Problem 1¶
Get familiar with real genetic gate designs by working through the following code.
Show hint
Have fun reading and playing with the code :)
In [61]:
from urllib.request import urlopen
import json
import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt
%matplotlib inline
figsize=(6, 4.5)
Obtaining model and experimental data¶
Cello is a genetic circuit compiler.
It compiles circuits written in a hardare description language (a sublanguage of Verilog) into
NOR and NOT gates, to then finally generate DNA with the genetic circuit in it.
Check out the paper by Nielsen et al. for a description of the compiler.
We will use modeling and experimental data from the Cello v2 compiler in the form of a user constraint file (UCF). Let's load it into a variable so that we can work with it.
In [62]:
def github_to_raw(url: str) -> str:
"""
Convert a GitHub file URL to its corresponding raw.githubusercontent.com URL.
Example:
https://github.com/user/repo/blob/branch/path/to/file
-> https://raw.githubusercontent.com/user/repo/branch/path/to/file
"""
if not url.startswith("https://github.com/"):
raise ValueError("Not a valid GitHub URL")
parts = url.replace("https://github.com/", "").split("/")
try:
user, repo, blob, branch = parts[:4]
path = "/".join(parts[4:])
except ValueError:
raise ValueError("Unexpected GitHub URL format")
if blob != "blob":
raise ValueError("URL must contain 'blob' to specify a branch")
raw_url = f"https://raw.githubusercontent.com/{user}/{repo}/{branch}/{path}"
return raw_url
# fetch it form this url
# url = "https://github.com/CIDARLAB/Cello-UCF/blob/develop/files/v2/ucf/Eco/Eco1C1G1T1.UCF.json"
url = "https://github.com/CIDARLAB/Cello-UCF/blob/develop/files/v2/ucf/Eco/Eco1C2G2T2.UCF.json"
# get & parse
response = urlopen(github_to_raw(url))
ucf_data = json.loads(response.read())
# if stored locally use this:
#
# with open('Eco1C1G1T1.UCF.json','r') as f:
# s = f.read()
# ucf_data = json.loads(s)
And check out what is inside. It is a list that starts with a header that includes general information from the used bacteria to experimental conditions under which data was obtained:
In [63]:
from pprint import pprint
pprint(ucf_data[0])
{'author': ['Jonghyeon Shin', 'Shuyi Zhang', 'Timothy Jones'],
'collection': 'header',
'date': 'Mon Jun 17 14:13:20 EDT 2019',
'description': 'TetR homologs: PhlF, SrpR, BM3R1, HlyIIR, BetI, AmtR, AmeR, '
'QacR, IcaRA',
'genome': 'NEB 10 ∆(ara-leu) 7697 araD139 fhuA ∆lacX74 galK16 galE15 e14- '
'φ80dlacZ∆M15 recA1 relA1 endA1 nupG rpsL (StrR) rph spoT1 '
'∆(mrr-hsdRMS-mcrBC)',
'growth': 'Inoculation: Individual colonies into M9 media, 16 hours overnight '
'in plate shaker. Dilution: Next day, cells dilute ~200-fold into '
'M9 media with antibiotics, growth for 3 hours. Induction: Cells '
'diluted ~650-fold into M9 media with antibiotics. Growth: shaking '
'incubator for 5 hours. Arrest protein production: PBS and 2 mg/ml '
'kanamycin. Measurement: flow cytometry, data processing for RPU '
'normalization.',
'media': 'M9 minimal media composed of M9 media salts (6.78 g/L Na2HPO4, 3 '
'g/L KH2PO4, 1 g/L NH4Cl, 0.5 g/L NaCl, 0.34 g/L thiamine '
'hydrochloride, 0.4% D-glucose, 0.2% Casamino acids, 2 mM MgSO4, and '
'0.1 mM CaCl2; kanamycin (50 μg/ml), spectinomycin (50 μg/ml)',
'organism': 'Escherichia coli NEB 10-beta',
'temperature': '37',
'version': 'Eco1C2G2T2'}
To get an overview on all the elements stored in the UCF file, let's see the collection names for all entries. These describe the type of the item. Since the list is quite long, we compact it into a set to remove multiples.
In [64]:
pprint(set([d['collection'] for d in ucf_data]))
{'circuit_rules',
'device_rules',
'functions',
'gates',
'genetic_locations',
'header',
'logic_constraints',
'measurement_std',
'models',
'motif_library',
'parts',
'structures'}
A NOR gate from the library¶
The library contains gates as can be seen in the collection variables.
In [65]:
gates_lib = [d for d in ucf_data if d['collection'] == 'gates']
gate_names = map(lambda x: x["name"], gates_lib[:100])
print(f"There are {len(gates_lib)} gates. in this library. Their names are:")
pprint(list(gate_names))
There are 18 gates. in this library. Their names are: ['P3_PhlF', 'S2_SrpR', 'B3_BM3R1', 'A1_AmtR', 'H1_HlyIIR', 'E1_BetI', 'F2_AmeR', 'N1_LmrA', 'B1_BM3R1', 'B2_BM3R1', 'P1_PhlF', 'P2_PhlF', 'S1_SrpR', 'S3_SrpR', 'S4_SrpR', 'F1_AmeR', 'C1_CymR', 'V1_VanR']
Let's pick a gate in the list and show some info on it.
In [66]:
gate_name = 'A1_AmtR'
# uncomment to try another gate
# gate_name = 'S1_SrpR'
gate = [g for g in gates_lib if g['name'] == gate_name][0]
pprint(gate)
{'collection': 'gates',
'color': '3BA9E0',
'gate_type': 'NOR',
'group': 'AmtR',
'model': 'A1_AmtR_model',
'name': 'A1_AmtR',
'regulator': 'AmtR',
'structure': 'A1_AmtR_structure',
'system': 'TetR'}
In fact all gates are NOR gates as we can check. This is not too surprising as we discussed in the lecture that NOR gates are particularly nice to implement as genetic components.
In [67]:
# check is all gates are NOR
all([g['gate_type'] == 'NOR' for g in gates_lib])
Out[67]:
True
Structure of the gate¶
It's structure, i.e., the genetic design, is obtained as follows:
In [68]:
structure_lib = [d for d in ucf_data if d['collection'] == 'structures']
print(f"There are {len(structure_lib)} structures in the dataset.\n")
# find matching structure for the chosen gate
structure = [s for s in structure_lib if s['name'] == gate['structure']][0]
pprint(structure)
There are 18 structures in the dataset.
{'collection': 'structures',
'devices': [{'components': ['#in2', '#in1', 'A1_AmtR_cassette'],
'name': 'A1_AmtR'},
{'components': ['BydvJ', 'A1', 'AmtR', 'L3S2P55'],
'name': 'A1_AmtR_cassette'}],
'inputs': [{'name': 'in1', 'part_type': 'promoter'},
{'name': 'in2', 'part_type': 'promoter'}],
'name': 'A1_AmtR_structure',
'outputs': ['pAmtR']}
The structure sounds familiar from the lecture:
It is a tandem promoter
NORgate with two input promotersin1andin2(seeinputs) followed by aA1_AmtR_cassette(a sequence of genetic parts). Just mind that the left input promoter that is potentially affected by roadblock is#in2(ourPAfrom the course) and the right one#in1and not vice versa.The gate's output is the
pAmtRpromoter (seeoutputs).
Let's take a look at the components used in the A1_AmtR_cassette.
In [69]:
parts = ['BydvJ', 'A1', 'AmtR', 'L3S2P55']
parts_lib = [d for d in ucf_data if d['collection'] == 'parts' and d["name"] in parts]
pprint(parts_lib)
[{'collection': 'parts',
'dnasequence': 'agGGTGTCTCAAGGTGCGTACCTTGACTGATGAGTCCGAAAGGACGAAACACCcctctacaaataattttgtttaa',
'name': 'BydvJ',
'type': 'ribozyme'},
{'collection': 'parts',
'dnasequence': 'AATGTTCCCTAATAATCAGCAAAGAGGTTACTAG',
'name': 'A1',
'type': 'rbs'},
{'collection': 'parts',
'dnasequence': 'ATGGCAGGCGCAGTTGGTCGTCCGCGTCGTAGTGCACCGCGTCGTGCAGGTAAAAATCCGCGTGAAGAAATTCTGGATGCAAGCGCAGAACTGTTTACCCGTCAGGGTTTTGCAACCACCAGTACCCATCAGATTGCAGATGCAGTTGGTATTCGTCAGGCAAGCCTGTATTATCATTTTCCGAGCAAAACCGAAATCTTTCTGACCCTGCTGAAAAGCACCGTTGAACCGAGCACCGTTCTGGCAGAAGATCTGAGCACCCTGGATGCAGGTCCGGAAATGCGTCTGTGGGCAATTGTTGCAAGCGAAGTTCGTCTGCTGCTGAGCACCAAATGGAATGTTGGTCGTCTGTATCAGCTGCCGATTGTTGGTAGCGAAGAATTTGCAGAATATCATAGCCAGCGTGAAGCACTGACCAATGTTTTTCGTGATCTGGCAACCGAAATTGTTGGTGATGATCCGCGTGCAGAACTGCCGTTTCATATTACCATGAGCGTTATTGAAATGCGTCGCAATGATGGTAAAATTCCGAGTCCGCTGAGCGCAGATAGCCTGCCGGAAACCGCAATTATGCTGGCAGATGCAAGCCTGGCAGTTCTGGGTGCACCGCTGCCTGCAGATCGTGTTGAAAAAACCCTGGAACTGATTAAACAGGCAGATGCAAAATAA',
'name': 'AmtR',
'type': 'cds'},
{'collection': 'parts',
'dnasequence': 'CTCGGTACCAAAGACGAACAATAAGACGCTGAAAAGCGTCTTTTTTCGTTTTGGTCC',
'name': 'L3S2P55',
'type': 'terminator'}]
The tandem input promoters drive a construct that comprises of: a ribozyme, an RBS, a CDS for the repressor AmtR, and a terminator.
Somewhere, and not necessarily after this first construct, is the output promoter pAmtR that is repressed by AmtR. This promoter can be an input of another gate, or be directly driving a reporter gene, e.g., a CDS that expresses GFP.
Model of the gate¶
We can also obtain a model for the gate from the library.
In [70]:
model_lib = [d for d in ucf_data if d['collection'] == 'models']
model = [m for m in model_lib if m['name'] == gate['model']][0]
pprint(model)
{'collection': 'models',
'functions': {'cytometry': 'A1_AmtR_cytometry',
'input_composition': 'tandem_input_composition',
'response_function': 'Hill_response',
'tandem_interference_factor': 'tandem_interference_factor',
'toxicity': 'A1_AmtR_toxicity'},
'name': 'A1_AmtR_model',
'parameters': [{'description': 'Maximal transcription',
'name': 'ymax',
'value': 3.13661101},
{'description': 'Minimal transcription',
'name': 'ymin',
'value': 0.035221608},
{'description': 'Half-maximum',
'name': 'K',
'value': 0.047427884},
{'description': 'Cooperativety',
'name': 'n',
'value': 1.656171138},
{'description': 'Tandem factor',
'name': 'alpha',
'value': 0.274797631},
{'description': 'Tandem factor', 'name': 'beta', 'value': 1.0},
{'description': 'Kinetics parameter (induction)',
'name': 'tau_on',
'value': 0.9},
{'description': 'Kinetics parameter (relaxation)',
'name': 'tau_off',
'value': 2.5}]}
It says that a Hill response_function is used as a model with the additional specification that the inputs are composed via a tandem_input_composition. We will check this out by looking into the collection of functions. Indeed the first entries are what we where looking for. The next (third) entry looks like experimental data, and we will come back to it later.
Side note: While we will not use it in this Problem Session, observe that the $\alpha$ and $\beta$ are set to account for static roadblocking only; in this gate at least.
In [71]:
functions_lib = [d for d in ucf_data if d['collection'] == 'functions']
print('The first two elements describe these theoretical models:\n')
pprint(functions_lib[0])
print()
pprint(functions_lib[1])
print()
pprint(functions_lib[2])
The first two elements describe these theoretical models:
{'collection': 'functions',
'equation': 'ymin + (ymax - ymin) / (1.0 + (x / K)^n)',
'name': 'Hill_response',
'parameters': [{'map': '#//model/parameters/ymax', 'name': 'ymax'},
{'map': '#//model/parameters/ymin', 'name': 'ymin'},
{'map': '#//model/parameters/K', 'name': 'K'},
{'map': '#//model/parameters/n', 'name': 'n'}],
'variables': [{'map': '#//model/functions/input_composition', 'name': 'x'}]}
{'collection': 'functions',
'equation': 't1 * x2 + x1',
'name': 'tandem_input_composition',
'variables': [{'map': '#//structure/inputs/in1/model/functions/response_function',
'name': 'x1'},
{'map': '#//structure/inputs/in2/model/functions/response_function',
'name': 'x2'},
{'map': '#//structure/inputs/in1/model/functions/tandem_interference_factor',
'name': 't1'}]}
{'collection': 'functions',
'equation': 'alpha * (K^n + beta * x^n) / (K^n + x^n)',
'name': 'tandem_interference_factor',
'parameters': [{'map': '#//model/parameters/alpha', 'name': 'alpha'},
{'map': '#//model/parameters/beta', 'name': 'beta'},
{'map': '#//model/parameters/K', 'name': 'K'},
{'map': '#//model/parameters/n', 'name': 'n'}],
'variables': [{'map': '#//model/functions/input_composition', 'name': 'x'}]}
Again the functions are familiar from the lecture.
Transfer Characteristics of the Gate¶
In [72]:
params = {}
for p in model['parameters']:
params[p['name']] = np.float64(p['value'])
print(f"{p['name']}: {p['value']}")
def inv(x):
return params['ymin'] + (params['ymax'] - params['ymin']) / (1.0 + (x / params['K'])**params['n'])
def nor(x, y):
inputs = x + y # linear input combination
return inv(inputs)
def contour_fun(x, y, z, title=None):
"""
Make a filled contour plot given x, y, z
in 2D arrays.
"""
plt.figure()
CS = plt.contourf(x, y, z)
cbar = plt.colorbar(CS)
if title is not None:
plt.title(title)
def contour_fun(x, y, z, title=None):
"""
Make a filled contour plot given x, y, z
in 2D arrays.
"""
plt.figure()
CS = plt.contourf(x, y, z)
cbar = plt.colorbar(CS)
if title is not None:
plt.title(title)
# Get x and y values for plotting
x = np.linspace(0, 0.1, 200)
y = np.linspace(0, 0.1, 200)
xx, yy = np.meshgrid(x, y)
# plot it
contour_fun(
xx, yy,
nor(xx, yy),
title=f"{gate_name} gate"
)
ymax: 3.13661101 ymin: 0.035221608 K: 0.047427884 n: 1.656171138 alpha: 0.274797631 beta: 1.0 tau_on: 0.9 tau_off: 2.5
Measurements¶
Intrestingly there are even measurments that give much greater detail. Remember that the steady state input-output behavior is deterministic with Hill functions. In fact, measurments show that there is significant noise on output behavior.
To see this, let's look at measurements: The measurements are (normalized) histograms of steady-state input-output measurements in terms of Relative Promotor Units (RPUs). Details are described in the supplementary material of Nielsen et al.. For example, Figure S30 shows how distributions are probagated and Section VII.C.9. “gate_cytometry” states that RPUs in UCFs are measured on the same RPU scale to allow for propagation between gates.
Let's plot the response distribution for 3 inputs to such a component and to be sure check if it is already normalized to be a distribution.
In [73]:
pprint([f["name"] for f in functions_lib])
['Hill_response', 'tandem_input_composition', 'tandem_interference_factor', 'P3_PhlF_toxicity', 'S2_SrpR_toxicity', 'B3_BM3R1_toxicity', 'A1_AmtR_toxicity', 'H1_HlyIIR_toxicity', 'E1_BetI_toxicity', 'F2_AmeR_toxicity', 'N1_LmrA_toxicity', 'B1_BM3R1_toxicity', 'B2_BM3R1_toxicity', 'P1_PhlF_toxicity', 'P2_PhlF_toxicity', 'S1_SrpR_toxicity', 'S3_SrpR_toxicity', 'S4_SrpR_toxicity', 'F1_AmeR_toxicity', 'C1_CymR_toxicity', 'V1_VanR_toxicity', 'P3_PhlF_cytometry', 'S2_SrpR_cytometry', 'B3_BM3R1_cytometry', 'A1_AmtR_cytometry', 'H1_HlyIIR_cytometry', 'E1_BetI_cytometry', 'F2_AmeR_cytometry', 'N1_LmrA_cytometry', 'B1_BM3R1_cytometry', 'B2_BM3R1_cytometry', 'P1_PhlF_cytometry', 'P2_PhlF_cytometry', 'S1_SrpR_cytometry', 'S3_SrpR_cytometry', 'S4_SrpR_cytometry', 'F1_AmeR_cytometry', 'C1_CymR_cytometry', 'V1_VanR_cytometry']
In [74]:
gate_cytometry_name = f"{gate_name}_cytometry"
gate_cytometry = [f for f in functions_lib if f["name"] == gate_cytometry_name][0]
pprint(gate_cytometry)
name = gate_cytometry['name']
measurements = gate_cytometry['table']
plt.figure(figsize=figsize)
plt.title(name)
plt.xlabel('RPU (consistent over all distributions)')
# Show some distributions
d = measurements[0]
plt.plot(d['bin'], d['output'], 'ro-', label=d['x'])
middle = int( len(measurements) / 2 )
d = measurements[middle]
plt.plot(d['bin'], d['output'], 'go-', label=d['x'])
d = measurements[-1]
plt.plot(d['bin'], d['output'], 'bo-', label=d['x'])
ax = plt.gca()
ax.set_xlim(0, 50)
plt.legend()
# Let's check if the last one was really a distribution
print(f"Checking if distribution. This should be 1: {sum(d['output'])}")
{'collection': 'functions',
'name': 'A1_AmtR_cytometry',
'table': [{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
5.005005005005005e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
7.507507507507507e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
5.005005005005005e-05,
0.0,
0.0,
0.0,
0.0,
0.00032532532532532533,
0.0,
0.0,
0.0,
0.00022522522522522523,
0.0,
0.0,
0.00012512512512512512,
0.0,
0.0,
0.00012512512512512512,
0.0,
2.5025025025025026e-05,
0.0,
7.507507507507507e-05,
0.0,
0.00017517517517517516,
0.0,
5.005005005005005e-05,
0.0001001001001001001,
0.0,
0.00015015015015015014,
5.005005005005005e-05,
7.507507507507507e-05,
5.005005005005005e-05,
0.0001001001001001001,
0.00022522522522522523,
7.507507507507507e-05,
7.507507507507507e-05,
0.00015015015015015014,
0.0002002002002002002,
0.00012512512512512512,
0.00022522522522522523,
0.0001001001001001001,
7.507507507507507e-05,
0.00017517517517517516,
0.00022522522522522523,
0.0002002002002002002,
0.00017517517517517516,
0.00015015015015015014,
0.00015015015015015014,
0.0001001001001001001,
0.00022522522522522523,
0.00012512512512512512,
0.00017517517517517516,
0.0002002002002002002,
5.005005005005005e-05,
0.00017517517517517516,
0.00012512512512512512,
0.00012512512512512512,
0.0,
5.005005005005005e-05,
0.0001001001001001001,
0.00015015015015015014,
2.5025025025025026e-05,
0.00012512512512512512,
2.5025025025025026e-05,
0.0001001001001001001,
0.0001001001001001001,
0.00015015015015015014,
7.507507507507507e-05,
5.005005005005005e-05,
0.0001001001001001001,
0.00015015015015015014,
0.00015015015015015014,
0.00012512512512512512,
0.00017517517517517516,
0.00017517517517517516,
0.0002752752752752753,
0.00012512512512512512,
0.0003003003003003003,
0.00022522522522522523,
0.0003503503503503503,
0.00015015015015015014,
0.00045045045045045046,
0.0002752752752752753,
0.0004254254254254254,
0.00045045045045045046,
7.507507507507507e-05,
0.00022522522522522523,
0.0002752752752752753,
0.0002002002002002002,
0.00017517517517517516,
0.0004004004004004004,
0.0002002002002002002,
0.0005755755755755755,
0.0004254254254254254,
0.00025025025025025025,
0.0004004004004004004,
0.00022522522522522523,
0.0006256256256256256,
0.0002002002002002002,
0.00032532532532532533,
0.00037537537537537537,
0.00037537537537537537,
0.00037537537537537537,
0.0007507507507507507,
0.0007257257257257257,
0.0009009009009009009,
0.0006506506506506507,
0.001076076076076076,
0.001076076076076076,
0.0012012012012012011,
0.001926926926926927,
0.0021271271271271273,
0.0036536536536536535,
0.004454454454454454,
0.005755755755755756,
0.007857857857857857,
0.011586586586586586,
0.01644144144144144,
0.02122122122122122,
0.026201201201201202,
0.03308308308308308,
0.03978978978978979,
0.04389389389389389,
0.04844844844844845,
0.05322822822822823,
0.057482482482482486,
0.05945945945945946,
0.05908408408408408,
0.05680680680680681,
0.05618118118118118,
0.04994994994994995,
0.04622122122122122,
0.04091591591591592,
0.03808808808808809,
0.03175675675675676,
0.029779779779779778,
0.022247247247247248,
0.01896896896896897,
0.01493993993993994,
0.013288288288288288,
0.010135135135135136,
0.008683683683683684,
0.0075075075075075074,
0.005805805805805806,
0.005530530530530531,
0.0038038038038038036,
0.0035035035035035035,
0.0023773773773773776,
0.0021271271271271273,
0.002177177177177177,
0.0016266266266266266,
0.0008508508508508508,
0.001151151151151151,
0.001001001001001001,
0.0005755755755755755,
0.0008508508508508508,
0.0006006006006006006,
0.00045045045045045046,
0.0003503503503503503,
0.00037537537537537537,
0.00037537537537537537,
0.0003503503503503503,
0.0002752752752752753,
0.00025025025025025025,
0.00025025025025025025,
0.00017517517517517516,
0.00037537537537537537,
0.0002002002002002002,
0.00022522522522522523,
0.00015015015015015014,
7.507507507507507e-05,
0.0001001001001001001,
5.005005005005005e-05,
5.005005005005005e-05,
2.5025025025025026e-05,
5.005005005005005e-05,
2.5025025025025026e-05,
0.0001001001001001001,
2.5025025025025026e-05,
2.5025025025025026e-05,
0.0,
5.005005005005005e-05,
0.0,
0.0,
2.5025025025025026e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.5025025025025026e-05,
0.0,
0.0,
0.0,
2.5025025025025026e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.006424},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.00022503262973131105,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.00011251631486565553,
0.0,
0.0,
0.0,
0.0,
0.0,
0.00015752284081191773,
0.0,
0.0,
0.0,
0.0,
0.00018002610378504882,
0.0,
0.0,
0.0,
9.001305189252441e-05,
0.0,
0.0,
0.00020252936675817994,
0.0,
0.0,
0.00011251631486565553,
0.0,
0.00013501957783878662,
0.0,
0.00015752284081191773,
0.0,
0.00022503262973131105,
0.0,
0.00011251631486565553,
0.00022503262973131105,
0.0,
0.00011251631486565553,
9.001305189252441e-05,
0.00018002610378504882,
6.750978891939331e-05,
9.001305189252441e-05,
6.750978891939331e-05,
0.00011251631486565553,
9.001305189252441e-05,
0.00013501957783878662,
9.001305189252441e-05,
4.5006525946262205e-05,
0.00015752284081191773,
9.001305189252441e-05,
0.00020252936675817994,
0.00011251631486565553,
9.001305189252441e-05,
0.00022503262973131105,
9.001305189252441e-05,
4.5006525946262205e-05,
0.00013501957783878662,
0.00013501957783878662,
9.001305189252441e-05,
9.001305189252441e-05,
0.00013501957783878662,
0.00018002610378504882,
6.750978891939331e-05,
9.001305189252441e-05,
0.00013501957783878662,
9.001305189252441e-05,
4.5006525946262205e-05,
9.001305189252441e-05,
2.2503262973131103e-05,
6.750978891939331e-05,
0.0,
4.5006525946262205e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
0.0,
4.5006525946262205e-05,
4.5006525946262205e-05,
4.5006525946262205e-05,
0.0,
2.2503262973131103e-05,
2.2503262973131103e-05,
6.750978891939331e-05,
4.5006525946262205e-05,
0.0,
0.00011251631486565553,
2.2503262973131103e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
6.750978891939331e-05,
6.750978891939331e-05,
0.00011251631486565553,
0.00018002610378504882,
0.00015752284081191773,
0.00018002610378504882,
0.00022503262973131105,
0.00036005220757009764,
0.00018002610378504882,
0.00018002610378504882,
0.00029254241865070435,
0.00029254241865070435,
0.00038255547054322876,
0.00031504568162383546,
0.00031504568162383546,
0.00029254241865070435,
0.0005850848373014087,
0.000652594626220802,
0.0009001305189252442,
0.0007651109410864575,
0.0012601827264953418,
0.0011026598856834241,
0.0014177055673072596,
0.0013501957783878663,
0.002002790404608668,
0.0024978621900175525,
0.00326297313110401,
0.004320626490841172,
0.0054232863765245965,
0.007831135514649624,
0.010554030334398487,
0.014762140510374003,
0.01856519195283316,
0.0225707727620505,
0.02853413744993024,
0.03479004455646069,
0.03868310905081237,
0.04399387911247131,
0.049417165488995905,
0.05358026913902516,
0.05632566722174715,
0.05576308564741887,
0.056775732481209776,
0.05688824879607543,
0.0515099689454971,
0.047751924028984205,
0.04361132364192808,
0.04084342229623295,
0.03515009676403078,
0.03019937890994194,
0.026463837256402178,
0.021715648769071515,
0.01894774742337639,
0.01590980692200369,
0.012151762005490795,
0.010959089067914847,
0.00978891939331203,
0.007426076781133264,
0.006210900580584185,
0.00510824069490076,
0.004185606913002385,
0.0042981232278680405,
0.003285476394077141,
0.002767901345695126,
0.0024528556640712905,
0.0018227643008236194,
0.0014402088302803906,
0.001507718619199784,
0.0013952023043341285,
0.0011476664116296864,
0.0009226337818983752,
0.0009901435708177687,
0.0007201044151401953,
0.0007201044151401953,
0.00038255547054322876,
0.0004500652594626221,
0.0005400783113551465,
0.00036005220757009764,
0.00040505873351635987,
0.00038255547054322876,
0.00018002610378504882,
0.00027003915567757323,
0.00024753589270444217,
0.00031504568162383546,
0.00022503262973131105,
9.001305189252441e-05,
4.5006525946262205e-05,
0.00015752284081191773,
4.5006525946262205e-05,
2.2503262973131103e-05,
4.5006525946262205e-05,
2.2503262973131103e-05,
2.2503262973131103e-05,
4.5006525946262205e-05,
6.750978891939331e-05,
0.0,
0.0,
2.2503262973131103e-05,
0.0,
0.0,
0.0,
2.2503262973131103e-05,
0.0,
0.0,
0.0,
2.2503262973131103e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.016211},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
7.528136409831747e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
7.528136409831747e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.000207023751270373,
0.0,
0.0,
0.0,
0.0,
7.528136409831747e-05,
0.0,
0.0,
0.0,
7.528136409831747e-05,
0.0,
0.0,
9.410170512289682e-05,
0.0,
0.0,
0.0001693830692212143,
0.0,
0.00018820341024579365,
0.0,
0.0001129220461474762,
0.0,
0.00013174238717205555,
0.0,
3.7640682049158734e-05,
5.64610230737381e-05,
0.0,
5.64610230737381e-05,
9.410170512289682e-05,
7.528136409831747e-05,
0.0001129220461474762,
9.410170512289682e-05,
0.00015056272819663494,
3.7640682049158734e-05,
9.410170512289682e-05,
0.00013174238717205555,
3.7640682049158734e-05,
0.0001129220461474762,
9.410170512289682e-05,
5.64610230737381e-05,
0.00015056272819663494,
0.0,
0.00013174238717205555,
0.0001129220461474762,
9.410170512289682e-05,
0.0001129220461474762,
0.0001129220461474762,
1.8820341024579367e-05,
0.00024466443331953175,
9.410170512289682e-05,
0.00013174238717205555,
0.0002258440922949524,
0.00013174238717205555,
5.64610230737381e-05,
3.7640682049158734e-05,
5.64610230737381e-05,
7.528136409831747e-05,
9.410170512289682e-05,
7.528136409831747e-05,
1.8820341024579367e-05,
7.528136409831747e-05,
1.8820341024579367e-05,
3.7640682049158734e-05,
5.64610230737381e-05,
3.7640682049158734e-05,
9.410170512289682e-05,
5.64610230737381e-05,
7.528136409831747e-05,
1.8820341024579367e-05,
3.7640682049158734e-05,
0.00015056272819663494,
9.410170512289682e-05,
0.00013174238717205555,
0.0001129220461474762,
0.0001693830692212143,
0.00018820341024579365,
0.00024466443331953175,
0.0004328678435653254,
0.0006210712538111191,
0.000414047502540746,
0.0006022509127865397,
0.0005081492076636428,
0.0004893288666390635,
0.0006587119358602778,
0.0007528136409831746,
0.0008092746640569127,
0.000978657733278127,
0.0011480408024993412,
0.0010915797794256031,
0.0009974780743027063,
0.0014303459178680318,
0.0016185493281138253,
0.0015809086460646666,
0.0017691120563104604,
0.002333722287047841,
0.00207023751270373,
0.0033688410433997066,
0.003086535928031016,
0.0032935596793013887,
0.0036135054767192382,
0.0046298038920465235,
0.004667444574095682,
0.005871946399668762,
0.007622238114954643,
0.00858207550720819,
0.01125456393269846,
0.013456543832574247,
0.015940828847818722,
0.019177927504046375,
0.0242594195806828,
0.029491474385515866,
0.03289795611096473,
0.0381300109157978,
0.04042609252079648,
0.044623028569277676,
0.04748372040501374,
0.04827417472804607,
0.05013738848947943,
0.051059585199683816,
0.04865058154853766,
0.047314337335792524,
0.04594045244099823,
0.041423570595099185,
0.03860051944141228,
0.03406481725448865,
0.03148643053412128,
0.027176572439492605,
0.02313019911920804,
0.018481574886136935,
0.016825384875973952,
0.013983513381262469,
0.011932096209583317,
0.00950427221741258,
0.0082997703918395,
0.006493017653479881,
0.005966048104791659,
0.005137953099710167,
0.004516881845899047,
0.0034817630895471827,
0.0028983325177852222,
0.0026536680844656906,
0.0019196747845070953,
0.00207023751270373,
0.001336244212745135,
0.0012421425076222382,
0.0009974780743027063,
0.0009410170512289683,
0.0006775322768848572,
0.000828095005081492,
0.0004893288666390635,
0.0006210712538111191,
0.0003764068204915873,
0.00031994579741784923,
0.0003387661384424286,
0.0005457898897128016,
0.0002258440922949524,
0.00013174238717205555,
0.0001693830692212143,
9.410170512289682e-05,
0.00013174238717205555,
0.00018820341024579365,
9.410170512289682e-05,
0.00013174238717205555,
7.528136409831747e-05,
3.7640682049158734e-05,
7.528136409831747e-05,
1.8820341024579367e-05,
1.8820341024579367e-05,
0.0,
3.7640682049158734e-05,
1.8820341024579367e-05,
1.8820341024579367e-05,
1.8820341024579367e-05,
1.8820341024579367e-05,
1.8820341024579367e-05,
0.0,
1.8820341024579367e-05,
1.8820341024579367e-05,
0.0,
1.8820341024579367e-05,
3.7640682049158734e-05,
0.0,
0.0,
3.7640682049158734e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.031392},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
4.538852578068264e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.00015885984023238924,
0.0,
0.0,
0.0,
0.0,
0.0,
9.077705156136529e-05,
0.0,
0.0,
0.0,
0.0,
0.00015885984023238924,
0.0,
0.0,
0.0,
0.00011347131445170662,
0.0,
0.0,
0.00013616557734204794,
0.0,
0.0,
0.0002950254175744372,
0.0,
0.00015885984023238924,
0.0,
0.00011347131445170662,
0.0,
6.808278867102397e-05,
0.0,
0.00015885984023238924,
4.538852578068264e-05,
0.0,
0.00011347131445170662,
2.269426289034132e-05,
9.077705156136529e-05,
0.00011347131445170662,
6.808278867102397e-05,
0.00013616557734204794,
9.077705156136529e-05,
0.00015885984023238924,
6.808278867102397e-05,
6.808278867102397e-05,
4.538852578068264e-05,
0.00013616557734204794,
9.077705156136529e-05,
0.00024963689179375453,
9.077705156136529e-05,
0.00011347131445170662,
6.808278867102397e-05,
0.00013616557734204794,
0.00018155410312273057,
0.00015885984023238924,
0.00011347131445170662,
0.00024963689179375453,
4.538852578068264e-05,
0.0002723311546840959,
0.00013616557734204794,
9.077705156136529e-05,
0.00011347131445170662,
6.808278867102397e-05,
9.077705156136529e-05,
0.00011347131445170662,
0.00011347131445170662,
9.077705156136529e-05,
6.808278867102397e-05,
6.808278867102397e-05,
0.00011347131445170662,
6.808278867102397e-05,
6.808278867102397e-05,
4.538852578068264e-05,
9.077705156136529e-05,
6.808278867102397e-05,
0.00015885984023238924,
0.00011347131445170662,
0.00011347131445170662,
0.00011347131445170662,
0.00015885984023238924,
0.00022694262890341323,
0.0003177196804647785,
0.00022694262890341323,
0.00036310820624546115,
0.0004084967320261438,
0.0004992737835875091,
0.0004311909949164851,
0.0007716049382716049,
0.0009531590413943355,
0.0009077705156136529,
0.0011120188816267247,
0.0015659041394335512,
0.0016112926652142338,
0.00240559186637618,
0.0022467320261437907,
0.0032679738562091504,
0.00360838779956427,
0.004788489469862019,
0.005401234567901234,
0.006717501815541031,
0.008442265795206972,
0.010893246187363835,
0.014773965141612201,
0.016521423384168482,
0.02081063907044299,
0.02351125635439361,
0.027800472040668118,
0.03188543936092956,
0.035062636165577345,
0.03982843137254902,
0.04513888888888889,
0.0481118373275236,
0.04793028322440087,
0.04863380537400145,
0.05022240377632534,
0.047680646332607116,
0.04675018155410312,
0.04484386347131445,
0.04162127814088598,
0.03803558460421205,
0.03524419026870007,
0.030501089324618737,
0.02766430646332607,
0.0240559186637618,
0.020833333333333332,
0.017383805374001454,
0.01563634713144517,
0.013071895424836602,
0.011869099491648511,
0.009667755991285403,
0.008896151053013798,
0.007171387073347858,
0.006082062454611474,
0.005287763253449528,
0.0055147058823529415,
0.0039261074800290485,
0.0035629992737835877,
0.003109114015976761,
0.00240559186637618,
0.0019290123456790122,
0.001906318082788671,
0.0014297385620915032,
0.0014524328249818446,
0.0010666303558460421,
0.0007942992011619463,
0.0007262164124909223,
0.0007942992011619463,
0.0005673565722585331,
0.0007262164124909223,
0.00045388525780682646,
0.0006127450980392157,
0.00038580246913580245,
0.0003177196804647785,
0.00045388525780682646,
0.0002042483660130719,
0.00024963689179375453,
0.00011347131445170662,
9.077705156136529e-05,
0.00011347131445170662,
0.00015885984023238924,
2.269426289034132e-05,
0.00013616557734204794,
0.00011347131445170662,
6.808278867102397e-05,
9.077705156136529e-05,
6.808278867102397e-05,
4.538852578068264e-05,
2.269426289034132e-05,
2.269426289034132e-05,
0.0,
2.269426289034132e-05,
2.269426289034132e-05,
0.0,
0.0,
0.0,
2.269426289034132e-05,
4.538852578068264e-05,
0.0,
2.269426289034132e-05,
2.269426289034132e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.076233},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.0001093039524309199,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0001093039524309199,
0.0,
0.0,
0.0,
0.0,
0.0,
0.00017488632388947185,
0.0,
0.0,
0.0,
0.0,
6.558237145855194e-05,
0.0,
0.0,
0.0,
0.00015302553340328787,
0.0,
0.0,
0.0002186079048618398,
0.0,
0.0,
8.744316194473592e-05,
0.0,
0.0001093039524309199,
0.0,
0.0001093039524309199,
0.0,
8.744316194473592e-05,
0.0,
0.00019674711437565583,
0.0001093039524309199,
0.0,
6.558237145855194e-05,
0.00015302553340328787,
0.00017488632388947185,
2.186079048618398e-05,
0.0001093039524309199,
8.744316194473592e-05,
0.00013116474291710389,
0.00015302553340328787,
2.186079048618398e-05,
0.00013116474291710389,
6.558237145855194e-05,
0.00019674711437565583,
6.558237145855194e-05,
0.0002186079048618398,
4.372158097236796e-05,
0.00013116474291710389,
0.00017488632388947185,
0.00015302553340328787,
8.744316194473592e-05,
0.0002841902763203917,
8.744316194473592e-05,
0.0002841902763203917,
0.00015302553340328787,
0.00026232948583420777,
0.00015302553340328787,
0.00013116474291710389,
0.00019674711437565583,
0.0001093039524309199,
0.0002186079048618398,
0.00013116474291710389,
0.00015302553340328787,
0.0002404686953480238,
0.0003279118572927597,
0.00026232948583420777,
0.0002841902763203917,
0.0003497726477789437,
0.00039349422875131166,
0.00030605106680657573,
0.0007651276670164394,
0.0007432668765302553,
0.0009181532004197271,
0.0009181532004197271,
0.001071178733823015,
0.0017051416579223506,
0.001989331934242742,
0.0023172437915355017,
0.002513990905911158,
0.003082371458551941,
0.0030605106680657575,
0.0043284365162644285,
0.005312172088142707,
0.006908009793634138,
0.006601958726827562,
0.009028506470793984,
0.009946659671213711,
0.01180482686253935,
0.014034627492130115,
0.01757607555089192,
0.020505421476040574,
0.022713361315145154,
0.028200419727177333,
0.028878104232249038,
0.03429958027282266,
0.03692287513116474,
0.04098898216159496,
0.04177597061909759,
0.044355543896467294,
0.04763466246939489,
0.04522997551591466,
0.0462574326687653,
0.04474903812521861,
0.0412075900664568,
0.04118572927597062,
0.0373819517313746,
0.03368747813920951,
0.03150139909059112,
0.02909671213711088,
0.023369185029730673,
0.021532878628891222,
0.0186909758656873,
0.01665792235047219,
0.014143931444561036,
0.012023434767401189,
0.011105281566981462,
0.009487583071003848,
0.008001049317943336,
0.007563833508219657,
0.006558237145855194,
0.005027981811822316,
0.004896817068905212,
0.004853095487932843,
0.003541448058761805,
0.0029512067156348375,
0.0028856243441762854,
0.002557712486883526,
0.0020111927247289264,
0.0017270024484085345,
0.0019456103532703743,
0.001202343476740119,
0.0009618747813920952,
0.001049317943336831,
0.0006776845050717034,
0.0008744316194473592,
0.0005465197621545995,
0.0004372158097236796,
0.0005246589716684155,
0.0002841902763203917,
0.0003497726477789437,
0.0002404686953480238,
0.0002186079048618398,
0.0002841902763203917,
0.0002404686953480238,
0.0001093039524309199,
0.00017488632388947185,
0.0001093039524309199,
0.0001093039524309199,
0.0001093039524309199,
4.372158097236796e-05,
8.744316194473592e-05,
4.372158097236796e-05,
6.558237145855194e-05,
6.558237145855194e-05,
0.00013116474291710389,
2.186079048618398e-05,
2.186079048618398e-05,
2.186079048618398e-05,
2.186079048618398e-05,
0.0,
2.186079048618398e-05,
4.372158097236796e-05,
2.186079048618398e-05,
2.186079048618398e-05,
4.372158097236796e-05,
0.0,
2.186079048618398e-05,
0.0,
0.0,
0.0,
0.0,
2.186079048618398e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.13223},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.0004804578972655679,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0006266842138246538,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0003969000020889474,
0.0,
0.0,
0.0,
0.0,
0.0002924526331181718,
0.0,
0.0,
0.0,
0.00043867894967725764,
0.0,
0.0,
0.00043867894967725764,
0.0,
0.0,
0.00045956842347141276,
0.0,
0.0004177894758831025,
0.0,
0.0005849052662363436,
0.0,
0.00045956842347141276,
0.0,
0.0002715631593240166,
0.00043867894967725764,
0.0,
0.0005640157924421884,
0.0004804578972655679,
0.0006057947400304987,
0.000501347371059723,
0.0005431263186480332,
0.0006266842138246538,
0.000501347371059723,
0.0005640157924421884,
0.000835578951766205,
0.000668463161412964,
0.0007311315827954294,
0.0016293789559440998,
0.0006475736876188089,
0.0012115894800609974,
0.0005640157924421884,
0.001524931586973324,
0.0018800526414739613,
0.001524931586973324,
0.0017756052725031856,
0.0013578157966200831,
0.0021307263270038228,
0.0027156315932401662,
0.001692047377326565,
0.0033005368594765097,
0.003655657913977147,
0.002172505274592133,
0.004449457918155042,
0.003697436861565457,
0.003822773704330388,
0.0055983789768335734,
0.005410373712686177,
0.006162394769275762,
0.007687326356249086,
0.007269536880365983,
0.009191368469428255,
0.009003363205280859,
0.012074115853021662,
0.011447431639197009,
0.015437321133880638,
0.014163063232437175,
0.01911386852165194,
0.018800526414739612,
0.02270685801424662,
0.024795805393662135,
0.025506047502663408,
0.02866035804558083,
0.03313070543753003,
0.032378684380940444,
0.03325604228029496,
0.037392158091537675,
0.03776816861983247,
0.040212237053748615,
0.038979758099893465,
0.03989889494683629,
0.03799795283156817,
0.036159679137682525,
0.03870819494056945,
0.03325604228029496,
0.031605773850556705,
0.027490547513108143,
0.02416912117983748,
0.021140147479684988,
0.020116563263771387,
0.01740093167053122,
0.015708884293204654,
0.013619936913789142,
0.012554573750287231,
0.009922500052223684,
0.008773578993545153,
0.00749932109210169,
0.007708215830043242,
0.005995278978922521,
0.005243257922332936,
0.004303231601595956,
0.004407678970566731,
0.003697436861565457,
0.0031543105429174237,
0.0029871947525641827,
0.0027783000146226317,
0.0021098368532096678,
0.002005389484238892,
0.0016293789559440998,
0.0014622631655908588,
0.0007520210565895845,
0.0010653631635019114,
0.0007938000041778948,
0.0006893526352071192,
0.0006475736876188089,
0.0007520210565895845,
0.00043867894967725764,
0.0003969000020889474,
0.0005222368448538781,
0.0002715631593240166,
0.0002924526331181718,
0.0003969000020889474,
0.0003133421069123269,
0.00018800526414739614,
4.177894758831025e-05,
0.0001462263165590859,
0.0001462263165590859,
4.177894758831025e-05,
0.00010444736897077563,
4.177894758831025e-05,
0.00010444736897077563,
0.0,
6.266842138246537e-05,
2.0889473794155127e-05,
8.35578951766205e-05,
2.0889473794155127e-05,
2.0889473794155127e-05,
4.177894758831025e-05,
4.177894758831025e-05,
2.0889473794155127e-05,
0.0,
6.266842138246537e-05,
0.0,
0.0,
0.0,
4.177894758831025e-05,
4.177894758831025e-05,
0.0,
0.0,
4.177894758831025e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.0889473794155127e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.278154},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.0009444009082323628,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0008640263628508851,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0010247754536138404,
0.0,
0.0,
0.0,
0.0,
0.0010649627263045794,
0.0,
0.0,
0.0,
0.0011252436353406876,
0.0,
0.0,
0.0010850563626499487,
0.0,
0.0,
0.0011051499989953183,
0.0,
0.0013261799987943819,
0.0,
0.0012056181807221652,
0.0,
0.0016878654530110314,
0.0,
0.0016275845439749231,
0.0014869290895573371,
0.0,
0.0015673036349388148,
0.0011654309080314264,
0.001285992726103643,
0.0015673036349388148,
0.0016878654530110314,
0.0018888018164647255,
0.0015673036349388148,
0.0018486145437739867,
0.0018486145437739867,
0.0016476781803202926,
0.0016074909076295538,
0.003536479996785018,
0.0024112363614443304,
0.004239757268872948,
0.0022102999979906365,
0.003857978178310929,
0.004561255450398859,
0.005324813631522897,
0.004963128177306247,
0.005103783631723833,
0.00590752908553861,
0.0090019490827255,
0.005987903630920088,
0.009584664536741214,
0.009986537263648603,
0.007334177266059839,
0.015009946349990958,
0.011614121807623525,
0.012598709988546628,
0.016898748166455684,
0.017099684529909377,
0.017521650893162134,
0.024192738159824784,
0.019008579982719473,
0.02495629634094882,
0.023650209978499807,
0.03094419997186891,
0.026543693612233007,
0.03725360178431491,
0.03208953724355497,
0.03562601724033999,
0.034902646331906685,
0.040548958144955495,
0.035706391785721464,
0.03494283360459743,
0.036610605421263084,
0.0364699499668455,
0.03460124178672614,
0.030281109972471718,
0.02817127815620793,
0.027930154520063494,
0.025277794522474733,
0.020053449072678683,
0.019269797255209276,
0.017843149074688047,
0.014809009986537263,
0.012779552715654952,
0.011312717262442984,
0.0097253199911588,
0.008519701810436636,
0.007736049992967228,
0.006409869994172845,
0.0054453754495951134,
0.004963128177306247,
0.004460787268672012,
0.003576667269475757,
0.0034561054514035405,
0.0026121727248980247,
0.002391142725098961,
0.002290674543372114,
0.0023308618160628528,
0.001527116362248076,
0.0015873972712841843,
0.0011654309080314264,
0.0012257118170675347,
0.0007032772720879298,
0.0008439327265055157,
0.0007434645447786686,
0.0005425281813249744,
0.0005626218176703438,
0.00044205999959812727,
0.00040187272690738845,
0.000522434544979605,
0.00044205999959812727,
0.00048224727228886614,
0.00022102999979906364,
0.0003014045451805413,
0.0001808427271083248,
0.0001808427271083248,
0.00014065545441758594,
0.00010046818172684711,
0.0001808427271083248,
4.0187272690738845e-05,
8.037454538147769e-05,
4.0187272690738845e-05,
8.037454538147769e-05,
8.037454538147769e-05,
4.0187272690738845e-05,
6.028090903610827e-05,
2.0093636345369423e-05,
0.00010046818172684711,
8.037454538147769e-05,
4.0187272690738845e-05,
4.0187272690738845e-05,
2.0093636345369423e-05,
0.0,
0.0,
2.0093636345369423e-05,
0.0,
4.0187272690738845e-05,
2.0093636345369423e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.0093636345369423e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.437547},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.002770083102493075,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.002707600024993231,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0030824984899922936,
0.0,
0.0,
0.0,
0.0,
0.002978360027492554,
0.0,
0.0,
0.0,
0.002978360027492554,
0.0,
0.0,
0.003228292337491929,
0.0,
0.0,
0.003061670797492346,
0.0,
0.003228292337491929,
0.0,
0.003832295419990419,
0.0,
0.0037489846499906276,
0.0,
0.0037698123424905754,
0.003957261574990107,
0.0,
0.004123883114989691,
0.003915606189990211,
0.0042071938849894824,
0.004144710807489638,
0.004311332347489222,
0.004165538499989586,
0.004540436964988649,
0.004477953887488805,
0.004290504654989273,
0.004665403119988336,
0.0049569908149876074,
0.00966404931997584,
0.005727615437485681,
0.01076791702247308,
0.00522775081748693,
0.010288880094974277,
0.011434403182471414,
0.011413575489971467,
0.01187178472497032,
0.011601024722470998,
0.012829858579967926,
0.01891154478995272,
0.012038406264969903,
0.01830754170745423,
0.019161477099952095,
0.01389207089746527,
0.027325932559931685,
0.020473621727448817,
0.02224397558994439,
0.029262907962426844,
0.02888800949742778,
0.027867452564930333,
0.035948597254910127,
0.027971591027430073,
0.03357424030991606,
0.03253285568491867,
0.036385978797409034,
0.028263178722429342,
0.03765646803990586,
0.030450086434923876,
0.033490929539916274,
0.030450086434923876,
0.03038760335742403,
0.02557640638993606,
0.023097910982442255,
0.020265344802449337,
0.020702726344948245,
0.016078978609959802,
0.014037864744964905,
0.011725990877470685,
0.01026805240247433,
0.009643221627475891,
0.008101972382479745,
0.006914793909982713,
0.006789827754983026,
0.005186095432487035,
0.0049569908149876074,
0.0037906400349905236,
0.0034365692624914084,
0.002686772332493283,
0.0026034615624934915,
0.0022702184824943245,
0.0021035969424947412,
0.0017078707849957303,
0.0014579384749963552,
0.0015204215524961988,
0.0013121446274967196,
0.0014162830899964592,
0.0006873138524982818,
0.0007497969299981255,
0.0008331076999979172,
0.0006664861599983338,
0.0005206923124986983,
0.000291587694999271,
0.0004998646199987503,
0.0006873138524982818,
0.0004998646199987503,
0.0002707600024993231,
0.000312415387499219,
0.00024993230999937515,
0.000312415387499219,
0.00024993230999937515,
0.00012496615499968757,
0.0001874492324995314,
0.00016662153999958345,
0.00016662153999958345,
0.0002707600024993231,
8.331076999979172e-05,
0.00016662153999958345,
0.0001457938474996355,
8.331076999979172e-05,
2.082769249994793e-05,
4.165538499989586e-05,
8.331076999979172e-05,
4.165538499989586e-05,
6.248307749984379e-05,
2.082769249994793e-05,
2.082769249994793e-05,
8.331076999979172e-05,
4.165538499989586e-05,
2.082769249994793e-05,
6.248307749984379e-05,
4.165538499989586e-05,
0.0,
0.0,
0.0,
0.0,
2.082769249994793e-05,
2.082769249994793e-05,
2.082769249994793e-05,
2.082769249994793e-05,
0.0,
0.0,
2.082769249994793e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.082769249994793e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 0.069681},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.006503589351216328,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.006166032810495758,
0.0,
0.0,
0.0,
0.0,
0.0,
0.006661115736885929,
0.0,
0.0,
0.0,
0.0,
0.007268717510182956,
0.0,
0.0,
0.0,
0.007201206202038841,
0.0,
0.0,
0.007156198663276099,
0.0,
0.0,
0.0067736345837927855,
0.0,
0.007966334361005469,
0.0,
0.008573936134302495,
0.0,
0.007403740126471184,
0.0,
0.008056349438530954,
0.0073362288183270695,
0.0,
0.00832639467110741,
0.008236379593581925,
0.00798883813038684,
0.008078853207912325,
0.008191372054819183,
0.008686454981209353,
0.00897900398316718,
0.008911492675023067,
0.00832639467110741,
0.008168868285437812,
0.009024011521929923,
0.017485428809325562,
0.008303890901726039,
0.0186331210477755,
0.008753966289353467,
0.01892567004973333,
0.01924072282107253,
0.019060692666021558,
0.018700632355919615,
0.019690798208699956,
0.018723136125300986,
0.02873731350001125,
0.01890316628035196,
0.027792155185993653,
0.02792717780228188,
0.01813803812138533,
0.036591129014109866,
0.027004523257645657,
0.02495668024394086,
0.031865337444021875,
0.031077705515673876,
0.02889483988568085,
0.03411571438215901,
0.026644462947543714,
0.030560118819902334,
0.027004523257645657,
0.029344915273308278,
0.021018520602200868,
0.026486936561874112,
0.018813151202826475,
0.019690798208699956,
0.017507932578706933,
0.015257555640569796,
0.012467088237279744,
0.010486756531719063,
0.009474086909557351,
0.008281387132344668,
0.00522087449647816,
0.005108355649571303,
0.004073182258028219,
0.003735625717307649,
0.003083016405247879,
0.0027454598645273083,
0.0027004523257645654,
0.0018903166280351959,
0.0017552940117469677,
0.0015077525485518825,
0.0011476922384499404,
0.0010801809303058263,
0.0009901658527803408,
0.0007876319283479983,
0.0006076017732970273,
0.00036006031010194205,
0.0007876319283479983,
0.0005850980039156558,
0.0005850980039156558,
0.00047257915700879896,
0.0002475414631950852,
0.0002925490019578279,
0.0004275716182460562,
0.0002250376938137138,
0.00036006031010194205,
0.0003150527713391993,
0.0002925490019578279,
0.0002250376938137138,
0.0002475414631950852,
0.0002025339244323424,
0.0001350226162882283,
0.0002250376938137138,
4.500753876274276e-05,
6.751130814411415e-05,
0.00015752638566959965,
4.500753876274276e-05,
0.00015752638566959965,
0.0001125188469068569,
6.751130814411415e-05,
2.250376938137138e-05,
2.250376938137138e-05,
2.250376938137138e-05,
0.0,
0.0,
4.500753876274276e-05,
2.250376938137138e-05,
4.500753876274276e-05,
2.250376938137138e-05,
0.0,
0.0,
2.250376938137138e-05,
2.250376938137138e-05,
0.0,
2.250376938137138e-05,
2.250376938137138e-05,
0.0,
0.0,
2.250376938137138e-05,
0.0,
0.0,
0.0,
0.0,
2.250376938137138e-05,
0.0,
2.250376938137138e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
2.250376938137138e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 1.343931},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.008458053787487815,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.008113997362234074,
0.0,
0.0,
0.0,
0.0,
0.0,
0.00842938241871667,
0.0,
0.0,
0.0,
0.0,
0.008716096106428121,
0.0,
0.0,
0.0,
0.008572739262572395,
0.0,
0.0,
0.008630082000114685,
0.0,
0.0,
0.008572739262572395,
0.0,
0.00865875336888583,
0.0,
0.009232180744308734,
0.0,
0.00989162222604507,
0.0,
0.009690922644647056,
0.009146166637995298,
0.0,
0.008974138425368428,
0.009346866219393313,
0.00943288032570675,
0.009834279488502781,
0.00937553758816446,
0.010264350020069958,
0.00960490853833362,
0.00989162222604507,
0.010149664544985377,
0.009633579907104764,
0.00989162222604507,
0.021818911634841447,
0.01083777739549286,
0.021876254372383736,
0.010407706863925684,
0.021188141521876255,
0.020700728252766788,
0.02104478467802053,
0.02027065772119961,
0.02050002867136877,
0.021188141521876255,
0.030477665003727276,
0.02027065772119961,
0.03059235047881186,
0.0315098342794885,
0.018607718332473194,
0.03730145077125982,
0.026549687482080395,
0.02523080451860772,
0.03234130397385171,
0.03099374964160789,
0.02746717128275704,
0.033574172831010954,
0.024026607030219624,
0.02657835885085154,
0.023481851023567864,
0.025374161362463444,
0.018579046963702047,
0.021847583003612593,
0.014765754917139745,
0.01591260966798555,
0.01261540225930386,
0.012300017202821263,
0.008687424737656976,
0.007253856299099719,
0.00653707207982109,
0.005934973335627043,
0.004845461322323528,
0.003411892883766271,
0.0028384655083433684,
0.0023797236080050463,
0.0015769252824129824,
0.0010895120133035151,
0.0016055966511841276,
0.0009174838006766443,
0.0007454555880497735,
0.000860141063134354,
0.0007167842192786284,
0.0006594414817363381,
0.0008888124319054992,
0.0006881128505074832,
0.000430070531567177,
0.0004013991627960319,
0.0003440564252537416,
0.00037272779402488675,
0.00028671368771145133,
0.0004013991627960319,
0.00020069958139801595,
0.0003153850564825965,
0.00022937095016916108,
0.00022937095016916108,
0.0001720282126268708,
0.0004874132691094673,
0.0001720282126268708,
0.00025804231894030623,
0.0001720282126268708,
0.00011468547508458054,
8.60141063134354e-05,
2.8671368771145135e-05,
5.734273754229027e-05,
5.734273754229027e-05,
0.0,
5.734273754229027e-05,
5.734273754229027e-05,
8.60141063134354e-05,
5.734273754229027e-05,
8.60141063134354e-05,
0.00014335684385572567,
0.0,
2.8671368771145135e-05,
0.0,
5.734273754229027e-05,
2.8671368771145135e-05,
5.734273754229027e-05,
2.8671368771145135e-05,
2.8671368771145135e-05,
0.0,
0.0,
2.8671368771145135e-05,
2.8671368771145135e-05,
0.0,
2.8671368771145135e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 1.941037},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.008160688397324978,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0073656643127718285,
0.0,
0.0,
0.0,
0.0,
0.0,
0.008277603703876911,
0.0,
0.0,
0.0,
0.0,
0.008488051255670393,
0.0,
0.0,
0.0,
0.007576111864565309,
0.0,
0.0,
0.008488051255670393,
0.0,
0.0,
0.00844128513304962,
0.0,
0.009446756769396249,
0.0,
0.008324369826497684,
0.0,
0.008113922274704205,
0.0,
0.008417902071739232,
0.008908946359257354,
0.0,
0.009680587382500118,
0.00965720432118973,
0.009189543094981996,
0.00930645840153393,
0.008862180236636581,
0.008815414114015808,
0.010124865547397464,
0.009540289014637797,
0.010265163915259785,
0.008932329420567741,
0.00930645840153393,
0.020436795585278025,
0.009984567179535145,
0.01975868680727681,
0.009891034934293597,
0.020694009259692277,
0.02001590048169106,
0.02031988027872609,
0.01938455782631062,
0.020436795585278025,
0.01989898517513913,
0.02955618949632886,
0.019127344151896368,
0.027942758265912172,
0.027849226020670626,
0.019524856194172942,
0.0372492166674461,
0.02478604498900996,
0.025557686012252723,
0.03222185848571295,
0.029883552354674273,
0.02960295561894963,
0.03353130991909461,
0.024248234578871066,
0.0282467380629472,
0.02429500070149184,
0.026422859280737034,
0.01975868680727681,
0.023032315390730956,
0.017724360473273162,
0.01688257026609924,
0.014146752092783987,
0.01311789739512697,
0.010779591264088294,
0.008230837581256138,
0.007903474722910723,
0.007201982883599121,
0.005869148388907076,
0.004092035729317683,
0.0037880559322826545,
0.0028293504185567973,
0.0028293504185567973,
0.001917411027451714,
0.002010943272693261,
0.0018004957208997802,
0.0011223869428985643,
0.0013328344946920451,
0.0011691530655193378,
0.0008184071458635365,
0.0006781087780012159,
0.0006547257166908292,
0.0005378104101388954,
0.00044427816489734837,
0.0005378104101388954,
0.00039751204227657486,
0.0002572136744142543,
0.0004910442875181219,
0.0003273628583454146,
0.0002572136744142543,
0.0002104475517934808,
0.00023383061310386756,
0.0002104475517934808,
0.00018706449048309405,
0.00018706449048309405,
0.00018706449048309405,
0.0001636814291727073,
0.00011691530655193378,
0.00011691530655193378,
0.0001636814291727073,
0.00014029836786232054,
0.0,
4.676612262077351e-05,
0.00011691530655193378,
7.014918393116027e-05,
2.3383061310386756e-05,
0.0,
7.014918393116027e-05,
2.3383061310386756e-05,
0.0,
0.0,
4.676612262077351e-05,
2.3383061310386756e-05,
2.3383061310386756e-05,
4.676612262077351e-05,
0.0,
0.0,
2.3383061310386756e-05,
0.0,
4.676612262077351e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.3383061310386756e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 2.14686},
{'bin': [0.001,
0.0010568175092136585,
0.001116863247780561,
0.0011803206356517297,
0.0012473835142429433,
0.0013182567385564075,
0.0013931568029453036,
0.0014723125024327193,
0.001555965631605075,
0.0016443717232149323,
0.0017378008287493763,
0.0018365383433483473,
0.0019408858775927793,
0.0020511621788255646,
0.002167704104819694,
0.0022908676527677724,
0.0024210290467361778,
0.0025585858869056452,
0.0027039583641088436,
0.0028575905433749467,
0.003019951720402016,
0.0031915378551007614,
0.003372873086588689,
0.0035645113342624426,
0.003767037989839089,
0.003981071705534973,
0.004207266283844442,
0.004446312674691089,
0.004698941086052156,
0.004965923214503363,
0.005248074602497723,
0.005546257129579105,
0.005861381645140285,
0.006194410750767812,
0.006546361740672747,
0.006918309709189363,
0.007311390834834172,
0.007726805850957022,
0.008165823713585922,
0.008629785477669702,
0.009120108393559097,
0.009638290236239706,
0.010185913880541169,
0.010764652136298349,
0.01137627285823431,
0.012022644346174132,
0.012705741052085419,
0.013427649611378642,
0.014190575216890926,
0.014996848355023733,
0.015848931924611134,
0.016749428760264373,
0.01770108958317421,
0.018706821403658005,
0.01976969640111861,
0.020892961308540396,
0.022080047330189003,
0.023334580622810033,
0.0246603933723434,
0.02606153549998895,
0.02754228703338166,
0.029107171180666053,
0.03076096814740708,
0.032508729738543435,
0.034355794789987466,
0.03630780547701014,
0.03837072454922788,
0.040550853544838394,
0.042854852039743964,
0.04528975799036209,
0.047863009232263824,
0.0505824662003114,
0.053456435939697164,
0.05649369748123025,
0.059703528658383694,
0.06309573444801933,
0.06668067692136222,
0.07046930689671471,
0.07447319739059892,
0.07870457896950989,
0.08317637711026708,
0.08790225168308842,
0.09289663867799362,
0.09817479430199844,
0.10375284158180126,
0.1096478196143185,
0.11587773561551262,
0.1224616199265049,
0.12941958414499863,
0.13677288255958495,
0.1445439770745928,
0.15275660582380732,
0.1614358556826487,
0.17060823890031243,
0.180301774085957,
0.19054607179632482,
0.20137242498623895,
0.21281390459827113,
0.22490546058357805,
0.23768402866248758,
0.25118864315095796,
0.2654605561975539,
0.2805433637951713,
0.2964831389524342,
0.31332857243155854,
0.3311311214825911,
0.3499451670283573,
0.3698281797802663,
0.3908408957924021,
0.41304750199016144,
0.4365158322401661,
0.46131757456037953,
0.4875284901033865,
0.5152286445817567,
0.5445026528424215,
0.5754399373371573,
0.6081350012787182,
0.64268771731702,
0.6792036326171843,
0.7177942912713615,
0.7585775750291835,
0.801678063387679,
0.8472274141405963,
0.8953647655495938,
0.946237161365793,
1.0,
1.0568175092136585,
1.1168632477805611,
1.1803206356517297,
1.2473835142429432,
1.3182567385564075,
1.3931568029453036,
1.4723125024327193,
1.555965631605075,
1.6443717232149324,
1.7378008287493762,
1.8365383433483473,
1.9408858775927793,
2.051162178825567,
2.167704104819694,
2.2908676527677723,
2.4210290467361775,
2.5585858869056453,
2.703958364108843,
2.8575905433749464,
3.019951720402016,
3.1915378551007616,
3.372873086588689,
3.5645113342624426,
3.767037989839089,
3.981071705534973,
4.207266283844442,
4.446312674691089,
4.698941086052156,
4.965923214503363,
5.248074602497728,
5.54625712957911,
5.86138164514029,
6.194410750767818,
6.5463617406727534,
6.918309709189363,
7.311390834834173,
7.726805850957021,
8.165823713585922,
8.629785477669701,
9.120108393559097,
9.638290236239705,
10.18591388054117,
10.76465213629835,
11.37627285823431,
12.02264434617413,
12.705741052085418,
13.427649611378643,
14.190575216890926,
14.99684835502374,
15.848931924611142,
16.749428760264383,
17.70108958317422,
18.706821403658015,
19.76969640111862,
20.892961308540407,
22.080047330189014,
23.334580622810044,
24.66039337234341,
26.061535499988977,
27.54228703338169,
29.107171180666082,
30.760968147407112,
32.50872973854347,
34.3557947899875,
36.30780547701018,
38.37072454922792,
40.55085354483843,
42.85485203974392,
45.28975799036204,
47.863009232263806,
50.58246620031137,
53.45643593969714,
56.49369748123023,
59.70352865838366,
63.0957344480193,
66.68067692136219,
70.46930689671467,
74.47319739059888,
78.70457896950985,
83.17637711026708,
87.90225168308842,
92.89663867799364,
98.17479430199843,
103.75284158180126,
109.64781961431851,
115.87773561551262,
122.4616199265049,
129.41958414499862,
136.77288255958496,
144.5439770745928,
152.75660582380732,
161.4358556826487,
170.60823890031244,
180.301774085957,
190.54607179632484,
201.37242498623894,
212.81390459827134,
224.90546058357828,
237.68402866248783,
251.18864315095823,
265.4605561975542,
280.5433637951716,
296.48313895243456,
313.3285724315589,
331.1311214825914,
349.9451670283577,
369.8281797802666,
390.8408957924025,
413.0475019901619,
436.51583224016565,
461.31757456037906,
487.528490103386,
515.2286445817562,
544.5026528424208,
575.4399373371566,
608.1350012787176,
642.6877173170194,
679.2036326171843,
717.7942912713615,
758.5775750291835,
801.678063387679,
847.2274141405964,
895.3647655495937,
946.237161365793],
'output': [0.0,
0.0077809798270893375,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.007309405292114226,
0.0,
0.0,
0.0,
0.0,
0.0,
0.008357348703170028,
0.0,
0.0,
0.0,
0.0,
0.007676185485983757,
0.0,
0.0,
0.0,
0.008278752947340843,
0.0,
0.0,
0.008514540214828399,
0.0,
0.0,
0.0075713911448781765,
0.0,
0.008435944458999214,
0.0,
0.008147760020958869,
0.0,
0.009326696358396646,
0.0,
0.008750327482315955,
0.009876866649200943,
0.0,
0.008802724652868745,
0.009221902017291067,
0.009641079381713387,
0.00995546240503013,
0.009379093528949436,
0.010296044013623265,
0.009117107676185485,
0.008855121823421535,
0.00882892323814514,
0.009745873722818968,
0.009850668063924548,
0.01930835734870317,
0.010820015719151166,
0.019937123395336653,
0.010191249672517683,
0.019937123395336653,
0.020827875294734084,
0.020303903589206182,
0.021692428608855122,
0.019544144616190726,
0.01946554886036154,
0.029552004191773645,
0.019596541786743516,
0.03020696882368352,
0.028635053707099817,
0.01831281110820016,
0.03793555148022007,
0.026617762640817395,
0.02431228713649463,
0.031097720723080955,
0.03046895467644747,
0.028373067854335864,
0.03185747969609641,
0.023919308357348703,
0.026853549908304953,
0.025543620644485197,
0.027587110296044014,
0.01972753471312549,
0.023919308357348703,
0.016321718627194132,
0.01663610165051087,
0.015771548336389836,
0.013125491223473932,
0.010138852501964894,
0.008488341629552004,
0.007676185485983757,
0.006811632171862719,
0.00526591564055541,
0.0045847524233691385,
0.003274823159549384,
0.0029866387215090385,
0.002698454283468693,
0.0016505108724128898,
0.0019386953104532354,
0.0018862981399004454,
0.0012313335079905685,
0.0011789363374377785,
0.001100340581608593,
0.0005763688760806917,
0.0007335603877390621,
0.00034058160859313597,
0.0004977731202515064,
0.0005501702908042965,
0.0004191773644223212,
0.00036678019386953103,
0.00036678019386953103,
0.00034058160859313597,
0.00036678019386953103,
0.00028818443804034583,
0.00028818443804034583,
0.00013099292638197538,
0.00013099292638197538,
0.00018339009693476552,
0.00013099292638197538,
0.0001047943411055803,
0.00018339009693476552,
0.00015719151165837045,
2.6198585276395076e-05,
7.859575582918523e-05,
0.0001047943411055803,
0.0001047943411055803,
5.239717055279015e-05,
7.859575582918523e-05,
0.0001047943411055803,
7.859575582918523e-05,
0.0,
7.859575582918523e-05,
0.0,
0.0,
2.6198585276395076e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.6198585276395076e-05,
0.0,
0.0,
0.0,
0.0,
2.6198585276395076e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.6198585276395076e-05,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0],
'x': 2.309624}],
'variables': [{'map': '#//model/functions/input_composition', 'name': 'x'},
{'name': 'bin'}]}
Checking if distribution. This should be 1: 1.0
Model based on experimental data¶
Let us plot the transfer characteristics from the distributions. Distributions can be shown in many different ways.
We go for the mean with quantiles in this case.
We will also plot the deterministic fitted Hill model on top to see how well it fits. For some gates the fit is very good, for some a bit less.
In [75]:
from scipy.stats import rv_discrete
x_vals = []
means = []
q10 = []
q90 = []
for d in measurements:
x = d['x']
vals = np.array(d['bin'], dtype=float)
probs = np.array(d['output'], dtype=float)
# Normalize probabilities
probs = probs / probs.sum()
# Create a discrete random variable
dist = rv_discrete(values=(vals, probs))
# Compute mean and quantiles
mean = dist.mean()
q10_val = dist.ppf(0.1)
q90_val = dist.ppf(0.9)
x_vals.append(x)
means.append(mean)
q10.append(q10_val)
q90.append(q90_val)
x_vals = np.array(x_vals)
means = np.array(means)
q10 = np.array(q10)
q90 = np.array(q90)
# We sort the data ascending in x_val (= the input)
# since unsorted data is in the library.
# Get sorting indices
sort_idx = np.argsort(x_vals)
# Apply sorting to all arrays
x_vals = x_vals[sort_idx]
means = means[sort_idx]
q10 = q10[sort_idx]
q90 = q90[sort_idx]
plt.figure(figsize=(6,4))
# Plot mean as a line
plt.plot(x_vals, means, marker='o', label='mean')
# Fill between 10% and 90% quantiles
plt.fill_between(x_vals, q10, q90, color='orange', alpha=0.3, label='10-90% quantile')
# Set log-log scale
plt.xscale('log')
plt.yscale('log')
# also add the deterministic Hill approximation
x = np.linspace(x_vals[0], x_vals[-1], 1000)
plt.plot(x, inv(x), 'red', label = 'Hill model')
plt.title(gate_name)
plt.legend()
Out[75]:
<matplotlib.legend.Legend at 0x12d522030>
The graph nicely shows the two transfer characteristics: the measurement and the fit.
In the measurements, one can clearly see an outlier experiment. When computing with the measurement distributions, we have to be careful to correct or clean this.
Problem 2: Gate characteristics¶
Plot all deterministic Hill models for all NOR gates in log-log plots.
You can plot them for a single combined input.
The plot should be nicely arranged so that the viewer can compare them next to each other. For example in a grid. Also think about common axis limits, gate names as titles, etc.
What do you observe in the gate library. What does this mean for composition of gates?
Show hint
Check out the log-log plot function in the lecture. Also check out plt.subplots for plotting grids of figures.
For the composition: check out input and resulting output ranges. The output range is the next input range. Further, does a logical value like a 0 get mapped to a 1 and then back to a 0 when being composed? For which values does this hold? Try solving this graphically.
Problem 3: Simulation of Inverter Chain¶
Propagate determinsitic input-output values from inputs to an output.
a) Write a function that allows you to call progagate(circuit: list[str], i: float) -> float.
Here, circuit is a linear circuit of NOR gates but with a single input (INV gates).
The circuit is encoded as a list[str] of NOR names from the library.
Argument i is an input value in RPUs.
The output of the function is the output of the circuit in RPUs.
Show hint
Since we are using only single promoters for the linear circuit, we can disregard the input composition.
b) Use the result of (a) to plot the transfer function for a linear circuit. Show a circuit that you consider good and one that you consider bad and tell us why.
Show hint
Good vs. bad: How are logical values mapped in a chain of 2 inverters? How large is the dynamic range (logical 0 to logical 1 in the output)?
License: © 2025 Matthias Függer and Thomas Nowak. Licensed under CC BY-NC-SA 4.0.