Boltzmann_with_running_example

last edited Dec 3, 2014, 9:46:56 AM by admin

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#Here are the results obtain for the 71 experiments used in the paper (parameter 1.696).
r1696=[[13.870000000000005, 280], [102.01599999999999, 2088], [307.131, 6286], [264.08500000000004, 5428], [28.57899999999995, 594],
[87.71199999999999, 1796], [8.395000000000095, 170], [31.55899999999997, 652], [37.563999999999965, 778],
[248.6049999999999, 5144], [187.66600000000005, 3892], [214.745, 4474],
[184.3610000000001, 3870],[2.475999999999999, 52], [87.67900000000009, 1830],
[147.31399999999985, 3076], [564.615, 11756], [345.44900000000007,
7180], [145.8130000000001, 3054], [58.18399999999974, 1220],
[128.37199999999984, 2674], [213.11400000000003, 4450],
[97.20699999999988, 2038], [177.9720000000002, 3724],
[71.79599999999982, 1398], [101.99000000000024, 2026],
[75.43399999999974, 1550], [119.82999999999993, 2494],
[71.48500000000013, 1500], [4.264999999999873, 92], [24.618000000000393,
520], [163.83199999999988, 3416], [110.19399999999996, 2298],
[47.43000000000029, 992], [202.76399999999967, 4226],
[165.28299999999945, 3440], [151.95800000000054, 3130],
[191.1180000000004, 3976], [267.9399999999996, 5576],
[5.3419999999996435, 112],
[223.54, 4638],[37.10499999999999, 784],[167.62300000000005, 3486],[14.645999999999958, 302],
[82.14800000000002, 1708],[305.578, 6350],[39.043000000000006, 820],[3.865000000000009, 82],[91.02299999999991, 1902],
[120.58600000000001, 2524],
[241.0110000000002, 5034],
[462.59199999999987, 9618],
[172.1199999999999, 3614],
[70.68900000000008, 1484],
[42.5300000000002, 890],
[6.618999999999687, 138],
[343.2350000000001, 7166],
[99.51100000000042, 2064],
[77.80099999999948, 1628],
[135.46800000000076, 2804],
[180.20099999999957, 3740],
[351.2060000000006, 7298],
[58.735999999999876, 1226],
[156.1210000000001, 3238],
[280.0079999999998, 5824],
[155.91400000000021, 3268],
[62.05399999999963, 1298],
[32.56100000000015, 678],
[291.9149999999995, 6066],
[142.45899999999983, 2976],
[123.19599999999991, 2574]];

(z, x)

(z, x)

[ 0 -1  0 -1]
[-1  0  0  0]
[ 0  1  0  1]
[ 0  0  1  0]

[ 0 -1  0 -1]
[-1  0  0  0]
[ 0  1  0  1]
[ 0  0  1  0]

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ 1 4 (e (2 2 \sqrt z) + 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) - 1 8 (4 z e (2 \sqrt z) + 2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) - 1 4 (e (2 2 \sqrt z) - 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) 1 8 (4 z e (2 \sqrt z) - 2 \sqrt e (2 2 \sqrt z) + 2 \sqrt) e (- 2 \sqrt z) - 1 4 (2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) 1 4 (e (2 2 \sqrt z) + 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) 1 4 (2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) 1 4 (e (2 2 \sqrt z) - 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) - 1 4 (e (2 2 \sqrt z) - 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) - 1 8 (4 z e (2 \sqrt z) - 2 \sqrt e (2 2 \sqrt z) + 2 \sqrt) e (- 2 \sqrt z) 1 4 (e (2 2 \sqrt z) + 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) 1 8 (4 z e (2 \sqrt z) + 2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) - 1 4 (2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) 1 4 (e (2 2 \sqrt z) - 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) 1 4 (2 \sqrt e (2 2 \sqrt z) - 2 \sqrt) e (- 2 \sqrt z) 1 4 (e (2 2 \sqrt z) + 2 e (2 \sqrt z) + 1) e (- 2 \sqrt z) ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} + 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & -\frac{1}{4} \, {\left(\sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & -\frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} - 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & -\frac{1}{4} \, {\left(\sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} \\ -\frac{1}{8} \, {\left(4 \, z e^{\left(\sqrt{2} z\right)} + \sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} + 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & -\frac{1}{8} \, {\left(4 \, z e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} + \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} - 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} \\ -\frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} - 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(\sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} + 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(\sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} \\ \frac{1}{8} \, {\left(4 \, z e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} + \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} - 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{8} \, {\left(4 \, z e^{\left(\sqrt{2} z\right)} + \sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, {\left(e^{\left(2 \, \sqrt{2} z\right)} + 2 \, e^{\left(\sqrt{2} z\right)} + 1\right)} e^{\left(-\sqrt{2} z\right)} \end{array}\right)$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 - 1 8 2 \sqrt e (2 \sqrt z) + 1 8 2 \sqrt e (- 2 \sqrt z) - 1 2 z - 1 4 e (2 \sqrt z) - 1 4 e (- 2 \sqrt z) + 1 2 - 1 8 2 \sqrt e (2 \sqrt z) + 1 8 2 \sqrt e (- 2 \sqrt z) + 1 2 z - 1 4 2 \sqrt e (2 \sqrt z) + 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 1 4 2 \sqrt e (2 \sqrt z) - 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) - 1 2 - 1 4 e (2 \sqrt z) - 1 4 e (- 2 \sqrt z) + 1 2 1 8 2 \sqrt e (2 \sqrt z) - 1 8 2 \sqrt e (- 2 \sqrt z) - 1 2 z 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 1 8 2 \sqrt e (2 \sqrt z) - 1 8 2 \sqrt e (- 2 \sqrt z) + 1 2 z - 1 4 2 \sqrt e (2 \sqrt z) + 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) - 1 2 1 4 2 \sqrt e (2 \sqrt z) - 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & -\frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} & -\frac{1}{4} \, e^{\left(\sqrt{2} z\right)} - \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & -\frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} \\ -\frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & \frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} - \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \\ -\frac{1}{4} \, e^{\left(\sqrt{2} z\right)} - \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & \frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} - \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & \frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} - \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} \\ -\frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} & \frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} - \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} \end{array}\right)$

 $⎡ ⎣ ⎢ ⎢ ⎛ ⎝ ⎜ ⎜ 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 - 1 8 2 \sqrt e (2 \sqrt z) + 1 8 2 \sqrt e (- 2 \sqrt z) - 1 2 z - 1 4 2 \sqrt e (2 \sqrt z) + 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) + 1 2 ⎞ ⎠ ⎟ ⎟, ⎛ ⎝ ⎜ ⎜ - 1 4 e (2 \sqrt z) - 1 4 e (- 2 \sqrt z) + 1 2 1 8 2 \sqrt e (2 \sqrt z) - 1 8 2 \sqrt e (- 2 \sqrt z) - 1 2 z - 1 4 2 \sqrt e (2 \sqrt z) + 1 4 2 \sqrt e (- 2 \sqrt z) 1 4 e (2 \sqrt z) + 1 4 e (- 2 \sqrt z) - 1 2 ⎞ ⎠ ⎟ ⎟ ⎤ ⎦ ⎥ ⎥$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rr} \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & -\frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} \\ -\frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} \end{array}\right), \left(\begin{array}{rr} -\frac{1}{4} \, e^{\left(\sqrt{2} z\right)} - \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} + \frac{1}{2} & -\frac{1}{4} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} \\ \frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} z\right)} - \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \, z & \frac{1}{4} \, e^{\left(\sqrt{2} z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} z\right)} - \frac{1}{2} \end{array}\right)\right]$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 8 ( 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt e ( - 2 \sqrt z ) ) z ⎛ ⎝ ⎜ ( 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt e ( - 2 \sqrt z ) + 4 z ) ( 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt e ( - 2 \sqrt z ) ) e ( 2 \sqrt z ) + e ( - 2 \sqrt z ) + 2 - 2 e ( 2 \sqrt z ) - 2 e ( - 2 \sqrt z ) - 4 ⎞ ⎠ ⎟ ( e ( 2 \sqrt z ) + e ( - 2 \sqrt z ) + 2 ) + 1 - 8 z ( 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt e ( - 2 \sqrt z ) + 4 z ) ( 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt e ( - 2 \sqrt z ) ) e ( 2 \sqrt z ) + e ( - 2 \sqrt z ) + 2 - 2 e ( 2 \sqrt z ) - 2 e ( - 2 \sqrt z ) - 4 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{r} -\frac{8 \, {\left(\sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(-\sqrt{2} z\right)}\right)} z}{{\left(\frac{{\left(\sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(-\sqrt{2} z\right)} + 4 \, z\right)} {\left(\sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(-\sqrt{2} z\right)}\right)}}{e^{\left(\sqrt{2} z\right)} + e^{\left(-\sqrt{2} z\right)} + 2} - 2 \, e^{\left(\sqrt{2} z\right)} - 2 \, e^{\left(-\sqrt{2} z\right)} - 4\right)} {\left(e^{\left(\sqrt{2} z\right)} + e^{\left(-\sqrt{2} z\right)} + 2\right)}} + 1 \\ -\frac{8 \, z}{\frac{{\left(\sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(-\sqrt{2} z\right)} + 4 \, z\right)} {\left(\sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2} e^{\left(-\sqrt{2} z\right)}\right)}}{e^{\left(\sqrt{2} z\right)} + e^{\left(-\sqrt{2} z\right)} + 2} - 2 \, e^{\left(\sqrt{2} z\right)} - 2 \, e^{\left(-\sqrt{2} z\right)} - 4} \end{array}\right)$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 - 2 z ( e ( 2 \sqrt z ) + 1 ) 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{r} -\frac{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ -\frac{2 \, z {\left(e^{\left(\sqrt{2} z\right)} + 1\right)}}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \end{array}\right)$

 $- 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2$  $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2}$

 $- 2 ( 4 z e ( 2 \sqrt z ) + 2 \sqrt e ( 2 2 \sqrt z ) - 2 \sqrt ) z z 2 e ( 2 2 \sqrt z ) - 2 z 2 e ( 2 \sqrt z ) + z 2 - 2 e ( 2 2 \sqrt z ) - 4 e ( 2 \sqrt z ) - 2$  $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2 \, {\left(4 \, z e^{\left(\sqrt{2} z\right)} + \sqrt{2} e^{\left(2 \, \sqrt{2} z\right)} - \sqrt{2}\right)} z}{z^{2} e^{\left(2 \, \sqrt{2} z\right)} - 2 \, z^{2} e^{\left(\sqrt{2} z\right)} + z^{2} - 2 \, e^{\left(2 \, \sqrt{2} z\right)} - 4 \, e^{\left(\sqrt{2} z\right)} - 2}$

 $256.708333711561$  $\newcommand{\Bold}[1]{\mathbf{#1}}256.708333711561$

 $2818.91488343021$  $\newcommand{\Bold}[1]{\mathbf{#1}}2818.91488343021$

 $1.69660180354$  $\newcommand{\Bold}[1]{\mathbf{#1}}1.69660180354$

 $[0, 0, 2, 0, 8, 0, 84, 0, 1632, 0, 51040, 0, 2340480, 0, 147985824, 0, 12338740736, 0, 1311694023168, 0]$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, 0, 2, 0, 8, 0, 84, 0, 1632, 0, 51040, 0, 2340480, 0, 147985824, 0, 12338740736, 0, 1311694023168, 0\right]$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ( 2 \sqrt e ( 2 \sqrt x z ) - 2 \sqrt e ( - 2 \sqrt x z ) ) z ( e ( 2 \sqrt z ) + 1 ) 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) - ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 ) ( e ( 2 \sqrt x z ) + e ( - 2 \sqrt x z ) + 2 ) 4 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) - 1 4 e (2 \sqrt x z) - 1 4 e (- 2 \sqrt x z) + 1 2 - 1 2 x z - z ( e ( 2 \sqrt x z ) + e ( - 2 \sqrt x z ) + 2 ) ( e ( 2 \sqrt z ) + 1 ) 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) + 1 8 2 \sqrt e (2 \sqrt x z) - 1 8 2 \sqrt e (- 2 \sqrt x z) + ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 ) ( 4 x z + 2 \sqrt e ( 2 \sqrt x z ) - 2 \sqrt e ( - 2 \sqrt x z ) ) 8 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) - ( 2 \sqrt e ( 2 \sqrt x z ) - 2 \sqrt e ( - 2 \sqrt x z ) ) z ( e ( 2 \sqrt z ) + 1 ) 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) + ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 ) ( e ( 2 \sqrt x z ) + e ( - 2 \sqrt x z ) - 2 ) 4 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) + 1 4 e (2 \sqrt x z) + 1 4 e (- 2 \sqrt x z) + 1 2 1 2 x z - z ( e ( 2 \sqrt x z ) + e ( - 2 \sqrt x z ) - 2 ) ( e ( 2 \sqrt z ) + 1 ) 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) + 1 8 2 \sqrt e (2 \sqrt x z) - 1 8 2 \sqrt e (- 2 \sqrt x z) - ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z + 2 e ( 2 \sqrt z ) + 2 ) ( 4 x z - 2 \sqrt e ( 2 \sqrt x z ) + 2 \sqrt e ( - 2 \sqrt x z ) ) 8 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{r} \frac{{\left(\sqrt{2} e^{\left(\sqrt{2} x z\right)} - \sqrt{2} e^{\left(-\sqrt{2} x z\right)}\right)} z {\left(e^{\left(\sqrt{2} z\right)} + 1\right)}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} - \frac{{\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2\right)} {\left(e^{\left(\sqrt{2} x z\right)} + e^{\left(-\sqrt{2} x z\right)} + 2\right)}}{4 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} - \frac{1}{4} \, e^{\left(\sqrt{2} x z\right)} - \frac{1}{4} \, e^{\left(-\sqrt{2} x z\right)} + \frac{1}{2} \\ -\frac{1}{2} \, x z - \frac{z {\left(e^{\left(\sqrt{2} x z\right)} + e^{\left(-\sqrt{2} x z\right)} + 2\right)} {\left(e^{\left(\sqrt{2} z\right)} + 1\right)}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} + \frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} x z\right)} - \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} x z\right)} + \frac{{\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2\right)} {\left(4 \, x z + \sqrt{2} e^{\left(\sqrt{2} x z\right)} - \sqrt{2} e^{\left(-\sqrt{2} x z\right)}\right)}}{8 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} \\ -\frac{{\left(\sqrt{2} e^{\left(\sqrt{2} x z\right)} - \sqrt{2} e^{\left(-\sqrt{2} x z\right)}\right)} z {\left(e^{\left(\sqrt{2} z\right)} + 1\right)}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} + \frac{{\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2\right)} {\left(e^{\left(\sqrt{2} x z\right)} + e^{\left(-\sqrt{2} x z\right)} - 2\right)}}{4 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} + \frac{1}{4} \, e^{\left(\sqrt{2} x z\right)} + \frac{1}{4} \, e^{\left(-\sqrt{2} x z\right)} + \frac{1}{2} \\ \frac{1}{2} \, x z - \frac{z {\left(e^{\left(\sqrt{2} x z\right)} + e^{\left(-\sqrt{2} x z\right)} - 2\right)} {\left(e^{\left(\sqrt{2} z\right)} + 1\right)}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} + \frac{1}{8} \, \sqrt{2} e^{\left(\sqrt{2} x z\right)} - \frac{1}{8} \, \sqrt{2} e^{\left(-\sqrt{2} x z\right)} - \frac{{\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z + 2 \, e^{\left(\sqrt{2} z\right)} + 2\right)} {\left(4 \, x z - \sqrt{2} e^{\left(\sqrt{2} x z\right)} + \sqrt{2} e^{\left(-\sqrt{2} x z\right)}\right)}}{8 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} \end{array}\right)$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ( 2 \sqrt z e ( 2 2 \sqrt x z ) - 2 \sqrt z e ( 2 \sqrt z ) - 2 e ( 2 \sqrt ( x + 1 ) z ) - 2 e ( 2 \sqrt x z ) ) e ( - 2 \sqrt x z ) 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ( 2 x e ( 2 \sqrt ( x + 1 ) z ) + 2 x e ( 2 \sqrt x z ) - e ( 2 \sqrt ( x + 1 ) z ) - e ( 2 2 \sqrt x z ) - e ( 2 \sqrt x z ) - e ( 2 \sqrt z ) ) z e ( - 2 \sqrt x z ) 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 - ( 2 \sqrt z e ( 2 2 \sqrt x z ) - 2 \sqrt z e ( 2 \sqrt z ) + 2 e ( 2 \sqrt ( x + 1 ) z ) + 2 e ( 2 \sqrt x z ) ) e ( - 2 \sqrt x z ) 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 - ( 2 x e ( 2 \sqrt ( x + 1 ) z ) + 2 x e ( 2 \sqrt x z ) - e ( 2 \sqrt ( x + 1 ) z ) + e ( 2 2 \sqrt x z ) - e ( 2 \sqrt x z ) + e ( 2 \sqrt z ) ) z e ( - 2 \sqrt x z ) 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{r} \frac{{\left(\sqrt{2} z e^{\left(2 \, \sqrt{2} x z\right)} - \sqrt{2} z e^{\left(\sqrt{2} z\right)} - 2 \, e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} - 2 \, e^{\left(\sqrt{2} x z\right)}\right)} e^{\left(-\sqrt{2} x z\right)}}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ \frac{{\left(2 \, x e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} + 2 \, x e^{\left(\sqrt{2} x z\right)} - e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} - e^{\left(2 \, \sqrt{2} x z\right)} - e^{\left(\sqrt{2} x z\right)} - e^{\left(\sqrt{2} z\right)}\right)} z e^{\left(-\sqrt{2} x z\right)}}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ -\frac{{\left(\sqrt{2} z e^{\left(2 \, \sqrt{2} x z\right)} - \sqrt{2} z e^{\left(\sqrt{2} z\right)} + 2 \, e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} + 2 \, e^{\left(\sqrt{2} x z\right)}\right)} e^{\left(-\sqrt{2} x z\right)}}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ -\frac{{\left(2 \, x e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} + 2 \, x e^{\left(\sqrt{2} x z\right)} - e^{\left(\sqrt{2} {\left(x + 1\right)} z\right)} + e^{\left(2 \, \sqrt{2} x z\right)} - e^{\left(\sqrt{2} x z\right)} + e^{\left(\sqrt{2} z\right)}\right)} z e^{\left(-\sqrt{2} x z\right)}}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \end{array}\right)$

 $⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 2 x e ( 2 \sqrt z ) + 2 x - e ( - 2 \sqrt ( x - 1 ) z ) - e ( 2 \sqrt x z ) + e ( 2 \sqrt z ) + 1 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 2 ( x e ( 2 \sqrt z ) + x - e ( 2 \sqrt z ) - 1 ) x z + 2 \sqrt e ( - 2 \sqrt ( x - 1 ) z ) - 2 \sqrt e ( 2 \sqrt x z ) - 2 \sqrt e ( 2 \sqrt z ) + 2 \sqrt 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) - 2 x e ( 2 \sqrt z ) + 2 x + e ( - 2 \sqrt ( x - 1 ) z ) + e ( 2 \sqrt x z ) - e ( 2 \sqrt z ) - 1 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 - 2 ( x e ( 2 \sqrt z ) + x - e ( 2 \sqrt z ) - 1 ) x z - 2 \sqrt e ( - 2 \sqrt ( x - 1 ) z ) + 2 \sqrt e ( 2 \sqrt x z ) + 2 \sqrt e ( 2 \sqrt z ) - 2 \sqrt 2 ( 2 \sqrt z e ( 2 \sqrt z ) - 2 \sqrt z - 2 e ( 2 \sqrt z ) - 2 ) ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟$  $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{r} -\frac{2 \, x e^{\left(\sqrt{2} z\right)} + 2 \, x - e^{\left(-\sqrt{2} {\left(x - 1\right)} z\right)} - e^{\left(\sqrt{2} x z\right)} + e^{\left(\sqrt{2} z\right)} + 1}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ \frac{2 \, {\left(x e^{\left(\sqrt{2} z\right)} + x - e^{\left(\sqrt{2} z\right)} - 1\right)} x z + \sqrt{2} e^{\left(-\sqrt{2} {\left(x - 1\right)} z\right)} - \sqrt{2} e^{\left(\sqrt{2} x z\right)} - \sqrt{2} e^{\left(\sqrt{2} z\right)} + \sqrt{2}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} \\ -\frac{2 \, x e^{\left(\sqrt{2} z\right)} + 2 \, x + e^{\left(-\sqrt{2} {\left(x - 1\right)} z\right)} + e^{\left(\sqrt{2} x z\right)} - e^{\left(\sqrt{2} z\right)} - 1}{\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2} \\ -\frac{2 \, {\left(x e^{\left(\sqrt{2} z\right)} + x - e^{\left(\sqrt{2} z\right)} - 1\right)} x z - \sqrt{2} e^{\left(-\sqrt{2} {\left(x - 1\right)} z\right)} + \sqrt{2} e^{\left(\sqrt{2} x z\right)} + \sqrt{2} e^{\left(\sqrt{2} z\right)} - \sqrt{2}}{2 \, {\left(\sqrt{2} z e^{\left(\sqrt{2} z\right)} - \sqrt{2} z - 2 \, e^{\left(\sqrt{2} z\right)} - 2\right)}} \end{array}\right)$

#The function Boltz does the generation of timed words with parameter zparam. It also does conversion the to permutations.  
#The precomputed generating functions as well as transition matrices are global variables
def Boltz(zparam):
    t_1=cputime();
    curx=0;
    n=0;
    delay=[];
    w=[];
    curloc=0;
    curx=0.0;
    while true:    
        gval=numerical_approx(Y[curloc,0](x=curx,z=zparam))        
        r=random();
        #print(curloc);
        if r< F[curloc,0]/gval: #epsilon is chosen
        	break
        n=n+1; 
        qs=Trans[0,curloc];
        if qs!=-1:
            qt=Trans[1,curloc]
            if qt==-1:
                b=1      #The only possible transition is S
                wis=gval-F[curloc,0] #weight of S
            else:
	        it=zparam*CDF_Y[qt,0](x=1-curx,z=zparam) #weight of T
                wis=gval-it-F[curloc,0] #weight of S
                r=random()
                if r*gval<F[curloc,0]+it: # T is chosen
                    b=0
                else:
                    b=1;
        else:
            b=0;      #The only possible transition is T
            it=gval-F[curloc,0]; #weight of T
            qt=Trans[1,curloc];
            p=0
        if b==1:#the next trans is S
            w=w+[0]
            curloc=qs
            r=random()
	    fg(t)=(zparam*(CDF_Y[qs,0](x=t,z=zparam)-CDF_Y[qs,0](curx,z=zparam))/wis) -r
            curdel=find_root(fg(t),curx,1)-curx
            delay=delay+[curdel]
            curx= curx+curdel
        else:#the next trans is T
            w=w+[1]
            curloc=qt
            r=random()
	    ff(t)=(zparam*CDF_Y[qt,0](x=t,z=zparam)/it)-r
            curdel=find_root(ff(t),0,1-curx)
            delay=delay+[curdel]
            curx=curdel
    #print delay;  #uncomment to see the vector of delays
    #print('computing the function phi');
#computing the function phi
    nu=vector(RDF,n);
    if n!=0:
        curad=ST_enc*(1-w[0])+(1-ST_enc)*w[0];
        nu[0]=curad*(1-delay[0])+(1-curad)*delay[0]; #type of the S-T-encoding l=0 means l=a, l=1 means l=d 
        for k in range(1,n):#a changer si n=0
            if w[k]==0:                                       #a straight 
                if curad==0:                                  #The previous letter is an ascent: pattern aa
                    nu[k]=nu[k-1]+delay[k]
                else:                                           #The previous letter is a descent: pattern dd
                    nu[k]=nu[k-1]-delay[k]
            else:        
                if curad==0:                                     #The previous letter is an ascent: pattern ad
                    nu[k]=1-delay[k]
                else:                                           #The previous letter is a descent: pattern da
                    nu[k]=delay[k]
                curad=1-curad;                                  #flip the value of l since w_k is a turn
    #print nu #uncomment to see the vector nu in the order polytopes.
        t_4=cputime();
    #print('sorting and answering');
        answer=Word(list(nu)[0:n]).standard_permutation();
    #print answer #return the permutation
    return([cputime(t_1),n]);

#Here
 are the results obtain for the 71 experiments used in the paper 
(parameter 1.69).
r169=[[6.470999999999549, 130], [6.154000000000451, 124],
[12.626999999999498, 256], [14.934000000000196, 308],
[44.86800000000039, 936], [7.634999999999309, 160], [9.576000000000022,
196], [31.430999999999585, 642], [12.031000000000859, 252],
[7.363999999999578, 154],[19.228999999999996, 390],
[0.8419999999999987, 18],
[24.375000000000007, 502],
[7.153000000000006, 146],
[0.08399999999998897, 2],
[4.403000000000006, 92],
[0.1910000000000025, 4],
[21.269999999999996, 444],
[9.242999999999995, 190],
[18.076999999999998, 378],
[13.240000000000009, 272],
[7.640999999999991, 160],
[16.818000000000012, 344],
[5.235000000000014, 110],
[8.758999999999986, 178],
[36.845999999999975, 774],
[5.925000000000011, 120],
[20.797000000000025, 430],
[0.2639999999999816, 6],
[47.93299999999999, 988],
[9.16500000000002, 194],
[5.168000000000006, 106],
[3.3029999999999973, 66],
[14.925999999999988, 312],
[8.430999999999983, 178],
[2.7379999999999995, 56],
[1.1550000000000296, 24],
[3.545000000000016, 74],
[2.0849999999999795, 44],
[16.581000000000017, 346],
[10.100000000000023, 206],
[0.5659999999999741, 12],
[11.962000000000046, 242],[12.997000000000298, 262], 
[12.135999999999513, 248],
[9.391999999999825, 196], [14.695000000000618, 306],
[23.792999999999665, 492], [35.766999999999825, 750],
[12.908000000000357, 268], [9.28899999999976, 198], [8.61999999999989,
176], [9.761999999999716, 196],
[2.3629999999999995, 46], [4.57, 94], [6.706000000000003, 130], 
[0.9599999999999973, 16], [1.6289999999999978, 32], [5.802, 118], 
[5.4140000000000015, 112], [28.168999999999997, 574], 
[3.2079999999999984, 66], [14.515999999999991, 292], 
[2.9950000000000188, 60], [28.576999999999984, 582], 
[0.6270000000000095, 12], [11.66000000000001, 240], [8.189999999999998, 
174], [44.375999999999976, 800], [8.177000000000021, 164]
];

#Here
 are the results obtain for the 71 experiments used in the paper 
(parameter 1.696).
r1696=[[13.870000000000005, 280], [102.01599999999999, 2088], [307.131, 
6286], [264.08500000000004, 5428], [28.57899999999995, 594], 
[87.71199999999999, 1796], [8.395000000000095, 170], [31.55899999999997,
 652], [37.563999999999965, 778],
[248.6049999999999, 5144], [187.66600000000005, 3892], [214.745, 4474],
[184.3610000000001, 3870],[2.475999999999999, 52], [87.67900000000009, 
1830],
[147.31399999999985, 3076], [564.615, 11756], [345.44900000000007,
7180], [145.8130000000001, 3054], [58.18399999999974, 1220],
[128.37199999999984, 2674], [213.11400000000003, 4450],
[97.20699999999988, 2038], [177.9720000000002, 3724],
[71.79599999999982, 1398], [101.99000000000024, 2026],
[75.43399999999974, 1550], [119.82999999999993, 2494],
[71.48500000000013, 1500], [4.264999999999873, 92], [24.618000000000393,
520], [163.83199999999988, 3416], [110.19399999999996, 2298],
[47.43000000000029, 992], [202.76399999999967, 4226],
[165.28299999999945, 3440], [151.95800000000054, 3130],
[191.1180000000004, 3976], [267.9399999999996, 5576],
[5.3419999999996435, 112],
[223.54, 4638],[37.10499999999999, 784],[167.62300000000005, 
3486],[14.645999999999958, 302],
[82.14800000000002, 1708],[305.578, 6350],[39.043000000000006, 
820],[3.865000000000009, 82],[91.02299999999991, 1902],
[120.58600000000001, 2524],
[241.0110000000002, 5034],
[462.59199999999987, 9618],
[172.1199999999999, 3614],
[70.68900000000008, 1484],
[42.5300000000002, 890],
[6.618999999999687, 138],
[343.2350000000001, 7166],
[99.51100000000042, 2064],
[77.80099999999948, 1628],
[135.46800000000076, 2804],
[180.20099999999957, 3740],
[351.2060000000006, 7298],
[58.735999999999876, 1226],
[156.1210000000001, 3238],
[280.0079999999998, 5824],
[155.91400000000021, 3268],
[62.05399999999963, 1298],
[32.56100000000015, 678],
[291.9149999999995, 6066],
[142.45899999999983, 2976],
[123.19599999999991, 2574]];