‡–Š‡‡ˆˆ‡ –•‘. ͳͶ͸. ‹ˆ‡”‡ ‡–Šƒ–—•–ƒ„Ž‡‡—”‘ƒŽƒ––”ƒ –‘”•ƒ›Šƒ˜‡ǤȌ —”–Š‡”‘”‡ǡƒ”‡–Š‡•‡. ͳͶ͹. ˆ‹†‹‰• ‘•‹•–‡–™‹–Š‹ œ–‡•–‡†ƒ–†‹ˆˆ‡”‡–‹ŽŽ‡••’Šƒ•‡•ǡƒ†ƒ”‡–Š‡›. ͳͶͺ. —‹“—‡–‘ œ‘”ƒŽ•‘’”‡•‡–‹‘–Š‡”‘Ǧ’•› Š‘–‹ ‘‘††‹•‘”†‡”•ǫ. . ‡ƒƒŽ›•‡†„‡Ž‹‡ˆ—’†ƒ–‹‰‹ œ—•‹‰–Š‡ ‹‡”ƒ” Š‹ ƒŽ ƒ—••‹ƒ ‹Ž–‡”. ͸.

(18)  ͳͶͻ. Methods and Materials. ͳͷͲ. Subject characteristics. ͳͷͳ ͳͷʹ.  ƒ–ƒ•‡–ͳ ‘’”‹•‡†ʹ͵’ƒ–‹‡–•™‹–Š†‡Ž—•‹‘•ȋͳͺ œȌǡʹʹ’ƒ–‹‡–•™‹–Š‘Ǧ. ͳͷ͵. ’•› Š‘–‹ ‘‘††‹•‘”†‡”•ǡƒ†͵ͷ‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ȋ‘˜‡”ƒŽŽǡͷͲƒŽ‡ƒ†͵Ͳ. ͳͷͶ. ˆ‡ƒŽ‡Ȃ•‡‡ƒ„Ž‡ͳˆ‘”†‡–ƒ‹Ž•‘ˆ–Š‡‰”‘—’•ȌǢ–Š‡ˆ‹”•––™‘‰”‘—’•™‡”‡•‡Ž‡ –‡†. ͳͷͷ. ˆ”‘‹’ƒ–‹‡–™ƒ”†•ƒ––Š‡ƒ—†•Ž‡›ƒ†–Š‡‡–ŠŽ‡‘›ƒŽ ‘•’‹–ƒŽ•ǤŽŽ. ͳͷ͸. ‰”‘—’•™‡”‡–‡•–‡†–™‹ ‡ȋ™‹–ŠŽ‘••‘ˆαʹͷˆ”‘–Š‡‰”‘—’•Ȃ•‡‡ƒ„Ž‡ͳȌǢ–Š‡. ͳͷ͹. Ž‹‹ ƒŽ‰”‘—’•™‡”‡–‡•–‡†‘ ‡™Š‡–Š‡›™‡”‡—™‡ŽŽȋǮ„ƒ•‡Ž‹‡ǯȌǡƒ†ƒ‰ƒ‹. ͳͷͺ. ‘ ‡–Š‡›Šƒ†”‡ ‘˜‡”‡†ȋǮˆ‘ŽŽ‘™Ǧ—’ǯȌǤŠ‡‡ƒ–‹‡„‡–™‡‡–‡•–‹‰•‡••‹‘•. ͳͷͻ. ™ƒ•ͳ͹ǤͶȋ”ƒ‰‡͸–‘ͶͳȌ™‡‡•‹–Š‡†‡Ž—†‡†‰”‘—’ǡ͵͵ǤͶȋ”ƒ‰‡Ͷ–‘͸ͺȌ™‡‡•. ͳ͸Ͳ. ‹–Š‡ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’ǡƒ†͵ͷǤ͸ȋ”ƒ‰‡ʹ͹–‘Ͷ͸Ȍ™‡‡•‹–Š‡‘Ǧ Ž‹‹ ƒŽ. ͳ͸ͳ. ‘–”‘Ž‰”‘—’ǤŠ‡†‡Ž—†‡†‰”‘—’ǯ••Š‘”–‡”‹–‡”Ǧ–‡•–‹–‡”˜ƒŽ™ƒ•†—‡–‘–Š‡‹”. ͳ͸ʹ. •Š‘”–‡”ƒ†‹••‹‘’‡”‹‘†ƒ†–‘–Š‡’”‹‘”‹–‹œƒ–‹‘‘ˆ–Š‡‹”ˆ‘ŽŽ‘™Ǧ—’‘˜‡”–Š‡. ͳ͸͵. ‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’Ǥƒ–ƒ•‡–ͳ‹•†‡• ”‹„‡†‹†‡–ƒ‹Ž‡Ž•‡™Š‡”‡ȋ‡–‡”•ƒ†. ͳ͸Ͷ. ƒ”‡–›ǡʹͲͲ͸ȌǤ. ͳ͸ͷ. ƒ–ƒ•‡–ʹ ‘’”‹•‡†ͷ͸•—„Œ‡ –•™‹–Šƒ†‹ƒ‰‘•‹•‘ˆ• Š‹œ‘’Š”‡‹ƒȋ œȌ. ͳ͸͸. ƒ†ͳͳͳ ‘–”‘Ž•ȋ‘˜‡”ƒŽŽǡͺ͵ƒŽ‡ƒ†ͺͶˆ‡ƒŽ‡Ȃ•‡‡ƒ„Ž‡ͳȌǤŽŽ•—„Œ‡ –•. ͳ͸͹. ’”‘˜‹†‡†‹ˆ‘”‡†ǡ™”‹––‡ ‘•‡–ǡƒ†‡–Š‹ ƒŽ’‡”‹••‹‘ˆ‘”–Š‡•–—†›™ƒ•. ͳ͸ͺ. ‘„–ƒ‹‡†ˆ”‘–Š‡Ž‘ ƒŽ ‡•‡ƒ” Š–Š‹ •‘‹––‡‡ȋ‡ˆ‡”‡ ‡. ͳ͸ͻ. ͳͶȀȀͲͷ͵ʹȌǤ ‹˜‡–Š‡ƒ–‹‘ƒŽ†—Ž–‡ƒ†‹‰‡•–ȋ‡Ž•‘ǡͳͻͺʹȌ™ƒ•—•‡†–‘. ͳ͹Ͳ. ‡•–‹ƒ–‡

(19) ‹–Š‡•‡’ƒ”–‹ ‹’ƒ–•ǡƒ”‡ ”—‹–‡– ‘†‹–‹‘™ƒ•–Šƒ–‰Ž‹•Š™ƒ•. ͳ͹ͳ. –Š‡‹”ˆ‹”•–Žƒ‰—ƒ‰‡Ǥ. . ͹.

(20)  ͳ͹ʹ. ‡ƒ•—”‡•‘ˆ ‘‰‹–‹˜‡ˆ— –‹‘ƒ††‡Ž—•‹‘Ǧ’”‘‡‡••ȋ‘”• Š‹œ‘–›’›Ȍ. ͳ͹͵. ™‡”‡ ‘ŽŽ‡ –‡†‹ƒŽŽ•—„Œ‡ –•Ǣ Ž‹‹ ƒŽ•›’–‘”ƒ–‹‰•™‡”‡ ‘ŽŽ‡ –‡†‹ Ž‹‹ ƒŽ. ͳ͹Ͷ. •—„Œ‡ –•‘Ž›ȋ•‡‡ƒ„Ž‡ͳˆ‘”†‡–ƒ‹Ž•ȌǤ. ͳ͹ͷ. . ͳ͹͸. Experimental design. ͳ͹͹. . ͳ͹ͺ. —„Œ‡ –•‹†ƒ–ƒ•‡–ͳ’‡”ˆ‘”‡†–Š‡Ǯ’”‘„ƒ„‹Ž‹–›‡•–‹ƒ–‡•ǯ„‡ƒ†•–ƒ•ƒ•—•‡†. ͳ͹ͻ. ’”‡˜‹‘—•Ž›ȋ ƒ”‡–›‡–ƒŽǤǡͳͻͻͳȌǡ™‹–Š–™‘—”•™‹–Š”ƒ–‹‘•‘ˆͺͷǣͳͷƒ†ͳͷǣͺͷ. ͳͺͲ. „Ž—‡ƒ†”‡†„‡ƒ†•”‡•’‡ –‹˜‡Ž›ǡƒ†˜‹‡™‹‰ƒ•‹‰Ž‡•‡“—‡ ‡‘ˆ–‡„‡ƒ†•. ͳͺͳ. ȋ ‹‰—”‡ʹȌǢƒˆ–‡”‡ƒ Š„‡ƒ†–Š‡›Šƒ†–‘ƒ”ƒƒƒŽ‘‰—‡• ƒŽ‡ȋˆ”‘ͳ–‘ͳͲͲȌ. ͳͺʹ. †‡‘–‹‰–Š‡’”‘„ƒ„‹Ž‹–›–Š‡—”™ƒ•ͺͷΨ”‡†Ǥ. ͳͺ͵. —„Œ‡ –•‹†ƒ–ƒ•‡–ʹ’‡”ˆ‘”‡†–Š‡Ǯ’”‘„ƒ„‹Ž‹–›‡•–‹ƒ–‡•ǯ„‡ƒ†•–ƒ•ǡ. ͳͺͶ. ™‹–Š–™‘—”•™‹–Š”ƒ–‹‘•‘ˆͺͲǣʹͲƒ†ʹͲǣͺͲ”‡†ƒ†„Ž—‡„‡ƒ†•”‡•’‡ –‹˜‡Ž›Ǥ. ͳͺͷ. Š‡›‡ƒ Š˜‹‡™‡†ˆ‘—”•‡’ƒ”ƒ–‡•‡“—‡ ‡•ȋ–™‘‹†‡–‹ ƒŽ’ƒ‹”•‘ˆ•‡“—‡ ‡•™‹–Š. ͳͺ͸. –Š‡ ‘Ž‘—”••™ƒ’’‡†™‹–Š‹‡ƒ Š’ƒ‹”Ȍ‘ˆ–‡„‡ƒ†•ȋ ‹‰—”‡ʹȌǢƒˆ–‡”‡ƒ Š„‡ƒ†. ͳͺ͹. –Š‡›Šƒ†–‘ƒ”ƒ‹‡”–• ƒŽ‡ȋˆ”‘ͳ–‘͹Ȍ†‡‘–‹‰–Š‡’”‘„ƒ„‹Ž‹–›–Š‡—”. ͳͺͺ. ™ƒ•–Š‡ͺͲΨ„Ž—‡‘‡Ǥ™‘•‡“—‡ ‡• ‘–ƒ‹‡†ƒƒ’’ƒ”‡– Šƒ‰‡‘ˆŒƒ”ǤŠ‡. ͳͺͻ. ‘”†‡”‘ˆ–Š‡ˆ‘—”•‡“—‡ ‡•™ƒ•”ƒ†‘‹•‡†Ǥ. ͳͻͲ. ‡—•‡†•‘‡‘ˆ–Š‡„‡Šƒ˜‹‘—”ƒŽ‡ƒ•—”‡•‡’Ž‘›‡†‹–Š‡‘”‹‰‹ƒŽ. ͳͻͳ. ƒƒŽ›•‹•‘ˆ†ƒ–ƒ•‡–ͳȋ‡–‡”•ƒ† ƒ”‡–›ǡʹͲͲ͸Ȍ–‘ƒƒŽ›•‡†ƒ–ƒ•‡–ʹǤŠ‡•‡™‡”‡. ͳͻʹ. Ǯ†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰ǯǡ–Š‡‡ƒ Šƒ‰‡‹„‡Ž‹‡ˆ‘•‡‡‹‰ƒ„‡ƒ†‘ˆƒ. ͳͻ͵. †‹ˆˆ‡”‡– ‘Ž‘—”–‘–Š‡ηʹ„‡ƒ†•’”‡ ‡†‹‰‹–ƒ†Ǯˆ‹ƒŽ ‡”–ƒ‹–›ǯȋ–Š‡”‡•’‘•‡–‘. ͳͻͶ. –Š‡Žƒ•–„‡ƒ†ȌǤ‡ƒŽ–‡”‡†–Š‡‹”Ǯ‹‹–‹ƒŽ ‡”–ƒ‹–›ǯ‡ƒ•—”‡ˆ”‘–Š‡‡ƒ. ͳͻͷ. ”‡•’‘•‡–‘–Š‡ˆ‹”•––Š”‡‡„‡ƒ†•–‘–Š‡”‡•’‘•‡–‘–Š‡ˆ‹”•–„‡ƒ†ǡ™Š‹ Š ‘‡•. . ͺ.

(21)  ͳͻ͸. Ž‘•‡”–‘ ƒ’–—”‹‰–Š‡ Žƒ••‹ ǮŒ—’‹‰–‘ ‘ Ž—•‹‘•ǯ„‹ƒ•ȋ‹™Š‹ Šƒ”‘—†. ͳͻ͹. ͷͲΨ‘ˆ œ†‡ ‹†‡‘–Š‡Œƒ” ‘Ž‘—”ƒˆ–‡”•‡‡‹‰‘Ž›‘‡„‡ƒ†Ǣȋ ƒ”‡–›‡–ƒŽǤǡ. ͳͻͺ. ͳͻͻͳȌǡƒŽ–Š‘—‰Š–Š‡”‡•—Ž–•‘ˆ„‘–Š‡ƒ•—”‡•ƒ”‡’”‡•‡–‡†„‡Ž‘™Ǥ. ͳͻͻ. . ʹͲͲ. Computational modelling. ʹͲͳ. . ʹͲʹ. Š‡‘’–‹ƒŽ™ƒ›–‘—•‡•‡•‘”›‹ˆ‘”ƒ–‹‘–‘—’†ƒ–‡‘‡ǯ•„‡Ž‹‡ˆ•—†‡”. ʹͲ͵. ‘†‹–‹‘•‘ˆ— ‡”–ƒ‹–›‹•–‘—•‡ƒ›‡•‹ƒ‹ˆ‡”‡ ‡Ǥ‡—”ƒŽ•›•–‡•ƒ”‡Ž‹‡Ž›. ʹͲͶ. –‘ƒ’’”‘š‹ƒ–‡ƒ›‡•‹ƒ‹ˆ‡”‡ ‡—•‹‰• Š‡‡•‘ˆ•‹’Ž‡—’†ƒ–‡‡“—ƒ–‹‘•. ʹͲͷ. ȋƒ‘ƒ†ƒŽŽƒ”†ǡͳͻͻͻǢ ”‹•–‘ǡʹͲͲͷȌǢ‘‡•— Š‘†‡Ž‹•–Š‡ ‹‡”ƒ” Š‹ ƒŽ. ʹͲ͸. ƒ—••‹ƒ ‹Ž–‡”ȋ ȌǤŠ‡ ‹•ƒŠ‹‡”ƒ” Š‹ ƒŽƒ›‡•‹ƒ‹ˆ‡”‡ ‡• Š‡‡–Šƒ–. ʹͲ͹. ‰‹˜‡•ƒ’”‹ ‹’Ž‡†ƒ ‘—–‘ˆŠ‘™„‡Ž‹‡ˆ•ƒ”‡—’†ƒ–‡†‘ƒ “—‹”‹‰‡™†ƒ–ƒǡ. ʹͲͺ. —•‹‰˜ƒ”‹ƒ–‹‘ƒŽƒ›‡•ƒ†‹†‹˜‹†—ƒŽ’”‹‘”•Ǥƒ”‹ƒ–‹‘ƒŽƒ›‡•‹ƒ• Š‡‡•ȋ‡Ǥ‰Ǥ. ʹͲͻ. ȋ‡ƒŽǡʹͲͲ͵Ȍ—•‡ƒƒŽ›–‹ ‡“—ƒ–‹‘•–‘†‡”‹˜‡ƒ‡šƒ –•‘Ž—–‹‘–‘ƒ. ʹͳͲ. ƒ’’”‘š‹ƒ–‹‘‘ˆ–Š‡’‘•–‡”‹‘”†‹•–”‹„—–‹‘‘˜‡”–Š‡Žƒ–‡–˜ƒ”‹ƒ„Ž‡•ƒ†. ʹͳͳ. ’ƒ”ƒ‡–‡”•ȋƒ•‘’’‘•‡†–‘•ƒ’Ž‹‰‡–Š‘†•™Š‹ Šƒ’’”‘š‹ƒ–‡ƒ•‘Ž—–‹‘–‘. ʹͳʹ. –Š‡‡šƒ –’‘•–‡”‹‘”ȌǤŠ‡ Šƒ•„‡‡—•‡†ƒ•ƒ‰‡‡”‹ •–ƒ–‡‘†‡Žˆ‘”Ž‡ƒ”‹‰. ʹͳ͵. —†‡”— ‡”–ƒ‹–›ƒ†Šƒ•”‡’‡ƒ–‡†Ž›„‡‡•Š‘™–‘‘—–’‡”ˆ‘”•‹‹Žƒ”. ʹͳͶ. ƒ’’”‘ƒ Š‡•ǡ•— Šƒ•”‡‹ˆ‘” ‡‡–Ž‡ƒ”‹‰‘†‡Ž•™‹–Šˆ‹š‡†ȋ‡Ǥ‰Ǥ‡• ‘”ŽƒǦ. ʹͳͷ. ƒ‰‡”Ȍ‘”†›ƒ‹ ȋ‡Ǥ‰Ǥȋ—––‘ǡͳͻͻʹȌŽ‡ƒ”‹‰”ƒ–‡•ȋ

(22) ‰Ž‡•‹ƒ•‡–ƒŽǤǡʹͲͳ͵Ǣ. ʹͳ͸. ‹ƒ ‘‡• —‡–ƒŽǤǡʹͲͳͶǢ ƒ—•‡”‡–ƒŽǤǡʹͲͳͶǢ‘••‡Ž‡–ƒŽǤǡʹͲͳͶȌǤ‡ƒ†˜ƒ–ƒ‰‡‘ˆ. ʹͳ͹. –Š‡ ‹•–Šƒ–‹– ‘–ƒ‹••—„Œ‡ –Ǧ•’‡ ‹ˆ‹ ’ƒ”ƒ‡–‡”•ȋƒ†’”‹‘”„‡Ž‹‡ˆ•Ȍ–Šƒ–. ʹͳͺ. ƒƒ ‘—–ˆ‘”„‡–™‡‡Ǧ•—„Œ‡ –†‹ˆˆ‡”‡ ‡•‹Ž‡ƒ”‹‰™Š‹Ž•–’”‡•‡”˜‹‰–Š‡. ʹͳͻ. ȋƒ›‡•Ȍ‘’–‹ƒŽ‹–›‘ˆƒ›‹†‹˜‹†—ƒŽǯ•Ž‡ƒ”‹‰ȋ”‡Žƒ–‹˜‡–‘Š‹•ȀŠ‡”‘†‡Ž. . ͻ.

(23)  ʹʹͲ. ’ƒ”ƒ‡–‡”•ƒ†’”‹‘”„‡Ž‹‡ˆ•ȌǤŠ‡•‡’ƒ”ƒ‡–‡”•ƒ›„‡‡ ‘†‡†„›–‘‹ Ž‡˜‡Ž•. ʹʹͳ. ‘ˆ‡—”‘‘†—Žƒ–‘”••— Šƒ•†‘’ƒ‹‡ȋƒ”•ŠƒŽŽ‡–ƒŽǤǡʹͲͳ͸Ȍǡ‘”„›–Š‡‹–”‹•‹ . ʹʹʹ. ’”‘’‡”–‹‡•‘ˆ‡—”‘ƒŽ‡–™‘”•ȋ‡Ǥ‰Ǥ–Š‡”ƒ–‹‘‘ˆ‡š ‹–ƒ–‘”›–‘‹Š‹„‹–‘”›‡—”ƒŽ. ʹʹ͵. ƒ –‹˜‹–› ƒƒˆˆ‡ –„‘–Š–Š‡•’‡‡†‘ˆ‡˜‹†‡ ‡ƒ ——Žƒ–‹‘ȋƒ‡–ƒŽǤǡʹͲͳ͹ȌȂ. ʹʹͶ. ƒƒŽ‘‰‘—•–‘–Š‡‡˜‘Ž—–‹‘”ƒ–‡‹–Š‡ Ȃƒ†ƒŽ•‘”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›. ʹʹͷ. ȋ—””ƒ›‡–ƒŽǤǡʹͲͳͶȌȌǤ‹ˆˆ‡”‡ ‡•‹‘†‡Ž’ƒ”ƒ‡–‡”•„‡–™‡‡ œƒ†. ʹʹ͸. ‘–”‘Ž•ƒ›–Š‡”‡ˆ‘”‡‡š’Žƒ‹ǡ‹ ‘’—–ƒ–‹‘ƒŽ–‡”•ǡŠ‘™’ƒ–Š‘’Š›•‹‘Ž‘‰›. ʹʹ͹. Ž‡ƒ†•–‘ƒ„‘”ƒŽ‹ˆ‡”‡ ‡ȋ†ƒ•‡–ƒŽǤǡʹͲͳͷȌǤ. ʹʹͺ.

(24) ‰‡‡”ƒŽǡ™Š‡‘†‡ŽŽ‹‰„‡Šƒ˜‹‘—”—†‡”ƒ›‡•‹ƒƒ••—’–‹‘•ǡ‹–‹•. ʹʹͻ. ‡ ‡••ƒ”›–‘†‹•–‹‰—‹•Š„‡–™‡‡–Š‡‘†‡Ž‘ˆ–Š‡™‘”Ž†—•‡†„›–Š‡•—„Œ‡ –ȋ–Š‡. ʹ͵Ͳ. ’‡” ‡’–—ƒŽ‘†‡ŽȌƒ†ƒ‘†‡Ž‘ˆŠ‘™ƒ•—„Œ‡ –ǯ•„‡Ž‹‡ˆ•–”ƒ•Žƒ–‡†‹–‘. ʹ͵ͳ. ‘„•‡”˜‡†„‡Šƒ˜‹‘—”ȋ–Š‡‘„•‡”˜ƒ–‹‘‘””‡•’‘•‡‘†‡ŽȌǤ‘•–‘ˆ–Š‡. ʹ͵ʹ. ’ƒ”ƒ‡–‡”•’‡”–ƒ‹–‘–Š‡’‡” ‡’–—ƒŽ‘†‡ŽȋŠ‡”‡ǡƒŽŽ’ƒ”ƒ‡–‡”•‡š ‡’–. ʹ͵͵. ”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›νȂ•‡‡ƒ„Ž‡ʹȌƒ†”‡ˆŽ‡ –ȋ‹ˆ‡””‡†Ȍ‡—”‘ƒŽ. ʹ͵Ͷ. ’”‘ ‡••‹‰Ǥ

(25)  ‘–”ƒ•–ǡ–Š‡’ƒ”ƒ‡–‡”•‘ˆ–Š‡”‡•’‘•‡‘†‡ŽŽ‹•—„Œ‡ –‹˜‡. ʹ͵ͷ. •–ƒ–‡•–‘„‡Šƒ˜‹‘—”ƒŽ‘—– ‘‡•ǡƒ†–Š—•ƒ›”‡ˆŽ‡ –•–‘ Šƒ•–‹ ‹–›‹‡—”‘ƒŽ. ʹ͵͸. ’”‘ ‡••‹‰ǡ‡ƒ•—”‡‡–‘‹•‡ȋ‹•‘‡’ƒ”ƒ†‹‰•Ȍǡ‘”‘Ǧ”ƒ†‘‡ˆˆ‡ –•–Šƒ–. ʹ͵͹. Šƒ˜‡‘–„‡‡ ƒ’–—”‡†„›–Š‡’‡” ‡’–—ƒŽ‘†‡ŽǤŠ‹•ƒ†”‡Žƒ–‡†Ž‡ƒ”‹‰. ʹ͵ͺ. ‘†‡Ž•ƒ”‡ˆ”‡‡Ž›ƒ˜ƒ‹Žƒ„Ž‡ˆ”‘. ʹ͵ͻ. Š––’ǣȀȀ™™™Ǥ–”ƒ•Žƒ–‹‘ƒŽ‡—”‘‘†‡Ž‹‰Ǥ‘”‰Ȁ–ƒ’ƒ•Ȁȋ˜‡”•‹‘ͷǤͳǤͲȌǣ–Š‹•. ʹͶͲ. ƒƒŽ›•‹•—•‡†–Š‡’‡” ‡’–—ƒŽ‘†‡Ž•ǮŠ‰ˆ̴„‹ƒ”›ǯ‘”ǮŠ‰ˆ̴ƒ”ͳ̴„‹ƒ”›ǯƒ†–Š‡. ʹͶͳ. ”‡•’‘•‡‘†‡ŽǮ„‡–ƒ̴‘„•ǯǤ. ʹͶʹ. ––Š‡„‘––‘‘ˆ–Š‡‘†‡Žȋ ‹‰—”‡͵•Š‘™••‘‡•‹—Žƒ–‡†”‡•’‘•‡•Ȍ‹• ሺ௞ሻ. ʹͶ͵. –Š‡„‡ƒ††”ƒ™‫ݑ‬ሺ௞ሻ ‘–”‹ƒŽkƒ†–Š‡’”‘„ƒ„‹Ž‹–›‫ݔ‬ଵ –Šƒ–†”ƒ™•ƒ”‡ ‘‹‰. ʹͶͶ. ˆ”‘–Š‡„Ž—‡Œƒ”Ǥ––Š‡Ž‡˜‡Žƒ„‘˜‡–Š‹•‹•‫ݔ‬ଶ ǡ–Š‡–‡†‡ ›–‘™ƒ”†•–Š‡„Ž—‡Œƒ” . ͳͲ.

(26)  ʹͶͷ. ȋƒ–”ƒ•ˆ‘”‘ˆ–Š‡’”‘„ƒ„‹Ž‹–›ǡ„‘—†‡†„›άλȌǢ„›†‡ˆ‹‹–‹‘ǡ‫ݔ‬ଵ ൌ ‫ݏ‬ሺ‫ݔ‬ଶ ሻǡ™Š‡”‡. ʹͶ͸. ‫ݏ‬ሺȈሻ‹•–Š‡Ž‘‰‹•–‹ •‹‰‘‹†ˆ— –‹‘Ǥ•‫ݔ‬ଶ ƒ’’”‘ƒ Š‡•‹ˆ‹‹–›ǡ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ. ʹͶ͹. –Š‡„Ž—‡Œƒ”ƒ’’”‘ƒ Š‡•ͳǢƒ•‹–ƒ’’”‘ƒ Š‡•‹—•‹ˆ‹‹–›ǡ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡. ʹͶͺ. „Ž—‡Œƒ”ƒ’’”‘ƒ Š‡•ͲǤ ‘”‫ݔ‬ଶ ൌ Ͳǡ„‘–ŠŒƒ”•ƒ”‡‡“—ƒŽŽ›’”‘„ƒ„Ž‡ǤŠ‹•“—ƒ–‹–›‹•. ʹͶͻ. Š‹††‡ˆ”‘–Š‡•—„Œ‡ –ƒ†—•–„‡‹ˆ‡””‡†ǣ–Š‡•—„Œ‡ –ǯ•’‘•–‡”‹‘”‡•–‹ƒ–‡‘ˆ. ʹͷͲ. ‫ݔ‬ଶ ‹•ߤଶ ǡƒ†–Š‡•—„Œ‡ –ǯ•’‘•–‡”‹‘”‡•–‹ƒ–‡‘ˆ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡Œƒ”„‡‹‰. ʹͷͳ. „Ž—‡‘–”‹ƒŽk‹•‫ݏ‬ቀߤଶ ቁȂ‡“—‹˜ƒŽ‡––‘–Š‡’”‡†‹ –‹‘ȋ†‡‘–‡†„›̰Ȍ‘–Š‡‡š–. ʹͷʹ. –”‹ƒŽߤƸ ଵ. ሺ௞ሻ. ሺ௞ାଵሻ. ʹͷ͵. Ǥ. ‡ˆ‘”‡•‡‡‹‰ƒ›‡™‹’—–‘–”‹ƒŽk–Š‡‘†‡Žǯ•‡š’‡ –‡†Œƒ” ሺ௞ሻ. ሺ௞ሻ. ሺ௞ሻ. ʹͷͶ. ’”‘„ƒ„‹Ž‹–›ߤƸ ଵ ƒ†’”‡ ‹•‹‘•ȋ‹˜‡”•‡˜ƒ”‹ƒ ‡•Ȍߨොଵ ǡ ߨොଶ ‘ˆ–Š‡‡š’‡ –ƒ–‹‘•. ʹͷͷ. ƒ–‡ƒ ŠŽ‡˜‡Žƒ”‡‰‹˜‡„›ǣ ሺ௞ሻ. ʹͷ͸. ሺ௞ିଵሻ. ߤƸ ଵ ‫ݏ ؠ‬ቀߢଵ ߤଶ ሺ௞ሻ. ʹͷ͹. ߨොଵ. ͳ. ‫ؠ‬. ሺ௞ሻ ߤƸ ଵ ሺͳ. ߨොଶ ‫ؠ‬. ሺ௞ሻ. െ ߤƸ ଵ ሻ. . ͳ. ሺ௞ሻ. ʹͷͺ. ቁ. ሺ௞ିଵሻ ߪଶ.  ൅ ‡š’ሺ߱ሻ ሺ௞ሻ. ʹͷͻ. ‘–‡–Šƒ–‹‘†‡Ž•ͳǦͶǡߢଵ ‹•ˆ‹š‡†–‘ͳǤ ‡™‹’—–‫ݑ‬ሺ௞ሻ ‫ߤ ؠ‬ଵ ‰‡‡”ƒ–‡•. ʹ͸Ͳ. ƒ’”‡†‹ –‹‘‡””‘”ߜଵ ƒ†–Š‡‘†‡Ž—’†ƒ–‡•ƒ†‰‡‡”ƒ–‡•ƒ‡™’”‡†‹ –‹‘ƒ•. ʹ͸ͳ. ˆ‘ŽŽ‘™•ǣ. ሺ௞ሻ. ሺ௞ሻ. ሺ௞ሻ. ሺ௞ሻ. ሺ௞ሻ. ߢଵଶ. ʹ͸ʹ. ߜଵ. ‫ߤ ؠ‬ଵ െ ߤƸ ଵ . ʹ͸͵. ߨଶ ൌ ߨොଶ ൅. ሺ௞ሻ. ሺ௞ሻ. ʹ͸Ͷ. ሺ௞ିଵሻ. ߤଶ ൌ ߤଶ ሺ௞ାଵሻ. ߤƸ ଵ. ʹ͸ͷ. . ൅. ሺ௞ሻ. ߨොଵ ߢଵ. ሺ௞ሻ ߜ ሺ௞ሻ ଵ. ߨଶ. ሺ௞ሻ. ‫ݏ ؠ‬ቀߢଵ ߤଶ ቁ ͳͳ.

(27)  Š‡•—„Œ‡ –ǯ•”‡•’‘•‡‫ ݕ‬ሺ௞ሻ ȋ‹Ǥ‡Ǥ™Š‡”‡‘–Š‡ ‘–‹—‘—•‘”‹‡”–• ƒŽ‡. ʹ͸͸. ሺ௞ାଵሻ. ʹ͸͹. –Š‡›”‡•’‘†‡†Ȍ‹•†‡–‡”‹‡†„›ߤƸ ଵ. ʹ͸ͺ. ‘†‡Žǯ•„‡–ƒ†‹•–”‹„—–‹‘ߥǤ. ʹ͸ͻ. ƒ†–Š‡’”‡ ‹•‹‘‘ˆ–Š‡”‡•’‘•‡. ‡’ƒ”ƒ‡–‡”‹œ‡–Š‡„‡–ƒ†‹•–”‹„—–‹‘‹–‡”•‘ˆ‹–•‡ƒߤƒ†. ʹ͹Ͳ. ’”‡ ‹•‹‘ߥǤŠ‡•‡•—ˆˆ‹ ‹‡–•–ƒ–‹•–‹ •”‡Žƒ–‡–‘–Š‡ ‘˜‡–‹‘ƒŽ. ʹ͹ͳ. ’ƒ”ƒ‡–‡”‹œƒ–‹‘‹–‡”•‘ˆ–Š‡•—ˆˆ‹ ‹‡–•–ƒ–‹•–‹ •ߙƒ†ߚ„›–Š‡ˆ‘ŽŽ‘™‹‰. ʹ͹ʹ. „‹Œ‡ –‹‘ǣ ߙ  ߙ൅ߚ. ʹ͹͵. ߤ ‫׷‬ൌ. ʹ͹Ͷ. ߥ ‫׷‬ൌ ߙ ൅ ߚ. ʹ͹ͷ. . ‘–‡–Šƒ–—’†ƒ–‡•–‘ߤଶ ƒ”‡†”‹˜‡„›–Š‡’”‘†— –‘ˆ–Š‡’”‡†‹ –‹‘‡””‘”. ʹ͹͸. ˆ”‘ƒ›‡•‹ƒ—’†ƒ–‹‰‡š’Žƒ‹‡†ƒ„‘˜‡ƒ†ƒŽ‡ƒ”‹‰”ƒ–‡™Š‹ Šǡ ”— ‹ƒŽŽ›ǡ ƒ. ʹ͹͹. Šƒ‰‡‘˜‡”–‹‡ǣ–Š‹•‹•ƒ‹’‘”–ƒ–ƒ•’‡ –‘ˆ–Š‡ ‹ ‘–”ƒ•––‘Ž‡ƒ”‹‰. ʹ͹ͺ. ‘†‡Ž••— Šƒ•‡• ‘”ŽƒǦƒ‰‡”–Šƒ–Šƒ˜‡ƒˆ‹š‡†Ž‡ƒ”‹‰”ƒ–‡Ǥƒ”ƒ‡–‡”•. ʹ͹ͻ. ™Š‹ Šƒˆˆ‡ ––Š‡†‡‰”‡‡–‘™Š‹ Šߤଶ  ƒ Šƒ‰‡†—”‹‰–Š‡‡š’‡”‹‡–‹ Ž—†‡ωǡ. ʹͺͲ. φǡκ1ƒ†σ2(0)ǤŠ‡ ‘–”‹„—–‹‘•‘ˆφƒ†κ1ƒ”‡‹ŽŽ—•–”ƒ–‡†‹ ‹‰—”‡ͶȋŽ‡ˆ–. ʹͺͳ. ’ƒ‡Ž•ȌǤ. ʹͺʹ. Š‡‘†‡Ž—•—ƒŽŽ›Šƒ•ƒ–Š‹”†Ž‡˜‡Žǡƒ–™Š‹ Š‫ݔ‬ଷ ‡ ‘†‡•–Š‡’Šƒ•‹ . ʹͺ͵. ˜‘Žƒ–‹Ž‹–›‘ˆ‫ݔ‬ଶ ȋ–Š‹•†‡–‡”‹‡•–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡Œƒ” Šƒ‰‹‰ƒ–ƒ›’‘‹–Ȍǣ. ʹͺͶ. ‰‹˜‡–Š‡˜‡”›•Š‘”–•‡“—‡ ‡•‡’Ž‘›‡†‹‘—”†ƒ–ƒ•‡–•ǡˆ”‘™Š‹ Š˜‘Žƒ–‹Ž‹–›. ʹͺͷ. ƒ‘–„‡”‡Ž‹ƒ„Ž›‡•–‹ƒ–‡†ǡ™‡‘‹––‡†–Š‹•Ž‡˜‡ŽǤ

(28) ƒ› ƒ•‡ǡ˜‘Žƒ–‹Ž‹–› ‘—Ž†. ʹͺ͸. ‘–ƒ ‘—–ˆ‘”–Š‡”ƒ’‹† Šƒ‰‡•‹Ž‡ƒ”‹‰”ƒ–‡ȋˆ”‘–”‹ƒŽ–‘–”‹ƒŽǡˆ‘ŽŽ‘™‹‰. ʹͺ͹. ‘ˆ‹”ƒ–‘”›˜•†‹• ‘ˆ‹”ƒ–‘”›‡˜‹†‡ ‡Ȍ’”‡•‡–‹–Š‡ œ‰”‘—’‹–Š‡•‡. ʹͺͺ. †ƒ–ƒ•‡–•Ǥ. . ͳʹ.

(29)  ʹͺͻ.

(30) ‘†‡Ž•ͳƒ†ʹǡ Šƒ‰‡•‹x2ˆ”‘–”‹ƒŽ–‘–”‹ƒŽ‘ —”‘Ž›ƒ ‘”†‹‰–‘. ʹͻͲ. –Š‡‡˜‘Ž—–‹‘”ƒ–‡ωǡ–Š‡˜ƒ”‹ƒ ‡‘ˆ–Š‡”ƒ†‘’”‘ ‡••ƒ––Š‡•‡ ‘†Ž‡˜‡ŽǤ. ʹͻͳ. Š‡•‡‘†‡Ž•™‡”‡‡“—‹˜ƒŽ‡––‘–Š‡•—„•‡“—‡–‘†‡Ž•™‹–Š‡‹–Š‡”φȋ‘†‡Ž•͵. ʹͻʹ. ƒ†ͶȌˆ‹š‡†–‘Ͳ‘”κ1ȋ‘†‡Ž•ͷƒ†͸Ȍˆ‹š‡†–‘ͳǤ

(31) ‘†‡Ž•͵ƒ†Ͷǡ Šƒ‰‡•‹x2ˆ”‘–”‹ƒŽ–‘–”‹ƒŽ‘ —”ƒ ‘”†‹‰–‘ƒ. ʹͻ͵ ʹͻͶ. ƒ—–‘”‡‰”‡••‹˜‡ȋȋͳȌȌ’”‘ ‡••–Šƒ–‹• ‘–”‘ŽŽ‡†„›–Š”‡‡’ƒ”ƒ‡–‡”•ǣmǡ–Š‡. ʹͻͷ. Ž‡˜‡Ž–‘™Š‹ Šx2‹•ƒ––”ƒ –‡†ǡφǡ–Š‡”ƒ–‡‘ˆ Šƒ‰‡‘ˆx2–‘™ƒ”†•mǡƒ†ωǡ–Š‡. ʹͻ͸. ˜ƒ”‹ƒ ‡‘ˆ–Š‡”ƒ†‘’”‘ ‡••ǣ ሺ௞ାଵሻ. ʹͻ͹. ‫݌‬ቀ‫ݔ‬ଶ. ሺ௞ሻ. ሺ௞ሻ. ቁ̱ࣨቀ‫ݔ‬ଶ ൅ ߮ሺ݉ െ ‫ݔ‬ଶ ሻǡ ‡š’ሺ ߱ሻቁ. ʹͻͺ. ˆ–‡”‹˜‡”•‹‘ǡ–Š‡‡˜‘Ž—–‹‘‘ˆx2ƒ ‘”†‹‰–‘–Š‹•‡“—ƒ–‹‘‹•”‡ˆŽ‡ –‡†‹–Š‡. ʹͻͻ. ’”‡†‹ –‹‘‘ˆߤଶ ǣ ሺ௞ାଵሻ. ͵ͲͲ. ߤƸ ଶ. ͵Ͳͳ. ሺ௞ሻ. ሺ௞ሻ. ൌ ߤଶ ൅ ߮ሺ݉ െ ߤଶ ሻ. 

(32) –Š‹••–—†›ǡ‰‹˜‡–Š‡”‡™ƒ•‘„‹ƒ•–‘™ƒ”†•‘‡Œƒ”‘”–Š‡‘–Š‡”ǡm™ƒ•. ͵Ͳʹ. ˆ‹š‡†–‘Ͳǡ•‘φ ƒŽ™ƒ›•ƒ –‡†–‘•Š‹ˆ––Š‡‘†‡Žǯ•„‡Ž‹‡ˆ•„ƒ –‘™ƒ”†•ƒš‹—. ͵Ͳ͵. — ‡”–ƒ‹–›ȋ‹Ǥ‡Ǥ†‹• ‘ˆ‹”–Š‡ —””‡–„‡Ž‹‡ˆȌƒ„‘—––Š‡Œƒ”•Ǥ ‹‰—”‡Ͷȋ—’’‡”Ž‡ˆ–. ͵ͲͶ. ’ƒ‡ŽȌ‹ŽŽ—•–”ƒ–‡•–Š‡‡ˆˆ‡ –‘ˆφ‘‫ݏ‬ቀߤଶ ቁ‘˜‡”–‹‡Ǥ. ሺ௞ሻ. ͵Ͳͷ.

(33) ‘†‡Ž•ͷƒ†͸ǡ Šƒ‰‡•‹μ2ˆ”‘–”‹ƒŽ–‘–”‹ƒŽ‘ —”ƒ ‘”†‹‰–‘–™‘. ͵Ͳ͸. ’ƒ”ƒ‡–‡”•ǣωǡ–Š‡˜ƒ”‹ƒ ‡‘ˆ–Š‡”ƒ†‘’”‘ ‡••ǡƒ†κ1ǡƒ• ƒŽ‹‰ˆƒ –‘”–Šƒ–. ͵Ͳ͹. Šƒ‰‡•–Š‡•‹œ‡‘ˆ—’†ƒ–‡•™Š‡ߤƸ ଵ αͲǤͷǡ‘”ƒš‹—— ‡”–ƒ‹–›ǡ”‡Žƒ–‹˜‡–‘. ͵Ͳͺ. ™Š‡ߤƸ ଵ ‹• Ž‘•‡”–‘Ͳ‘”ͳǡ‹Ǥ‡Ǥ™Š‡–Š‡•—„Œ‡ –‹•‘”‡ ‘ˆ‹†‡–ƒ„‘—–‡‹–Š‡”. ͵Ͳͻ. Œƒ”Ǥ ‹‰—”‡ͶȋŽ‘™‡”Ž‡ˆ–’ƒ‡ŽȌ‹ŽŽ—•–”ƒ–‡•–Š‡‡ˆˆ‡ –‘ˆκ1‘ߤƸ ଵ ‘˜‡”–‹‡Ǥ. ͵ͳͲ. ‘”ƒŽŽ›ǡ–Š‡• ƒŽ‹‰‘ —”•ƒ•ǣ ሺ௞ାଵሻ. ͵ͳͳ. ߤƸ ଵ. . ሺ௞ሻ. ‫ݏ ؠ‬ቀߤଶ ߢଵ ቁ. ͳ͵.

(34)  ͵ͳʹ. Š‡κ1 εͳǡ—’†ƒ–‹‰–‘™ƒ”†•ͳ‘‘„•‡”˜‹‰ƒ„Ž—‡„‡ƒ†ȋuαͳȌ‹•. ͵ͳ͵. ‰”‡ƒ–‡•–ȋ‹Ǥ‡Ǥ•™‹– Š‹‰„‡–™‡‡Œƒ”•„‡ ‘‡•‘”‡Ž‹‡Ž›Ȍ™Š‡ߤƸ ଵ δͲǤ͵Ǣ™Š‡. ͵ͳͶ. κ1 δͳǡ—’†ƒ–‹‰‹• ‘’ƒ”ƒ–‹˜‡Ž›ˆƒ”Ž‘™‡”™Š‡ߤƸ ଵ δͲǤ͵ǤŠ‹•‹•‹ŽŽ—•–”ƒ–‡†‹. ͵ͳͷ. ‹‰—”‡Ͷȋ‹††Ž‡’ƒ‡ŽȌǣˆ‘”Š‹‰Š˜ƒŽ—‡•‘ˆκ1ȋ„”‘™Ž‹‡Ȍǡ„‡Ž‹‡ˆ—’†ƒ–‡•–Šƒ–. ͵ͳ͸. ”‘••–Š‡ߤƸ ଵ ൌ ͲǤͷŽ‹‡‡ ‘—–‡”Ž‹––Ž‡”‡•‹•–ƒ ‡ȋ‹Ǥ‡ǤŽ‹––Ž‡‡˜‹†‡ ‡‹•”‡“—‹”‡†. ͵ͳ͹. –‘ ƒ—•‡ƒŽƒ”‰‡•Š‹ˆ–Ȍǡ™Š‹Ž‡ƒ’’”‘ƒ Š‹‰–Š‡‡š–”‡‡•‘ˆߤƸ ଵ ൌ Ͳƒ†ߤƸ ଵ ൌ ͳ‹. ͵ͳͺ. ”‡•’‘•‡–‘ ‘ˆ‹”ƒ–‘”›‡˜‹†‡ ‡‹•”‡•‹•–‡†ȋ„‡Ž‹‡ˆ•Š‹ˆ–•ƒ”‡˜‡”›•ƒŽŽˆ‘”ߤƸ ଵ . ͵ͳͻ. ‡ƒ”ͳȌǤ› ‘–”ƒ•–ǡˆ‘”Ž‘™˜ƒŽ—‡•‘ˆκ1 ȋ„Žƒ Ž‹‡ǡ ‹‰—”‡Ͷ‹††Ž‡’ƒ‡ŽȌǡ–Š‡”‡. ͵ʹͲ. ‹•”‡Žƒ–‹˜‡Ž›Ž‡••”‡•‹•–ƒ ‡ƒ‰ƒ‹•–ƒ’’”‘ƒ Š‹‰–Š‡‡š–”‡‡•™Š‹Ž‡‹––ƒ‡•‘”‡. ͵ʹͳ. ‡˜‹†‡ ‡ˆ‘”„‡Ž‹‡ˆ•–‘ ”‘••–Š‡ߤƸ ଵ ൌ ͲǤͷŽ‹‡Ǥ. ͵ʹʹ. ‹‰—”‡Ͷȋ”‹‰Š–’ƒ‡ŽȌ‹ŽŽ—•–”ƒ–‡•–Š‡ƒ˜‡”ƒ‰‡ƒ„•‘Ž—–‡•Š‹ˆ–•‹„‡Ž‹‡ˆ•‘. ͵ʹ͵. ‘„•‡”˜‹‰„‡ƒ†•‘ˆ‡‹–Š‡” ‘Ž‘—”ǤŠ‹•Ǯ˜—Ž‡”ƒ„‹Ž‹–›–‘—’†ƒ–‹‰ǯ‹•Š‹‰ŠŽ›. ͵ʹͶ. ”‡‹‹• ‡–‘ˆ–Š‡Ǯ‡‡”‰›•–ƒ–‡ǯ‘ˆƒ‡—”ƒŽ‡–™‘”‘†‡ŽȂ‹Ǥ‡Ǥ‹Ž‘™‡‡”‰›. ͵ʹͷ. •–ƒ–‡•ǡŽ‡••—’†ƒ–‹‰‘ —”•ǤŠ‡‡ˆˆ‡ –‘ˆ‹ ”‡ƒ•‹‰κ1‹•–‘ ‘˜‡”– ‘ˆ‹†‡–. ͵ʹ͸. „‡Ž‹‡ˆ•ƒ„‘—––Š‡Œƒ”ȋ‡ƒ”Ͳƒ†ͳȌˆ”‘Ž‘™–‘Š‹‰ŠǮ‡‡”‰›•–ƒ–‡•ǯǡ‹Ǥ‡Ǥ–‘ƒ‡. ͵ʹ͹. –Š‡— Š‘”‡—•–ƒ„Ž‡ǤŠ‹•”‡ ƒ’‹–—Žƒ–‡•–Š‡ƒ––”ƒ –‘”‡–™‘”’”‘’‡”–‹‡•. ͵ʹͺ. ‹ŽŽ—•–”ƒ–‡†‹ ‹‰—”‡ͳǣƒ—•–ƒ„Ž‡‡–™‘”‡ƒ•‹Ž›•™‹– Š‡•ˆ”‘‘‡•–ƒ–‡–‘. ͵ʹͻ. ƒ‘–Š‡”„—–Šƒ•†‹ˆˆ‹ —Ž–›•–ƒ„‹Ž‹•‹‰ƒ›‘‡•–ƒ–‡ǡ™Š‡”‡ƒ•ƒ•–ƒ„Ž‡‡–™‘”. ͵͵Ͳ. ”‡“—‹”‡•‘”‡‡‡”‰›ȋŠ‡”‡ǡ‹ˆ‘”ƒ–‹‘Ȍ–‘‘˜‡” ‘‡–Š‡„‘—†ƒ”›„‡–™‡‡. ͵͵ͳ. –™‘•–ƒ–‡•ȋŠ‡”‡ǡ„‡Ž‹‡ˆ•ȌǤ‘†‡Ž•ͷƒ†͸–Š‡”‡ˆ‘”‡ ƒ’–—”‡–Š‡‡ˆˆ‡ –•‘ˆ. ͵͵ʹ. ƒ––”ƒ –‘”ȋ‹Ȍ•–ƒ„‹Ž‹–›‘„‡Ž‹‡ˆ—’†ƒ–‹‰ǡ‘”ƒ–Ž‡ƒ•––Š‡‹†‘ˆ—’†ƒ–‹‰ˆ‘”. ͵͵͵. ™Š‹ Šȋ—Ȍ•–ƒ„Ž‡ƒ––”ƒ –‘”•–ƒ–‡•ƒ”‡ƒ‰‘‘†ƒƒŽ‘‰›Ǥ. ͵͵Ͷ. •‰”‘—’†‹ˆˆ‡”‡ ‡•‹‹‹–‹ƒŽ—’†ƒ–‹‰Šƒ†„‡‡‘„•‡”˜‡†‹†ƒ–ƒ•‡–ͳǡ. ͵͵ͷ. ™‡ƒŽ•‘‡•–‹ƒ–‡†–Š‡•–ƒ†ƒ”††‡˜‹ƒ–‹‘‘ˆμ2„‡ˆ‘”‡–Š‡•‡“—‡ ‡„‡‰‹•ǡσ2(0)ǡ. ͵͵͸. ‹‘†‡Ž•ʹǡͶƒ†͸Ǥ. . ͳͶ.

(35)  ͵͵͹. ˆ‘”‹–‡”‡†‹ƒ–‡˜ƒŽ—‡•‘ˆκ1ǡ‘†‡Ž•ͷƒ†͸’”‘†— ‡•‹‹Žƒ”„‡Ž‹‡ˆ. ͵͵ͺ. —’†ƒ–‹‰–”ƒŒ‡ –‘”‹‡•–‘‘†‡Ž•͵ƒ†Ͷȋ ‘–ƒ‹‹‰–Š‡†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰. ͵͵ͻ. ’ƒ”ƒ‡–‡”φȌǣ„‘–Šƒ‡‰”‡ƒ–‡”—’†ƒ–‡•ˆ‘ŽŽ‘™‹‰†‹• ‘ˆ‹”ƒ–‘”›‡˜‹†‡ ‡Ǥ. ͵ͶͲ. ‘”‘”‡‡š–”‡‡˜ƒŽ—‡•‘ˆκ1ǡŠ‘™‡˜‡”ǡ‘†‡Ž•ͷƒ†͸’”‘†— ‡–”ƒŒ‡ –‘”‹‡•. ͵Ͷͳ. –Šƒ–‘†‡Ž•͵ƒ†Ͷ ƒ‘–ǣφ ƒ‘–’—ŽŽ„‡Ž‹‡ˆ•ˆƒ”–‘™ƒ”†• ‡”–ƒ‹–›‹–Š‡. ͵Ͷʹ. ‘’’‘•‹–‡Œƒ”ȋ ǤˆǤ„”‘™Ž‹‡‹ ‹‰—”‡ͶǡŽ‘™‡”Ž‡ˆ–’ƒ‡ŽȌǡƒ†‡‹–Š‡” ƒ‹–ƒ‡. ͵Ͷ͵. ‹–more†‹ˆˆ‹ —Ž––‘—’†ƒ–‡–‘†‹• ‘ˆ‹”ƒ–‘”›‡˜‹†‡ ‡ȋ ǤˆǤ„Žƒ Ž‹‡‹ ‹‰—”‡Ͷǡ. ͵ͶͶ. Ž‘™‡”Ž‡ˆ–’ƒ‡ŽȌǤ. ͵Ͷͷ. Š‡’ƒ”ƒ‡–‡”•ωƒ†νΪȀǦσ2(0)ΪȀǦ φ‘” κ1™‡”‡‡•–‹ƒ–‡†‹†‹˜‹†—ƒŽŽ›. ͵Ͷ͸. ˆ‘”‡ƒ Š•—„Œ‡ –Ǥ

(36) ˆ‡•–‹ƒ–‡†ǡ–Š‡’”‹‘”’”‘„ƒ„‹Ž‹–›†‹•–”‹„—–‹‘•ˆ‘”–Š‡‹”˜ƒŽ—‡•. ͵Ͷ͹. ƒ”‡‰‹˜‡‹ƒ„Ž‡ʹǤŠ‡‡ƒ•‰‹˜‡Š‡”‡”‡ˆ‡”–‘–Š‡’ƒ”ƒ‡–‡”•ǯƒ–‹˜‡•’ƒ ‡ǡ. ͵Ͷͺ. „—––Š‡˜ƒ”‹ƒ ‡•”‡ˆ‡”‘––‘–Š‡’ƒ”ƒ‡–‡”•ǯƒ–‹˜‡•’ƒ ‡ǡ™Š‹ Š‹ƒ› ƒ•‡•. ͵Ͷͻ. ‹•„‘—†‡†ǡ„—––‘–Š‡—„‘—†‡†•’ƒ ‡–Š‡›™‡”‡–”ƒ•ˆ‘”‡†–‘ˆ‘”‡•–‹ƒ–‹‘. ͵ͷͲ. ’—”’‘•‡•Ǥ–Š‡”™‹•‡–Š‡›™‡”‡ˆ‹š‡†ƒ•߮ ൌ Ͳȋ‘†‡Ž•ͳƒ†ʹȌƒ†ߪଶ. ͵ͷͳ. ͲǤͲͲ͸ȋ‘†‡Ž•ͳǡ͵ƒ†ͷȌ.Š‡‘†‡Žǯ•’”‹‘”„‡Ž‹‡ˆ•ƒ„‘—––Š‡Œƒ”•ƒ––Š‡•–ƒ”–‘ˆ. ͵ͷʹ. –Š‡•‡“—‡ ‡™‡”‡ˆ‹š‡†ƒ–μ2(0)αͲȋ‹Ǥ‡Ǥ„‡Ž‹‡˜‹‰‡ƒ Š–‘„‡‡“—ƒŽŽ›Ž‹‡Ž›ȌǤŠ‡. ͵ͷ͵. ’”‹‘”•™‡”‡•—ˆˆ‹ ‹‡–Ž›—‹ˆ‘”ƒ–‹˜‡–‘„‡‡ƒ•‹Ž›—’†ƒ–‡†„›–Š‡†ƒ–ƒǣƒŽŽ’”‹‘”. ͵ͷͶ. ‡ƒ•ƒ”‡•–ƒ†ƒ”†ˆ‘”–Š‡ ‡š ‡’–σ2(0)ǡ™Š‹ ŠŠƒ†–‘„‡‹ ”‡ƒ•‡†ˆ”‘. ͵ͷͷ. ͲǤͲͲ͸–‘ͲǤͺ–‘ƒŽŽ‘™–Š‡†ƒ–ƒ–‘ Šƒ‰‡‹–ǤŠ‡Žƒ––‡” Šƒ‰‡‡•—”‡†–Šƒ–‰”‘—’. ͵ͷ͸. †‹ˆˆ‡”‡ ‡•‹‹‹–‹ƒŽ„‡Ž‹‡ˆ—’†ƒ–‹‰ƒŽ‘‡™‘—Ž† ƒ—•‡‰”‘—’†‹ˆˆ‡”‡ ‡•‹σ2(0). ͵ͷ͹. ”ƒ–Š‡”–Šƒκ1Ǥ. ͵ͷͺ. . ͵ͷͻ. Model fitting and statistical analysis. ͵͸Ͳ. . ሺ଴ሻ. . ͳͷ. ൌ.

(37)  ͵͸ͳ. ‡–‡•–‡†‘†‡Ž•™‹–Š†‹ˆˆ‡”‡– ‘„‹ƒ–‹‘•‘ˆ’ƒ”ƒ‡–‡”•ωǡνǡφ‘”κ1ƒ†. ͵͸ʹ. σ2(0)ȋ•‡‡ƒ„Ž‡ʹȌǤ

(38) ƒƒŽ›•‹‰†ƒ–ƒ•‡–ʹǡ™‡ ‘ ƒ–‡ƒ–‡†ƒŽŽˆ‘—”•‡“—‡ ‡•ˆ‘”. ͵͸͵. ‡ƒ Š•—„Œ‡ –‹‘”†‡”–‘‡•–‹ƒ–‡–Š‡‘†‡Ž’ƒ”ƒ‡–‡”•ƒ•ƒ —”ƒ–‡Ž›ƒ•’‘••‹„Ž‡. ͵͸Ͷ. ȋ”‡•‡––‹‰–Š‡„‡Ž‹‡ˆ•ƒ„‘—––Š‡Œƒ”•ƒ––Š‡•–ƒ”–‘ˆ‡ƒ Š•‡“—‡ ‡ȌǤ. ͵͸ͷ. . ͵͸͸. ‘†‡Ž•‡Ž‡ –‹‘‘ƒŽŽ‰”‘—’••‡’ƒ”ƒ–‡Ž›‹„‘–Š†ƒ–ƒ•‡–ͳȋƒ–„ƒ•‡Ž‹‡ƒ†. ͵͸͹. ˆ‘ŽŽ‘™Ǧ—’Ȍƒ††ƒ–ƒ•‡–ʹǤŠ‹•’”‘ ‡†—”‡™‡‹‰Š–•‘†‡Ž•ƒ ‘”†‹‰–‘–Š‡‹”. ͵͸ͺ. ƒ —”ƒ ›„—–’‡ƒŽ‹•‡•–Š‡ˆ‘” ‘’Ž‡š‹–›ȋ‹Ǥ‡Ǥ—‡ ‡••ƒ”›‡š–”ƒ’ƒ”ƒ‡–‡”•Ȍ. ͵͸ͻ. –‘’”‡˜‡–‘˜‡”ˆ‹––‹‰ȋ–‡’Šƒ‡–ƒŽǤǡʹͲͲͻǢ‹‰‘—š‡–ƒŽǤǡʹͲͳͶȌǤŠ‡™‹‹‰. ͵͹Ͳ. ‘†‡Ž‹ƒŽŽ‡‹‰Š–‰”‘—’•™ƒ•‘†‡Ž͸ȋ ‹‰—”‡͸ȌǡƒŽ–Š‘—‰Šƒ”‘—†ƒ–Š‹”†‘ˆ. ͵͹ͳ. ’•› Š‘–‹ •—„Œ‡ –•ƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•‹†ƒ–ƒ•‡–ͳȋƒ–„ƒ•‡Ž‹‡Ȍƒ†‹. ͵͹ʹ. †ƒ–ƒ•‡–ʹ™‡”‡„‡––‡”ˆ‹–„›‘†‡ŽͶǤ

(39) –‹•— Ž‡ƒ”™Š›–Š‹• Šƒ‰‡‘ —”•ǡ„—–. ͵͹͵. ‰‹˜‡–Šƒ–‘†‡Ž͸ ƒ’”‘†— ‡˜‡”›•‹‹Žƒ”–”ƒŒ‡ –‘”‹‡•–‘‘†‡ŽͶˆ‘”. ͵͹Ͷ. ‹–‡”‡†‹ƒ–‡˜ƒŽ—‡•‘ˆκ1ȋ ‹‰—”‡ͶȌǡƒ›‹ ”‡ƒ•‡‹”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›‹•. ͵͹ͷ. Ž‹‡Ž›–‘†‹‹‹•Š–Š‡•–”‡‰–Š‘ˆ‡˜‹†‡ ‡ˆ‘”‘‡‘†‡Ž‘˜‡”ƒ•‹‹Žƒ”‘‡Ǥ. ͵͹͸. . ͵͹͹. ™‹‹‰‘†‡Žǡ‘†‡Ž͸ǡ™‡•‹—Žƒ–‡†ͳͲͲ†ƒ–ƒ•‡–•—•‹‰–Š‡‘†ƒŽ˜ƒŽ—‡•‘ˆ. ͵͹ͺ. –Š‡’ƒ”ƒ‡–‡”•ˆ‘”„‘–Š ‘–”‘Žƒ† œ‰”‘—’•ȋ ‹‰—”‡ͷǡ—’’‡”ƒ†Ž‘™‡””‘™•. ͵͹ͻ. ”‡•’‡ –‹˜‡Ž›Ǣƒ‡šƒ’Ž‡•‹—Žƒ–‡††ƒ–ƒ•‡–‹••Š‘™‹ ‹‰—”‡͵ȌǤ‡–Š‡. ͵ͺͲ. ‡•–‹ƒ–‡†–Š‡’ƒ”ƒ‡–‡”•ˆ‘”–Š‡•‹—Žƒ–‡††ƒ–ƒǡƒ†•Š‘™‡†–Šƒ–‹‘•– ƒ•‡•ǡ. ͵ͺͳ. –Š‡’ƒ”ƒ‡–‡”•ƒ”‡”‡ ‘˜‡”‡†”‡ƒ•‘ƒ„Ž›ƒ —”ƒ–‡Ž›ǤŠ‡‡š ‡’–‹‘™ƒ•σ2(0)‹. ͵ͺʹ. –Š‡ œ‰”‘—’•‹—Žƒ–‹‘ǡ™Š‹ Š™ƒ•†‹•–”‹„—–‡†ƒ”‘—†–Š‡’”‹‘”‡ƒ‘ˆͲǤͺ. ͵ͺ͵. ”ƒ–Š‡”–Šƒ–Š‡–”—‡˜ƒŽ—‡‘ˆͳǤͷǤ‡”‡–ƒ‹‡†ƒ’”‹‘”‡ƒ‘ˆͲǤͺˆ‘”σ2(0). ͵ͺͶ. „‡ ƒ—•‡—•‹‰ƒŠ‹‰Š‡”’”‹‘”‡ƒŽ‡†–‘‘˜‡”‡•–‹ƒ–‹‘‘ˆσ2(0)‹‘–Š‡”. ͵ͺͷ. •‹—Žƒ–‹‘•ȋ‘–•Š‘™ȌǤ. . ˆ–‡”ˆ‹––‹‰–Š‡•‹š‘†‡Ž•–‘‡ƒ Š•—„Œ‡ –ǯ•†ƒ–ƒǡ™‡’‡”ˆ‘”‡†ƒ›‡•‹ƒ.

(40) ‘”†‡”–‘ ‘ˆ‹”™‡ ‘—Ž†”‡Ž‹ƒ„Ž›‡•–‹ƒ–‡–Š‡’ƒ”ƒ‡–‡”•‘ˆ–Š‡. ͳ͸.

(41)  ͵ͺ͸. . ͵ͺ͹. Results. ͵ͺͺ. . ͵ͺͻ. Behavioural results: dataset 1. ͵ͻͲ. . ͵ͻͳ. ƒ Š‰”‘—’ǯ•‡ƒ”‡•’‘•‡•ƒ”‡’Ž‘––‡†‹ ‹‰—”‡ʹǡƒ†•–ƒ–‹•–‹ ƒŽ–‡•–•. ͵ͻʹ. †‡–ƒ‹Ž‡†‹ƒ„Ž‡ͳȋp(adj) ”‡ˆ‡”•–‘–Š‡ƒ†Œ—•–‡†p ˜ƒŽ—‡‘ˆ—‡›ǯ• post hoc. ͵ͻ͵. –‡•–ȌǤ•†‡• ”‹„‡†’”‡˜‹‘—•Ž›ȋ‡–‡”•ƒ† ƒ”‡–›ǡʹͲͲ͸Ȍǡƒ–„ƒ•‡Ž‹‡–Š‡”‡™ƒ•ƒ. ͵ͻͶ. •‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡‹†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰„‡–™‡‡–Š‡‰”‘—’•ȋFȋʹǡ͹͹Ȍα. ͵ͻͷ. ͸ǡpαͲǤͲͲͶǡȌǡƒ†–Š‡’•› Š‘–‹ ‰”‘—’Šƒ†‰”‡ƒ–‡”†‹• ‘ˆ‹”ƒ–‘”›. ͵ͻ͸. —’†ƒ–‹‰–Šƒ–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ȋp(adj)αͲǤͲͲ͵Ȍ„—–‘––Š‡ Ž‹‹ ƒŽ. ͵ͻ͹. ‘–”‘Ž•ȋp(adj)αͲǤͶȌǤŠ‡”‡™ƒ•‘†‹ˆˆ‡”‡ ‡„‡–™‡‡–Š‡ Ž‹‹ ƒŽƒ†‘Ǧ. ͵ͻͺ. Ž‹‹ ƒŽ ‘–”‘Ž•ȋp(adj)αͲǤͳ͵ȌǤŠ‡”‡™‡”‡ƒŽ•‘•‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡•‹‹‹–‹ƒŽ. ͵ͻͻ. ‡”–ƒ‹–›ƒ ”‘••–Š‡–Š”‡‡‰”‘—’•ȋFȋʹǡ͹͹ȌαͺǤ͹ǡpαͲǤͲͲͲͶǡȌǢ–Š‡. ͶͲͲ. ’•› Š‘–‹ ‰”‘—’ǯ•‹‹–‹ƒŽ ‡”–ƒ‹–›™ƒ•Š‹‰Š‡”–Šƒ–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ǯ. ͶͲͳ. ȋp(adj)αͲǤͲͲͲ͵Ȍ„—–‘––Š‡ Ž‹‹ ƒŽ ‘–”‘Ž•ǯȋp(adj) αͲǤʹͷȌǤŠ‡”‡™ƒ•ǯ–ƒ. ͶͲʹ. •‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡„‡–™‡‡–Š‡ Ž‹‹ ƒŽƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’•ȋp(adj). ͶͲ͵. αͲǤͲ͸ȌǤŠ‡”‡™‡”‡‘‰”‘—’†‹ˆˆ‡”‡ ‡•‹ˆ‹ƒŽ ‡”–ƒ‹–›ȋFȋʹǡ͹͹ȌαͲǤ͹ǡ’αͲǤͷǡ. ͶͲͶ. ȌǤ. ͶͲͷ. . ͶͲ͸. ‰”‘—’•™ƒ•‘Ž‘‰‡”•‹‰‹ˆ‹ ƒ–ȋFȋʹǡͷʹȌ αʹǤͻǡpαͲǤͲ͸ǡȌǢ–Š‡’•› Š‘–‹ . ͶͲ͹. ‰”‘—’Šƒ†‰”‡ƒ–‡”†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰–Šƒ–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•. ͶͲͺ. ȋp(adj)αͲǤͲͶͻȌ„—–‘––Š‡ Ž‹‹ ƒŽ ‘–”‘Ž•ȋp(adj)αͲǤͶȌǤŠ‡”‡™ƒ•‘. . –ˆ‘ŽŽ‘™Ǧ—’ǡ–Š‡†‹ˆˆ‡”‡ ‡‹†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰„‡–™‡‡–Š‡. ͳ͹.

(42)  ͶͲͻ. •‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡‹‹‹–‹ƒŽ ‡”–ƒ‹–›ƒ ”‘••–Š‡‰”‘—’•ȋFȋʹǡͷʹȌαͲǤͻǡpαͲǤͶǡ. ͶͳͲ. ȌǤ‹ˆˆ‡”‡ ‡•‹ˆ‹ƒŽ ‡”–ƒ‹–›™‡”‡‘Ž‘‰‡”•‹‰‹ˆ‹ ƒ–ȋFȋʹǡͷʹȌαʹǤͺǡp. Ͷͳͳ. αͲǤͲ͹ǡȌǢ–Š‡„‹‰‰‡•–†‹ˆˆ‡”‡ ‡™ƒ•–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ǯˆ‹ƒŽ. Ͷͳʹ. ‡”–ƒ‹–›™Š‹ Š™ƒ•—‡”‹ ƒŽŽ›Š‹‰Š‡”–Šƒ–Š‡ Ž‹‹ ƒŽ ‘–”‘Ž•ǯȋp(adj)α. Ͷͳ͵. ͲǤͲͷ͹ȌǤ. ͶͳͶ. . Ͷͳͷ. †‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰ƒ–„‘–Š„ƒ•‡Ž‹‡ȋραǦͲǤͶͳǡp αͲǤͲͲͲͳͷȌƒ†ˆ‘ŽŽ‘™Ǧ—’. Ͷͳ͸. ȋραǦͲǤͶͳǡp αͲǤͲͲʹȌǡ„—–‘–„‡–™‡‡ˆ‹ƒŽ ‡”–ƒ‹–›ƒ†–Š‡‘–Š‡”–™‘. Ͷͳ͹. ‡ƒ•—”‡•ȋp εͲǤͳ‹ƒŽŽˆ‘—” ‘’ƒ”‹•‘•ȌǤ. Ͷͳͺ. . Ͷͳͻ. Behavioural results: dataset 2. ͶʹͲ. . Ͷʹͳ. Š‡‡ƒ”‡•’‘•‡•‘ˆ•—„Œ‡ –•‹‡ƒ Š‰”‘—’ƒ”‡’Ž‘––‡†‹ ‹‰—”‡ʹǤŠ‡”‡. Ͷʹʹ. ™ƒ•ƒ•‹‰‹ˆ‹ ƒ–‹ ”‡ƒ•‡‹†‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰‹ œ ‘’ƒ”‡†™‹–Š. Ͷʹ͵. ‘–”‘Ž•ȋtȋͺͺǤ͸ȌαʹǤͳǡpαͲǤͲͶǡ‡Ž Šǯ•tǦ–‡•–ȌǤŠ‡”‡™ƒ•‹š‡†‡˜‹†‡ ‡ˆ‘”ƒ. ͶʹͶ. †‹ˆˆ‡”‡ ‡‹‹‹–‹ƒŽ ‡”–ƒ‹–›„‡–™‡‡ œƒ† ‘–”‘Ž•ǣ œ™‡”‡‘”‡ ‡”–ƒ‹. Ͷʹͷ. ƒˆ–‡”–Š‡ˆ‹”•–„‡ƒ†‹•‡“—‡ ‡•ƒ†„—–‘–‘”ȋ ‹‰—”‡ʹƒ†ƒ„Ž‡ʹȌǡ. Ͷʹ͸. „—––Š‡†‹ˆˆ‡”‡ ‡‹‡ƒ‹‹–‹ƒŽ ‡”–ƒ‹–›ˆ‡ŽŽ•Š‘”–‘ˆ•–ƒ–‹•–‹ ƒŽ•‹‰‹ˆ‹ ƒ ‡. Ͷʹ͹. ȋtȋͳͳͲȌαǦͳǤͻǡpαͲǤͲͷͻǡ‘Š‡ǯ•dαͲǤ͵ʹǡ‡Ž Šǯ•tǦ–‡•–ȌǤ ‹ƒŽ ‡”–ƒ‹–›™ƒ•. Ͷʹͺ. ‘Ž›ƒ••‡••‡†‹•‡“—‡ ‡•ƒ†ȋƒ† ‘–ƒ‹‡†–™‘ Šƒ‰‡•‘ˆ ‘Ž‘—”‹. Ͷʹͻ. –Š‡Žƒ•––Š”‡‡„‡ƒ†•Ȍǣ‹„‘–Š•‡“—‡ ‡•ǡ œ™‡”‡Ž‡•• ‡”–ƒ‹–Šƒ ‘–”‘Ž•. Ͷ͵Ͳ. ȋ•‡“—‡ ‡ǣtȋͺͲǤͳȌα͵ǤͲǡpαͲǤͲͲͶǡ•‡“—‡ ‡ǣtȋͺͷǤͷȌα͵ǤͶǡpαͲǤͲͲͳǡ‡Ž Šǯ•. Ͷ͵ͳ. tǦ–‡•–•ȌǤ. . Š‡”‡™‡”‡‡‰ƒ–‹˜‡ ‘””‡Žƒ–‹‘•„‡–™‡‡‹‹–‹ƒŽ ‡”–ƒ‹–›ƒ†. ͳͺ.

(43)  Ͷ͵ʹ. . Ͷ͵͵. ™‹–Š‹„‘–Š œȋραǦͲǤͶ͸ǡpαͲǤͲͲͲ͵Ȍƒ† ‘–”‘ŽȋραǦͲǤͷ͹ǡpαͳͲǦͳͳȌ‰”‘—’•Ǥ. Ͷ͵Ͷ. ‹ƒŽ ‡”–ƒ‹–›†‹†‘– ‘””‡Žƒ–‡™‹–Š‡‹–Š‡”‡ƒ•—”‡‹‡‹–Š‡”‰”‘—’ȋp εͲǤͶ‹. Ͷ͵ͷ. ˆ‘—” ‘’ƒ”‹•‘•ȌǤ. Ͷ͵͸. . Ͷ͵͹. Modelling results: dataset 1. Ͷ͵ͺ. . Ͷ͵ͻ. ‘†‡Ž•‡Ž‡ –‹‘”‡•—Ž–•ˆ‘”–Š‡–Š”‡‡‰”‘—’•ƒƒŽ›•‡†•‡’ƒ”ƒ–‡Ž›ƒ–„‘–Š„ƒ•‡Ž‹‡. ͶͶͲ. ƒ†ˆ‘ŽŽ‘™Ǧ—’ƒ”‡’Ž‘––‡†‹ ‹‰—”‡͸ȋ ‘Ž—•ͳǡʹǡͶƒ†ͷȌǢ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ. ͶͶͳ. ‡ƒ Š‘†‡Ž„‡‹‰„‡•–ˆ‘”ƒ›‰‹˜‡•—„Œ‡ –‹••Š‘™‹–Š‡Ž‡ˆ–’ƒ‡Žǡƒ†–Š‡. ͶͶʹ. ’”‘„ƒ„‹Ž‹–›‘ˆ‡ƒ Š‘†‡Ž„‡‹‰–Š‡„‡•–‘˜‡”ƒŽŽ‹••Š‘™‹–Š‡”‹‰Š–’ƒ‡ŽǤ. ͶͶ͵. ‘†‡Ž͸‹•–Š‡ Ž‡ƒ”™‹‡”ƒ–‡ƒ Š–‹‡’‘‹–ǡƒŽ–Š‘—‰Šƒ‹‘”‹–›‘ˆ’•› Š‘–‹ . ͶͶͶ. ƒ† Ž‹‹ ƒŽ ‘–”‘Ž•ƒ”‡„‡•–ˆ‹–„›‘†‡ŽͶǤ. ͶͶͷ. . ͶͶ͸. •‡™‡†ǡŠ‡ ‡‘Ǧ’ƒ”ƒ‡–”‹ –‡•–•™‡”‡—•‡†–‘†‡–‡”‹‡‰”‘—’†‹ˆˆ‡”‡ ‡•. ͶͶ͹. ȋˆ—ŽŽ†‡–ƒ‹Ž•‹ƒ„Ž‡͵Ǣp(adj) ”‡ˆ‡”•–‘–Š‡ƒ†Œ—•–‡†p˜ƒŽ—‡‘ˆ—ǯ•post hoc. ͶͶͺ. –‡•–ȌǤ–„ƒ•‡Ž‹‡–Š‡”‡™‡”‡Žƒ”‰‡‰”‘—’†‹ˆˆ‡”‡ ‡•‹„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›κ1. ͶͶͻ. ȋχ2ȋʹǡαͺͲȌαͻǤ͸ͶǡpαͲǤͲͲͺǡηʹαͲǤͳʹǡ”—•ƒŽǦƒŽŽ‹•ǯ‘‡Ǧ™ƒ›‘. ͶͷͲ. ”ƒ•Ȍƒ†”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›νȋχ2ȋʹǡαͺͲȌαͳͳǤͻǡpαͲǤͲͲ͵ǡηʹαͲǤͳͷȌ„—–. Ͷͷͳ. ‘–‹σ2(0)‘”ωǤŠ‡”‡™‡”‡•–ƒ–‹•–‹ ƒŽŽ›•‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡•‹κ1„‡–™‡‡–Š‡. Ͷͷʹ. ‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ƒ†„‘–Š–Š‡’•› Š‘–‹ ‰”‘—’ȋp(adj) αͲǤͲͳǡ—ǯ•–‡•–Ȍ. Ͷͷ͵. ƒ†–Š‡ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’ȋp(adj)αͲǤͲͳȌǡ„—–‘–„‡–™‡‡–Š‡Žƒ––‡”–™‘. ͶͷͶ. ‰”‘—’•ȋp(adj) αͲǤͶȌǤ‹‹Žƒ”Ž›ǡ–Š‡”‡™‡”‡•–ƒ–‹•–‹ ƒŽŽ›•‹‰‹ˆ‹ ƒ–†‹ˆˆ‡”‡ ‡•‹. Ͷͷͷ. 턇–™‡‡–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ƒ†„‘–Š–Š‡’•› Š‘–‹ ‰”‘—’ȋp(adj) αͲǤͲͲʹǡ. .

(44) ‹–‹ƒŽ ‡”–ƒ‹–›ƒ††‹• ‘ˆ‹”ƒ–‘”›—’†ƒ–‹‰‡‰ƒ–‹˜‡Ž› ‘””‡Žƒ–‡†. ‘†‡Ž͸ǯ•’ƒ”ƒ‡–‡”†‹•–”‹„—–‹‘•ƒ”‡•Š‘™‹ ‹‰—”‡͹Ǣ–Š‡›ƒ”‡. ͳͻ.

(45)  Ͷͷ͸. —ǯ•–‡•–Ȍƒ†–Š‡ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’ȋp(adj)αͲǤͲͳȌǡ„—–‘–„‡–™‡‡–Š‡. Ͷͷ͹. Žƒ––‡”–™‘‰”‘—’•ȋp(adj) αͲǤ͵ȌǤ. Ͷͷͺ. . Ͷͷͻ. ͺǤͲǡpαͲǤͲʹǡηʹαͲǤͳͷǡ”—•ƒŽǦƒŽŽ‹•ǯ‘‡Ǧ™ƒ›‘”ƒ•Ȍƒ†ν. Ͷ͸Ͳ. ȋχ2ȋʹǡαͷͷȌαͺǤͷǡpαͲǤͲͳǡηʹαͲǤͳ͸Ȍ„—–‘–‹σ2(0)‘”ωǤŠ‡”‡™ƒ•ƒ•‹‰‹ˆ‹ ƒ–. Ͷ͸ͳ. †‹ˆˆ‡”‡ ‡‹κ1„‡–™‡‡–Š‡’•› Š‘–‹ ƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’•ȋp(adj)α. Ͷ͸ʹ. ͲǤͲͲ͹ǡ—ǯ•–‡•–Ȍ„—–‘––Š‡ Ž‹‹ ƒŽƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’•ȋp(adj)α. Ͷ͸͵. ͲǤͳȌǢ픇ƒ‹‡†•‹‰‹ˆ‹ ƒ–Ž›†‹ˆˆ‡”‡–„‡–™‡‡–Š‡‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ƒ†. Ͷ͸Ͷ. „‘–Š–Š‡’•› Š‘–‹ ‰”‘—’ȋp(adj) αͲǤͲͳǡ—ǯ•–‡•–Ȍƒ†‘™ƒŽ•‘„‡–™‡‡–Š‡. Ͷ͸ͷ. ’•› Š‘–‹ ƒ† Ž‹‹ ƒŽ ‘–”‘Ž‰”‘—’•ȋp(adj)αͲǤͲͳȌǡ„—–‘–„‡–™‡‡–Š‡ Ž‹‹ ƒŽ. Ͷ͸͸. ƒ†‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•ȋp(adj)αͲǤͷȌǤ. Ͷ͸͹. . Ͷ͸ͺ. —’‹‰Š–„‡ƒ• ”‹„ƒ„Ž‡–‘

(46) ȋ—‹ ‡•–• ‘”‡ȋ‘•ƒ†‘•ǡͳͻ͸ʹȌȌǡ. Ͷ͸ͻ. ƒ•–Š‡‰”‘—’•ǯ

(47) • ‘”‡•™‡”‡‘–‡“—‹˜ƒŽ‡–ȋƒ„Ž‡ͳȌǤ

(48)  Ž—†‹‰„‘–Š

(49) ƒ†. Ͷ͹Ͳ. ‰”‘—’•–ƒ–—•™‹–Š‹‘‡”‡‰”‡••‹‘‘†‡Ž‹•ƒ—•‘—†‡–Š‘†‘ˆ–‡•–‹‰ˆ‘”. Ͷ͹ͳ. ‘ˆ‘—†‹‰„›

(50) „‡ ƒ—•‡‰”‘—’ƒ†

(51) ƒ”‡ Ž‡ƒ”Ž›‘–‹†‡’‡†‡–Š‡”‡ȋ‹ŽŽ‡”. Ͷ͹ʹ. ƒ†Šƒ’ƒǡʹͲͲͳȌǡ•‘™‡–‡•–‡†ˆ‘””‡Žƒ–‹‘•Š‹’•„‡–™‡‡–Š‡’ƒ”ƒ‡–‡”•ƒ†. Ͷ͹͵.

(52) •‡’ƒ”ƒ–‡Ž›™‹–Š‹‡ƒ Š‰”‘—’ƒ–‡ƒ Š–‹‡’‘‹–Ǥ‘”‡Žƒ–‹‘•Š‹’•”‡ƒ Š‡†. Ͷ͹Ͷ. •–ƒ–‹•–‹ ƒŽ•‹‰‹ˆ‹ ƒ ‡ȋƒŽŽpεͲǤͳȌǡ–Š‡ Ž‘•‡•–„‡‹‰ƒ–”‡†„‡–™‡‡κ1ƒ†

(53) ‹. Ͷ͹ͷ. ‘Ǧ Ž‹‹ ƒŽ ‘–”‘Ž•‘Ž›ȋrαǦͲǤ͵ͲǡpαͲǤͲͺȌǢ‡˜‡”–Š‡Ž‡••ǡ‰‹˜‡–Š‡•ƒŽŽ‡”. Ͷ͹͸. ‰”‘—’•‹œ‡•ƒ†Žƒ”‰‡”„‡–™‡‡Ǧ˜‡”•—•™‹–Š‹Ǧ‰”‘—’˜ƒ”‹ƒ ‡•ǡ‹–”‡ƒ‹•. Ͷ͹͹. ’Žƒ—•‹„Ž‡–Šƒ–

(54) †‹ˆˆ‡”‡ ‡• ‘–”‹„—–‡–‘‰”‘—’’ƒ”ƒ‡–‡”†‹ˆˆ‡”‡ ‡•Ǥ. Ͷ͹ͺ. –ˆ‘ŽŽ‘™Ǧ—’ǡ–Š‡”‡™‡”‡•–‹ŽŽŽƒ”‰‡‰”‘—’†‹ˆˆ‡”‡ ‡•‹κ1ȋχ2ȋʹǡαͷͷȌα. ‡‡š’Ž‘”‡†™Š‡–Š‡”‰”‘—’†‹ˆˆ‡”‡ ‡•‹κ1‘”νƒ–„ƒ•‡Ž‹‡ƒ†ˆ‘ŽŽ‘™. ‡–‡•–‡†™Š‡–Š‡”κ1‘”νƒ–„ƒ•‡Ž‹‡”‡Žƒ–‡†–‘†‡Ž—•‹‘Ǧ’”‘‡‡••. Ͷ͹ͻ. ȋ‡–‡”•‡Ž—•‹‘

(55) ˜‡–‘”›• ‘”‡Ȍƒ ”‘••ƒŽŽ‰”‘—’•ǡƒˆ–‡”ˆ‹”•–‡š Ž—†‹‰ƒ›. ͶͺͲ. ‹–‡”ƒ –‹‘„‡–™‡‡

(56) ƒ†‰”‘—’Ǣ

(57) •‹‰‹ˆ‹ ƒ–Ž› ‘””‡Žƒ–‡†™‹–ŠνȋFȋͳǡ͸͹Ȍα. . ʹͲ.

(58)  Ͷͺͳ. ͹ǤͳǡpαͲǤͲͳǡȌ„—–‘–κ1ȋFȋͳǡ͸͹Ȍα͵ǤʹǡpαͲǤͲ͹ͻǡȌǤ‡–‡•–‡†. Ͷͺʹ. ™Š‡–Š‡”κ1‘”νƒ–„ƒ•‡Ž‹‡™ƒ• ‘””‡Žƒ–‡†™‹–Šƒ›’ƒ”–‹ —Žƒ”•—„‰”‘—’‘ˆ. Ͷͺ͵. •›’–‘•ȋ‡ƒ•—”‡†—•‹‰–Š‡ƒ Š‡•–‡” ƒŽ‡ȋ”ƒ™‹‡ ƒ‡–ƒŽǤǡͳͻ͹͹ȌȌ‹. ͶͺͶ. „‘–Š Ž‹‹ ƒŽ‰”‘—’•‘Ž›ǡ—•‹‰–Š‡”‡‰”‡••‹‘‘†‡Ž•κ1ȏ‘”νȐ ̱ ‘•–Ϊ. Ͷͺͷ. νͳȗƒˆˆ‡ –‹˜‡Ϊ νʹȗ’‘•‹–‹˜‡Ϊν͵ȗ‡‰ƒ–‹˜‡ǣ‘‡‘ˆ–Š‡‘†‡Ž•™‡”‡. Ͷͺ͸. •‹‰‹ˆ‹ ƒ–ǡŠ‘™‡˜‡”ȋƒŽŽpεͲǤͳȌǤ. Ͷͺ͹. –„ƒ•‡Ž‹‡ǡ–Š‡”‡™ƒ•‘‡˜‹†‡ ‡‘ˆƒ ‘””‡Žƒ–‹‘„‡–™‡‡κ1ƒ†. Ͷͺͺ. ƒ–‹’•› Š‘–‹ ‡†‹ ƒ–‹‘†‘•‡ȋp αͲǤ͵Ȍǡ„—––Š‡ ‘””‡Žƒ–‹‘„‡–™‡‡νƒ†. Ͷͺͻ. ‡†‹ ƒ–‹‘†‘•‡ƒ’’”‘ƒ Š‡†•‹‰‹ˆ‹ ƒ ‡ȋρ αǦͲǤͶǡpαͲǤͲ͸͹ȌǤ. ͶͻͲ. ‡–‡•–‡†ˆ‘” ‘””‡Žƒ–‹‘•„‡–™‡‡–Š‡‘†‡Ž͸’ƒ”ƒ‡–‡”•ȋ’‡ƒ”ƒǯ•. Ͷͻͳ. ρ ™ƒ•—•‡†™Š‡”‡†‹•–”‹„—–‹‘•™‡”‡‘–’ƒ”ƒ‡–”‹ Ȍǣκ1ƒ†ν ™‡”‡‡‰ƒ–‹˜‡Ž›. Ͷͻʹ. ‘””‡Žƒ–‡†„‘–Šƒ–„ƒ•‡Ž‹‡ȋρ αǦͲǤ͵ͺǡp αͲǤͲͲͲͶȌƒ†ƒ–ˆ‘ŽŽ‘™—’ȋρ αǦͲǤͷʹǡp α. Ͷͻ͵. ͲǤͲͲͲͳȌǡƒ•™‡”‡κ1ƒ†ωƒ–„ƒ•‡Ž‹‡ȋρ αǦͲǤͶ͹ǡp αͳͲǦͷȌƒ†ˆ‘ŽŽ‘™—’ȋρ αǦ. ͶͻͶ. ͲǤͷ͵ǡp αͳͲǦͷȌǤ

(59) ‡•–‹ƒ–‹‰–Š‡’ƒ”ƒ‡–‡”•ˆ”‘simulated†ƒ–ƒǡ–Š‡‘Ž›. Ͷͻͷ. ‘””‡Žƒ–‹‘’”‡•‡–‹„‘–Š•‹—Žƒ–‹‘•ȋ‹†‹ ƒ–‹‰•‘‡ ‘•‹•–‡––”ƒ†‹‰Ǧ‘ˆˆ. Ͷͻ͸. „‡–™‡‡–Š‡•‡’ƒ”ƒ‡–‡”•†—”‹‰‡•–‹ƒ–‹‘Ȍ™ƒ•„‡–™‡‡κ1ƒ†ωǡ™‹–Šr αǦ. Ͷͻ͹. ͲǤͷ‹‡ƒ Š ƒ•‡ǤŠ‹•‹•‘–•—”’”‹•‹‰ǡƒ•„‘–Šκ1ƒ†ωƒˆˆ‡ –—’†ƒ–‹‰–‘‡™. Ͷͻͺ. ‹ˆ‘”ƒ–‹‘–Š”‘—‰Š‘—––Š‡•‡“—‡ ‡ȋ—Ž‹‡σ2(0)Ȍ‹ƒ†‡–‡”‹‹•–‹ ™ƒ›ȋ—Ž‹‡. Ͷͻͻ. νȌǤ‡˜‡”–Š‡Ž‡••ǡκ1™ƒ•‡•–‹ƒ–‡†˜‡”›”‡Ž‹ƒ„Ž›‹–Š‡ˆ‹”•–•‹—Žƒ–‹‘ȋ ‹‰—”‡ͷǡ. ͷͲͲ. –‘’”‘™Ȍƒ†™‹–Š”‡ƒ•‘ƒ„Ž‡ƒ —”ƒ ›‹–Š‡•‡ ‘†ȋ ‹‰—”‡ͷǡ„‘––‘”‘™Ȍǡ•‘. ͷͲͳ. ™‡ƒ”‡ ‘ˆ‹†‡––Šƒ––Š‡‰”‘—’†‹ˆˆ‡”‡ ‡•‹κ1ƒ”‡‰‡—‹‡ǤŠ‡ ‘””‡Žƒ–‹‘•‘ˆ. ͷͲʹ. ρ γǦͲǤͷ„‡–™‡‡ωƒ†κ1‹†ƒ–ƒ•‡–ͳƒ”‡—Ž‹‡Ž›–‘„‡”‡Ž‹ƒ„Ž‡ǡŠ‘™‡˜‡”Ǥ. ͷͲ͵. . . ʹͳ.

(60)  ͷͲͶ. Modelling results: dataset 2. ͷͲͷ. . ͷͲ͸. ‡–‡•–‡†–Š‡•ƒ‡•‹š‘†‡Ž•ƒ†’‡”ˆ‘”‡†ƒ›‡•‹ƒ‘†‡Ž•‡Ž‡ –‹‘ƒ•. ͷͲ͹. „‡ˆ‘”‡Ǥ•‹†ƒ–ƒ•‡–ͳǡ–Š‡™‹‹‰‘†‡Ž™ƒ•‘†‡Ž͸‘˜‡”ƒŽŽƒ†‹‡ƒ Š‰”‘—’. ͷͲͺ. •‡’ƒ”ƒ–‡Ž›ȋ ‹‰—”‡͸ȌǡƒŽ–Š‘—‰Š‹–Š‡ œ‰”‘—’ƒ‹‘”‹–›™‡”‡„‡•– ƒ’–—”‡†. ͷͲͻ. „›‘†‡ŽͶǤ‘†‡Ž͸ǯ•’ƒ”ƒ‡–‡”†‹•–”‹„—–‹‘•ƒ”‡•Š‘™‹ ‹‰—”‡ͺǢ–Š‡›ƒ”‡. ͷͳͲ. •‡™‡†ǡ•‘‘Ǧ’ƒ”ƒ‡–”‹ –‡•–•™‡”‡—•‡†ȋˆ—ŽŽ†‡–ƒ‹Ž•‹ƒ„Ž‡͵ȌǤ. ͷͳͳ. . ͷͳʹ. ‘–”‘Ž•ȋZαǦͷǤ͸ǡpαͳͲǦͺǡƒǦŠ‹–‡›–‡•–Ȍ™‹–Šƒ‡†‹—Ǧ–‘ǦŽƒ”‰‡‡ˆˆ‡ –. ͷͳ͵. •‹œ‡ȋrαͲǤͶ͵ȌǢƒŽ•‘”‡•’‘•‡•–‘ Šƒ•–‹ ‹–›ν ™ƒ•Ž‘™‡”‹ œ–Šƒ‹ ‘–”‘Ž•ȋZ. ͷͳͶ. α͵ǤͻǡpαͲǤͲͲͲͳǡr αͲǤ͵ǡƒǦŠ‹–‡›–‡•–Ȍǡƒ•™ƒ•‹‹–‹ƒŽ„‡Ž‹‡ˆ˜ƒ”‹ƒ ‡σ2(0). ͷͳͷ. ȋZα͵ǤͳǡpαͲǤͲͲʹǡr αͲǤʹͶǡƒǦŠ‹–‡›–‡•–ȌǤŠ‡”‡™‡”‡‘•–ƒ–‹•–‹ ƒŽŽ›. ͷͳ͸. •‹‰‹ˆ‹ ƒ–‰”‘—’†‹ˆˆ‡”‡ ‡•‹‡˜‘Ž—–‹‘”ƒ–‡ωǤ‡‡ ‹‰—”‡•͸ƒ†͹ˆ‘”. ͷͳ͹. ‡šƒ’Ž‡•‘ˆ‘†‡Žˆ‹–•‹•—„Œ‡ –•™‹–ŠŽ‘™‡”κ1˜ƒŽ—‡•ȋ–™‘ ‘–”‘Ž•‹ ‹‰—”‡ͻȌ. ͷͳͺ. ƒ†Š‹‰Š‡”κ1˜ƒŽ—‡•ȋ–™‘ œ•—„Œ‡ –•‹ ‹‰—”‡ͳͲȌǢ‡ƒ Šˆ‹‰—”‡ƒŽ•‘‹ŽŽ—•–”ƒ–‡•. ͷͳͻ. –Š‡‡ˆˆ‡ –•‘ˆŽ‘™‡”ƒ†Š‹‰Š‡”ω ˜ƒŽ—‡•ȋ‹–Š‡–‘’ƒ†„‘––‘”‘™•. ͷʹͲ. ”‡•’‡ –‹˜‡Ž›ȌǤ‡”‡’‡ƒ–‡†–Š‡ƒƒŽ›•‹•—•‹‰ƒ•—„•‡–‘ˆ–Š‡ ‘–”‘Ž•ȋα͸ͲȌ–Šƒ–. ͷʹͳ. ™‡”‡„‡––‡”ƒ– Š‡†‹ƒ‰‡ƒ†•‡šǡƒ•–Š‡‘”‹‰‹ƒŽ ‘–”‘Ž‰”‘—’™ƒ•›‘—‰‡”. ͷʹʹ. ƒ†‘”‡ˆ‡ƒŽ‡–Šƒ–Š‡’ƒ–‹‡–‰”‘—’ȋƒ„Ž‡ͳȌǤŠ‡‰”‘—’†‹ˆˆ‡”‡ ‡•‹κ1. ͷʹ͵. ƒ†ν™‡”‡— Šƒ‰‡†‹–Š‹•ƒƒŽ›•‹•ȋZαǦͶǤͳǡpαͲǤͲͲͲͲͶǢZα͵ǤͶǡpαͲǤͲͲͲ͹. ͷʹͶ. ”‡•’‡ –‹˜‡Ž›ǡƒǦŠ‹–‡›–‡•–•Ȍǡ„—––Šƒ–‹σ2(0)™ƒ•‘Ž‘‰‡”•‹‰‹ˆ‹ ƒ–ȋZ. ͷʹͷ. αͳǤͻǡpαͲǤͲͷ͸ǡƒǦŠ‹–‡›–‡•–ȌǤ. ͷʹ͸. . ͷʹ͹. ‡˜‡Ž›ƒ– Š‡†‹–Š‡•‡‰”‘—’•ǡ™‘”‹‰‡‘”›ȋ‡––‡”—„‡”‡“—‡ ‹‰. ͷʹͺ. • ‘”‡ȋ‡ Š•Ž‡”ǡͳͻͻ͹ȌȌ™ƒ•Ž‘™‡”‹ œ–Šƒ‹ ‘–”‘Ž•ȋ•‡‡ƒ„Ž‡ͳȌǤ‡ . •‹†ƒ–ƒ•‡–ͳǡ„‡Ž‹‡ˆ‹•–ƒ„‹Ž‹–›κ1™ƒ••‹‰‹ˆ‹ ƒ–Ž›Š‹‰Š‡”‹ œ–Šƒ‹. Ž–Š‘—‰Š

(61) ȋƒ–‹‘ƒŽ†—Ž–‡ƒ†‹‰‡•–• ‘”‡ȋ‡Ž•‘ǡͳͻͺʹȌȌ™ƒ•. ʹʹ.

(62)  ͷʹͻ. ‡š’Ž‘”‡†™Š‡–Š‡”–Š‡‰”‘—’’ƒ”ƒ‡–‡”†‹ˆˆ‡”‡ ‡•‹‰Š–„‡”‡Žƒ–‡†–‘™‘”‹‰. ͷ͵Ͳ. ‡‘”›ǡ„›–‡•–‹‰ˆ‘” ‘””‡Žƒ–‹‘•„‡–™‡‡κ1‘”탐†™‘”‹‰‡‘”›‹‡ƒ Š. ͷ͵ͳ. ‰”‘—’•‡’ƒ”ƒ–‡Ž›ȋ‹ŽŽ‡”ƒ†Šƒ’ƒǡʹͲͲͳȌǣ‘‡™‡”‡•–ƒ–‹•–‹ ƒŽŽ›•‹‰‹ˆ‹ ƒ–. ͷ͵ʹ. ȋƒŽŽp εͲǤͳȌǤ‡ƒŽ•‘–‡•–‡†ˆ‘””‡Žƒ–‹‘•Š‹’•„‡–™‡‡κ1‘”탐†

(63) ȋȌ‹. ͷ͵͵. ‡ƒ Š‰”‘—’ǣν ƒ†

(64) ȋȌ™‡”‡ ‘””‡Žƒ–‡†‹ œȋrαͲǤ͵͵ǡpαͲǤͲͳͶȌǡ„—–‘. ͷ͵Ͷ. ‘–Š‡””‡Žƒ–‹‘•Š‹’•™‡”‡•‹‰‹ˆ‹ ƒ–ȋƒŽŽpεͲǤͳȌǤ. ͷ͵ͷ. . ͷ͵͸. —‡•–‹‘ƒ‹”‡• ‘”‡Ȍƒ ”‘••ƒŽŽ‰”‘—’•„—–‡‹–Š‡”†‹†•‘ȋ„‘–ŠpαͲǤͶǡȌǤ. ͷ͵͹. ‡–‡•–‡†™Š‡–Š‡”κ1‘”홇”‡’”‡†‹ –‡†„›ƒ›’ƒ”–‹ —Žƒ”•—„‰”‘—’‘ˆ. ͷ͵ͺ. •›’–‘•ȋ‡ƒ•—”‡†—•‹‰–Š‡‘•‹–‹˜‡ƒ†‡‰ƒ–‹˜‡›’–‘ ƒŽ‡ȋƒ›‡–ƒŽǤǡ. ͷ͵ͻ. ͳͻͺ͹ȌȌ‹–Š‡ œ‰”‘—’‘Ž›ǡ—•‹‰–Š‡”‡‰”‡••‹‘‘†‡Žκ1 ȏ‘”νṞ̏ ‘•–Ϊ. ͷͶͲ. νͳȗ‰‡‡”ƒŽΪ νʹȗ’‘•‹–‹˜‡Ϊν͵ȗ‡‰ƒ–‹˜‡ǣ–Š‡κ1‘†‡Ž™ƒ•‘–. ͷͶͳ. •‹‰‹ˆ‹ ƒ–ȋF αͲǤͻǡp αͲǤͶȌǡ„—–ν ™ƒ•™‡ƒŽ›’”‡†‹ –‡†„›‡‰ƒ–‹˜‡•›’–‘•. ͷͶʹ. ȋ‘˜‡”ƒŽŽF αʹǤ͹͸ǡp αͲǤͲͷͳǢˆ‘”ν͵ǡtαǦʹǤͳǡpαͲǤͲͶȌǤ‡Šƒ†‘”‡ ‘”†‘ˆ. ͷͶ͵. ‡†‹ ƒ–‹‘†‘•‡‹†ƒ–ƒ•‡–ʹǤ. ͷͶͶ. . ͷͶͷ. ͳǡκ1ƒ†ν ™‡”‡‡‰ƒ–‹˜‡Ž› ‘””‡Žƒ–‡†ȋ ‹‰—”‡ͺǢρ αǦͲǤ͵ͷǡp αͳͲǦ͸Ȍǡ„—–—Ž‹‡. ͷͶ͸. †ƒ–ƒ•‡–ͳǡ–Š‡‘Ž›‘–Š‡”•–ƒ–‹•–‹ ƒŽŽ›•‹‰‹ˆ‹ ƒ– ‘””‡Žƒ–‹‘™ƒ•„‡–™‡‡κ1ƒ†. ͷͶ͹. σ2(0)ȋρ αǦͲǤͷͶǡp αͳͲǦͳ͵ȌǤŠ‡”‡™ƒ•ƒ ‘””‡Žƒ–‹‘‘ˆr αǦͲǤʹ„‡–™‡‡κ1ƒ†ν‹. ͷͶͺ. –Š‡†ƒ–ƒ•‹—Žƒ–‡†ˆ”‘‘†ƒŽ œ’ƒ”ƒ‡–‡”˜ƒŽ—‡•ȋ ‹‰—”‡ͷǡ„‘––‘”‘™Ȍǡ„—–. ͷͶͻ. ‘ ‘””‡Žƒ–‹‘‹–Š‡ˆ‹”•–ǤŠ‹•‹’Ž‹‡•–Šƒ––Š‡ ‘•‹•–‡– ‘””‡Žƒ–‹‘•„‡–™‡‡. ͷͷͲ. –Š‡•‡’ƒ”ƒ‡–‡”•‘ˆρ αǦͲǤ͵ͺǡρ αǦͲǤͷʹȋ†ƒ–ƒ•‡–ͳ„ƒ•‡Ž‹‡ƒ†ˆ‘ŽŽ‘™Ǧ—’Ȍƒ†ρ. ͷͷͳ. αǦͲǤ͵ͷȋ†ƒ–ƒ•‡–ʹȌƒ”‡—Ž‹‡Ž›–‘„‡Œ—•–‡•–‹ƒ–‹‘ƒ”–‡ˆƒ –•ǤŠ‡‘Ž›‘–Š‡”. ͷͷʹ. ‘””‡Žƒ–‹‘„‡–™‡‡’ƒ”ƒ‡–‡”•‹–Š‡•‹—Žƒ–‡††ƒ–ƒ™ƒ•„‡–™‡‡σ2(0)ƒ†κ1ǡ. . ‡–‡•–‡†™Š‡–Š‡”κ1‘”픇Žƒ–‡†–‘• Š‹œ‘–›’›ȋ Š‹œ‘–›’ƒŽ‡”•‘ƒŽ‹–›. ‡–‡•–‡†ˆ‘” ‘””‡Žƒ–‹‘•„‡–™‡‡–Š‡‘†‡Ž͸’ƒ”ƒ‡–‡”•ǣƒ•‹†ƒ–ƒ•‡–. ʹ͵.

(65)  ͷͷ͵. ‘ˆr αǦͲǤʹͷǡ‹–Š‡ˆ‹”•–•‹—Žƒ–‹‘‘Ž›ǤŠ‡•‡’ƒ”ƒ‡–‡”•™‡”‡ ‘””‡Žƒ–‡†‹. ͷͷͶ. †ƒ–ƒ•‡–ʹ„—–‘–†ƒ–ƒ•‡–ͳǤ . ͷͷͷ. Discussion. ͷͷ͸.  œ–‡†–‘—’†ƒ–‡–Š‡‹”„‡Ž‹‡ˆ•‘”‡–‘—‡š’‡ –‡†‹ˆ‘”ƒ–‹‘ƒ†Ž‡••–‘. ͷͷ͹. ‘•‹•–‡–‹ˆ‘”ƒ–‹‘ǡ ‘’ƒ”‡†–‘ ‘–”‘Ž•Ǥ‡Šƒ˜‡”‡’Ž‹ ƒ–‡†–Š‡•‡. ͷͷͺ. „‡Šƒ˜‹‘—”ƒŽ‡ˆˆ‡ –•ǡƒ††‡‘•–”ƒ–‡†ƒ ‘’—–ƒ–‹‘ƒŽ„ƒ•‹•ˆ‘”–Š‡–Šƒ–‹•. ͷͷͻ. ‹ˆ‘”‡†„›–Š‡—•–ƒ„Ž‡ƒ––”ƒ –‘”Š›’‘–Š‡•‹•‘ˆ• Š‹œ‘’Š”‡‹ƒǤ

Riferimenti

Scarica adesso ( PDF - 63 pagine - 6.67 MB )

Documenti correlati

The UK and London

Leggi il breve testo su Londra e il Regno Unito e rispondi alle domande.. People from Northern

Lithuanian University Of Health Sciences Faculty of Medicine Department of Psychiatry

The chosen substances were: alcohol, caffeine, cannabis, hallucinogens (without separate categories for phencyclidine nor for arylcyclohexylamines and other hallucinogens),

Ulrich Beck (London School of Economics/University of Munich ) Introduce

del Centro Studi MEDÌ di Genova, della rivista MONDI migranti e dell’Accademia della Casa della Carità Con il contributo della Fondazione

EMPLOYMENT APPEAL TRIBUNAL FLEETBANK HOUSE, 2-6 SALISBURY SQUARE, LONDON EC4Y 8AE

Customer acknowledges and agrees that once a Driver has accepted (either directly or through … [ULL] acting as agent for the Customer/Driver) a User’s request

Department of Psychology

The present study revealed that the modulatory effect of monetary stimuli, which emerged in studies using non-social stimuli, does not emerge if the attentional cue is a

Civilization, culture, and race in John Crawfurd's discourses on Southeast Asia : continuities and changes, c.1814-1868

tensions; in Gascoigne 19994 (pp.119-183), J. Bank’s formative years are interpreted as a transformations from an antiquarian to an anthropologist deeply influenced by the

Handbook of Juvenile Forensic Psychology and Psychiatry

In a comprehensive study conducted to exam- ine mental health problems and substance abuse disorders among youth involved in the juvenile justice system, the National

About some Medical Bibliographical Sources of Jacobinic and Napoleonic Age

BOTTA C., Storia naturale e medica dell’isola di Corfù di […], autore della Storia dell’indipendenza d’America, seconda edizione, Milano, per Giovanni Silvestri, 1823, p..