I am developing Python software for reducing residual gas analysis mass spectrometry data, specifically focusing on outlier detection via helium-3 spike intensities. We use helium-3 as a reference spike to measure helium-4, however, erroneous spike intensities due to e.g. hydrogen deuteride interference can invalidate the analysis. Before I can identify such outliers, however, I need to correct for the effects of beam suppression.
Beam Suppression
Beam suppression is where a large concentration of one gas, say $^4$He at 4 amu, suppresses the mass spec's ability to measure the full intensity of another gas, like $^3$He at 3 amu. Beam suppression is roughly linear (note the log scale on the $x$-axis):
Without correcting for beam suppression, the scatter in raw 3 amu intensities is high:
In the above figure, purple triangles and some green circles show significant beam suppression with data scatter reaching up to 5 error ranges. Samples with even higher helium-4 concentrations experience further suppression, pushing this scatter even higher. This limits my outlier detection capacity to extreme values only.
Challenge
The optimal outlier detection method should first correct for beam suppression, then identify outliers within a smaller range.
To accomplish this, I need to programmatically identify the 4 amu intensity threshold above which beam suppression occurs.
This is further complicated by the following:
- $^3$He spike depletes with each analysis following $y = ae^{bx}$ where $x$ is analysis number and $y$ is intensity. This decay is so small that it is practically linear over a single sequence; in some cases the decay is lost in the scatter completely. Still, this trend makes traditional statistical methods like the mean and standard deviation inappropriate, as the data do not have a normal distribution.
- The proportion of analyses requiring correction may vary, with some sequences having more analyses needing correction than not.
How can I programmatically identify the 4 amu intensity threshold where beam suppression begins, and distinguish which analyses need correction?
Here are some example data:
analysis number: [3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139]
3 amu: [7.902247180966696e-10, 7.894322788473899e-10, 7.75192352846054e-10, 7.73938454990039e-10, 7.751150261600025e-10, 7.902661264530252e-10, 7.88887076907539e-10, 7.88710449681167e-10, 7.892751658033371e-10, 7.889499885195002e-10, 7.882350356665988e-10, 7.904308872238497e-10, 7.898302812219745e-10, 7.925021509317708e-10, 7.843025375921496e-10, 7.952036488404707e-10, 7.971472344684745e-10, 7.844056568346896e-10, 7.979437149185154e-10, 7.980422393636198e-10, 7.990720170108935e-10, 7.970410742958998e-10, 7.97018793957161e-10, 7.956195848829496e-10, 8.004119381549109e-10, 7.972656498101729e-10, 7.966864772687667e-10, 7.790114913438407e-10, 7.969479656000517e-10, 7.996934862896009e-10, 7.841333194332546e-10, 7.97034686449044e-10, 7.977992943579927e-10, 7.96762771694868e-10, 7.966966797283409e-10, 7.957027686461644e-10, 7.970077213244511e-10, 7.987547855356413e-10, 7.990928143485798e-10, 7.872294314913151e-10, 7.991282952126249e-10, 7.996996154320075e-10, 7.840188084382355e-10, 7.974592802090021e-10, 7.979831441559331e-10, 7.94313708313506e-10, 7.974202496222153e-10, 7.945769899770333e-10, 7.989189319332251e-10, 7.96391846920186e-10, 7.982638977817534e-10, 7.82989201718891e-10, 7.974257092665038e-10, 7.96637400681832e-10, 7.847531512165508e-10, 7.954547701859193e-10, 7.951978488429227e-10, 7.951657032060133e-10, 7.963988837735334e-10, 7.9666641848498e-10, 7.974257077249156e-10, 7.951288772463126e-10, 7.953641614139227e-10, 7.875991133163015e-10, 7.95915408669814e-10, 7.938317201604924e-10, 7.832400164007236e-10, 7.935808337220685e-10]
4 amu: [3.4531613676106733e-13, 3.3366166766220147e-13, 3.6988393114508855e-13, 5.961258499688195e-10, 5.970954234076243e-10, 3.3135943383048437e-13, 3.174663651862393e-11, 3.429288558679257e-13, 1.498399412104261e-11, 3.5220279314430447e-13, 2.5262369198935363e-11, 3.653210774058152e-13, 1.5874799493237576e-11, 3.7591848853645757e-13, 5.688803077892193e-10, 4.034124020003251e-13, 4.0035327970012827e-13, 6.042332602054686e-10, 1.4183267421644794e-11, 3.831671585218368e-13, 3.6760320465208133e-13, 2.3341252415085237e-12, 3.844970580704981e-13, 1.0571451687178263e-11, 3.8382660954355845e-13, 8.200382190821025e-12, 3.913148573404574e-13, 1.560203809184596e-09, 4.0489182829201056e-13, 3.795900104505717e-13, 6.042755762441724e-10, 1.3988539372116802e-12, 3.846049343112061e-13, 1.3319585168540297e-11, 3.9771840308213876e-13, 4.805999006071973e-12, 3.867074959999706e-13, 3.313577766561125e-12, 3.744314402797234e-13, 6.988886300943138e-10, 4.042693494216982e-13, 3.8217513835498493e-13, 6.043691789681499e-10, 5.944734086176057e-12, 3.7644022305327873e-13, 1.0931464175829169e-11, 3.821912123145932e-13, 5.821603916411063e-12, 3.853558180169586e-13, 6.074935756081214e-12, 3.761774399661647e-13, 1.0734844854098086e-09, 5.4860372258075055e-12, 3.7660101885287676e-13, 6.050900851245702e-10, 8.540715457007659e-12, 3.6749344852280326e-13, 8.384015787133257e-12, 3.7729690113938666e-13, 9.574894653551193e-12, 3.7085506394298535e-13, 3.2667374998333825e-12, 3.7503327170460714e-13, 5.528634421707689e-10, 3.802721615638516e-13, 3.6080139240454957e-13, 6.042719499645437e-10, 3.656337191419462e-13]
analysis number: [3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 3350, 3351, 3352, 3353, 3354, 3355, 3356]
3 amu: [2.993232809745656e-10, 2.758432308019711e-10, 2.7500800747963717e-10, 2.7309891076894257e-10, 2.4891889666588953e-10, 2.4017748982710046e-10, 2.4498267634135793e-10, 2.6695249088891075e-10, 2.697818888003866e-10, 2.7146816958418764e-10, 2.7134379274303456e-10, 2.715824008867223e-10, 2.7414563103702527e-10, 2.7582827916439875e-10, 2.747061461560547e-10, 2.7469316491596424e-10, 2.733921376055414e-10, 2.7485445834777047e-10, 2.7271860166605506e-10, 2.7440322167566896e-10, 2.7086236930879e-10, 2.7311954349770675e-10, 2.7200216558810403e-10, 2.743303626686615e-10, 2.651454063525448e-10, 2.7471636992180705e-10, 2.731570097334424e-10, 2.7277664283728946e-10, 2.685016315502734e-10, 2.7261991926158883e-10, 2.724281199854046e-10, 2.738517010536505e-10, 2.7140154617544906e-10, 2.7299974365340646e-10, 2.6096206203779177e-10, 2.7242167114922815e-10, 2.7108413210229964e-10, 2.717861550914157e-10, 2.7202408601173795e-10, 2.707864708041623e-10, 2.4940511841347725e-10, 2.461652614907221e-10, 2.4246508641506813e-10, 2.6521951097088415e-10, 2.672916209288258e-10, 2.6858653313129376e-10, 2.6979554808516567e-10, 2.676215807945852e-10, 2.701442584075416e-10, 2.6875091534724346e-10, 2.702144207500158e-10, 2.6932728761634265e-10, 2.6858993860787203e-10, 2.687085903398567e-10, 2.690223304534166e-10, 2.682607740755479e-10, 2.6735134462693204e-10, 2.686139942817035e-10, 2.684564201291062e-10, 2.691410875207599e-10, 2.629699754477367e-10, 2.6770128502575184e-10, 2.6755871596406563e-10, 2.676093792402415e-10, 2.668953077617681e-10, 2.6896299136178434e-10, 2.664378248537012e-10, 2.673890239282435e-10, 2.662775878835712e-10, 2.6944785152766334e-10, 2.6335368711754856e-10, 2.725970405733179e-10, 2.642439630403252e-10, 2.6778472172982503e-10, 2.696591097866928e-10, 2.713658459608838e-10, 2.4942324490500977e-10, 2.4534836885412227e-10, 2.450282527014461e-10, 2.634997426429196e-10, 2.6707617826498506e-10]
4 amu: [1.1778226488399289e-13, 1.1585969396306585e-13, 1.194103819842898e-13, 1.110306745185171e-13, 3.343506759203781e-10, 3.2415976000194466e-10, 3.282822362672445e-10, 1.1368210514297983e-13, 1.0784323455737277e-13, 1.2252633319139738e-13, 1.0337789671801992e-13, 1.1948118773957652e-13, 1.1530731069669136e-13, 1.087507763002924e-13, 1.0065382119863639e-13, 8.988573899103181e-14, 8.616948381805773e-14, 8.630813426522908e-14, 2.065211529647099e-11, 8.097864890969572e-14, 4.935261064431398e-11, 9.443768042736721e-14, 3.5429267630749507e-11, 9.370858756318766e-14, 1.4708677657728752e-10, 1.064393497146623e-13, 1.691462545564634e-11, 1.086172160780605e-13, 7.11236626150374e-11, 1.2198298032064658e-13, 2.572786927143115e-11, 1.1398954224042433e-13, 5.207922529362331e-11, 1.0626233693275609e-13, 1.5137372340521278e-10, 8.928064881900744e-14, 2.765965410143622e-11, 1.1904457541093595e-13, 1.2458065896252615e-13, 1.267490112546463e-13, 3.3468996648376433e-10, 3.297490557974959e-10, 3.2649394068634107e-10, 1.3033422865392657e-13, 1.3132583312101482e-13, 1.4267438105644652e-13, 1.1546736588819987e-13, 1.292593882627721e-13, 1.0988411045108127e-13, 1.1854053405701426e-13, 1.1156879563126661e-13, 1.1748508333343027e-13, 1.2530082584774972e-13, 1.330727013555199e-13, 1.9563760972579177e-11, 1.3928606813206969e-13, 4.590337788670679e-11, 1.201366376692417e-13, 1.1878442557653435e-11, 1.0688522317697435e-13, 1.0668920783160711e-10, 1.2092274513094857e-13, 4.0233200255329735e-11, 1.2085573595859198e-13, 4.429122526454737e-11, 1.284394024941915e-13, 7.461929082605818e-11, 1.0309329230748312e-13, 5.04149131491202e-11, 1.8194920452638716e-13, 5.668594243578721e-11, 1.2206938883881162e-13, 1.4093116652971717e-10, 1.206067135396686e-13, 1.0978170708248181e-13, 9.419702653975424e-14, 3.3434307587675236e-10, 3.290596125523293e-10, 3.288131176473908e-10, 1.282689820885239e-13, 1.225893324032757e-13]
analysis number: [6859, 6860, 6861, 6862, 6863, 6864, 6865, 6866, 6867, 6868, 6869, 6870, 6871, 6872, 6873, 6874, 6875, 6876, 6877, 6878, 6879, 6880, 6881, 6882, 6883, 6884, 6885, 6886, 6887, 6888, 6889, 6890, 6891, 6892, 6893, 6894, 6895, 6896, 6897, 6898, 6899, 6900, 6901, 6902, 6903, 6904, 6905, 6906, 6907, 6908, 6909, 6910, 6911, 6912, 6913, 6914, 6915, 6916, 6917, 6918, 6919, 6920, 6921, 6922, 6923, 6924, 6925, 6926, 6927, 6928, 6929, 6930, 6931, 6932, 6933, 6934, 6935, 6936, 6937, 6938, 6939, 6940, 6941, 6942, 6943, 6944, 6945, 6946, 6947, 6948, 6949, 6950, 6951, 6952, 6953, 6954, 6955, 6956, 6957, 6958, 6959, 6960, 6961, 6962, 6963, 6964, 6965, 6966, 6967, 6968, 6969, 6970, 6971, 6972, 6973, 6974, 6975, 6976, 6977, 6978, 6979, 6980, 6981, 6982, 6983, 6984, 6985, 6986, 6987, 6988, 6989, 6990, 6991, 6992, 6993, 6994, 6995, 6996, 6997, 6998, 6999, 7000, 7001, 7002, 7003, 7004, 7005, 7006, 7007, 7008, 7009, 7010, 7011, 7012, 7013, 7014, 7015, 7016, 7017, 7018, 7019, 7020, 7021, 7022, 7023, 7024, 7025, 7026, 7027, 7028, 7029, 7030, 7031, 7032, 7033, 7034, 7035, 7036, 7037, 7038, 7039, 7040, 7041, 7042, 7043, 7044, 7045, 7046, 7047, 7048, 7049, 7050]
3 amu: [3.6255764022151506e-10, 3.508510161840758e-10, 3.217814266815697e-10, 3.179376549891513e-10, 3.194778623624382e-10, 3.401444058291269e-10, 3.4223388678594747e-10, 3.440489401063371e-10, 3.441057437695379e-10, 3.425749620155861e-10, 3.435744386811953e-10, 3.4489191568630124e-10, 3.434716905499254e-10, 3.425260524167747e-10, 3.43461984597375e-10, 3.439188052414678e-10, 3.435774248953598e-10, 3.4383101118885907e-10, 3.449123916761429e-10, 3.4290760314430305e-10, 3.4280669764925373e-10, 3.4397652806580837e-10, 3.4461231511951843e-10, 3.437634944102224e-10, 3.4172525670125826e-10, 3.477274668516251e-10, 3.4958634673293644e-10, 3.490095226658467e-10, 3.4883622619984005e-10, 3.4827992864831115e-10, 3.484871000283174e-10, 3.4539380102373657e-10, 3.4949889360766894e-10, 3.461791015909947e-10, 3.473576066805718e-10, 3.4687587165429547e-10, 3.502428914546513e-10, 3.4661039108758977e-10, 3.476744036012117e-10, 3.4673375574695467e-10, 3.484904917692616e-10, 3.430785920617636e-10, 3.4719520295415734e-10, 3.460715206577883e-10, 3.485013280301459e-10, 3.425313275190909e-10, 3.450513766954601e-10, 3.44540303364892e-10, 3.459360571733889e-10, 3.4086939780074047e-10, 3.4551435852961704e-10, 3.4551965165372766e-10, 3.447387429296374e-10, 3.3539611321753234e-10, 3.473991794645757e-10, 3.4727868411658677e-10, 3.471920319378224e-10, 3.452501067141513e-10, 3.4313765813352933e-10, 3.452251201245261e-10, 3.4493446463194697e-10, 3.4717811582825653e-10, 3.4328004844544023e-10, 3.4196982494004094e-10, 3.4412315935490977e-10, 3.4466862719102705e-10, 3.47596219236958e-10, 3.4625275413097686e-10, 3.47132845098501e-10, 3.4547803433554077e-10, 3.4238740885210175e-10, 3.456655555868335e-10, 3.4816307833737724e-10, 3.4774824288539e-10, 3.473801573260447e-10, 3.433386138236303e-10, 3.4226474466968337e-10, 3.4224013535827093e-10, 3.429253350139061e-10, 3.429791155256504e-10, 3.389800568146646e-10, 3.387964758853137e-10, 3.43279299723862e-10, 3.417311237130251e-10, 3.4107453219714175e-10, 3.1616841428928924e-10, 3.1645565619827947e-10, 3.1606963934053716e-10, 3.3703103359216717e-10, 3.3857185026857926e-10, 3.403011739148351e-10, 3.3965642261787963e-10, 3.4224761009864215e-10, 3.403131541693085e-10, 3.407340254648663e-10, 3.416729431072837e-10, 3.4176817148726347e-10, 3.4000314727141564e-10, 3.4114803792419063e-10, 3.402940524124258e-10, 3.402685547806598e-10, 3.4253518896261156e-10, 3.390903832777625e-10, 3.4197493826295586e-10, 3.4278716482642597e-10, 3.3878884973446745e-10, 3.416973242779153e-10, 3.4199735705397183e-10, 3.4528719278713487e-10, 3.455919437079698e-10, 3.44611027806822e-10, 3.459704819427114e-10, 3.4518756948277017e-10, 3.450548418122571e-10, 3.455295753730432e-10, 3.4260222173453664e-10, 3.4419521838354026e-10, 3.453971532179556e-10, 3.453820797948062e-10, 3.459635300719046e-10, 3.4410455731363674e-10, 3.460494013265236e-10, 3.4648258817096355e-10, 3.486318647996109e-10, 3.408929854394461e-10, 3.422273781909444e-10, 3.437119121872867e-10, 3.4624646576825474e-10, 3.261418415733458e-10, 3.439730461327148e-10, 3.4718673165724445e-10, 3.423200582333211e-10, 3.430154826767904e-10, 3.4324072674119334e-10, 3.458457865506733e-10, 3.452066918463927e-10, 3.429010947143837e-10, 3.461007265192867e-10, 3.4424749735859486e-10, 3.448006688012594e-10, 3.458284856407212e-10, 3.4420381107170645e-10, 3.424458220889927e-10, 3.4198377980417427e-10, 3.4329421592589523e-10, 3.430758917157396e-10, 3.422898688710079e-10, 3.449468653388248e-10, 3.434908034990462e-10, 3.444671373451212e-10, 3.4387857291249254e-10, 3.4582875178117944e-10, 3.4418676540293166e-10, 3.432756865571895e-10, 3.4572690964747247e-10, 3.434853534507701e-10, 3.454413458278558e-10, 3.4710999354880977e-10, 3.4265161735350964e-10, 3.396879937980639e-10, 3.366602886636423e-10, 3.391096555459298e-10, 3.401192119060491e-10, 3.3720408846535306e-10, 3.3693816651527765e-10, 3.3590043834572743e-10, 3.3627056281641927e-10, 3.3958849119392304e-10, 3.1615597804003225e-10, 3.1171008739236775e-10, 3.137278712787108e-10, 3.1262213841779304e-10, 3.1150763658181847e-10, 3.1198696830524167e-10, 3.094293018984173e-10, 3.3313476728492545e-10, 3.3634960209093403e-10, 3.1138057893085315e-10, 3.325633407288151e-10, 3.1173323313760973e-10, 3.3312770858031297e-10, 3.1192969441473545e-10, 3.336159228867155e-10, 3.1351583525732356e-10, 3.348838746937062e-10, 3.108374904052273e-10, 3.340030639317837e-10, 3.1104279821773107e-10, 3.3260851296317647e-10, 3.110176857863856e-10, 3.3455048003228917e-10, 3.354825534291982e-10]
4 amu: [3.3101361978669214e-14, 4.146407133070773e-14, 3.8464600151370457e-10, 3.7963540805461484e-10, 3.8222815769902544e-10, 7.316644418396674e-14, 5.18292075607939e-14, 4.4366476617626473e-14, 4.4766944262047194e-14, 5.60781643502124e-14, 3.882287433469317e-14, 3.369855206340818e-14, 4.041942883722857e-14, 5.0717494307246745e-14, 4.917725215040309e-14, 3.4327442463349075e-14, 4.7628251245258705e-14, 3.704984089120418e-14, 3.637035082699088e-14, 4.331504500036978e-14, 3.584480311668591e-14, 4.0188425740746565e-14, 4.521133060708128e-14, 3.967489159883654e-14, 4.7297310164724074e-14, 4.302990037294614e-14, 3.3454929600493866e-14, 5.822706353885703e-14, 4.073999885580924e-14, 5.214789428758753e-14, 5.041742932561961e-14, 4.042398006519017e-14, 4.148910745335829e-14, 5.747826405197776e-14, 4.2689319703184144e-14, 3.2631935556374465e-14, 4.7572963933387944e-14, 2.634205411137258e-11, 2.5257412136927374e-14, 4.3735104441346613e-14, 4.889800583281691e-14, 2.2352831080115307e-11, 4.0536792322871984e-14, 5.0783532591792995e-14, 5.3982005182701933e-14, 6.66156159607468e-11, 5.752026924290862e-14, 4.8363496375356645e-14, 4.4263841568911176e-14, 7.680922498153327e-11, 4.577275293657866e-14, 3.6343975307978394e-14, 4.830266547786961e-14, 1.3217493362975924e-10, 5.691012936221051e-14, 4.624805551981382e-14, 5.191044431642304e-14, 7.35598046588805e-14, 4.032273723346593e-14, 5.475821830681722e-14, 3.572362676067935e-14, 4.53792267029052e-14, 4.811150381617244e-14, 4.18870247568556e-14, 5.269425371163631e-14, 4.749954821050258e-14, 3.659440562889052e-14, 4.0618464298095687e-14, 2.457723337204267e-14, 5.17645245024611e-14, 3.028353821051941e-14, 3.8090818295311995e-14, 4.0785927578973433e-14, 2.8305244090869045e-14, 4.241041689114752e-14, 4.11345055897064e-14, 4.2660570038734026e-14, 4.043589749262442e-14, 3.248775113507995e-14, 3.579286664449709e-14, 4.837611831081787e-14, 3.1654015572088e-14, 3.578682399679274e-14, 2.8659530832379557e-14, 3.7500902793910864e-14, 3.7910551589975395e-10, 3.8001259116141904e-10, 3.7917414959777875e-10, 6.919239229840155e-14, 4.638295045447225e-14, 4.2281261745635005e-14, 4.689993397406153e-14, 4.145679893439644e-14, 5.301270362402919e-14, 5.54318765004603e-14, 2.889297680780083e-14, 2.2165609621229645e-14, 6.552388545157717e-16, 4.1485735572339217e-14, 4.180138910440657e-14, 4.4891456417402014e-14, 4.436565493115589e-14, 6.45665060306906e-14, 4.3465977067901715e-14, 4.6683688055107376e-14, 3.8500651765732604e-14, 3.11936705001375e-14, 3.0385240224120554e-14, 4.320332364320882e-14, 3.2078816198818235e-14, 4.158664276801585e-14, 3.7535506365951966e-14, 4.618522896670219e-14, 3.690459532838156e-14, 5.048828597118978e-14, 2.925271758588507e-14, 2.5413549811533986e-14, 4.9393102062324443e-14, 4.657551007595595e-14, 3.94134839225784e-14, 1.7427666865630518e-11, 2.1353374163224927e-14, 5.610865680587635e-14, 3.264729990705068e-14, 6.069825759162198e-11, 4.67248561610634e-14, 4.15335284559848e-14, 5.1439924765759663e-14, 2.4147614489828565e-10, 4.8014476530530357e-14, 6.285631018121028e-14, 4.1762026240590943e-14, 8.077915690862838e-12, 4.276969119633478e-14, 1.6556310800242732e-14, 4.8000055585905586e-14, 2.8866036952655548e-11, 4.0328744198179854e-14, 4.980894462203276e-14, 4.106879860099725e-14, 5.1096309070337053e-14, 3.020088699257153e-14, 3.2657773289848625e-14, 5.2618974165599034e-14, 4.502629377009243e-14, 2.893613996870109e-14, 3.677504465995457e-14, 3.71930615926864e-14, 2.7404005154562947e-14, 3.9521121796552014e-14, 4.0545310857880814e-14, 2.8390214328469127e-14, 4.124354881093567e-14, 4.9514233184564065e-14, 4.720026077121709e-14, 4.107593530984168e-14, 4.560105491515524e-14, 3.9012756458184725e-14, 4.7409714785179807e-14, 3.727409729275244e-14, 4.78755482287444e-14, 4.5461439431259405e-14, 2.3543509362318603e-14, 3.5079202249607776e-14, 3.9289578578539414e-14, 4.1378692858654526e-14, 2.666006418858889e-14, 5.1138270939919936e-14, 3.825896960099374e-10, 3.786718269713149e-10, 3.808311043196966e-10, 3.7943461684820726e-10, 3.778783725761114e-10, 3.7916225638860694e-10, 3.7465904378822767e-10, 7.361306857492091e-14, 6.550083181745619e-14, 3.7718206905798687e-10, 6.188546465519851e-14, 3.764141728416682e-10, 5.919675518997156e-14, 3.785038369646022e-10, 6.641770717734108e-14, 3.806240038986748e-10, 5.728379344637129e-14, 3.769801139051104e-10, 5.869522147391884e-14, 3.7689230408369244e-10, 5.658865207851127e-14, 3.779555026303843e-10, 5.522906103262253e-14, 5.363501621434117e-14]
