Information processing via physical soft body. Supplementary Information

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Informtion processing vi physicl soft body Supplementry Informtion Kohei Nkjim 1, Helmut Huser 2, o Li 3, Rolf Pfeifer 4,5 1 he Hkubi Center for Advnced Reserch & Grdute School of Informtics, Kyoto University, 66-851 Kyoto, Jpn. 2 Deprtment of Engineering Mthemtics, University of Bristol, Bristol BS8 1UB, United Kingdom. 3 Deprtment of Engineering nd Informtion echnology, Bern University of Applied Sciences, 251 Biel, Switzerlnd. 4 Institute for Acdemic Inititives, Osk University, Osk 56-8531, Jpn. 5 Deprtment of Automtion, Shnghi Jio ong University, Shnghi 224, Chin. o whom correspondence should be ddressed; emil: k nkjim@cs.i.kyoto-u.c.jp

Supplementry ble Supplementry ble S1: he verged NMSE system, NMSE LR, NMSE, nd NMSEverge re shown. For NMSE LR, NMSE, nd NMSEverge, the results of significnt tests in terms of p-vlue compring with NMSE system re lso depicted for ech experimentl condition. Note tht n.s. represents not significnt. sk NMSE system NMSE LR NMSE NMSE verge men ± SD men ± SD p-vlue men ± SD p-vlue men ± SD p-vlue NARMA2 1 1.36±.7 ( 1 5 ) 1.89±.1 ( 1 5 ) p <.1 2.3±2.35 ( 1 6 ) p <.1.94±.2 ( 1 5 ) p <.1 15 1.2±.2 ( 1 5 ) 2.7±.3 ( 1 5 ) p <.1 1.99±2.72 ( 1 6 ) p <.1 1.12±.3 ( 1 5 ) n.s. 2 1.11±.16 ( 1 5 ) 2.15±.5 ( 1 5 ) p <.1 1.59±1.81 ( 1 6 ) p <.1 1.18±.32 ( 1 5 ) n.s. 25 1.41±.6 ( 1 5 ) 2.24±.5 ( 1 5 ) p <.1.86±1.2 ( 1 6 ) p <.1 1.13±.25 ( 1 5 ) p <.1 3 1.73±.12 ( 1 5 ) 2.3±.6 ( 1 5 ) p <.1.56±.94 ( 1 6 ) p <.1 1.8±.33 ( 1 5 ) p <.1 35 1.91±.1 ( 1 5 ) 2.37±.5 ( 1 5 ) p <.1.72±1.33 ( 1 6 ) p <.1 1.1±.32 ( 1 5 ) p <.1 4 1.96±.7 ( 1 5 ) 2.39±.7 ( 1 5 ) p <.1.36±.5 ( 1 6 ) p <.1.9±.28 ( 1 5 ) p <.1 NARMA5 1 1.5±.4 ( 1 3 ) 3.1±.1 ( 1 3 ) p <.1.53±.76 ( 1 3 ) p <.1 1.72±.9 ( 1 3 ) n.s. 15 3.14±.1 ( 1 3 ) 6.69±.7 ( 1 3 ) p <.1.57±1.25 ( 1 3 ) p <.1 2.91±2.13 ( 1 3 ) n.s. 2 3.57±.25 ( 1 3 ) 8.88±.14 ( 1 3 ) p <.1.54±1.6 ( 1 3 ) p <.1 3.4±2.55 ( 1 3 ) n.s. 25 3.54±.7 ( 1 3 ) 1.2±1.75 ( 1 4 ) p <.1.5±1.66 ( 1 3 ) p <.1 3.94±2.82 ( 1 3 ) n.s. 3 4.6±.9 ( 1 3 ) 1.1±2.1 ( 1 4 ) p <.1.65±2.15 ( 1 3 ) p <.1 4.34±3.1 ( 1 3 ) n.s. 35 2.9±.55 ( 1 3 ) 1.16±1.61 ( 1 4 ) p <.1.4±1.73 ( 1 3 ) p <.1 4.96±3.6 ( 1 3 ) p <.1 4 2.54±.38 ( 1 3 ) 1.19±2.65 ( 1 4 ) p <.1.92±2.6 ( 1 3 ) p <.1 5.43±3.53 ( 1 3 ) p <.1 NARMA1 1 1.97±.2 ( 1 3 ) 2.2±.1 ( 1 3 ) p <.1.84±.46 ( 1 3 ) p <.1 1.75±.31 ( 1 3 ) p <.1 15 1.9±.1 ( 1 3 ) 1.33±.1 ( 1 3 ) p <.1.39±.25 ( 1 3 ) p <.1.98±.25 ( 1 3 ) p <.1 2 1.68±.16 ( 1 3 ) 2.76±.4 ( 1 3 ) p <.1.37±.45 ( 1 3 ) p <.1 1.46±.74 ( 1 3 ) n.s. 25 2.61±.46 ( 1 3 ) 4.84±.8 ( 1 3 ) p <.1.36±.9 ( 1 3 ) p <.1 2.16±1.18 ( 1 3 ) p <.5 3 3.27±.59 ( 1 3 ) 6.81±.13 ( 1 3 ) p <.1.67±1.57 ( 1 3 ) p <.1 3.12±2.16 ( 1 3 ) n.s. 35 2.79±.44 ( 1 3 ) 8.56±.13 ( 1 3 ) p <.1.67±1.77 ( 1 3 ) p <.1 3.82±2.78 ( 1 3 ) p <.5 4 2.97±.65 ( 1 3 ) 9.86±.23 ( 1 3 ) p <.1.68±1.83 ( 1 3 ) p <.1 4.34±2.97 ( 1 3 ) p <.1 NARMA15 1 2.81±.3 ( 1 3 ) 3.76±.1 ( 1 3 ) p <.1 1.15±.66 ( 1 3 ) p <.1 2.87±.57 ( 1 3 ) n.s. 15 2.4±.7 ( 1 3 ) 2.7±.5 ( 1 3 ) p <.1.93±.56 ( 1 3 ) p <.1 2.13±.35 ( 1 3 ) p <.1 2 1.34±.2 ( 1 3 ) 1.44±.2 ( 1 3 ) p <.1.43±.29 ( 1 3 ) p <.1 1.9±.2 ( 1 3 ) p <.1 25 1.46±.11 ( 1 3 ) 1.75±.1 ( 1 3 ) p <.1.36±.32 ( 1 3 ) p <.1 1.11±.32 ( 1 3 ) p <.1 3 1.94±.17 ( 1 3 ) 2.84±.4 ( 1 3 ) p <.1.34±.56 ( 1 3 ) p <.1 1.47±.64 ( 1 3 ) p <.1 35 2.15±.22 ( 1 3 ) 4.39±.7 ( 1 3 ) p <.1.32±.64 ( 1 3 ) p <.1 2.12±1.8 ( 1 3 ) n.s. 4 2.62±.46 ( 1 3 ) 6.4±.15 ( 1 3 ) p <.1.61±1.41 ( 1 3 ) p <.1 2.93±1.71 ( 1 3 ) n.s. NARMA2 1 1.66±.1 ( 1 3 ) 1.73±.1 ( 1 3 ) p <.1.83±.22 ( 1 3 ) p <.1 1.51±.12 ( 1 3 ) p <.1 15 3.69±.8 ( 1 3 ) 4.26±.9 ( 1 3 ) p <.1 1.26±.64 ( 1 3 ) p <.1 3.34±.51 ( 1 3 ) p <.1 2 2.55±.8 ( 1 3 ) 2.95±.8 ( 1 3 ) p <.1.92±.51 ( 1 3 ) p <.1 2.41±.3 ( 1 3 ) p <.1 25 1.77±.5 ( 1 3 ) 1.84±.4 ( 1 3 ) p <.1.55±.35 ( 1 3 ) p <.1 1.48±.18 ( 1 3 ) p <.1 3 1.6±.6 ( 1 3 ) 1.81±.2 ( 1 3 ) p <.1.47±.31 ( 1 3 ) p <.1 1.37±.22 ( 1 3 ) p <.1 35 1.81±.11 ( 1 3 ) 2.36±.2 ( 1 3 ) p <.1.43±.31 ( 1 3 ) p <.1 1.55±.4 ( 1 3 ) p <.1 4 2.18±.19 ( 1 3 ) 3.35±.6 ( 1 3 ) p <.1.54±.74 ( 1 3 ) p <.1 2.±.77 ( 1 3 ) n.s.

Supplementry Figures power source plexiglss plte b θ(t) = 1. θ(t) = -1. 46.4 46.4 6 cm Supplementry Figure S1: Pictures showing the overll pltform () nd close-up of the rm bse (b). For (b), the mximum left (θ(t) = 1.) nd right (θ(t) = 1.) bse positions, which re 46.4 degrees, re depicted. See Methods section for detils.

NMSE motor vrince vrince b odd-numbered sensors even-numbered sensors s1 s3 s5 s7 s9 s2 s4 s6 s8 s1 Supplementry Figure S2: he verged NMSE motor between m(t) nd θ(t) () nd the verged vrince for ech sensory vlue ccording to the prmeter of the input mong 2 experimentl trils (b). For (b), left nd right digrms plot the odd-numbered sensors nd even-numbered sensors, respectively. For ll plots, the verticl xis is in log scle, nd the error brs show the stndrd devitions.

NMSE NMSE 2. 1..6.4.2 1-5 1-2 NARMA2 1. NARMA5 1-9 1-7 1-5 1-3 1-1 NMSE 1-2.5 1-2 NARMA1 NARMA15 NMSE.5.4.3.2.1 1-9 1-7 1-5 1-3 1-1 NMSE.3.2.1 1-9 1-7 1-5 1-3 1-1.4 1-2 NARMA2 1-9 1-7 1-5 1-3 1-1 1-9 1-7 1-5 1-3 1-1 =1 =15 =2 =25 =3 =35 =4 Supplementry Figure S3: Plots showing the verged NMSE ccording to ech noise intensity for 5 NARMA tsks. For ech plot, the cses from = 1 to = 4 re overlid. he verged NMSE is clculted by using 3 different s for ech condition, nd the error brs show the stndrd devitions for ech plot.

SD rtio NARMA2 NARMA5 NARMA1 NARMA15 NARMA2 NARMA2 NARMA1 NARMA2 b =1 =15 =2 =25 =3 =35 =4 1. ρ Condition A Condition B Condition C.. 1. Supplementry Figure S4: he verged rtio of NMSEs for the tht shows lower vlue thn the NMSEsystem ginst the entire (, ρ)-spce (), nd typicl exmple of the NMSE for ech prmeter of nd ρ (b). For (), the verged rtios for NARMA tsks for ech setting of re overlid in the left plot, nd the corresponding stndrd devitions re plotted in the right for clrity. he plots show the verged vlue over 5 different s. For (b), NMSEs in the condition of NMSE < NMSEsystem re clssified s Condition A, NMSEs in the condition of NMSEsystem NMSE < NMSELR re clssified s Condition B, nd NMSEs in the condition of NMSELR NMSE re clssified s Condition C nd colored differently in the plot. he plots for NARMA5 nd NARMA15 tsks showed tendency tht ws similr to NARMA1 nd NARMA2 tsks.

Supplementry Video (Cption) Supplementry Video S1: A video showing the rm motion, the corresponding sensory responses, nd the system performnce for 5 NARMA tsks for ech setting of during the evlution phse. he cses for = 1, 2, 3, nd 4 re shown for exmple.

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