posted online on 4 June 2014 as doi: /jeb
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- Calvin Melton
- 5 years ago
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1 First posted online on 4 June 2014 as /jeb J Exp Biol Advance Access the Online most recent Articles. version First at posted online on 4 June 2014 as doi: /jeb Access the most recent version at & ƒ ƒ Ž ƒ ƒ ƒ ƒ ƒ ƒš ŽŽ Žƒ ƒ ˆ ƒžš Ž ƒ Ž ƒ ƒ ƒ ƒ ƒ Zd ƒ ƒ Ž Ž ƒ Ž <t ƒ Šƒ Šƒ Ž œƒ ƒš ŽŽ Žƒ Š Žƒ ˆ ƒ ƒ ƒ ˆ ƒžš Ž ƒ Ž ƒ ƒ ƒ ƒ Published by The Company of Biologists Ltd
2 Ž ˆ ƒ Šƒ œ Š ƒ Šˆ ˆ Ž Šƒ ƒˆƒ ƒ ƒ Ž œƒ Ž Š œƒ Š ƒ Š Š Š Šƒ ŽŽ ˆ Ž ƒ ƒžž Ž ˆ Š Ž ƒ Šƒ ƒ ˆ ƒž ˆ ƒ Ž Š Š ƒ Š ƒ ƒ Œ ˆ ŽŽ ƒ ˆ ƒ ƒ Š ƒ ƒ Œ ˆ ˆ ŽŽ ƒ Š ˆ ˆˆ ƒ ƒ š ˆ Šƒ Š Žƒ Š š Œ ƒ ˆ ƒ Ž Šƒ Š ˆ ƒ Š ˆ ƒ ƒ Š Ž Ž ƒ Œ Š ƒ Š ˆ ƒ ƒ Žƒ ˆ Š Š ˆƒ ƒ Š Ž ƒž ˆ Šƒ Š ˆƒ Š Ž ƒ ƒ Ž ƒ Ž ƒ Š ƒ Œ Š ƒ ˆ Š Ž ƒ š ƒ Šƒ Ž ƒ ƒ Ž Š ƒ Ž ƒ Ž Ž Š Ž ƒ ƒ ˆ Š ˆ ƒ ƒ Š ƒ ƒžž ˆ Šƒ Ž Šƒ œƒ ˆ / Š Š ˆƒŽ Š ƒ Š Šƒ ƒ Ž Š Šƒ Š ˆ Šƒ ƒ ˆ ƒž Ž ˆ ƒ Š œ ƒ ƒ ƒ ƒ Žƒ ƒž Žˆ ƒ ƒž Ž ƒ Š ˆ Žƒ ƒ Šƒ ƒ Ž ƒ Š Šƒ Š Š Š Š Š Š ƒ Ž Š ƒžž ƒž ƒ ˆ ƒ Šƒ ƒ Ž Š Ž ˆ ˆ ƒ ƒ ƒž Šƒ ƒ ˆ Ž Šƒ ƒ ƒ Ž ƒ Žƒ ƒ ƒ Šƒ ƒ ˆˆ ƒ Ž ƒ ƒ Š ŠŽ œ ƒž ƒ ƒž ƒž ƒ ƒ ƒ ƒ ŠŠƒ ƒ Š Š ƒ ƒ ƒ ƒ Šƒ
3 Ž ƒžž ƒž ƒ ƒž Šƒ ƒ šƒ ŽŽ Š ƒ ƒ Š ƒ šƒ Ž Šƒ Ž ƒ Šƒ ƒ ŽŽ ƒ Š ŽŽ ƒ ŽŽ ƒž ƒ ƒ Š Ž ƒ ƒ Œ ˆ ˆ ƒ Š ˆ ƒž ƒ ƒ Š ƒ ƒž Š Šƒ Š Šƒ ƒ ˆˆ ƒž ƒ ƒ Ž Š Ž ˆ ˆ ˆ ƒ ŽŽ ƒž ˆƒ ƒ Ž ˆ ƒ ƒžž ƒž ƒž Š Š ˆ ˆ ˆ ŽŽ ƒ Šƒ ƒž ƒ ƒž ƒ Ž ˆ ƒ Ž ƒ Šƒ Š Ž ˆ ƒ ƒ š ƒžž ƒž ˆ ƒ ƒžš Ž Ž ˆ Š ƒ ˆ Š Šƒ ˆ ƒ ƒ ˆ ƒ Ž ˆ ˆ ƒžž ƒž ƒž ƒ ƒž š Šƒ ƒ Šƒ ˆƒ ƒ Ž ƒž Ž ˆ ƒ Œ Š ƒ ƒ Šƒ Š ƒ ˆ ƒ ƒž ƒ ˆ Ž ƒžž ƒž ˆ ƒž Ž ˆ Š ƒ ˆ Š Š ƒ ƒ ˆ œƒ ƒ ƒ ƒ Ž ƒ ƒž Ž ƒ ƒ ƒžž ˆƒ Ž ƒ š Š Ž œƒ ƒž Ž Ž ƒ ƒžž ƒžƒ Œ Šƒ Š Ž Š ƒ ƒ ƒ Ž ƒ ˆ Ž ƒ Šƒ ƒ ˆ ƒ Šƒ Šƒ ƒ ƒ ˆ Ž Š ƒ ˆ ˆ Ž Žƒ ƒ Ž Šƒ Š ƒ ˆƒ ƒ Ž œƒ ƒ Ž Š Ž ˆ ƒž Š ƒ Š ƒ Ž ƒž ƒ Œ ƒž ƒ Žˆ ƒ ƒ ŽŽ ƒ ƒž ˆ Ž ƒž Š Ž ˆƒ Šƒ Š ƒžž ˆ Œ ˆ ƒ Ž ƒ Œ Š ƒž Š ƒ Š ƒžž Ž Š ˆ Š
4 Š Ž Ž Š ˆ ƒ ƒ Ž ƒžž ƒž ƒž Š Ž Š Ž ƒ ˆ ƒ Ž Ž Ž ƒ Š ˆ Š Š ˆ Š ˆ Ž š Š ƒž Šƒ Ž ˆ ƒžž ƒ Š ƒˆˆ Š ƒ ˆ ƒ Šƒ Ž Œ ˆ ƒ Œ Š Š ƒ ˆ Ž ƒ Ž ƒ ˆˆ Ž Š Š Ž ŽŽ Š ƒ ƒ ƒ ˆ Š ƒ Š Š Š Ž ˆ ˆ ˆ ƒ ˆ ƒ Š ƒ Ž Šƒ ƒ Ž Š Š Œ ƒ Ž ƒ ƒž š ƒ Š ƒ ƒ Œ ƒ ƒ Š ˆ ƒ Š ˆ š Š ƒ ˆ ˆ Ž ƒ ƒ ŽŽ ƒž Š š Š ƒ ˆ Ž ˆ ƒ ƒž ƒž œƒ Š ˆ Š ˆ Ž Š ƒ ƒ Œ ƒ ŽŽ ƒ Š ˆ ƒ ƒ ˆ ƒ Š Š Š ˆƒ ƒ Ž Ž Š Ž ˆ Š ˆ ƒ ƒ Š ˆ ƒ Š ˆ ƒ Š ˆ Š š Z ˆ Šƒ ˆƒ ƒ Ž ƒ ƒ Š Ž ˆ Š ˆ ˆ ƒ ˆ Š š Œ ƒ ˆ ƒ Ž Šƒ Š ƒ ƒ Š ˆ ƒ ƒ Š Ž Ž ˆ Š ƒ Ž Š ƒ ƒ ƒž Š ƒ ƒ Š ˆƒˆƒ ƒ Ž Š Š Šƒ Žƒ ƒ ˆ ƒ ˆˆ Š ˆ ƒžž Š ˆƒ ƒ Ž Ž ˆ Ž Š ƒ š Šƒ ˆ ƒ ƒ ƒ ƒ ƒ š ƒ Žƒ Ž Ž ˆƒ ƒ Ž
5 ƒ š Š ˆ ƒ š ƒ š Š ˆƒ ƒž Žƒ ƒ Š Ž ƒ ƒžž ˆˆ š Š Ž ˆ ƒ Ž ˆˆ Œ ƒž šš Žƒ ˆ Žƒ ƒ Š ƒ Š ƒ ƒ ƒ Ž ƒ Žƒ ˆ ˆ ˆ Šƒ ƒ ƒ ˆ Šƒ ˆ ƒ š Š ˆƒ ƒ Š ƒ ƒ Œ Š ˆ ƒ ƒž ƒ ƒ Š ˆƒ ƒ Ž ƒ Ž ƒ ˆ ƒ ˆ ƒ š Ž Š Ž Š Ž ƒ Ž ƒ Ž œ ƒ ˆ ƒ ˆ ƒ š Ž Š ƒ ƒ Š ˆƒ ƒ Ž ƒ ƒ ƒ Ž ƒ Œ ƒ ƒ Š ˆ ƒž ƒ ƒ ƒž Ž Ž ˆ ƒ Œ ˆ Š Ž Š ƒ ƒ ƒ ƒ Ž Š Š Žƒ ˆ Š ƒ ˆ ƒž ƒž šƒ Ž Š ˆƒ ƒ Ž ƒ ƒ Š Ž ˆ Š ƒ ƒž ƒ ƒ Š Ž Š ˆ ƒ ƒž ˆ ƒž ƒ ƒ Ž ƒ Šƒ ƒ ƒž ƒ Œ Šƒ Š Š ˆ ƒž ƒ ƒ ƒž Š Ž Š Ž Šƒ ƒ ƒž Šƒ Š Š ƒ ƒ ƒž Š ˆƒ Š ƒ ˆƒ Š ƒž Š Ž Š ƒ ƒ Œ Ž Ž Š Œ ƒ ƒ ƒž Š ƒž Š Š Š Š Œ Ž Š ˆ ƒ ƒ ƒ Ž ƒˆƒ ƒ Ž Ž Š ˆƒ ƒ ƒ ƒž ˆ Š ƒ ˆ ƒ Š ˆ Š Ž ƒ ƒžž ƒ Š ƒ ƒ Ž ˆ Š ƒ š ˆ Š ˆ ˆƒ Š ˆƒ Š ƒ ˆƒ ƒ ƒ Š ˆ ƒ š ˆ Š ˆƒ Š ˆƒ Š ƒ ˆƒ ƒ ƒ Š Ž ˆˆ ˆ ƒ ƒ
6 ƒ Š ƒž Š š ˆ ƒ Šƒ Œ Ž Ž Š Š ƒ š Š Š ƒ ˆƒ ƒ Ž Š ƒ Š Ž ƒ ƒ Ž Š ƒ ƒ Š š ƒž ˆ ƒž ƒž ˆ ƒ Šƒ Š Ž š Žƒ ƒ ˆ Š ƒ ƒ ƒ ˆ Š ƒ ˆ ƒ š Ž Š ƒ ƒ Ž ˆ Šƒ Š Ž ƒ š Žƒ Š ƒ ƒ Ž ƒ ƒ ƒž Š ˆ ƒ ƒ Š ˆ Š ƒ ƒ Šƒ Š ƒž ƒ Œ ƒ ˆ ƒ Š ƒžˆ Š ƒ ƒ ƒ ƒ Š ƒ Ž ˆ ƒ Š ƒ ƒ Š ƒž ˆ ƒž ƒ Žƒ Ž Žƒ ƒ ˆ ƒ ˆ Š ƒ Œ ˆ ƒ Ž ˆ Š Š Ž Š ŽŽ Š ƒ ƒ ˆ Š ƒžˆ Š ƒ ƒ ƒ Š ƒ ƒ Š ˆ ƒ ƒ ƒ ƒ Ž Š ƒ ƒ Œ ƒ ˆ ƒž ƒž Š ƒ ƒ ƒ Œ ƒ Žƒ Š ƒ Š Ž Š ƒ ƒ ˆƒ Š ˆ ƒ ˆƒ Š ˆ ƒž ƒ Š ˆƒ ƒ ƒ ƒž ƒ ƒ ƒ ƒ Ž Ž Š ƒž ˆ Š ˆ Š ƒ ƒž ƒ Šƒ Š Ž š Žƒ ƒ ˆ Š ƒ ƒ ˆƒ Š ƒ ˆƒ Š Ž Žƒ Ž Š ƒž ˆ Š Š ˆ ƒ ƒž ƒ Šƒ Š Ž š Žƒ ˆ Š ƒ ƒ ˆƒ Š ƒ ˆ Š ƒ ƒ ˆƒ Š Š Š ƒž ƒžžƒ Š Ž ƒ ƒ ŽŽ Ž Š Ž ƒ Šƒ Š Ž ŽŽ š Žƒ Š ƒ ˆ Š ƒž ƒ ˆ Ž ƒ Š Ž ƒ Ž š Ž Šƒ Š Ž Š ƒ ƒ ˆˆ Š ƒ ƒ Ž Ž ˆˆ ƒ ƒ ƒ Š ƒ ƒžž ƒ ˆ Š
7 ƒ ƒž Š Šƒ Šƒ ƒ ƒ Š ˆ Š ƒž ˆ Š š Š ƒ Ž ƒ ƒ Š Š ƒ ƒž ƒ Œ ƒ ƒ ŽŽƒ Š Ž ˆ Š Ž Š ƒ Ž ƒ ˆ ƒ Ž š Ž Š ƒ Ž š ƒ ƒ Š ŽŽ Š Ž ˆ Š ƒž Š ƒ ƒ ƒ ƒ ƒƒ Š Ž ƒ ƒžžƒ ƒ ƒ ƒ Ž ƒ œ ƒ Šƒ ƒ Ž Ž ƒ Ž Ž ƒ ƒ ƒ Ž š Žƒ ƒ ƒž Ž š Ž Š Šƒ ƒ ƒ Š Ž ˆ ˆ ƒ ƒ ƒ Ž Žƒ Š Šƒ Ž ƒž Š ˆƒ ˆ Š ƒ Ž ƒ Œ ˆ ƒ Ž ƒ Š ˆ ƒ Š ƒˆ Š Ž ƒ ƒ Ž Ž ˆ ƒ ˆ Ž Ž Ž Š ƒžž ˆˆ ƒ ƒ ƒ Ž Š ƒœ ˆˆ š ƒž ƒ ƒ ˆ Ž š Šƒ Žƒ ƒ ƒ ŽŽ ƒ Š ƒžž ƒ Ž š Šƒ ƒ Ž Š ƒž ƒ ƒž š ˆ Šƒ Žƒ ˆƒ ƒ Ž ƒ ƒ ˆ Ž ƒ Š Š ƒž Š Š Šƒ ƒž Šƒ Ž Š ƒ ƒ ƒ ƒ ƒž ƒžš ŽŽ ˆ Ž Šƒ Š ˆŽ Ž Šƒ ˆ Ž ˆ ƒ ƒ Š ˆ ƒ Žƒ Š š ƒž ˆˆ ƒ š Š ƒž ƒž Šƒ ƒ Ž ˆ Ž ƒ ˆ ƒ Š Šƒ ƒ ƒ Š ƒ Š ƒ Žƒ ƒ ƒ Šƒ ƒ Ž Ž Ž Ž Šƒ ˆ Šƒ ƒ Š ˆ Ž Š ƒ Ž ƒ ˆ Š ƒ ˆ Š Š Ž Š Ž Š Žƒ Ž Š ƒ Ž ƒ
8 ˆ Š ƒ ˆ Ž Š ƒ ƒ Ž š Žƒ ƒ ƒ Š Š ˆ ˆƒ ƒ ƒ ƒžž ˆƒ Š ƒ š Š ƒ Š ˆ ƒ š Š Ž Œ ƒž Šƒ ƒ Œ Š ƒ š ƒ ˆ Š ˆ ƒ š Š ƒ Œ ˆ Š š ƒž ƒ ƒ ƒ Š ƒ ˆ Š ƒž Ž Ž Š Ž ˆ ˆ ƒ ˆˆ ƒ ƒ š Šƒ ƒ ƒžž ˆˆ Ž ƒ Œ ƒ ƒ Š ƒ Ž ƒ ƒ Š ƒžž ˆ ˆ ƒ ˆˆ Š ƒ ˆ Š Ž š Žƒ ƒ ˆ ˆ ƒ ƒ ˆƒ Š Ž ˆ Šƒ Š ƒ ŽŽ Š ƒžž ƒ ƒ Šˆ Šƒ ƒ Šƒ ƒž ƒ Ž ƒ ˆ ƒ Š ˆ ƒž ˆ Š ƒžž Š Ž ˆ Š ƒ ˆ Š Ž Ž ƒ ƒ ƒž ˆ Šƒ ƒž ƒžž ˆ ƒ Š Ž Ž Š Ž ƒ Š Ž Š ˆ Š Ž Šƒ ƒž ƒžž ˆˆ Š ˆ š Š Ž ƒ ˆˆ Š Ž ƒž Ž Š Ž Šƒ šƒ Š ˆ Ž ˆ š ƒ Š Ž Š Š Ž Šƒ Š Ž Š Ž Š š Š Žƒ Š ˆ ƒ Ž Š Ž Š ƒ ˆ ƒ ˆ Šƒ Œ ƒž Ž ƒ Ž Š Š Š Ž ƒˆ ƒ Š ƒ Ž ˆ Š Ž Š ƒ Ž Šƒ ˆ Š Š ˆ ƒ ƒ Ž šƒ Ž ˆ ˆ ƒžž Š ƒ ƒ ƒ ƒ ƒž Ž Š Ž Š Š Ž Š ƒ Ž ƒ Š ˆ Ž Š Ž Ž šƒ Ž ƒ Š Šƒ ˆ Š Š ƒ ƒ ƒ Ž Šƒ ƒ ˆ ƒ Š ƒžˆ Šƒ Žƒ ƒ Ž Š š ƒž ƒ ƒ Ž ƒ Š ƒ Šƒ ˆ ƒ ƒž Ž Š Š Š Š Š Ž ˆ Ž Š Ž Š ƒž ˆ Ž ƒ ƒ Ž ƒ Š š ˆˆ ŠƒŽŽ
9 Š Šƒ Ž ƒ Ž š Š ƒ Ž Š ƒž ƒ ƒ ƒ ƒ ˆ Š Š Ž Š ƒž ƒ ƒ ƒ ˆ Ž Šƒ ƒž Ž ƒ Š ƒ Ž Ž Š Š ƒžž ƒž ƒ ƒˆƒ Ž Šƒ Ž ƒ œƒ ˆ ƒ ƒ ƒ Ž ƒ ƒ Ž Šƒ Ž ˆ Š ˆƒ ƒ Ž œƒ ˆ Ž Ž ƒ Ž Ž Š Ž Š ˆ ƒ Žƒ ƒ ƒ Š ˆ Ž ƒž ƒ ƒž ƒ ˆ ƒ ƒ ƒ ƒ ˆ ƒ ƒž Ž ƒ Š ŽŽ ƒž Š ƒ ˆ œƒ Šƒ œƒ ƒ ƒ ƒ ƒ ˆ ƒ ƒ Ž ƒ Œ ƒ ƒ ƒ Ž Ž ƒ ƒ ƒ Ž Š ƒž ƒ Š Šƒ œƒ ŽŽ ƒ ˆ Ž Š ƒ Š Š Ž ƒ ˆƒ Ž Ž ˆ Š ƒ ˆƒ ƒ Œ Ž Šƒ Ž ƒ Š ˆƒ Š ƒ ˆ Š ƒžž ƒž ƒž ƒ ƒ ˆ ƒ ˆ Ž ˆ Š Žƒ Š ƒ ƒ ƒ ƒ ƒž Ž ƒ Šƒ Š Ž ƒ ˆ Š ˆ Š Š ƒ ƒ ˆ œƒ Ž ˆ ˆ Ž ƒž ˆ Š ƒž Ž ˆ ƒžž ƒž Š ˆƒ ƒ Œ š ˆƒ ƒ ƒ ˆ ƒ Ž ƒ ƒ Ž ˆ ƒž ƒž Š Ž Ž Š ˆƒ ƒ Ž ƒ š ƒ Š ˆ ƒž ƒ ƒ ƒž šƒ Ž Š ƒ Š Š ƒ Œ Š ƒ Ž ƒ Ž Š Š ƒ ƒ ƒž ƒžƒ ƒ Ž Š ƒ Š ƒžž Š ˆƒ ƒ ƒ Ž ƒ Œ ƒ Š ƒž ƒ Šƒ ƒ ƒ ƒ Ž Š Šƒ ƒ ƒ Ž Š ƒž ƒ ƒ Œ Š ƒ ƒ ƒ ƒ Š Š ƒ ƒ Ž Ž ƒ ƒ ƒ ƒ ƒ Œ Ž Šƒ Š
10 ƒ ƒ Š ˆƒ ƒ ƒ Œ ˆ Š Š Š ˆ ƒ ƒ ƒ ˆ ƒ ƒ ƒ ƒ Š ƒ ƒ Ž Š ƒ ƒ Š ƒ ˆ š Œ ƒ ƒšƒ ƒ Šƒ ƒ ˆ Š ƒ ƒ ƒ ƒ Œ Šƒ ƒ ƒ Š ƒž Ž ƒ Š ƒ ƒ š ƒž ƒ Šƒ Š ƒ ƒžƒ Ž ƒ ƒžž ƒ ƒ Šƒ Š ƒž ˆƒ ˆ Šƒ Š ˆƒ ƒ ƒ ƒ ƒ ƒ Š Š Ž Šƒ ƒ ƒ ƒ Šƒ ƒ ƒ ƒ ƒ ƒ ˆ ƒ Ž ˆ ˆƒ ƒ ƒ ƒ ƒ ƒ ƒ Š ƒ ˆ Š ƒ ƒ ˆ ƒ Œ ƒˆ Š Ž Š ƒ Ž ƒž Š Š ƒž ƒ Œ ƒ ˆ Š ˆ ƒž ƒ ƒ ƒž Š œ ƒž Š Š Š ƒžƒ Œ Š Šƒ Š ƒ ƒž ƒ ƒ ƒ ƒ ƒ Ž ˆ Š ˆƒ ƒ Œ ƒž ƒ Ž ˆ Š ˆƒ ƒ ƒ Šƒ Š ƒ ƒž Ž Š Œ ˆ Š ƒ ƒž ƒž Š ƒ ˆƒ ƒ Š œƒ ŽŽ ƒžž Š ƒ Šƒ Š Š š Žƒ ƒ ƒ ƒ Š ƒž Ž ƒ Š ˆ Ž Šƒ Š ƒ Ž Š Š ƒ œƒ ŽŽ Šƒ Š ƒ ƒž ƒž ƒ ƒ ƒ Ž Ž ƒ ˆ Ž ƒž ˆ Ž ƒž œƒ ƒ ƒ Ž ƒ ˆ Š Ž ˆ Ž ƒ Žƒ Ž ƒžž ˆ ƒ ƒ ƒ ˆ šƒ Ž Šƒ Ž ƒžž ƒžš Š Ž Ž ƒ ƒ Ž ƒ ˆ Š ƒ ƒ Ž ˆ ˆ Š ƒ ˆ Š ˆ Š ƒž ƒ ˆ ƒ ƒ Ž Ž Ž Š Š ˆ ƒ ƒ Š ƒ Š ƒž ŽŽŠƒ ƒž ƒ Š ˆˆ ˆƒ Šƒ ƒ Š ƒ ƒ ŽŽ Ž ƒ Š Š ƒ ƒ ƒ ƒž ƒ Žƒ Ž Š Žƒ Ž Šƒ ˆˆ ƒžž ƒ Ž Ž
11 ˆ Ž ƒž œƒ Š ƒ ƒ Ž Šƒ ƒž œƒ ˆ ƒ ƒžž ˆ ƒ ƒ ƒ Šƒ Šƒ Š ƒ ˆ Ž Š ˆˆ ƒ Šƒ ƒ ˆ Šƒ Š Ž ŽŽˆ Žˆ ŽŽ Š ƒ ƒ ƒ ƒ ƒ Š Š ƒ Ž Š Š Ž Ž ƒ ƒ ƒ Ž ƒ Ž Ž Ž ƒ ƒ ƒ ƒ Š ƒ š ƒ Ž ˆ Š Šƒ Š ƒž Ž ƒ ƒ œ ƒ š ƒ ƒ Œ Šƒ œ Š ƒ Ž ƒ ˆ ƒ ƒž Š Šƒ œ Š ƒ Ž ƒ ƒ Š ƒ ˆ š Š Ž ˆ Š š ƒž ƒ Š Š ˆ Š Œ ˆ ƒ ƒ œ ƒž Š Š ƒ ˆ ƒ š Š œ ƒ Ž Ž ˆ ƒ ˆ ƒ ƒ Š ˆˆ ˆ Š ˆ œ ˆ ƒ ƒ ˆ š ƒžž ˆ š ˆ ƒž Š Š Š Ž Ž Š ƒ Š Š Ž Ž Ž Šƒ œ ƒ Ž Žƒ ƒž Œ Š ƒ ƒ Ž ƒž ˆƒ Š Š ƒ Š Š ŠƒŠ Š ˆ ƒ Š ƒ ƒ ƒ Ž Š Œ ˆ Žˆ ŽŽ Š ˆ ˆ ƒž ƒ Ž Š ƒ ƒ Ž Šƒ ˆ ˆƒ Œ ˆ ƒ š Š ˆ Š ƒ Š Šƒ Š œ ˆ ƒ Š Š œ ƒ ƒ ˆ œ ƒž ˆ ƒ Š ˆ ƒ Žƒ ƒžš ƒžƒ ˆ Š Š Ž ƒ Šƒ Ž ˆ ƒ ƒ ƒ œ ˆ ƒ ƒ ƒ ƒ ƒ Žƒ ƒž Žˆ ƒ ƒž Š ƒ Š ƒž ƒ ˆ Š ˆ
12 Š ƒ ˆ ƒ Ž ƒ ƒ ŽŽ ƒ Š Šƒ ƒ ƒž Œ ƒ Š Š ƒ ƒ ˆ ƒ ˆ ƒ š Œ ƒ ƒ Ž ˆˆ ˆ Š ƒ ŽŽ ƒžž Š Ž ƒ ƒ ˆ ƒ Š Ž Š Ž Š Ž Ž ƒ ƒžž ˆˆ Š ƒ ˆˆ Š ˆ Ž Š Š Œ ˆƒŽŽ ˆˆ Š Ž Ž Š Ž Šƒ ƒ ƒ Šƒ ƒ ƒ Š ƒ ƒž Š ƒ ƒ Š ˆ ƒ š Š Š ƒ ˆ ƒ Š Šƒ Š ˆ ƒ Š ƒ œ Š Š Š Œ ˆ Š š ƒžž Œ ˆ Š ƒ š ˆ Š ˆ ƒ š Ž Š Š Š š ˆ ˆˆ Ž Šƒ ƒ ƒ œ Š ƒ Š ˆƒ Ž ƒ ˆ Œ Š Š š ƒž Ž Š Ž ƒ Š ƒ ƒ ˆ Š ƒ ƒ ˆ ˆ ˆƒ ƒ Ž Š ˆ ƒž ƒ ƒ Ž Ž Š š ƒž ƒ Š ƒ ƒ Š ƒ ƒ ƒ Š Ž ƒ Š œƒ ˆ Š ˆ ƒ ƒ Šƒ ˆ ƒ ƒ Š Š ˆ ƒ Š Š ƒ ƒ ƒ Žƒƒ ƒž ƒž Ž Š ƒ ƒ ˆˆ Š ƒ ƒ ƒ Š Šƒ ƒ ƒ Ž ƒ ƒ ƒ ˆ ƒ ƒ š Ž Š ƒ Ž ƒ ƒ ƒž ƒ ƒ Š ˆˆ ƒ ƒ Š Šƒ Ž ˆ Šƒ Š Ž ˆ ˆ ƒ ƒ ƒ Šƒ ƒ ˆˆ ƒž Š Š Ž Š ƒžƒ Š ƒ ˆ ƒ Š ƒž Š ƒž ˆ ƒž ƒ Š ƒž ƒ ˆ ƒ Š š ƒž ƒž ƒ ƒ Ž Ž Š ˆ Œ Š ƒ Š ƒž œƒ ˆ ƒ Š ƒž ƒ ƒ ƒ Šƒ Š Œ Šƒ ƒ Š ƒ ƒ Š Žƒ ˆ ƒ Š ƒž ˆ Œ Š ƒ Žƒ Ž Ž ƒ Š ƒ Ž ƒ š ƒ ƒ ƒ Ž ƒ ƒ ˆ ƒž ƒ ˆ Š Ž ƒ ƒžž ˆ Š š ˆ œƒ
13 Š Ž ƒ ƒ Ž ƒ Šƒ Ž ƒ Š ƒ ˆ ˆˆ ƒ ƒ ƒ ˆ š ƒž Ž Š ŠŠƒ ƒžž ƒ Šƒ Š ˆ ƒ ƒ ˆ ƒ œ ƒ Ž ƒ ƒ ƒ ƒ Žƒ ƒž Žˆ ƒ ƒž ƒ Ž ƒ ƒ Ž Ž Š ƒžž ƒž ƒ Š ƒˆƒ ƒ Ž Ž Š ˆ ƒ ƒ Š ƒ ƒžž ˆ Šƒ Ž ƒ Š œƒ ˆ Š Ž ƒ Ž Š ƒž ƒ ƒ Ž Š ˆ ˆ ƒ ˆ Šƒ Š ƒ ƒž Š Ž ƒž Šƒ ˆ œƒ Š ƒ ˆ ƒ œƒ Šƒ ƒ Ž ƒ ƒ ƒ ƒ Š Žƒ Šƒ Š ƒ Ž ƒ Œ ƒ Š ƒ ƒ ˆŽ Š Ž ŽŽ ƒ Ž ˆ ƒžž ƒž ƒ š DD Š Š ƒž Š ƒ Ž ƒ ƒ Ž Ž Š ƒ ƒ ƒ ƒ ƒ ƒ ƒ Š ƒž ƒ ƒ ˆ ƒ Š Šƒ Š ˆ ƒž ƒ Š ˆ Š ƒ š Š ˆ ƒ ƒ Š ˆ ƒ š Š ƒ ƒ ˆˆ ˆ ƒ Š Š ƒ Š Ž ƒ ƒ ƒ ƒ Š ˆ ˆ š ƒ ˆƒ Ž ƒ œ Š Œ ŠƒŽŽ Š š ƒ š ƒ Ž ƒ Œ ƒž ƒ ƒ ŽŽ ƒ Šƒ Ž ƒ Š Ž ƒ Œ ˆ Š ƒ ˆ Œ Ž Šƒ Š Š Ž ƒ Š ƒ ƒ Ž ˆ Š ˆ Š ƒ Œ
14 ˆ Ž ƒ Ž Š ƒ ƒž ƒ Œ ƒ Š Š ƒ ƒ Š ƒ Œ ƒ Ž ƒ Ž Šƒ ˆ Ž Š ˆ ƒ ˆ Š ˆ ˆ Ž ˆ Ž Š Š ƒ Šƒ Ž Š ƒž Ž ƒž Ž ˆ Š Š ƒ ƒ ƒ Š Ž ƒ ƒ ƒ Š ƒ ƒ Ž ƒ ˆ Š ƒ ƒ ˆ Šƒ ƒ ƒ ƒ Ž Š ƒ ƒ Š ƒ ƒ ƒ ˆ Œ ƒ ƒ Š ˆ ƒ ƒ ƒ Š ƒ ƒ ˆ Š ƒ Š ƒ ƒ œ Š š ƒ ˆ ƒ ƒ ŽŽ ƒ Ž ƒžž ˆ ˆ Š ƒ ˆ Š ˆ ƒž Š ˆ ƒˆ ƒž ˆ ƒ Ž ƒž Š ƒ Š ƒ ŽŽ Š ƒ ŽŽ Š Ž ƒ ƒž Š Ž ŽŽ ƒ ƒ ƒž ƒ ŽŽ Š Š ƒš Ž ƒ Ž ƒ ƒ Ž Ž Šƒ Šƒ ƒžž ŠƒŽŽ ƒžƒ Ž Ž ƒ ˆŽ š œ ƒž Š Ž ŽŽ Žƒ Ž Šƒ Š ƒ ƒš Ž ƒ Ž ƒ Š ˆˆ ƒ ˆ ƒ Ž Šƒ Žƒ ˆ ƒ š ƒ Ž ˆ ƒ ˆ ƒ Šƒ ˆ Œ ƒž ƒ Š Ž ƒ Œ ƒž Š ƒ Œ Ž Šƒ Š ˆ ƒžž Š ƒ Œ Š ƒž ƒ Š ŠƒŽŽ ƒžƒ ƒ Œ Ž ˆ ƒ Ž ƒ Š ƒ ˆ ƒ Œ Žƒ Š ƒ Ž Œ Ž ƒ ƒž ˆˆ ˆ ƒ ˆ ˆˆ ƒ ˆ ˆ Š ƒ ˆ ƒ Š Œ ˆ ˆ ƒ ˆ ƒ ƒ
15 ƒ Š ƒ š Š Œ ˆ ˆ ƒ ƒ œƒ ƒ œƒ ƒ Š ˆ Š ˆ ƒ ˆ ƒ ƒ ƒ Ž Š ƒ ˆ ƒ Š ˆ ƒ ƒ ƒ ˆ ƒ ˆ Š ƒ Š ƒ ƒ œ ƒ ƒ š Ž Ž ƒ Š Š Š ƒ ƒ ƒ Š ƒ ƒž ƒ Šƒ Š ƒ ƒ Ž Š ƒ ƒ ƒ ƒ ƒ ˆ ƒ ƒ ƒ Œ ƒ Ž Š ˆ ƒ š ˆ ƒ ƒ ƒ ƒ ŠŽ ƒ ƒ ˆ ˆ Ž Š Œ Š Ž ƒ ƒž ƒ Ž ƒž ˆ Š Š ƒ ƒ ƒ Ž Šƒœ ƒ Ž ˆ Žƒ ƒž ƒ Š ƒ ƒ ˆ Š ƒ ˆ ƒ ƒ ƒ ˆ ƒž ƒ ƒ Ž ƒ Šƒ ˆ ƒ Š Ž Š ƒ ƒž Š ƒ ƒ ƒ ƒ Ž ŽŽ ƒ ƒ ƒž Ž Š ƒ ƒ ƒ ƒž ƒ Š Ž ƒ ŽŽ ƒ Š ˆ Š Š ƒ Š ŽŽ ƒ ƒž Š Š ƒ ƒ Šƒ Š Œ Š š ƒž ƒ ƒ ƒ ƒž Š š ƒ Š ˆ ƒ ƒž ˆ ƒ ƒ Š ˆ ˆ Š ƒ ƒ ƒž ƒ ƒž Š ƒ ˆ ƒ š ƒ ŽŽ ƒ ƒ ƒž ˆ ˆˆ ƒ ƒ ƒ ˆ Š Š ƒ š ƒž œ Š ƒ ƒ ƒ œ ˆ Š ƒ ƒ ƒˆ Š ƒ ˆ œ ƒ Š ƒ ƒ ˆ Š ˆ ƒ ƒ ƒ Ž Š ƒ
16 ƒ ƒ Š ƒ ƒ ˆ Š ƒž Žƒ ˆ ƒ ƒ ƒ Ž ˆ Š ˆ ŽŽ š Š ˆ ƒ Ž Š ƒ Ž Š Ž ˆ ƒ ƒ ƒ ¹» Ê» 1 Ê» 1 ¹ ¹» 1, Š Š ƒ Š Š ƒ ƒ ˆƒ Š ƒ ˆ Š ˆƒ ƒ Ž Š ƒ ƒ ˆ ƒ Š ƒ Ž ˆ Š ˆƒ ƒ Ž Š Š Š Žƒ ƒ Š ƒ Ž ˆ ˆ Š ƒ ƒ ƒ Žƒ ƒ ˆ Š Ž ƒž Žƒ Š Šƒ ˆ Š Šƒ ƒ Ž ƒž œ Š Š ƒ ƒ ƒ ˆ Š Š Š ˆ š ƒžˆ Šƒ ƒ ƒ Ž ƒ Šƒ ƒ ƒ Ž Ž ƒ ƒž ƒž ƒ ƒ ˆ ƒ Š ƒ Š ˆ Š ˆ ƒž ƒž ƒ š ƒ Ž ƒ ƒ Š Œ Ž Š ƒž Ž ƒ ƒ ˆ ƒ Š ˆ Š š ƒ Š š œƒ ƒ Šƒ Š ˆ Š ˆƒ ƒ Ž Ž Š ƒ ƒ ƒžž ƒž ˆ ƒ ƒžƒ Š ƒ Š ˆ ƒ Ž ƒ ˆ ˆƒ ƒ Ž ƒ Šƒ ˆ Š ƒ ƒ š Š ˆ Š ƒ ˆ ƒž ƒž ƒž ƒžž Šƒ ˆˆ ˆ ƒ Ž ƒž ƒ Ž ƒ ƒ Ž ƒ Ž ƒ ƒ œƒ Š Œ ˆ œ ƒ Š ˆ Š ƒ ˆˆ ƒ ƒ ƒ ƒ Ž Š ƒ Š ƒž ƒ ƒžž ƒž ˆ ƒ Š Œ Š
17 ƒ Š š Š œƒ œ Š Œ ˆ Š ƒ ƒ ƒž Š ± Ž Š Ž ˆ ˆ ƒ Š ƒ ƒ Ž ƒ ƒ Š ƒ ƒ œƒ Žƒ ƒ ƒž ƒžž ƒ ƒ Š ƒž Žƒ ƒ Š Šƒ ƒ ƒ ƒ ƒ ƒ œ ƒž òžž ƒž ƒ Š ˆ ˆ ˆ Š ƒ ˆ ƒ ƒ ƒž Š Š ˆ Š ƒ ƒ ƒ ƒ š Žƒ Š Ž ƒ šƒ Š ƒž Š Ž ƒ Š ƒ ƒ ƒ ƒ ˆ ƒ ƒž ˆˆ Š ƒ ƒ ˆ Š ˆƒ ƒ Ž Š š ƒ Š ƒ ƒ ˆ Š ƒ ƒ ƒ ƒ ƒ ƒ ƒ Š ƒ ˆ ƒž ƒ Žƒ ˆ Š Žƒ Š Žƒ Ž œ ˆ Ž ƒ Š ƒ ƒ Ž š ƒ ˆ ƒ ƒž ˆˆ Žƒ Š š ƒ Š ƒ ƒ ˆ Žƒ ƒ ƒ ƒ Ž ƒ ƒžž Š ƒ Š Š Š ƒ ˆ Š ƒž Š ƒ ƒ ƒžž ƒ ˆ ƒ & Š ƒ ƒ ƒ Šˆˆ ƒ ƒ ŽŽƒ ƒ ƒ ƒ ˆ ƒž Š ƒ Šƒ Šƒ Ž Š ƒ ˆ ƒž Š ƒ Š ƒžƒ ƒ ƒ ŽŽƒ Š Ž Š ƒ ƒ ƒ Š Ž Š ƒ Š ƒ ˆ Š š ƒ ƒ ƒƒ ƒž Š ƒ ƒ ŽŽ ƒ Š ƒ ƒ Š ƒ
18 / Š ƒ Š Šƒ
19 & ƒ ƒ Š ƒ Žƒƒ ƒž ƒž ƒ Š ƒ ƒ ƒ Šƒ ƒž Ž Š ƒžž ƒž ƒ ˆ ƒ ƒ Žƒ ƒ ƒ Œ ƒ Žƒ ƒž ƒ Š ƒ šƒ ŽŽ Š ƒ ƒ Š ƒ ƒ ˆ Š œ Šƒ ƒ ƒ ˆ Š Ž ƒž ƒ ˆˆ ƒž ƒ ƒžž Ž Ž ƒžž ƒž ƒž ƒ ƒ ˆ Š ƒ Ž ƒ Ž ˆŽ ƒ Šƒ Ž š ƒ ˆ Šƒ Ž Ž ƒž ƒ Š ƒ Š Ž Ž ˆŽ ƒ œƒ Šƒ ƒ Ž ƒ Ž œ Š Ž ƒ Š ˆ Š ˆƒ ƒ Ž ƒ Ž Š ƒ ƒ ƒ Š ƒ ƒžž Ž Š ˆƒ ƒ Ž ƒ ƒ ƒžž Žˆ Š ƒ ƒ Ž ƒ Ž ƒ Š Ž Š ˆ š ƒžˆ Šƒ Š Š ƒ ƒ ƒ
20 Ž ƒ š ƒ ƒ Šƒ ƒ ŽŽ Ž ƒ ƒ Œ ˆ ˆ ŽŽ Ž ƒ Œ ƒ Š ƒ ƒ ƒž Š ƒž ƒ ƒ Œ ƒ ˆ ƒž ƒž Š Š Š ˆ ƒž ƒ ƒ ƒž ˆ ƒ Ž ƒ Ž Š ƒ ƒ ƒž œ ˆƒ Š ƒ ˆƒ Š š ƒž ƒ ƒ Žƒ Ž Š ƒ ŽŽ Ž ƒ Š Š Š ƒž Š Žƒ Š š ƒž ƒ ƒ ŽŽ ƒ Šƒ Š Ž ƒ ˆˆ Š ƒ ˆ Ž Š ƒž ƒžž ƒ ƒ š ƒ Ž ƒ Ž ƒ œ ƒ š ƒ ƒ Šƒ ˆ Ž ƒ ƒ ƒ Œ ƒž ˆ ŽŽ Ž ƒ Œ ƒ Š ƒ ƒ Š ƒž ŽŽ ƒ Šƒ Š ƒ Ž Ž ˆ Šƒ Ž Ž ƒ Š Š š ƒž ƒ ƒ Šƒ Š Ž ƒž ˆˆ š Žƒ Š ƒ Š Š Ž ˆ ƒž ƒ ƒž Š ˆˆ ƒ ƒ ƒ ƒ ŽŽƒ ƒ š ƒž œ ƒ Š ƒž ƒ ƒ Ž ƒ ƒ ˆœ Š ƒ ƒ ƒ ƒ ˆ ƒ Š ˆ ƒž ƒ ƒ ƒž ƒžž ƒ Ž Š ƒ ƒ ƒ Š Š ƒ
21 ƒ ƒ Ž ˆ ˆ ƒžž Œ ƒ ƒžž ƒž ˆ Š Š ƒ š ƒ Š ˆ ƒ š ƒ ƒž ƒ ƒ Š ƒž œ ƒ Š ƒž ƒ ƒ ˆ ƒ Šƒ Š ŽŽ ƒ ƒ Š ƒ ƒ Šƒ ƒ ƒ Š ˆƒ Š Š ˆ ƒ Ž Š ˆ ƒž ƒ ƒ ƒž Š ˆ Š ˆƒ Š ƒžž ƒ ƒ Ž ˆ ƒž ƒž ƒ ƒ Š ƒ ˆ Š Žƒ ˆ ƒž Šƒˆƒ ƒ Ž Ž Šƒƒ ˆƒ Š ƒž Š ƒ ˆƒ ƒ Ž ƒ Šƒ ƒ ˆƒ Š ƒ ƒž Š ˆƒ ƒ Ž ƒ ƒ ˆƒ ƒ ƒ Š ˆƒ ƒ Ž ƒ Ž ˆ Š ƒ Š ƒ ˆ Š ˆƒ ƒ Ž ˆ Š Žƒ Š ˆ Š Ž Š ƒžž
22 š ƒž Š Ž Š ƒ š Œ ƒž ƒ ƒ ŽŽ Šƒ ƒžž Ž ƒ ƒ ˆ Œ Š ƒ Šƒ ƒ ŽŽ ˆ ƒ ƒ ˆ ƒ ƒ ƒ ˆ Œ Ž ƒ Œ Š ƒž Š Ž ƒžž Š ˆ Ž ƒ Œ Š ˆ ƒ ƒ Š Ž ƒ ˆ ƒ Š ƒ ƒ ŽŽ ƒ Š ˆ ˆ ƒ ƒ Ž Œ ƒ ƒ ƒ ˆ Š ˆ ƒ š Œ ƒž Š Ž Š œ Š ƒ ƒ ƒž ƒ ƒ ƒ Š Œ ƒ ƒžž ƒ ƒ Œ Š ƒ Šƒ ˆ ˆ ƒ ƒ ƒ ˆ ƒ ƒ ˆ ˆ Œ Ž ƒ Œ Š ˆ Š Ž ƒžž Š ˆ Ž ƒ Œ Š ƒž ƒ ƒ ˆ ƒ Š Ž ƒ ˆ Š ƒ ƒ ŽŽ ƒ Š ˆ ƒ ƒ Ž Œ ƒ ƒ ƒ ˆ ƒž Š ˆ ˆ Š ƒž ƒ
23 ƒ ƒ ŽŽ Ž ƒ Ž ƒ Š ƒ š Š š ƒž Žˆ Š ƒ š ƒ ƒ ƒ Ž Š ƒ Š ƒ ƒ Ž ƒ ƒ ˆ Šƒ Ž Ž ƒ Ž ƒ ƒ Ž Š ƒ Š ƒš Ž ƒ Ž ƒ ƒ Ž Šƒ Žƒ ˆ
24 > ƒ Ž Ž ƒž ƒ ƒ Š Ž ƒž Žƒ Ž Ž ƒ > ˆ ˆƒ Ž
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28 A person Indirect sensors Sensed gait Prediction Task and environmental constraints + + Body dynamics Gait Direct sensors Metabolic rate Optimization B 1 τ s + 1 f A f Commanded input 1 τ s + 1 s A s + + Measured output
29 A Step frequency (normalized) Speed perturbation experiments Average fast overshoot response Input Two-process model fit Average fast undershoot response C Speed (normalized) Frequency perturbation experiments Input Average fast overshoot response Two-process model fit Average fast undershoot response 0 0 B 0.2 D 0.2 Step frequency (normalized) Fast overshoot residuals Fast undershoot residuals Time (s) Speed (normalized) Fast undershoot residuals Fast overshoot residuals Time (s)
30 ANumber of trials Speed perturbation experiments B Frequency perturbation experiments Fast undershoot Fast overshoot 50 Fast undershoot Fast overshoot Fast amplitude Number of trials Fast amplitude
31 A Speed perturbation experiments C Frequency perturbation experiments Metronome Instantaneous speed Treadmill speed Step frequency B D Speed (m/s) Treadmill speed (controlled) Step frequency (measured) Step frequency (Hz) Speed (m/s) Metronome frequency (controlled) Speed (measured) Step frequency (Hz) Time (s) Time (s)
32 ± 25% at 1.0 m/s ± 25% at 1.5 m/s Acceleration (m/s 2 ) ± 50% at 1.0 m/s ± 50% at 1.5 m/s Time (s)
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