1proposition,case,quantity,theory,simulation,rel_error2P1-P2,"single model, phi=0",tau,0.9589566551591868,0.9588458450583444,0.000115552773158519613P1-P2,"single model, phi=0",lam,0.019179133103183737,0.019175752481317396,0.00017626562411098934P1-P2,"single model, phi=0",mse,0.04104334484081318,0.04129126465884099,0.0060404389308271455P1-P2,"single model, phi=0",rhobar,0.3787878787878788,0.37947533265704547,0.00181487821460005526P1-P2,"single model, phi=0",sync,0.6236590070768526,0.6237815836734695,0.00019654425772086617P1-P2,"single model, phi=0.1",tau,0.9516558812333461,0.9516118476031707,4.6270538588263265e-058P1-P2,"single model, phi=0.1",lam,0.01903311762466692,0.019018044989802807,0.00079191623576055269P1-P2,"single model, phi=0.1",mse,0.0483441187666539,0.04828641424547546,0.00119362029240756310P1-P2,"single model, phi=0.1",rhobar,0.3818800247371676,0.3817584348587759,0.0003183981107033696611P1-P2,"single model, phi=0.1",sync,0.6248831487706711,0.6249644571428571,0.0001301177225629525712P1-P2,"single model, phi=0.2",tau,0.9269558769002596,0.926803288755423,0.0001646120906497798813P1-P2,"single model, phi=0.2",lam,0.018539117538005193,0.01853558630569371,0.00019047467088142614P1-P2,"single model, phi=0.2",mse,0.0730441230997404,0.07321495387982196,0.002338734080609049715P1-P2,"single model, phi=0.2",rhobar,0.39270253555967843,0.3927190039434333,4.1936026034011325e-0516P1-P2,"single model, phi=0.2",sync,0.6291676446990355,0.6290899428571428,0.000123499424274871517P1-P2,"single model, phi=0.5",tau,0.7795447458684129,0.7814543864299311,0.002449686912315560718P1-P2,"single model, phi=0.5",lam,0.015590894917368259,0.015603423881791543,0.00080360777810942219P1-P2,"single model, phi=0.5",mse,0.22045525413158706,0.21987004006908134,0.0026545707191737720P1-P2,"single model, phi=0.5",rhobar,0.471552257266543,0.47343561787020266,0.00399395947031829521P1-P2,"single model, phi=0.5",sync,0.6603832578914052,0.6608069224489797,0.000641543456033746322P1-P2,"single model, phi=1",tau,0.49436424757761516,0.49184955889597654,0.00508671226521860423P1-P2,"single model, phi=1",lam,0.009887284951552304,0.009859406617159425,0.002819614740495706224P1-P2,"single model, phi=1",mse,0.5056357524223849,0.5068518891714339,0.00240516368398147525P1-P2,"single model, phi=1",rhobar,0.7575757575757576,0.7571975042536527,0.00049929438517838626P1-P2,"single model, phi=1",sync,0.773616364569609,0.7735689387755101,6.130402130941514e-0527P1(i),tau strictly decreasing over phi grid (1=yes),monotone,1.0,1.0,0.028P1(i),Omega(phi=1/N) / Omega(phi=0),ratio,1.0,1.0,0.029P1(ii),"N->inf limit, phi=0.2",tau_inf,0.9615384615384615,0.9615383284021541,1.3846175960452457e-0730P1(ii),"bound tau(N=50)<=tau_inf, phi=0.2 (1=yes)",bound,1.0,1.0,0.031P1(ii),"N->inf limit, phi=0.5",tau_inf,0.8,0.7999999270398466,9.120019184294392e-0832P1(ii),"bound tau(N=50)<=tau_inf, phi=0.5 (1=yes)",bound,1.0,1.0,0.033P1(iii),"phi=0, N=1e7",tau->1,1.0,0.9999998359997768,1.640002231795279e-0734P2(ii),phi=0.5,rho_same,0.7575757575757576,0.7570963864431715,0.000632769895013671735P2(ii),phi=0.5,rho_cross,0.3787878787878788,0.3779700431514435,0.002159086080189145436P2(iv),"phi=0.5, same-model pair",S(rho1)=1/2+asin(rho1)/pi,0.773616364569609,0.7733414666666667,0.0003553413753020386437P2 placebo,sigma_eta=0: Omega(phi=1)/Omega(phi=0),ratio,1.0,1.0,0.038P3,"Phi=1, G=1 (50)",tau,0.49436424757761516,0.49341141461729443,0.001927390512136765539P3,"Phi=1, G=1 (50)",rhobar,0.7575757575757576,0.7569853104346328,0.000779390226284699740P3,"Phi=1, G=1 (50)",sync,0.773616364569609,0.7736320367346939,2.025831639902203e-0541P3,"Phi=1, G=2 uniform (25,25)",tau,0.6566850538481743,0.6574905050550102,0.001226541097769615642P3,"Phi=1, G=2 uniform (25,25)",rhobar,0.5643166357452072,0.5660294353951645,0.003035174831759944643P3,"Phi=1, G=2 uniform (25,25)",sync,0.6971075087059577,0.6976120734693878,0.000723797631109592844P3,"Phi=1, G=5 uniform (10x5)",tau,0.8177952240758913,0.8172375337609343,0.000681943717129425145P3,"Phi=1, G=5 uniform (10x5)",rhobar,0.4483611626468769,0.44833526158669923,5.776829559631221e-0546P3,"Phi=1, G=5 uniform (10x5)",sync,0.6512021951877671,0.6512468040816326,6.85023702240756e-0547P3,"Phi=1, G=3 skewed (30,10,10)",tau,0.6836204539239814,0.6831971941831166,0.00061914434893698248P3,"Phi=1, G=3 skewed (30,10,10)",rhobar,0.5411255411255411,0.5400367440856554,0.002012096929708840449P3,"Phi=1, G=3 skewed (30,10,10)",sync,0.6879264460023196,0.6872304367346939,0.001011749543385558550P3,"Phi=0.6, G=1 (30)",tau,0.719010641357492,0.7188837757769287,0.0001764446494474316251P3,"Phi=0.6, G=1 (30)",rhobar,0.5132962275819418,0.513237234068623,0.0001149307361886298552P3,"Phi=0.6, G=1 (30)",sync,0.6769091707579539,0.6769316775510205,3.324935462373573e-0553P3,"Phi=0.6, G=2 uniform (15,15)",tau,0.8259002312520647,0.8253527513594462,0.000662888653982475654P3,"Phi=0.6, G=2 uniform (15,15)",rhobar,0.44372294372294374,0.44365069827898973,0.000162816561496356555P3,"Phi=0.6, G=2 uniform (15,15)",sync,0.6493659826470395,0.6495021346938776,0.0002096692011539352856P3,"Phi=0.6, G=3 uniform (10,10,10)",tau,0.8689607229753215,0.8685960391342109,0.0004196781643500173657P3,"Phi=0.6, G=3 uniform (10,10,10)",rhobar,0.4205318491032777,0.4195118784420024,0.00242543023423845558P3,"Phi=0.6, G=3 uniform (10,10,10)",sync,0.6401849199434013,0.6396935102040816,0.000767605927617226959P3(iii),simulated tau decreasing in H within each Phi (1=yes),ordering,1.0,1.0,0.060P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=1 (50) (1=yes)",bounds,1.0,1.0,0.061P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=2 uniform (25,25) (1=yes)",bounds,1.0,1.0,0.062P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=5 uniform (10x5) (1=yes)",bounds,1.0,1.0,0.063P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=3 skewed (30,10,10) (1=yes)",bounds,1.0,1.0,0.064P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=1 (30) (1=yes)",bounds,1.0,1.0,0.065P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=2 uniform (15,15) (1=yes)",bounds,1.0,1.0,0.066P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=3 uniform (10,10,10) (1=yes)",bounds,1.0,1.0,0.067P4(i),lambda*gamma=0.3,variance amplification 1/(1-lg)^2,2.0408163265306127,2.040816326530612,4.3520742565306126e-1668P4(iii),lambda*gamma=0.3,Var(P1-v)=sv^2[(1-tau)+tau(kappa-1)^2],0.24330132497937995,0.24370288120040037,0.001650448147187253869P4(i),lambda*gamma=0.3,max|dP - kappa*lam*Y| (abs),0.0,8.881784197001252e-16,8.881784197001252e-1670P4(i),lambda*gamma=0.6,variance amplification 1/(1-lg)^2,6.249999999999999,6.249999999999997,2.8421709430404013e-1671P4(iii),lambda*gamma=0.6,Var(P1-v)=sv^2[(1-tau)+tau(kappa-1)^2],2.1586948461253246,2.160366856281589,0.0007745467865759372P4(i),lambda*gamma=0.6,max|dP - kappa*lam*Y| (abs),0.0,3.552713678800501e-15,3.552713678800501e-1573P4(ii),lambda*gamma=1.0: |dP| after 60 rounds >= 50 * |lam*Y| (1=yes),divergence,1.0,1.0,0.074P4(ii),lambda*gamma=1.2: |dP| after 60 rounds >= 50 * |lam*Y| (1=yes),divergence,1.0,1.0,0.075P5(ii),"a=0.60, b=0.0, dP0=-1.0",fixed point (dP0+lam*b/m)/(1-a),-2.5,-2.5,0.076P5(ii),"a=0.60, b=5.0, dP0=-1.0",fixed point (dP0+lam*b/m)/(1-a),-2.25,-2.25,0.077P5(ii),"a=0.60, b=0",multiplier 1/(1-a),2.5,2.5,0.078P5(i),"a=0.60, b=5, dP0=-0.1 (inside buffer)",dP = dP0,-0.1,-0.1,0.079P5(iii),a=1.00: cascade below -1e3 (1=yes),no finite fixed point,1.0,1.0,0.080P5(iii),a=1.20: cascade below -1e3 (1=yes),no finite fixed point,1.0,1.0,0.081P5(iv),phi_L=0,sd(X_net),10.788883167408942,10.758877785651544,0.0027811388159284682P5(iv),phi_L=0,E|X| = sigX*sqrt(2/pi),8.60828330758151,8.575270770976026,0.003834973295594240783P5(iv),"phi_L=0, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.31731050786291415,0.31466,0.00835304157043307684P5(iv),phi_L=0.5,sd(X_net),11.679041056525145,11.63964211855805,0.003373473710419236685P5(iv),phi_L=0.5,E|X| = sigX*sqrt(2/pi),9.318526543984198,9.282062585089383,0.00391306058127351286P5(iv),"phi_L=0.5, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.35560003994636147,0.352595,0.00845061757252545687P5(iv),phi_L=1,sd(X_net),14.366627996854378,14.356194803386284,0.000726210316740872588P5(iv),phi_L=1,E|X| = sigX*sqrt(2/pi),11.462910669488306,11.450867751700944,0.00105059859006118989P5(iv),"phi_L=1, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.45267169342522484,0.4527,6.253223955967488e-0590