numbers from subjective comparisons/partial ordering | AN #1517
Run
Tick Action: "S"S
every
Min Step Time: 100100
ms
Expression 31: "R" Subscript, 2 , BaselineR2
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differentiable cost function
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Expression 33: "E" left parenthesis, "K" , "L" , right parenthesis equals Start sum from "i" equals 1 to length left parenthesis, "K" , right parenthesis , end sum, Start sum from "j" equals 1 to length left parenthesis, "K" , right parenthesis , end sum, left brace, "A" left parenthesis, "A" Subscript, "L" , Baseline , "i" , "j" , right parenthesis equals 0 : 1 , "C" left parenthesis, "L" , "i" , "j" , right parenthesis equals 0 : cosh left parenthesis, "K" left bracket, "i" , right bracket minus "K" left bracket, "j" , right bracket , right parenthesis , "C" left parenthesis, "L" , "i" , "j" , right parenthesis equals 1 : exp left parenthesis, "K" left bracket, "j" , right bracket minus "K" left bracket, "i" , right bracket , right parenthesis , "C" left parenthesis, "L" , "i" , "j" , right parenthesis equals negative 1 : exp left parenthesis, "K" left bracket, "i" , right bracket minus "K" left bracket, "j" , right bracket , right parenthesis , 0 , right braceEK,L=lengthK∑i=1lengthK∑j=1AAL,i,j=0:1,CL,i,j=0:coshKi−Kj,CL,i,j=1:expKj−Ki,CL,i,j=−1:expKi−Kj,0
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Expression 34: "h" equals 0.0 0 1h=0.001
00
11
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convergence process
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Expression 36: "b" left parenthesis, "x" , "l" , right parenthesis equals left brace, StartAbsoluteValue, "x" , EndAbsoluteValue greater than "l" : sgn left parenthesis, "x" , right parenthesis "l" , "x" , right bracebx,l=x>l:sgnxl,x
Expression 38: "d" Subscript, "t" , Baseline to StartFraction, "d" Subscript, "t" , Baseline Over 2 , EndFractiondt→dt2
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Expression 39: "S" equals left parenthesis, "Y" to "Y" minus "d" Subscript, "t" , Baseline times left bracket, left brace, "p" less than or equal to "s" : 0 , "b" left parenthesis, StartFraction, "E" left parenthesis, "Y" plus left bracket, left brace, "m" equals "p" : "h" , 0 , right brace for "m" equals left bracket, 1...length left parenthesis, "Y" , right parenthesis , right bracket , right bracket , "X" , right parenthesis minus "E" left parenthesis, "Y" , "X" , right parenthesis Over "h" , EndFraction , 10 , right parenthesis , right brace for "p" equals left bracket, 1...length left parenthesis, "Y" , right parenthesis , right bracket , right bracket , right parenthesisS=Y→Y−dt·p≤s:0,bEY+m=p:h,0form=1...lengthY,X−EY,Xh,10forp=1...lengthY
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actual error
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Expression 41: StartRoot, mean left parenthesis, left parenthesis, "Y" minus "X" , right parenthesis squared , right parenthesis , EndRootmeanY−X2
equals=
0.6 5 5 6 2 5 5 8 0 9 3 80.655625580938
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Expression 42: correlation left parenthesis, "X" , "Y" , right parenthesiscorrX,Y
undefined
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Expression 43: StartFraction, Start sum from "u" equals 1 to "N" , end sum, Start sum from "v" equals 1 to "N" , end sum, "A" left parenthesis, "A" Subscript, "L" , Baseline , "u" , "v" , right parenthesis left parenthesis, "C" left parenthesis, "Y" , "u" , "v" , right parenthesis minus "C" left parenthesis, "X" , "u" , "v" , right parenthesis , right parenthesis squared Over 2total left parenthesis, "A" Subscript, "L" , Baseline , right parenthesis plus "N" , EndFractionN∑u=1N∑v=1AAL,u,vCY,u,v−CX,u,v22totalAL+N
equals=
0.5 1 3 5 1 3 5 1 3 5 1 40.513513513514
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Expression 44: StartFraction, Start sum from "u" equals 1 to "N" , end sum, Start sum from "v" equals 1 to "N" , end sum, left parenthesis, "C" left parenthesis, "Y" , "u" , "v" , right parenthesis minus "C" left parenthesis, "X" , "u" , "v" , right parenthesis , right parenthesis squared Over "N" squared , EndFractionN∑u=1N∑v=1CY,u,v−CX,u,v2N2
equals=
0.5 0 3 9 0 6 2 50.50390625
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rescale affinely
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Expression 46: "F" Subscript, "r" , Baseline equals left parenthesis, "Y" to "Y" times StartFraction, stddev left parenthesis, "X" , right parenthesis Over stddev left parenthesis, "Y" , right parenthesis , EndFraction plus left parenthesis, mean left parenthesis, "X" , right parenthesis minus mean left parenthesis, "Y" , right parenthesis , right parenthesis , right parenthesisFr=Y→Y·stddevXstddevY+meanX−meanY
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Expression 47: "q" equals 2q=2
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22
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Hidden Label: left parenthesis, 0 , 0 , right parenthesis0,0
Run
Min Step Time: left parenthesis, left brace, "q" equals 0 : "R" Subscript, 1 , Baseline , "q" equals 1 : "R" Subscript, 2 , Baseline , "q" equals 2 : "F" Subscript, "r" , Baseline , right brace , "q" to mod left parenthesis, "q" plus 1 , 3 , right parenthesis , right parenthesisq=0:R1,q=1:R2,q=2:Fr,q→modq+1,3