From d887b765b093a1bcb284e21ecd135fcfa7058c14 Mon Sep 17 00:00:00 2001
From: SciPost Editorial Administration <edadmin@scipost.org>
Date: Tue, 12 Dec 2023 16:23:44 +0100
Subject: [PATCH] Include TASEPy-1.1
---
TASEPy-1.1/LICENSE | 21 +
TASEPy-1.1/README.md | 20 +
TASEPy-1.1/TASEPy.py | 500 ++++++++
TASEPy-1.1/applications/YAL008W_rates.dat | 198 ++++
.../info_a02_L100_ll10_iter1e6.log | 2 +
.../applications/info_a02_L20_ll1_iter1e6.log | 2 +
.../applications/kappa_L20-inferred.dat | 20 +
.../applications/kappa_L20-minimize.log | 109 ++
TASEPy-1.1/applications/rates_L100.dat | 100 ++
TASEPy-1.1/applications/rates_L20.dat | 20 +
.../rho_a02_L100_ll10_iter1e6.dat | 100 ++
.../applications/rho_a02_L20_ll1_iter1e6.dat | 20 +
TASEPy-1.1/applications_TASEPy.ipynb | 783 ++++++++++++
TASEPy-1.1/benchmarks_TASEPy.ipynb | 1046 +++++++++++++++++
TASEPy-1.1/exact/current-coeff_L4_ll1.csv | 1 +
TASEPy-1.1/exact/current-coeff_L4_ll2.csv | 1 +
TASEPy-1.1/exact/current-coeff_L4_ll3.csv | 1 +
TASEPy-1.1/exact/exact-small-system.nb | 795 +++++++++++++
TASEPy-1.1/exact/prob-coeff_L4_ll1.csv | 16 +
TASEPy-1.1/exact/prob-coeff_L4_ll2.csv | 8 +
TASEPy-1.1/exact/prob-coeff_L4_ll3.csv | 6 +
TASEPy-1.1/exact/rates_L4.csv | 4 +
TASEPy-1.1/exact/rho-coeff_L4_ll1.csv | 4 +
TASEPy-1.1/exact/rho-coeff_L4_ll2.csv | 4 +
TASEPy-1.1/exact/rho-coeff_L4_ll3.csv | 4 +
.../current_a02_L50_ll1_iter1e6.dat | 51 +
.../current_a02_L50_ll5_iter1e6.dat | 51 +
TASEPy-1.1/simulations/dTASEPe.dat | 7 +
TASEPy-1.1/simulations/dTASEPe.f90 | 264 +++++
TASEPy-1.1/simulations/mt19937.f90 | 200 ++++
TASEPy-1.1/simulations/rates_L50.dat | 50 +
.../simulations/rho_a02_L50_ll1_iter1e6.dat | 50 +
.../simulations/rho_a02_L50_ll5_iter1e6.dat | 50 +
TASEPy-1.1/tutorial_TASEPy.ipynb | 589 ++++++++++
34 files changed, 5097 insertions(+)
create mode 100644 TASEPy-1.1/LICENSE
create mode 100644 TASEPy-1.1/README.md
create mode 100644 TASEPy-1.1/TASEPy.py
create mode 100644 TASEPy-1.1/applications/YAL008W_rates.dat
create mode 100644 TASEPy-1.1/applications/info_a02_L100_ll10_iter1e6.log
create mode 100644 TASEPy-1.1/applications/info_a02_L20_ll1_iter1e6.log
create mode 100644 TASEPy-1.1/applications/kappa_L20-inferred.dat
create mode 100644 TASEPy-1.1/applications/kappa_L20-minimize.log
create mode 100644 TASEPy-1.1/applications/rates_L100.dat
create mode 100644 TASEPy-1.1/applications/rates_L20.dat
create mode 100644 TASEPy-1.1/applications/rho_a02_L100_ll10_iter1e6.dat
create mode 100644 TASEPy-1.1/applications/rho_a02_L20_ll1_iter1e6.dat
create mode 100644 TASEPy-1.1/applications_TASEPy.ipynb
create mode 100644 TASEPy-1.1/benchmarks_TASEPy.ipynb
create mode 100644 TASEPy-1.1/exact/current-coeff_L4_ll1.csv
create mode 100644 TASEPy-1.1/exact/current-coeff_L4_ll2.csv
create mode 100644 TASEPy-1.1/exact/current-coeff_L4_ll3.csv
create mode 100644 TASEPy-1.1/exact/exact-small-system.nb
create mode 100644 TASEPy-1.1/exact/prob-coeff_L4_ll1.csv
create mode 100644 TASEPy-1.1/exact/prob-coeff_L4_ll2.csv
create mode 100644 TASEPy-1.1/exact/prob-coeff_L4_ll3.csv
create mode 100644 TASEPy-1.1/exact/rates_L4.csv
create mode 100644 TASEPy-1.1/exact/rho-coeff_L4_ll1.csv
create mode 100644 TASEPy-1.1/exact/rho-coeff_L4_ll2.csv
create mode 100644 TASEPy-1.1/exact/rho-coeff_L4_ll3.csv
create mode 100644 TASEPy-1.1/simulations/current_a02_L50_ll1_iter1e6.dat
create mode 100644 TASEPy-1.1/simulations/current_a02_L50_ll5_iter1e6.dat
create mode 100644 TASEPy-1.1/simulations/dTASEPe.dat
create mode 100644 TASEPy-1.1/simulations/dTASEPe.f90
create mode 100644 TASEPy-1.1/simulations/mt19937.f90
create mode 100644 TASEPy-1.1/simulations/rates_L50.dat
create mode 100644 TASEPy-1.1/simulations/rho_a02_L50_ll1_iter1e6.dat
create mode 100644 TASEPy-1.1/simulations/rho_a02_L50_ll5_iter1e6.dat
create mode 100644 TASEPy-1.1/tutorial_TASEPy.ipynb
diff --git a/TASEPy-1.1/LICENSE b/TASEPy-1.1/LICENSE
new file mode 100644
index 0000000..319a0cc
--- /dev/null
+++ b/TASEPy-1.1/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2023 Ciandrini, Crisostomo, Szavits-Nossan
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/TASEPy-1.1/README.md b/TASEPy-1.1/README.md
new file mode 100644
index 0000000..161bc71
--- /dev/null
+++ b/TASEPy-1.1/README.md
@@ -0,0 +1,20 @@
+# TASEPy
+TASEPy is a python package providing a numerical solution for the inhomogeneous Totally Asymmetric Simple Exclusion Process (TASEP) in the stationary state. The TASEP is a paradigmatic lattice model for one-dimensional particle transport subject to excluded-volume interactions. The package TASEPy provides an implementation of the Power Series Approximation (PSA) introduced in [1,2] for solving the TASEP in the limit in which the initiation rate at which new particles are added to the lattice is small. The iterative solution proposed here is detailed in the affiliated paper [3].
+
+All numerical methods are implemented in Python 3.
+
+## Tutorial
+
+A short tutorial demonstrating TASEPy is given in this [python notebook](<tutorial_TASEPy.ipynb>).
+
+## Benchmarks
+
+The TASEPy has been tested using exact results obtained by solving the master equation for small systems, and numerical results obtained by stochastic simulations for large systems. These tests can be found in this [python notebook](<benchmarks_TASEPy.ipynb>).
+
+## Bibliography
+[1] J. Szavits-Nossan, L. Ciandrini and M. C. Romano, Deciphering mRNA Sequence Determinants of Protein Production Rate, *Physical Review Letters* 120, 128101 (2018) \[[url](https://doi.org/10.1103/PhysRevLett.120.128101)\]
+
+[2] J. Szavits-Nossan, M. C. Romano and L. Ciandrini, Power series solution of the inhomogeneous exclusion process, *Physical Review E* 97, 052139 (2018) \[[url](https://doi.org/10.1103/PhysRevE.97.052139)\]
+
+[3] L. Ciandrini, R. Crisostomo, J. Szavits-Nossan, *preprint* arXiv:2308.00847 \[[url](https://arxiv.org/abs/2308.00847)\] (2023)
+
diff --git a/TASEPy-1.1/TASEPy.py b/TASEPy-1.1/TASEPy.py
new file mode 100644
index 0000000..3af3044
--- /dev/null
+++ b/TASEPy-1.1/TASEPy.py
@@ -0,0 +1,500 @@
+###############################################################################
+#
+# TASEPy v1.1
+# October 2023
+#
+# Based on Ciandrini et al., 2023
+#
+###############################################################################
+
+import numpy as np
+import matplotlib.pyplot as plt
+import pandas as pd
+import csv
+from scipy.special import comb as choose
+
+###############################################################################
+#
+# DEFINE: Returns the maximum number of particles that can fit on the lattice.
+#
+###############################################################################
+
+def N_max(L, ll=1):
+ '''
+ Returns the maximum number of particles that can fit onto the lattice of
+ size L. Particle size ll is optional (=1 by default).
+ '''
+
+ Nmax = 0
+ i = 1
+ xi = 1
+ while xi <= L:
+ Nmax += 1
+ i += 1
+ xi = 1 + (i-1)*ll
+
+ return Nmax
+
+
+
+###############################################################################
+#
+# DEFINE: Returns the stacked particle configuration for a given PSA order.
+#
+###############################################################################
+
+def stacked_config(npsa, L, ll=1):
+ '''
+ Returns a stacked configuration of order npsa. The result is a list x of
+ size npsa, where x[i-1] is the position of the i-th particle. If npsa is
+ smaller or equal to Nmax, where Nmax is the maximum number of particles
+ that can fit onto the lattice, then the resulting configuration has npsa
+ particles, otherwise it has Nmax particles.
+ '''
+
+ Nmax = N_max(L, ll)
+ if npsa > Nmax:
+ npsa = Nmax
+
+ # initialize list
+ x = []
+
+ if npsa > 0:
+ # stack all particles
+ i = 1
+ xi = 1
+ while (xi <= L and i <= npsa):
+ x.append(xi)
+ i += 1
+ if i <= npsa:
+ xi = 1 + (i-1)*ll
+
+ return x
+
+
+
+###############################################################################
+#
+# DEFINE: Returns the number of non-zero coefficients of a given PSA order.
+#
+###############################################################################
+
+def nonzero_coeffs(n, L, ll=1):
+ '''
+ Returns the number of non-zero coefficients of a given order PSA order n,
+ given the lattice size L and the particle size ll.
+ '''
+
+ if n == 0:
+ return 1
+
+ elif n > 0:
+ sum_i = np.zeros(n)
+ for ii in range(n):
+ i = ii + 1
+ term_i1 = choose(L-i*ll+i,i)
+ sum_k = np.zeros(ll-1)
+ for kk in range(ll-1):
+ k = kk + 1
+ term_k = choose(L-k-(i-1)*ll+i-1,i-1)
+ sum_k[kk] = term_k
+ term_i2 = np.sum(sum_k)
+ sum_i[ii] = term_i1 + term_i2
+
+ Cn = 1 + np.sum(sum_i)
+
+ return Cn
+
+
+###############################################################################
+#
+# DEFINE: Returns the total number of all non-zero coefficients up to a given
+# PSA order.
+#
+###############################################################################
+
+def total_coeffs(K, L, ll=1):
+ '''
+ Returns the total number of all non-zero coefficients up to a given PSA order
+ K, given the lattice size L and the particle size ll. It is advised to use
+ this function if one is calling psa_compute with save_coeffs=True, in order to
+ check how much lines the resulting file will have.
+ '''
+
+ Nmax = N_max(L, ll)
+ sum_Cn = np.zeros(K+1)
+ for n in range(K+1):
+ Cn = nonzero_coeffs(n, L, ll)
+ sum_Cn[n] = Cn
+
+ if K <= Nmax:
+
+ result = np.sum(sum_Cn)
+ return result.astype(int)
+
+ elif K > Nmax:
+
+ result = np.sum(sum_Cn) + ((K-Nmax)*nonzero_coeffs(Nmax, L, ll))
+ return result.astype(int)
+
+
+
+###############################################################################
+#
+# DEFINE: Returns the next configuration in the PSA iteration.
+#
+###############################################################################
+
+def next_config(xlist, L, ll=1):
+ '''
+ Returns next configuration in the PSA iteration from the input configuration
+ xlist. The input configuration is a list of size equal to the order of the
+ PSA. The elements of xlist are particle positions. The values of xlist for
+ particles that are missing are set to zero.
+
+ For example, xlist = [1,2,0] means that the PSA order is 3, the 1st
+ particle is at lattice site 1, the 2nd particle is at lattice site 2, and
+ the 3rd particle is missing. On the other hand, xlist = [1,2] means that
+ the PSA order is 2, the 1st particle is at lattice site 1 and the 2nd
+ particle is at lattice site 2.
+ '''
+
+ # the order of the PSA, also the maximum number of particles for which
+ # the PSA coefficient is non-zero
+ npsa = len(xlist)
+
+ # number of zeros in xlist
+ nzeros = xlist.count(0)
+
+ # number of particles in xlist
+ N = npsa - nzeros
+
+ if xlist[N-1] < L:
+
+ # moves rightmost particle one lattice site to the right
+ xlist[N-1] += 1
+
+ # stackes npsa - N particles next to the rightmost particle,
+ # if possible
+ if N < npsa:
+ j = N
+ xj = xlist[N-1] + ll
+ while (xj <= L and j < npsa):
+ xlist[j] = xj
+ j += 1
+ if j < npsa:
+ xj = xlist[j-1]+ll
+ else:
+ xlist[N-1] = 0
+
+ return xlist
+
+
+
+###############################################################################
+#
+# DEFINE: Returns the total exit rate excluding initiation rate.
+#
+###############################################################################
+
+def e_0(xlist, wlist, ll=1):
+ '''
+ Returns the total exit rate excluding initiation, see Eq. 30 in the main
+ text.
+ '''
+
+ # number of particles
+ N = len(xlist) - xlist.count(0)
+
+ if N == 0:
+ total = 0
+ elif N == 1:
+ pos_x = xlist[0]-1 # particle position shifted by -1
+ total = wlist[pos_x]
+ else:
+ total = 0
+ for particle_number in range(N-1):
+ site = xlist[particle_number]
+ next_site = xlist[particle_number+1]
+ if next_site-site > ll:
+ total += wlist[site-1]
+ site = xlist[N-1]
+ total += wlist[site-1]
+
+ return total
+
+
+
+###############################################################################
+#
+# DEFINE: Computes the 1st order coefficient for a given configuration.
+#
+###############################################################################
+
+def c_1(xlist, wlist):
+ '''
+ Returns the 1st order coefficient c_1, see Eqs. 27 and 28 in the main text.
+ '''
+
+ if xlist[0] == 0: # empty configuration, implement Eq.(28)
+ total = 0.0
+ for w in wlist:
+ total += 1.0/w
+ coeff = - total
+
+ else: # non-empty configuration, implement Eq.(27)
+ coeff=1.0/wlist[xlist[0]-1] #-1 since we start with position 0
+
+ return coeff
+
+
+
+###############################################################################
+#
+# DEFINE: Performs the PSA up to a given order.
+#
+###############################################################################
+
+def psa_compute(wlist, K, ll=1, save_coeffs=False, coeffs_file='Pcoeff.csv'):
+ '''
+ Computes coefficients of the current and local density for orders 0,...,K.
+ '''
+
+ # finds lattice size
+ L = len(wlist)
+
+ # finds maximum number of particles
+ Nmax = N_max(L, ll)
+
+ # open file for storing probability coefficients
+ if save_coeffs == True:
+ f=open(coeffs_file, 'w', newline='')
+ writer = csv.writer(f, quoting=csv.QUOTE_NONNUMERIC)
+ writer.writerow([0,[],1.0]) # add zeroth order coefficient
+
+ # initializes the dictionary
+ c_n = {}
+
+ # initializes the list for storing local density coefficients
+ rhocoeff = []
+
+ # initializes the list for storing current coefficients
+ Jcoeff = []
+
+ # order = 0
+ Jcoeff.append(1.0) # the current coefficient is 1
+ for site_i in range(L):
+ rhocoeff.append([0.0]) # the local density coefficients are 0
+
+ # main loop over orders n = 1,...,K
+ for n in range(1,K+1):
+
+ c_n_minus1 = c_n.copy()
+ c_n.clear()
+
+ # resets current and local density coefficients
+ Jcoeff_sum = 0
+ rhocoeff_sum = [0 for site_i in range(L)]
+
+ # stacked configuration
+ X = stacked_config(n, L, ll)
+
+ # number of particles in the stacked configuration
+ N = len(X)
+
+ if n == 1: # order = 1
+
+ # computes c_1 for the stacked configuration
+ coeff = c_1(X, wlist)
+
+ else: # order > 1
+ xn = X[-1]-1 # position of the last particle shifted by -1
+ if n <= Nmax:
+ Xtemp = X[1:]
+ else:
+ Xtemp = X[1:]
+ Xtemp.append(0)
+
+ # computes c_n for the stacked configuration
+ coeff = c_n_minus1[str(Xtemp)]/wlist[xn]
+
+ # adds the stacked configuration coefficient to the dictionary c_n
+ c_n[str(X)] = coeff
+
+ # writes the stacked configuration coefficient to the file
+ if save_coeffs == True:
+ writer.writerow([n,np.trim_zeros(X,'b'),coeff])
+
+ # updates the local density coefficients
+ for particle_number in range(N):
+ pos_x = particle_number*ll # particle position shifted by -1
+ rhocoeff_sum[pos_x] += coeff
+
+ # iterates over all configurations belonging to the nth order
+ while X[0] != 0: # iteration ends when the last particle leaves the lattice
+
+ # selects next configuration
+ X = next_config(X, L, ll)
+
+ # number of particles in X
+ N = len(X) - X.count(0)
+
+ if n == 1: # order = 1
+
+ # computes c_1 for configuration X
+ coeff = c_1(X, wlist)
+
+ else: # order > 1
+
+ if X[0] == 0: # empty configuration
+
+ # computes c_n for configuration X
+ coeff = -sum(c_n.values())
+
+ else:
+ # total exit rate excluding initiation
+ e_0X = e_0(X, wlist, ll)
+
+ # computes term (a) in Eq.(29)
+ a = 0
+ if X[0] == 1 :
+ if n <= Nmax:
+ Xtemp = X[1:]
+ else:
+ Xtemp = X[1:]
+ Xtemp.append(0)
+
+ a = c_n_minus1[str(Xtemp)]
+
+ # computes term (b1) in Eq.(29)
+ b1 = 0
+ if X[0] > 1 :
+ Xtemp = X.copy()
+ Xtemp[0] = Xtemp[0]-1
+ pos_x1_min1 = Xtemp[0]-1 # -1 because wlist starts from index 0
+ b1 = wlist[pos_x1_min1] * c_n[str(Xtemp)]
+
+ # computes term (b2) in Eq.(29)
+ b2 = 0
+ if N > 1: # do this only if there is more than one particle
+ for particle_number in range(N-1):
+ Xtemp = X.copy()
+ if X[particle_number + 1] - X[particle_number] > ll:
+ Xtemp[particle_number+1] -= 1
+ pos_x_min1 = Xtemp[particle_number+1]-1 #-1 again because wlist starts from index 0
+ b2 += wlist[pos_x_min1] * c_n[str(Xtemp)]
+
+ # computes term (c) in Eq.(29)
+ c = 0
+ if (X[N-1] <= L-ll) and (n >= N +1):
+ Xtemp = X.copy()
+ Xtemp[N] = L
+ c = wlist[-1] * c_n[str(Xtemp)]
+
+ # computes term (d) in Eq.(29)
+ d = 0
+ if (X[0] > ll) and (n-1 >= N):
+ Xtemp = X.copy()
+ if n <= Nmax:
+ Xtemp.pop()
+ d = c_n_minus1[str(Xtemp)]
+
+ # computes c_n for configuration X
+ coeff = (a + b1 + b2 + c - d)/e_0X
+
+ # adds the computed coefficient to the dictionary c_n
+ c_n[str(X)] = coeff
+
+ # writes the coefficient to the file
+ if save_coeffs == True:
+ writer.writerow([n,np.trim_zeros(X,'b'),coeff])
+
+ # updates the current coefficient
+ if X[0] >= ll+1 or X[0] == 0:
+ Jcoeff_sum += coeff
+
+ # updates the local density coefficients
+ for particle_number in range(N):
+ pos_x = X[particle_number]-1 # particle position shifted by -1
+ rhocoeff_sum[pos_x] += coeff
+
+ Jcoeff.append(Jcoeff_sum)
+
+ for site_i in range(L):
+ rho_i_n = rhocoeff_sum[site_i]
+ rhocoeff[site_i].append(rho_i_n)
+
+ # closes the file
+ if save_coeffs == True:
+ f.close()
+
+ return rhocoeff, Jcoeff
+
+
+
+###############################################################################
+#
+# DEFINE: Returns local density for a given initiation rate.
+#
+###############################################################################
+
+def local_density(rhocoeff, alpha):
+ '''
+ Returns local density up to every PSA order contained in rhocoeff. The
+ output is a list of local density profiles rho such that rho[i] is the local
+ density profile up to the PSA order i. The size of rho is the maximum PSA
+ order plus 1.
+ '''
+
+ Kplus1 = len(rhocoeff[0]) # maximum order of the PSA increased by 1
+
+ rho = [[] for order in range(Kplus1)]
+ for coefficients in rhocoeff: # iteration over all lattice sites
+ rho_sum = 0
+ for order, coeff in zip(range(Kplus1), coefficients):
+ rho_sum += alpha**order * coeff
+ rho[order].append(rho_sum)
+
+ return rho
+
+
+
+###############################################################################
+#
+# DEFINE: Returns mean density given the local density.
+#
+###############################################################################
+
+def mean_density(local_density):
+
+ mean_rho = []
+ n = 0
+ for local_density_n in local_density:
+ rho_n = sum(local_density_n)/len(local_density_n)
+ mean_rho.append(rho_n)
+ n += 0
+
+ return mean_rho
+
+
+
+###############################################################################
+#
+# DEFINE: Returns particle current for a given initiation rate.
+#
+###############################################################################
+
+def current(Jcoeff, alpha):
+ '''
+ Returns particle current up to every PSA order contained in Jcoeff. The
+ output is a list of currents J such that J[i] is the values of the current
+ up to the PSA order i. The size of J is the maximum PSA order plus 1.
+ '''
+
+ J = []
+ J_sum = 0
+ for order, coeff in zip(range(len(Jcoeff)), Jcoeff):
+ J_sum += alpha**(order+1) * coeff
+ J.append(J_sum)
+
+ return J
diff --git a/TASEPy-1.1/applications/YAL008W_rates.dat b/TASEPy-1.1/applications/YAL008W_rates.dat
new file mode 100644
index 0000000..653d40b
--- /dev/null
+++ b/TASEPy-1.1/applications/YAL008W_rates.dat
@@ -0,0 +1,198 @@
+ATG 6.735
+ACT 12.034
+TTG 11.296
+GCT 12.034
+TTT 7.88
+AAT 7.88
+ATG 6.735
+CAA 10.505
+CGG 1.594
+TTG 11.296
+GTG 3.049
+TTT 7.88
+CGT 7.784
+AAT 7.88
+TTG 11.296
+AAT 7.88
+GTT 14.006
+GGG 3.049
+AAG 14.006
+CGC 5.411
+ATG 6.735
+TTC 11.296
+AAG 14.006
+AAC 11.296
+GTC 10.471
+CCC 2.008
+TTA 8.752
+TGG 7.784
+AGG 1.594
+TTT 7.88
+AAT 7.88
+GTC 10.471
+GCC 8.791
+AAT 7.88
+AAA 8.752
+TTA 8.752
+GGA 4.375
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+GGT 11.112
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+GAA 14.006
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+GGT 11.112
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diff --git a/TASEPy-1.1/applications/info_a02_L100_ll10_iter1e6.log b/TASEPy-1.1/applications/info_a02_L100_ll10_iter1e6.log
new file mode 100644
index 0000000..769c548
--- /dev/null
+++ b/TASEPy-1.1/applications/info_a02_L100_ll10_iter1e6.log
@@ -0,0 +1,2 @@
+INFO: Program started.
+INFO: Program finished successfully in 84.015 seconds.
diff --git a/TASEPy-1.1/applications/info_a02_L20_ll1_iter1e6.log b/TASEPy-1.1/applications/info_a02_L20_ll1_iter1e6.log
new file mode 100644
index 0000000..e4edb1b
--- /dev/null
+++ b/TASEPy-1.1/applications/info_a02_L20_ll1_iter1e6.log
@@ -0,0 +1,2 @@
+INFO: Program started.
+INFO: Program finished successfully in 2.968 seconds.
diff --git a/TASEPy-1.1/applications/kappa_L20-inferred.dat b/TASEPy-1.1/applications/kappa_L20-inferred.dat
new file mode 100644
index 0000000..d3dcf28
--- /dev/null
+++ b/TASEPy-1.1/applications/kappa_L20-inferred.dat
@@ -0,0 +1,20 @@
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\ No newline at end of file
diff --git a/TASEPy-1.1/applications/kappa_L20-minimize.log b/TASEPy-1.1/applications/kappa_L20-minimize.log
new file mode 100644
index 0000000..70d7ed7
--- /dev/null
+++ b/TASEPy-1.1/applications/kappa_L20-minimize.log
@@ -0,0 +1,109 @@
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+nit : 17
+nfev : 10180
+status : 0
+success : True
+message : Optimization terminated successfully.
+x : [53.0816606 25.74548617 5.386643 46.38115968 47.31065604 31.73327289
+ 35.73037314 8.74086531 41.21601188 15.93889603 6.45272429 40.7306943
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diff --git a/TASEPy-1.1/applications/rates_L100.dat b/TASEPy-1.1/applications/rates_L100.dat
new file mode 100644
index 0000000..213eecd
--- /dev/null
+++ b/TASEPy-1.1/applications/rates_L100.dat
@@ -0,0 +1,100 @@
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\ No newline at end of file
diff --git a/TASEPy-1.1/applications/rates_L20.dat b/TASEPy-1.1/applications/rates_L20.dat
new file mode 100644
index 0000000..c558a3b
--- /dev/null
+++ b/TASEPy-1.1/applications/rates_L20.dat
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\ No newline at end of file
diff --git a/TASEPy-1.1/applications/rho_a02_L100_ll10_iter1e6.dat b/TASEPy-1.1/applications/rho_a02_L100_ll10_iter1e6.dat
new file mode 100644
index 0000000..fe29251
--- /dev/null
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+ 1.6108389034079986E-002
+ 1.4792693971434795E-002
+ 2.3952006227687402E-002
+ 7.3589331056299279E-002
+ 2.6410997728064527E-002
+ 8.4225168163708508E-002
+ 3.3674273710989522E-002
+ 8.9488432917911365E-002
diff --git a/TASEPy-1.1/applications/rho_a02_L20_ll1_iter1e6.dat b/TASEPy-1.1/applications/rho_a02_L20_ll1_iter1e6.dat
new file mode 100644
index 0000000..5ed1fd7
--- /dev/null
+++ b/TASEPy-1.1/applications/rho_a02_L20_ll1_iter1e6.dat
@@ -0,0 +1,20 @@
+ 2.8377368146100968E-002
+ 7.4917697617000331E-002
+ 0.18363304599744704
+ 2.1445347885518159E-002
+ 2.1494760277422604E-002
+ 3.3463171864036571E-002
+ 3.9985657303745301E-002
+ 0.11411485954287399
+ 3.3424756625394084E-002
+ 8.9238634356349697E-002
+ 0.15349130193644472
+ 2.5722789858787575E-002
+ 4.8404129163899877E-002
+ 3.1262031289618061E-002
+ 3.8920638617442681E-002
+ 9.6862197614576526E-002
+ 9.5008375367119660E-002
+ 0.13148233675044022
+ 0.17416313627333171
+ 3.6140391247000407E-002
diff --git a/TASEPy-1.1/applications_TASEPy.ipynb b/TASEPy-1.1/applications_TASEPy.ipynb
new file mode 100644
index 0000000..189ac19
--- /dev/null
+++ b/TASEPy-1.1/applications_TASEPy.ipynb
@@ -0,0 +1,783 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "4ed33961",
+ "metadata": {},
+ "source": [
+ "# TASEPy applications"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6eddb3fe",
+ "metadata": {},
+ "source": [
+ "The totally asymmetric simple exclusion process (TASEP) has been introduced as a model of biopolymerization, where the mRNA is represented as a one-dimensional lattice with discrete sites corresponding to codons. The dynamics of ribosomes on the mRNA is modeled with particles moving from site to site on the lattice."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "22d51495",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import methods from TASEPy\n",
+ "\n",
+ "from TASEPy import psa_compute\n",
+ "from TASEPy import local_density\n",
+ "from TASEPy import mean_density\n",
+ "from TASEPy import current\n",
+ "\n",
+ "# to measure computation time\n",
+ "import time"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0f0c98bd",
+ "metadata": {},
+ "source": [
+ "## Estimating translation initiation rate $\\alpha$ from polysome profiling data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5555726b",
+ "metadata": {},
+ "source": [
+ "As an application of the TASEPy package, we demonstrate how to infer the initiation rate $\\alpha$ when the hopping rates $\\omega_i$ (representing codon-dependent ribosome speed) and the mean density $\\rho$ (indicating the average number of ribosomes divided by the length of the mRNA in codon units) are known. The mean ribosome density can be measured using polysome profiling, and the codon-dependent hopping rates have been estimated based on tRNA concentrations.\n",
+ "\n",
+ "Thus, by predicring $\\rho(\\alpha)$ with TASEPy and with the experimental value $\\rho_\\textrm{exp}$, we can infer the value of $\\alpha$. First, we import a file containing hopping rates for the YAL008W gene of *S. cerevisiae*, which have been estimated in Ciandrini L, Stansfield I, Romano MC (2013) *Ribosome Traffic on mRNAs Maps to Gene Ontology: Genome-wide Quantification of Translation Initiation Rates and Polysome Size Regulation*. PLoS Comput Biol 9(1): e1002866. https://doi.org/10.1371/journal.pcbi.1002866"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 250,
+ "id": "ddd9e56f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# imports hopping rates YAL008W_rates.dat\n",
+ "\n",
+ "with open('applications/YAL008W_rates.dat', 'r') as file:\n",
+ " rates = [float(line.split()[1]) for line in file]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c8396870",
+ "metadata": {},
+ "source": [
+ "Next, we set particle size $\\ell=9$ as in the reference above, and choose the order of PSA $K=3$. This takes about 11 seconds to solve on a laptop with Intel i7-8565U CPU and 16 GB of RAM, and less than 7 seconds on an Apple M1 Pro with 32 GB of RAM."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 251,
+ "id": "edcc836b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Lattice size: 198 codons\n",
+ "Computation time: 8.366 seconds\n"
+ ]
+ }
+ ],
+ "source": [
+ "# computes the PSA for order K = 3\n",
+ "\n",
+ "L = len(rates) # lattice size\n",
+ "ll = 9 # particle size\n",
+ "K = 3 # maximum PSA order\n",
+ "\n",
+ "print('Lattice size:',L,'codons')\n",
+ "\n",
+ "start = time.time()\n",
+ "rhocoeff, Jcoeff = psa_compute(rates, K, ll)\n",
+ "end = time.time()\n",
+ "print('Computation time:',round(end-start,3),'seconds')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "973bbfee",
+ "metadata": {},
+ "source": [
+ "We then need to compute the mean density coefficients $\\rho_n=\\sum_{i=1}^{L}\\rho_{i,n}/L$ for $n=0,\\dots,K$ as in Eq.(25c) of the paper introducing the algorothm used in TASEPy (Ciandrini, Crisostomo and Szavits-Nossan, 2023)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 252,
+ "id": "e0eb7dc4",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.0, 0.1806069864721105, -0.20947619500711065, 0.32647921092495436]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# computes mean density coefficients\n",
+ "\n",
+ "mean_rhocoeff = []\n",
+ "for order in range(0,K+1):\n",
+ " rhocoeff_sum = 0\n",
+ " for site in range(L):\n",
+ " rhocoeff_sum += rhocoeff[site][order]\n",
+ " mean_rhocoeff.append(rhocoeff_sum/L)\n",
+ "print(mean_rhocoeff)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f030a787",
+ "metadata": {},
+ "source": [
+ "Next, we set up the function whose root we want to find: \n",
+ "$$f(\\alpha)=\\rho(\\alpha)-\\rho_{\\text{exp}},$$\n",
+ "where $\\rho(\\alpha)\\approx\\sum_{n=0}^{K}\\rho_n \\alpha^n$ is the mean density computed using TASEPy for a given value of the initiation rate $\\alpha$, and $\\rho_{\\text{exp}}$ is the mean density measured experimentally, see the cited Ciandrini et (2013) reference for more details. Since $f(\\alpha)$ is a polynomial, we can also find its derivative, in which case we can use the Newton-Raphson method for solving $f(\\alpha)=0$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 253,
+ "id": "2d2df6b5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# root finding algorithm\n",
+ "from scipy import optimize\n",
+ "\n",
+ "# experimental mean density\n",
+ "rhoexp = 0.023226\n",
+ "\n",
+ "# in the functions below x is the initation rate (alpha)\n",
+ "def f(x,a):\n",
+ " result = -rhoexp\n",
+ " for order,coeff in enumerate(a):\n",
+ " result += coeff * x**order\n",
+ " return result\n",
+ "\n",
+ "def fprime(x,a):\n",
+ " result = 0\n",
+ " for order,coeff in enumerate(a):\n",
+ " if order > 0:\n",
+ " result += coeff * order * x**(order-1)\n",
+ " return result"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "74439bf8",
+ "metadata": {},
+ "source": [
+ "As the initial guess, we can use the first-order approximation of the PSA, $\\rho_{\\text{exp}}\\approx \\rho_{1}\\alpha$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 254,
+ "id": "feb1231b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Initial value: 0.12859967631200458\n"
+ ]
+ }
+ ],
+ "source": [
+ "# initial guess\n",
+ "alpha0 = rhoexp/mean_rhocoeff[1]\n",
+ "print('Initial value:',alpha0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a9e4e3cd",
+ "metadata": {},
+ "source": [
+ "Finally, we call the optimize function from the scipy package to find the root."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 255,
+ "id": "9c74cb36",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Optimal value: 0.14818676243771686\n"
+ ]
+ }
+ ],
+ "source": [
+ "alpha = optimize.newton(f, alpha0, fprime, args=(mean_rhocoeff,))\n",
+ "print('Optimal value:',alpha)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2b366f01",
+ "metadata": {},
+ "source": [
+ "This value is very close to the one obtained from stochastic simulations in the cited Ciandrini et al (2013) paper. The relative error is about 1.5\\%."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 257,
+ "id": "957eb3a1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Relative percentage error: 1.5363806817873418\n"
+ ]
+ }
+ ],
+ "source": [
+ "# value reported in Ciandrini L, Stansfield I, Romano MC (2013) \n",
+ "# Ribosome Traffic on mRNAs Maps to Gene Ontology: Genome-wide \n",
+ "# Quantification of Translation Initiation Rates and Polysome \n",
+ "# Size Regulation. PLoS Comput Biol 9(1): e1002866. \n",
+ "# https://doi.org/10.1371/journal.pcbi.1002866\n",
+ "\n",
+ "alpha_paper = 0.150499\n",
+ "per_err = 100 * abs(alpha_paper-alpha)/alpha_paper\n",
+ "print('Relative percentage error:',per_err)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e68ec0a2",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "## Estimating translation elongation rates from ribosome profiling data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3851a361",
+ "metadata": {},
+ "source": [
+ "We now solve a different problem, in which the mean density $\\rho_{\\text{exp}}$ is known, as well as the local densities $\\rho_{i}$ for $i=1,\\dots,L$, but the elongation rates $\\omega_i$ for $i=1,\\dots,L$ and the initiation rate $\\alpha$ are unknown. This problem is inspired by experimental ribosome profiling data, in which the occupancy of the ribosomes (particles) is known on each codon (lattice site). Here we present a simplifed version of that, and assume that the ratio $\\rho_i/\\rho$ is known. \n",
+ "\n",
+ "The approach is explained in detail in J. Szavits-Nossan , L. Ciandrini (2020) *Inferring efficiency of translation initiation and elongation from ribosome profiling*. Nucleic Acids Research 48(17):9478-9490, https://doi.org/10.1093/nar/gkaa678, which makes use of the power series approximation (PSA) of the TASEP (up to order $n=3$).\n",
+ "\n",
+ "First, we note that since the local density $\\rho_i$ is dimensionless, we can only find the ratios $\\omega_i/\\alpha$ for $i=1,\\dots,L$, not the absolute elongation rates $\\omega_i$. Let us denote by $\\kappa_i$ the ratio\n",
+ " $$\\kappa_i=\\frac{\\omega_i}{\\alpha}, \\quad i=1,\\dots,L.$$\n",
+ "We want to find $\\kappa_1,\\dots,\\kappa_L$ such that\n",
+ "\\begin{equation}\n",
+ " \\rho_i(\\kappa_1,\\dots,\\kappa_L)=\\rho_{i,\\text{exp}},\\quad i=1,\\dots,L, \\tag{1}\n",
+ "\\end{equation}\n",
+ "\n",
+ "where the left-hand side is the local density predicted by the TASEP, and the right-hand side is the experimentally measured density. This problem can be solved by minimising the objective function\n",
+ "\\begin{equation}\n",
+ " D(\\kappa_1,\\dots,\\kappa_L)=\\sqrt{\\frac{\\sum_{i=1}^{L}[\\rho_{i}(\\kappa_1,\\dots,\\kappa_L)-\\rho_{i,\\text{exp}}]^2}{L}}, \\tag{2}\n",
+ "\\end{equation}\n",
+ "\n",
+ "which is also known as the root mean square deviation (RMSD). Here we demonstrate how to solve this problem using TASEPy and SciPy repositories. We will not use real ribosome profiling data, instead we use mock data obtained using stochastic simulations for a given set of randomly selected hopping rates $\\omega_i$ and a given value of the initiation rate $\\alpha$. We will then use TASEPy to restore the values of $\\kappa_i=\\omega_i/\\alpha$ and compare them to the original ones."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 258,
+ "id": "01545121",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import random number generator\n",
+ "from statistics import random\n",
+ "\n",
+ "# import minimization algoritm\n",
+ "from scipy import optimize"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9d03a3d6",
+ "metadata": {},
+ "source": [
+ "In order to demonstrate the methodology, we select a relatively small lattice size $L=20$ and $\\ell=1$. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 259,
+ "id": "349646f5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# declare parameters\n",
+ "\n",
+ "# lattice size\n",
+ "L = 20\n",
+ "\n",
+ "# particle size (in lattice sites)\n",
+ "ll = 1\n",
+ "\n",
+ "# list of particle hopping rates selected randomly from interval [1,10]\n",
+ "# unless changing the seed, the outcome can be compared to the stochastic simulations\n",
+ "# stored in this directory\n",
+ "random_seed = random.seed(1234)\n",
+ "rates = [random.uniform(1,10) for site in range(L)] \n",
+ " \n",
+ "# maximum order of the PSA\n",
+ "K = 3\n",
+ "\n",
+ "# initiation rate\n",
+ "alpha = 0.2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eb95b344",
+ "metadata": {},
+ "source": [
+ "The rates are stored in the file *applications/rates_L20.dat*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 260,
+ "id": "7460518d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "with open('applications/rates_L20.dat', 'w') as file:\n",
+ " n = 0\n",
+ " for rate in rates:\n",
+ " if n < L-1: \n",
+ " file.write(str(rate)+'\\n')\n",
+ " else:\n",
+ " file.write(str(rate))\n",
+ " n += 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1966d256",
+ "metadata": {},
+ "source": [
+ "For these set of parameters, we obtained the local densities using stochastic simulations (see *simulations/dTASEPe.f90* for the Fortran source file), which are stored in the file *applications/rho_a02_L20_ll1_iter1e6.dat*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 261,
+ "id": "c04e63e9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# imports local densities (mock data)\n",
+ "\n",
+ "with open('applications/rho_a02_L20_ll1_iter1e6.dat', 'r') as file:\n",
+ " rhoexp = [float(line) for line in file]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "18d61679",
+ "metadata": {},
+ "source": [
+ "Let us see first how the local density obtained using TASEPy with the original hopping rates compares to the one obtained by stochastic simulations. For real data, we can only check this at the end with the inferred rates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 262,
+ "id": "15dc66c1",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 700x233.333 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "kappa_original = [rate/alpha for rate in rates]\n",
+ "\n",
+ "rhocoeff, Jcoeff = psa_compute(kappa_original, K, ll)\n",
+ "rho = local_density(rhocoeff, 1.0)[-1]\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "# Create a figure \n",
+ "plt.figure(figsize=(7,7/3))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "plt.plot(sites, rhoexp, linewidth=2, label='sims')\n",
+ "plt.plot(sites, rho, linewidth=2, label='n='+str(K))\n",
+ "\n",
+ "plt.xlabel(r'lattice site $i$', fontsize=10)\n",
+ "plt.ylabel(r'density $\\rho_{i}$', fontsize=10)\n",
+ "\n",
+ "plt.legend(loc='best',ncol=2)\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1c4e70bb",
+ "metadata": {},
+ "source": [
+ "We see that the order of $K=3$ is applicable to our problem, so we proceed with the minimization procedure. \n",
+ "\n",
+ "For the initial values of the ratios $\\kappa_i$, we employ the mean-field approximation, which ignores correlations between neighbouring lattice sites, leading to the following set of equations:\n",
+ "\\begin{align}\n",
+ " & \\kappa_i=\\frac{\\left(1-\\sum_{s=1}^{\\ell}\\rho_{s,\\text{exp}}\\right)\\left(1-\\sum_{s=1}^{\\ell}\\rho_{i+s,\\text{exp}}+\\rho_{i+\\ell,\\text{exp}}\\right)}{\\rho_{i,exp}\\left(1-\\sum_{s=1}^{\\ell}\\rho_{s,\\text{exp}}\\right)},\\quad i=1,\\dots,L-\\ell \\tag{3}\\\\\n",
+ " & \\kappa_i=\\frac{\\left(1-\\sum_{s=1}^{\\ell}\\rho_{s,\\text{exp}}\\right)}{\\rho_{i,exp}},\\quad i=L-\\ell+1,\\dots,L . \\tag{4}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 263,
+ "id": "1e0c799d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "kappa0 = []\n",
+ "for site in range(L):\n",
+ " sum1 = sum(rhoexp[:ll])\n",
+ " if site < L-ll:\n",
+ " sum2 = sum(rhoexp[site:site+ll+1])\n",
+ " kappa_site = (1-sum1)*(1-sum2+rhoexp[site+ll])/(rhoexp[site]*(1-sum1))\n",
+ " else:\n",
+ " kappa_site = (1-sum1)/rhoexp[site]\n",
+ " kappa0.append(kappa_site)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c9884070",
+ "metadata": {},
+ "source": [
+ "We can check how close these initial values are to the real ones: they are close but there are obvious deviations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 264,
+ "id": "cc3d3818",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 600x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create a figure \n",
+ "plt.figure(figsize=(6,4))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "min_kappa = min(rates)/alpha\n",
+ "max_kappa = max(rates)/alpha\n",
+ "linearx = [min_kappa,max_kappa]\n",
+ "\n",
+ "plt.scatter(kappa0, kappa_original,label='mean-field')\n",
+ "plt.plot(linearx, linearx, linestyle='--', color='gray',label='y=x')\n",
+ "\n",
+ "plt.xlim(0,1.1*max(rates)/alpha)\n",
+ "plt.ylim(0,1.1*max(rates)/alpha)\n",
+ "\n",
+ "plt.xlabel(r'$\\kappa_i$ (mean-field)', fontsize=12)\n",
+ "plt.ylabel(r'$\\kappa_i$ (original)', fontsize=12)\n",
+ "\n",
+ "# Set the title\n",
+ "plt.title(r'Comparing initial (mean-field) and original $\\kappa$', fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='best')\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d3f0f1df",
+ "metadata": {},
+ "source": [
+ "We now set up the minimisation procedure using the Powell method and `scipy.optimize.minimize`, which has an option to set up parameter bounds. In our case, we know that $0<\\kappa_i<\\infty$ for $i=1,\\dots,L$. In practice, we can use smaller bounds, e.g. $10^{-2}$ instead of $0$ and $10^{5}$ instead of $\\infty$. This optimization procedure takes about 3 minutes on a laptop with Intel i7-8565U CPU and 16 GB of RAM, and about 2 minutes on an Apple M1 Pro with 32 GB of RAM."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 266,
+ "id": "368ef9ba",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import math\n",
+ "\n",
+ "# set up the objective function\n",
+ "def fun(kappa, K, ll, rhoexp):\n",
+ " rhocoeff, Jcoeff = psa_compute(kappa, K, ll)\n",
+ " rho = local_density(rhocoeff, 1.0)[-1]\n",
+ " D = 0\n",
+ " for i in range(L):\n",
+ " D += (rho[i]-rhoexp[i])**2\n",
+ " D = math.sqrt(D/L)\n",
+ " return D\n",
+ "\n",
+ "# set up linear constraint\n",
+ "A = np.identity(L)\n",
+ "lower = np.array([1e-2 for site in range(L)]) # lower bound\n",
+ "upper = np.array([1e5 for site in range(L)]) # upper bound\n",
+ "cons = optimize.LinearConstraint(A, lower, upper)\n",
+ "\n",
+ "# set up bounds (must be tuples)\n",
+ "bnds = ((1e-2,1e5),)*L"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 267,
+ "id": "6ef6e60b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Started optimization... Optimization terminated successfully.\n",
+ " Current function value: 0.000001\n",
+ " Iterations: 17\n",
+ " Function evaluations: 10180\n",
+ "Done.\n",
+ "Computation time: 175.317 seconds\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ " message: Optimization terminated successfully.\n",
+ " success: True\n",
+ " status: 0\n",
+ " fun: 1.143017831702802e-06\n",
+ " x: [ 5.308e+01 2.575e+01 ... 5.707e+00 2.712e+01]\n",
+ " nit: 17\n",
+ " direc: [[ 0.000e+00 0.000e+00 ... 0.000e+00 1.000e+00]\n",
+ " [ 0.000e+00 1.000e+00 ... 0.000e+00 0.000e+00]\n",
+ " ...\n",
+ " [ 0.000e+00 0.000e+00 ... 1.000e+00 0.000e+00]\n",
+ " [ 2.464e-03 7.772e-04 ... 9.703e-06 -4.073e-05]]\n",
+ " nfev: 10180"
+ ]
+ },
+ "execution_count": 267,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "start = time.time()\n",
+ "\n",
+ "# COBYLA method (constrained optimization, derivative-free)\n",
+ "#kappa = optimize.minimize(fun, kappa0, args=(K, ll, rhoexp), method='COBYLA', constraints=cons, options={'maxiter':5e4,'disp': True})\n",
+ "\n",
+ "# Powell method (bounded optimization, derivative-free)\n",
+ "kappa = optimize.minimize(fun, kappa0, args=(K, ll, rhoexp), method='Powell', bounds=bnds, options={'ftol': 1e-3, 'xtol': 1e-3, 'disp': True})\n",
+ "\n",
+ "end = time.time()\n",
+ "print('Computation time:',round(end-start,3),'seconds')\n",
+ "\n",
+ "# print info\n",
+ "kappa"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4a3e7970",
+ "metadata": {},
+ "source": [
+ "Having inferred the set of $\\kappa_i$'s stored in `kappa` from the particle density profile, we now compare them to the `kappa_original` which have been used to produce the density profile with stochastic simulations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 268,
+ "id": "5d0e3c4c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 600x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create a figure \n",
+ "plt.figure(figsize=(6,4))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "min_kappa = min(rates)/alpha\n",
+ "max_kappa = max(rates)/alpha\n",
+ "linearx = [min_kappa,max_kappa]\n",
+ "\n",
+ "plt.scatter(kappa.x, kappa_original,label='inferred')\n",
+ "plt.plot(linearx, linearx, linestyle='--', color='gray',label='y=x')\n",
+ "\n",
+ "plt.xlim(0,1.1*max(rates)/alpha)\n",
+ "plt.ylim(0,1.1*max(rates)/alpha)\n",
+ "\n",
+ "plt.xlabel(r'$\\kappa_i$ (inferred)', fontsize=12)\n",
+ "plt.ylabel(r'$\\kappa_i$ (original)', fontsize=12)\n",
+ "\n",
+ "# Set the title\n",
+ "plt.title(r'Comparing inferred and original $\\kappa$', fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='best')\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ca391811",
+ "metadata": {},
+ "source": [
+ "The Pearson's correlation coefficient for these two data set is:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 274,
+ "id": "f882a168",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pearson's correlation coefficient: 0.9980523506928205\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy import stats\n",
+ "\n",
+ "R = stats.pearsonr(kappa_original,kappa.x)\n",
+ "\n",
+ "print('Pearson\\'s correlation coefficient:', R.statistic)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "70a83264",
+ "metadata": {},
+ "source": [
+ "Finally, we store the inferred ratios $\\kappa_i$ for $i=1,\\dots,L$ in the file *applications/rates_L20-inferred.dat*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 275,
+ "id": "a1c4407b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "with open('applications/kappa_L20-inferred.dat', 'w') as file:\n",
+ " n = 0\n",
+ " for rate in kappa.x:\n",
+ " if n < L-1: \n",
+ " file.write(str(rate)+'\\n')\n",
+ " else:\n",
+ " file.write(str(rate))\n",
+ " n += 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8a178904",
+ "metadata": {},
+ "source": [
+ "We also save all the information from the minimization procedure in a separate file *kappa_L20-minimize.log*, except the inferred ratios."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "ba81c2c9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "dict_keys = []\n",
+ "dict_values = []\n",
+ "for keys, value in kappa.items():\n",
+ " dict_keys.append(keys)\n",
+ " dict_values.append(value)\n",
+ " \n",
+ "with open('applications/kappa_L20-minimize.log', 'w') as file:\n",
+ " for i in range(1,len(dict_keys)):\n",
+ " file.write(dict_keys[i]+' : '+str(dict_values[i])+'\\n')"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.15"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/TASEPy-1.1/benchmarks_TASEPy.ipynb b/TASEPy-1.1/benchmarks_TASEPy.ipynb
new file mode 100644
index 0000000..1a620d4
--- /dev/null
+++ b/TASEPy-1.1/benchmarks_TASEPy.ipynb
@@ -0,0 +1,1046 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "167da728",
+ "metadata": {},
+ "source": [
+ "# TASEPy benchmarks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "32ed9e40",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from TASEPy import psa_compute\n",
+ "from TASEPy import local_density\n",
+ "from TASEPy import mean_density\n",
+ "from TASEPy import current\n",
+ "\n",
+ "import csv\n",
+ "from tabulate import tabulate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6ec2ca97",
+ "metadata": {},
+ "source": [
+ "## Benchmark 1: comparison with exact results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a9f7f5a9",
+ "metadata": {},
+ "source": [
+ "Exact results were obtained by solving the stationary master equation $MP=0$ \\[Eq. (5) in the main text\\], where $M$ is the stochastic transition matrix, and $P$ is the probability vector. This system of equations was solved exactly using Mathematica (*exact/exact-small-system.nb*) for the system size $L=4$, and for three particles sizes $\\ell=1,2$ and $3$. The initiation rate $\\alpha$ was kept as a variable, and the results were expanded in Taylor series around $\\alpha=0$ up to the order $K=5$.\n",
+ "\n",
+ "The hopping rates for all three particle sizes are stored in file:\n",
+ "- *rates_L4.csv*. \n",
+ "\n",
+ "The local density coefficients are stored in files:\n",
+ "- *exact/rho-coeff_L4_ll1.csv* for $\\ell=1$, \n",
+ "- *exact/rho-coeff_L4_ll2.csv* for $\\ell=2$ and \n",
+ "- *exact/rho-coeff_L4_ll3.csv* for $\\ell=3$. \n",
+ "\n",
+ "The particle current coefficients are stored in files:\n",
+ "- *exact/current-coeff_L4_ll1.csv* for $\\ell=1$, \n",
+ "- *exact/current-coeff_L4_ll2.csv* for $\\ell=2$ and \n",
+ "- *exact/current-coeff_L4_ll3.csv* for $\\ell=3$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6e597e05",
+ "metadata": {},
+ "source": [
+ "### Example 1: L = 4 and $\\ell$ = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "8cdd7a77",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Maximum order of the PSA: K = 5\n",
+ "Hopping rates are [1.88, 1.52, 1.09, 1.38]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# imports hopping rates (example L=4 and ll=1)\n",
+ "\n",
+ "file = open('exact/rates_L4.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rates = []\n",
+ "for lines in reader:\n",
+ " rates.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact local density coefficients (example L=4 and ll=1) \n",
+ "\n",
+ "file = open('exact/rho-coeff_L4_ll1.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rhocoeff1 = []\n",
+ "for lines in reader:\n",
+ " rhocoeff1.append([float(x) for x in lines])\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact particle current coefficients (example L=4 and ll=1)\n",
+ "\n",
+ "file = open('exact/current-coeff_L4_ll1.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "Jcoeff1 = []\n",
+ "for row in reader:\n",
+ " Jcoeff1.append([float(x) for x in row])\n",
+ "file.close()\n",
+ "Jcoeff1 = Jcoeff1[0]\n",
+ "\n",
+ "print('Maximum order of the PSA: K =',len(rhocoeff1[0])-1)\n",
+ "print('Hopping rates are',rates)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "07b9ddad",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes the PSA for order K = 5\n",
+ "\n",
+ "L = 4 # lattice size\n",
+ "ll = 1 # particle size\n",
+ "K = 5 # maximum PSA order\n",
+ "\n",
+ "rhocoeff2, Jcoeff2 = psa_compute(rates, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "4cf40404",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (local density):\n",
+ " site order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "------ --------- --------- --------- --------- --------- ---------\n",
+ " 1 0 0.531915 0.149892 0.846462 -1.08538 -4.66958\n",
+ " 2 0 0.657895 0.564896 0.134411 -3.24941 1.19327\n",
+ " 3 0 0.917431 0.176094 -0.902102 -0.936768 0.818141\n",
+ " 4 0 0.724638 -0.385446 -0.108617 -0.613378 0.786505\n",
+ "\n",
+ "TASEPy results (local density):\n",
+ " site order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "------ --------- --------- --------- --------- --------- ---------\n",
+ " 1 0 0.531915 0.149892 0.846462 -1.08538 -4.66958\n",
+ " 2 0 0.657895 0.564896 0.134411 -3.24941 1.19327\n",
+ " 3 0 0.917431 0.176094 -0.902102 -0.936768 0.818141\n",
+ " 4 0 0.724638 -0.385446 -0.108617 -0.613378 0.786505\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the local density\n",
+ "\n",
+ "headers = ['order ' + str(x) for x in range(K+1)]\n",
+ "headers.insert(0, 'site')\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff1):\n",
+ " coeff.insert(0,site+1)\n",
+ " \n",
+ "print('Exact results (local density):')\n",
+ "print(tabulate(rhocoeff1, headers = headers)) # exact results\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff2):\n",
+ " coeff.insert(0,site+1)\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (local density):')\n",
+ "print(tabulate(rhocoeff2, headers = headers)) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "69ec88c1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1, 2, 3]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = [1,2,3]\n",
+ "y = x\n",
+ "print(y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "c1f3c0af",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -0.531915 -0.149892 -0.846462 1.08538 4.66958\n",
+ "\n",
+ "TASEPy results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -0.531915 -0.149892 -0.846462 1.08538 4.66958\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the particle current\n",
+ "\n",
+ "print('Exact results (current):')\n",
+ "print(tabulate([Jcoeff1], headers = ['order ' + str(x) for x in range(K+1)])) # exact results\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (current):')\n",
+ "print(tabulate([Jcoeff2], headers = ['order ' + str(x) for x in range(K+1)])) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d03b85ef",
+ "metadata": {},
+ "source": [
+ "### Example 2: L = 4 and $\\ell = 2$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "5ce9c7c8",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Maximum order of the PSA: K = 5\n",
+ "Hopping rates are [1.88, 1.52, 1.09, 1.38]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# imports hopping rates (example L=4 and ll=2)\n",
+ "\n",
+ "file = open('exact/rates_L4.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rates = []\n",
+ "for lines in reader:\n",
+ " rates.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact local density coefficients (example L=4 and ll=2) \n",
+ "\n",
+ "file = open('exact/rho-coeff_L4_ll2.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rhocoeff1 = []\n",
+ "for lines in reader:\n",
+ " rhocoeff1.append([float(x) for x in lines])\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact particle current coefficients (example L=4 and ll=2)\n",
+ "\n",
+ "file = open('exact/current-coeff_L4_ll2.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "Jcoeff1 = []\n",
+ "for row in reader:\n",
+ " Jcoeff1.append([float(x) for x in row])\n",
+ "file.close()\n",
+ "Jcoeff1 = Jcoeff1[0]\n",
+ "\n",
+ "print('Maximum order of the PSA: K =',len(rhocoeff1[0])-1)\n",
+ "print('Hopping rates are',rates)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "c4d931dc",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes the PSA for order K = 5\n",
+ "\n",
+ "L = 4 # lattice size\n",
+ "ll = 2 # particle size\n",
+ "K = 5 # maximum PSA order\n",
+ "\n",
+ "rhocoeff2, Jcoeff2 = psa_compute(rates, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "6bfa3c7e",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (local density):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "-- --------- --------- ---------- ---------- --------- ---------\n",
+ " 1 0 0.531915 0.208803 -1.83332 3.43302 -2.47067\n",
+ " 2 0 0.657895 -0.0965666 -1.73927 4.22138 -4.58057\n",
+ " 3 0 0.917431 -1.09157 -0.102969 3.27761 -7.02239\n",
+ " 4 0 0.724638 -0.862181 -0.0813304 2.58883 -5.54667\n",
+ "\n",
+ "TASEPy results (local density):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "-- --------- --------- ---------- ---------- --------- ---------\n",
+ " 1 0 0.531915 0.208803 -1.83332 3.43302 -2.47067\n",
+ " 2 0 0.657895 -0.0965666 -1.73927 4.22138 -4.58057\n",
+ " 3 0 0.917431 -1.09157 -0.102969 3.27761 -7.02239\n",
+ " 4 0 0.724638 -0.862181 -0.0813304 2.58883 -5.54667\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the local density\n",
+ "\n",
+ "headers = ['order ' + str(x) for x in range(K+1)]\n",
+ "headers.insert(0, 'site')\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff1):\n",
+ " coeff.insert(0,site+1)\n",
+ "\n",
+ "print('Exact results (local density):')\n",
+ "print(tabulate(rhocoeff1, headers = ['order ' + str(x) for x in range(K+1)])) # exact results\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff2):\n",
+ " coeff.insert(0,site+1)\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (local density):')\n",
+ "print(tabulate(rhocoeff2, headers = ['order ' + str(x) for x in range(K+1)])) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "76bf82a4",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -1.18981 -0.112236 3.57259 -7.65441 7.05124\n",
+ "\n",
+ "TASEPy results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -1.18981 -0.112236 3.57259 -7.65441 7.05124\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the particle current\n",
+ "\n",
+ "print('Exact results (current):')\n",
+ "print(tabulate([Jcoeff1], headers = ['order ' + str(x) for x in range(K+1)])) # exact results\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (current):')\n",
+ "print(tabulate([Jcoeff2], headers = ['order ' + str(x) for x in range(K+1)])) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "465ba083",
+ "metadata": {},
+ "source": [
+ "### Example 3: L = 4 and $\\ell = 3$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "74f5845a",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Maximum order of the PSA: K = 5\n",
+ "Hopping rates are [1.88, 1.52, 1.09, 1.38]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# imports hopping rates (example L=4 and ll=3)\n",
+ "\n",
+ "file = open('exact/rates_L4.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rates = []\n",
+ "for lines in reader:\n",
+ " rates.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact local density coefficients (example L=4 and ll=3) \n",
+ "\n",
+ "file = open('exact/rho-coeff_L4_ll3.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rhocoeff1 = []\n",
+ "for lines in reader:\n",
+ " rhocoeff1.append([float(x) for x in lines])\n",
+ "file.close()\n",
+ "\n",
+ "# imports exact particle current coefficients (example L=4 and ll=3)\n",
+ "\n",
+ "file = open('exact/current-coeff_L4_ll3.csv','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "Jcoeff1 = []\n",
+ "for row in reader:\n",
+ " Jcoeff1.append([float(x) for x in row])\n",
+ "file.close()\n",
+ "Jcoeff1 = Jcoeff1[0]\n",
+ "\n",
+ "print('Maximum order of the PSA: K =',len(rhocoeff1[0])-1)\n",
+ "print('Hopping rates are',rates)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "004f27db",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes the PSA for order K = 5\n",
+ "\n",
+ "L = 4 # lattice size\n",
+ "ll = 3 # particle size\n",
+ "K = 5 # maximum PSA order\n",
+ "\n",
+ "rhocoeff2, Jcoeff2 = psa_compute(rates, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "1675e26c",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (local density):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "-- --------- --------- --------- --------- --------- ----------\n",
+ " 1 0 0.531915 -0.595773 0.595622 -0.464151 0.0921524\n",
+ " 2 0 0.657895 -1.38634 2.5759 -4.44973 7.31514\n",
+ " 3 0 0.917431 -1.93325 3.59208 -6.20513 10.2009\n",
+ " 4 0 0.724638 -1.52699 2.83722 -4.90116 8.05726\n",
+ "\n",
+ "TASEPy results (local density):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "-- --------- --------- --------- --------- --------- ----------\n",
+ " 1 0 0.531915 -0.595773 0.595622 -0.464151 0.0921524\n",
+ " 2 0 0.657895 -1.38634 2.5759 -4.44973 7.31514\n",
+ " 3 0 0.917431 -1.93325 3.59208 -6.20513 10.2009\n",
+ " 4 0 0.724638 -1.52699 2.83722 -4.90116 8.05726\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the local density\n",
+ "\n",
+ "headers = ['order ' + str(x) for x in range(K+1)]\n",
+ "headers.insert(0, 'site')\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff1):\n",
+ " coeff.insert(0,site+1)\n",
+ "\n",
+ "print('Exact results (local density):')\n",
+ "print(tabulate(rhocoeff1, headers = ['order ' + str(x) for x in range(K+1)])) # exact results\n",
+ "\n",
+ "for site,coeff in zip(range(K+1),rhocoeff2):\n",
+ " coeff.insert(0,site+1)\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (local density):')\n",
+ "print(tabulate(rhocoeff2, headers = ['order ' + str(x) for x in range(K+1)])) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "2dacfce0",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Exact results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -2.10724 3.91536 -6.7636 11.119 -17.6082\n",
+ "\n",
+ "TASEPy results (current):\n",
+ " order 0 order 1 order 2 order 3 order 4 order 5\n",
+ "--------- --------- --------- --------- --------- ---------\n",
+ " 1 -2.10724 3.91536 -6.7636 11.119 -17.6082\n"
+ ]
+ }
+ ],
+ "source": [
+ "# compares the particle current\n",
+ "\n",
+ "print('Exact results (current):')\n",
+ "print(tabulate([Jcoeff1], headers = ['order ' + str(x) for x in range(K+1)])) # exact results\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (current):')\n",
+ "print(tabulate([Jcoeff2], headers = ['order ' + str(x) for x in range(K+1)])) # TASEPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "299db2c3",
+ "metadata": {},
+ "source": [
+ "## Benchmark 2: comparison with simulations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "20c2fce9",
+ "metadata": {},
+ "source": [
+ "For large systems, solving the master equation explicitely is not feasible, and one has to use stochastic simulations. We have simulated the inhomogeneous TASEP for using the code written in Fortran. The Fortran source code, *simulations/dTASEPe.f90*, was compiled using the following commands:\n",
+ "\n",
+ "```\n",
+ "$ gfortan -c mt19937.f90\n",
+ "$ gfortran dTASEPe.f90 -o dTASEPe mt19937.o\n",
+ "```\n",
+ "\n",
+ "The first command creates a module for the Mersenne Twister pseaudorandom number generator, whereas the second command compiles the dTASEPe program. The input file for *dTASEPe.f90* is *dTASEPe.dat* which contains the following parameters, one in each line:\n",
+ "- particle size $\\ell$\n",
+ "- initiation rate $\\alpha$\n",
+ "- number of iterations of the Gillespie algorithm $N_{\\text{iter}}$ in multiples of the system size $L$\n",
+ "- filename where the hopping rates $\\omega_1,\\dots,\\omega_L$ are stored\n",
+ "- filename for storing local density\n",
+ "- filename for storing particle current\n",
+ "- filename for storing computation time\n",
+ "\n",
+ "The results were obtained for $L=50$, $\\ell=1$ and $5$, $\\alpha = 0.2$, and $N_{\\text{iter}}=10^6$.\n",
+ "\n",
+ "The hopping rates for both particle sizes are stored in file\n",
+ "- *simulations/rates_L50.dat*. \n",
+ "\n",
+ "The local density profiles are stored in files \n",
+ "- *simulations/rho_a02_L50_ll1_iter1e6.dat* for $\\ell=1$ and\n",
+ "- *simulations/rho_a02_L50_ll5_iter1e6.dat* for $\\ell=5$. \n",
+ "\n",
+ "The particle current (for each lattice site including current into the lattice) is stored in files:\n",
+ "- *simulations/current_a02_L50_ll1_iter1e6.dat* for $\\ell=1$ and\n",
+ "- *simulations/current_a02_L50_ll5_iter1e6.dat* for $\\ell=5$.\n",
+ "\n",
+ "These results were compared to the ones obtained by TASEPy up to $K=3$ for $\\ell=1$ and up to $K=4$ for $\\ell=5$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c97ce6fc",
+ "metadata": {},
+ "source": [
+ "### Example 1: L = 50, $\\ell = 1$ and $K=3$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "ca7bc065",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# imports hopping rates (example L=50 and ll=1)\n",
+ "\n",
+ "file = open('simulations/rates_L50.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rates = []\n",
+ "for lines in reader:\n",
+ " rates.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports simulated density profile (example L=50 and ll=1)\n",
+ "\n",
+ "file = open('simulations/rho_a02_L50_ll1_iter1e6.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "profile_simulations = []\n",
+ "for lines in reader:\n",
+ " profile_simulations.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports simulated current and average (example L=50 and ll=1)\n",
+ "\n",
+ "file = open('simulations/current_a02_L50_ll1_iter1e6.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "currents_sim = []\n",
+ "for lines in reader:\n",
+ " currents_sim.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "J_simulations = sum(currents_sim)/len(currents_sim)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "9e63af46",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes the PSA for order K = 3\n",
+ "\n",
+ "L = len(rates) # lattice size\n",
+ "ll = 1 # particle size\n",
+ "K = 3 # maximum PSA order\n",
+ "\n",
+ "rhocoeff, Jcoeff = psa_compute(rates, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "6b2e324d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# initiation rate\n",
+ "\n",
+ "alpha = 0.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "02d4b17c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes local density profiles\n",
+ "\n",
+ "profile_TASEPy = local_density(rhocoeff, alpha)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "74d36ba4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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7eyGXy1FeXh6UrMDZGaE/RCIRbDZbyAPZtrY23HTTTfj5z3+O2tpa7Ny5E9dff32/koJ//OMfkMvl+O6773DPPffgzjvvxI9+9CPMmTMHhw8fxpIlS7BixQr09fUBAB555BGcOHECX3zxBWpra/Haa6+FXR4RM4Hs+vXrUVBQAIlEgmnTpmHPnj39btvW1oaf/OQnGDduHPh8PlatWuWxzYYNG8Dj8Tz+jEZjGN/F8KZR4/CQlUvliBfFU0aWIAgiBnBxLEhwBLIj+fotl8shGCvAqZRTaElsQbu0HQ3xDZg/fz4qKiqQmpoa8L7dnREGgs/nw2w2B/xa3mhra4PVasX111+PMWPGYNKkSbjrrruQmJjodfvy8nI8/PDDKC4uxpo1ayCVSiGXy/GLX/wCxcXFePTRR9HV1YWamhoAQFNTE6ZMmYLp06djzJgxuOyyy3DNNdeE9D24ExOB7KZNm7Bq1So89NBDqKqqwvz587F06VI0NXm2QwUAk8mEjIwMPPTQQygvL+93vzKZDG1tbS5/EglV1geC3qLnsq55SXkAMCKLBQiCIGINd8cCAEgUJSJOEAdgZF6/W/Qt6BX3oiWhBY1JjTgrOYuE1ISgbbHcnREGwm63QywWB/V67pSXl2PRokWYNGkSfvSjH+Hvf/871Gp1v9uXlZVxjwUCAdLT0zFp0iRuWWam4/uiVDqkKXfeeSc2btyIyZMn43e/+x327dsX0vF7IyYC2RdffBG333477rjjDpSUlGDdunXIzc3Fa6+95nX7MWPG4OWXX8Ytt9yC5OTkfvfL4/GQlZXl8tcfJpMJGo3G5Y+4gIv1lswRyFKxF0EQRPTj3AyBDWR5PB6XjBiJ12/n3zQW5+5ngeLsjDAQFosFAoEAGRkZQb+mMwKBANu2bcMXX3yBCRMm4C9/+QvGjRuH+vp6r9u7SyB4PJ7LMlbnywbnS5cuRWNjI1atWoXz589j0aJFeOCBB0L6HtzxK5CtrKzEqlWrMGPGDOTm5qK4uBjLli3D66+/jt7e3sF3EABmsxmHDh3C4sWLXZYvXrw46Ehfp9MhPz8fOTk5uPrqq1FVVdXvtmvXrkVycjL3l5ubG9RrDzfcC70AkEaWIAgiBnDOyLLFXsCFa7jadEFDO1LwFsg6SzACxdkZoT9dKsMwUKvVSEtLC3kgCziCz7lz5+KJJ55AVVUVxGIxNm/eHLL9Z2Rk4LbbbsM///lPrFu3Dm+88UbI9u0NnwPZK6+8Eu+88w4uv/xyfP7556ivr0d1dTWefPJJmM1m3HDDDWEx0WWF0Wz6miUzMxPt7YHfHY0fPx4bNmzA559/jg8++AASiQRz587FmTNnvG6/Zs0a9Pb2cn/NzZ5f8pGMs/VWrswR5IsFYiSJkwCMPI0VQRBErOBNIwu4zqp1G0ZOq3Gb3YZWXavH8lAEss7OCJ2dnR6ZWdYZISEhAWVlZSHv8FVZWYlnn30WBw8eRFNTEz755BN0dnaipKQkJPt/9NFH8dlnn6Gurg7Hjx/Hf/7zn5Dtuz98NkFbsGABHnzwQdcnC4UoLy9HeXk5fvOb36CnpyfU4+Nwt6lgGCYg6wuWWbNmYdasWdz/586di6lTp+Ivf/kLXnnlFY/t4+LiEBcXF/DrDXfcu3qxyKVyaM1aCmQJgiCiFPf2tCwuBV9GlUuQO5xR9im5DHScIA4mmwmAa+Y6GFhnhP46e8nl8rB19pLJZNi9ezfWrVsHjUaD/Px8vPDCC1i6dCk2bdoU9P7FYjHWrFmDhoYGSKVSzJ8/Hxs3bgzByPvH50B227ZtGDVqFG655RaX5Xa7HY899hieeuqpsBjpsnoS9+yrUqn0yNIGA5/Px4wZM/rNyBID4ywtyE26ILtIl6SjvrceBqsBfZY+xIviIzE8giAIoh/YAC1JlIQEUQK3fKQW7DonZsozyvFd+3cAXLXEwSKXy1FRUYHOzk50dnbCbDZDLBYjIyMDGRkZIc/EspSUlODLL7/0um7Dhg0u/9+5c6fHNg0NDR7LnCUSDz/8MB5++OFghug3Pn9Smzdvxl/+8hf897//5Za1trZi4cKFXt9YqBCLxZg2bRq2bdvmsnzbtm2YM2dOyF6HYRhUV1cjOzs7ZPscSbDSgjRJGicnAEbuhZAgCCIWYBiGy8i6Z1xH6vXbOZCdnjWdexyqjCwLn89HZmYmSktLMXXqVJSWliIzMzNsQexwxeeMrEwmw7///W9cdtllSEtLQ2dnJ37zm9/giSeewK233hrOMWL16tVYsWIFpk+fjtmzZ+ONN95AU1MTVq5cCcChX21tbcW7777LPae6uhqAo6Crs7MT1dXVEIvFmDBhAgDgiSeewKxZs1BcXAyNRoNXXnkF1dXV+Otf/xrW9zIcMVgNXFcY52ws4FnwxepnCYIgiMjTY+rhps7dA1mXpggjSB7mHMhOkk+CmC+G2W4OiUaWCD0+B7KPPvooJk2ahGeffRY33ngjsrOzsX37dhQVFYVzfACA5cuXo6urC08++STa2tpQWlqKLVu2ID8/H4DD4NfdU3bKlCnc40OHDuH9999Hfn4+lz3u6enBL3/5S7S3tyM5ORlTpkzB7t27cfHFF4f9/Qw3nE/6fFm+y7qRbKpNEAQR7TgHZ1nxrhaUzsVeI+n67V7zkZmQiWZtc8gzskRo8DmQTUlJwRdffIFjx46hp6cHSUlJeOyxx1BaWorS0lJcffXV4Rwn7rrrLtx1111e17nrOgD0a2vB8tJLL+Gll14KxdBGPM0a19a0zpCXLEEQRPTirRkCy0hNRLCBrIAnQHZiNjLjHYGs1qKF3qKHAI72tIPFGcTAhOrz8zmQXb16tcv/z507h2PHjuHYsWPYuHFj2ANZInpxtt5ydiwARm6/boIgiFigP+stYGRKCxiGQYu2BYDDU1fEF7l8Lh36DuQnOWYe+/r6IJVKIzLO4UBfXx8Az6YL/uJzIOtOYWEhCgsL8YMf/CCoARCxj0sgK+s/kKWMLEEQRHTh3K3KPSMrFUqRKEqEzqJDt3Fk+Mj2mnqhtWgBXJhhdJZctPe1ozClECkpKVxb1vj4+KDsQEcaDMOgr68PSqUSKSkpEAgEQe3P50B2yZIl+NGPfoQf/OAHUCgU3HK73Y7vvvsO//znPzFjxgz09PTg3nvvxalTp1BcXEzVdyOAgaQFcsnInJoiCIKIBVw0sgmebdrlUjl0Ft2IuX4762PZ3zP3jCwArqU9G8wS/pOSksJ9jsHgcyC7efNmvPXWW1i2bBna29uRkpICo9EIo9GIhQsX4s4778TMmTOxfft2AMB9992Huro6JCYmYuLEiZyW9qqrrgp60ER0wWZkk+OSkRyX7LIuTZrGPaY2tQRBENHFQBpZwGGp2KBpgM6ig8FqgFQ4vKfSvQayTp8LG/jzeDxkZ2dDoVB4dOciBkckEgWdiWXxOZCNj4/HPffcg3vuuQcWiwUqlQoSiQSpqaku2y1atAgAsGXLFgCARqPhtLTbtm2jQHaYYbKZuKkpd30sAIj4IqTEpaDH1EPSAoIgiCiDDcwSRAlIFCd6rHf3ks1JyhmysUWCwTKyzlIMABAIBCELyIjACEgjKxKJXBoH1NfXY9euXYiLi8PUqVMxbtw4bp1MJsOcOXNC2ryAiB5atC1g4Kg8dJcVsKRL0rlANtjWwgRBEERocGmG4CUbC3g6F4zIQNZLRpaIHgIu9mJZt24d7r//fiQmJkIoFEKtVmPatGl48803UV5eHooxElGMc2ta90IvFrlUjrO9Z2G0GaG36L3e9RMEQRBDi8asgcFqAOBbIDsS5GHOgSwbtKdJ0iDii2CxWyiQjUKCrsR65plnsGbNGqjVanR1deHs2bOYP38+5syZg71794ZijEQYsNvtaG9vx7Fjx3D48GEcO3YM7e3tsNvtfu1nIOstFtLJEgRBRB8ujgUJPgSyI0AexlpvpUnSkCBKAADweXwo4h1F7tQUIfoIOiOr0+lw2223ce4EBQUFePHFF5GWlob7778flZWVQQ+SCC0qlQo1NTXo7u6GzWYDn8+H3W6HQCBAWloaysrKIJfLB98R3DqgDJCR5V7boPLo/kUQBEEMPYM5FgAjy0vWaDVCafDebj0zPhOtulZozBr0WfoQL4qPxBAJLwSdkS0rK8P+/fs9li9fvhw1NTXB7p4IMSqVCpWVlVCpVEhOTkZmZiYyMjKQmZmJ5ORkl/W+4CIt6CcjS929CIIgog+XZgj9SAtGUiDLZmMBL4FsAulko5WgA9kXXngB999/PzZt2uTSbmz//v0oLi4OdvdECLHb7aipqYFer0dGRgZsPBs+Ov0RPjn9CYxWI0QiETIyMqDX61FTU+OTzICVFiSJkpASl+J1m5Ha5pAgCCKaGagZAstI8gL3VujF4pyxpkA2ughaWjBv3jxs2LABK1euxD333IPy8nKYzWYcP34c//znP0MxRiJEKJVKdHd3IzU1FTweD6fVp9HZ1wkAONF1AlMzp4LH4yE1NRXd3d3o7OxEZqb3ixsAWGwWtOnbAAC5stx+3QhGWrEAQRBELODiIduPRnYk1Tg413x4kxawkE42ughJ260rr7wSZ86cwYYNGzBlyhSIxWLweDxcddVVyMjIwKWXXopVq1aF4qWIIFCpVLDZbFxfY+e760ZNI/dYJBLBZrOhs7NzwP216lphZxxZ2/5kBQC1qSUIgohGfJEWiPgipMY5/OKH+/V7wIxsPGVko5WgM7IscXFxuPLKK3HllVdyy5qbm1FdXY2qqipUVVWF6qWIADGbzS4tg50D2XZ9u0vXFj6fD7PZPOD+Brp7dWakVb0SBEHEAmxAJhVKIRPL+t0uXZoOtUkNlUE1rL3AnTWy7n65AzVFICJLyAJZb+Tm5iI3NxfXXHNNOF+G8BGxWMzpXm12G9RGtcv6Jk0TxqU5mlnY7XaIxeIB9+eLhywApMSlgAceGDDDXmNFEAQRCzAMwwVkmfGZAwan6dJ01PXUwWQzQWfRIUmcNFTDHFLYjKxUKHUpUgaoKUI0E9ZAlogu5HI5BAIBLBYLeq29nCyApVHTiHFp42CxWCAQCJCRkTHg/pwzsgNZagn5QqRKUtFt7B72Giti+GC326FUKqFSqWA2myEWiyGXy6FQKFxmNggiFtFatBeaIfSjj2VxL9gdjoGs1W7Fed15AI4ZRvfAPl2aDiFPCCtjJY1slEGB7AhCoVAgLS0NKpUKKr5nZrRZ2wyrzQq1Wg25XO5XIDuQtABwXAS6jd3DfmqKGB6E0muZIKIRl0KvfvSxLM7OBV2GLhQkF4RtXJGiXd8OK2MF4P33jG2KcF5/njKyUQalFUYQfD4fZWVlSEhIgKpLBYFdAABcy1ibxYa683VISEhAWVnZoFmnZo1jGiZeGO8xDeMOeyG02C3QWrTBvhWCCBuh9lomiGjEl0IvFpeMrHF4fu8HKvRiYTPXPaYeLptNRB4KZEcYcrkcM2fORDe/G1KbFDKzDBPiJkBmlkFqk0LFU2HmzJmDZpssdgs3DZMnyxs0wzqSTLWJ2MXda5l1+GAJxGuZIKIR54xsf129WEaC84xPgaxTwK/sU4Z9TIRvBB3I3nbbbdi9e3coxkIMEWnpaaiMr8SplFPQpeswu2w2zieex6mUU9gn3Yf09IGzqwDQrht4GsYdci4gYgF3r+UWbQs+r/scZ9RnuG3cvZYJIhbxpT0ty0hIRAzkWMDi0hSBdLJRQ9CBrFarxeLFi1FcXIxnn30Wra2toRgXEUZada3QWXXoFfdCPkaOOTPmILMoE73iXjTrmlGvqR90H8762IE8ZFmoTS0RC7h7LX/b+i1ada3Y3bLbpXOhr17LBBGt+NLVi2UkdGf0NyNLOtnoIehA9uOPP0ZrayvuvvtufPjhhxgzZgyWLl2Kjz76CBaLJRRjJELMye6T3OPx6eMBAAtzFnLLdjcPnmF3bqAwkPUWy0i4oydiH2evZZPNhG5jt2O5zeyh7fbFa5kgopVANbLDNRHBBrJCnhDZCdlet3F2d6BANnoIiUY2PT0d9957L6qqqvDdd99h7NixWLFiBUaNGoX77rsPZ86cGXwnxJDhEsimegayO1t2DroPX+5enXHRWJEFFxGlOHsts+2bWdx9l33xWh6J2O12tLe349ixYzh8+DCOHTuG9vZ20hNHGezUeJwgDslxyQNumxKXAgHPURw8HBMRDMNwv2nZidkQ8r0bOjkH/NQUIXoIqf1WW1sbtm7diq1bt0IgEODKK6/E8ePHMWHCBDz//PO47777QvlyRICc6j7FPWYbIIxJHoMxsjFo0DSgWlmNXlPvgBc3f6UFI2Fqioh9nL2W3Ys51EY155fsq9fySINsy2IHNqOYlZA1aLEun8dHuiQdSoNyWGZku43d6LP2ARg4MUMa2egk6IysxWLBxx9/jKuvvhr5+fn48MMPcd9996GtrQ3/+Mc/sHXrVrz33nt48sknQzFeIgTUdtcCAJJESRidOJpbviBnAQDAxtiwt3XvgPtgu3pJBBIo4hWDviZpZIlYgPVaVqvV6NR7z8gyDAO1Wo20tDQKZJ0g27LYQWfWQWfRARhcVsDCzqp1Gbs8munEOr7OMKZL0rnMNEkLooegA9ns7Gz84he/QH5+Pr777jscPHgQK1euRFLShc4fS5YsQUpKSrAvRYSAbmM3l2kalzbO5U7cWV6wq2VXv/uw2W1o0TkqPHNlnh1QvDHcp6aI4YGz17K2R8t5LQOOQNZisaCzs9Nnr+WRAtmWxRb+6GNZ2EDWxtjQY+oJx7Aihq+BrIAvQEa84+aVAtnoIeir8L333ouWlhb89a9/xeTJk7nlDMOgqcmRtUtNTUV9/eCV8ET4cZYVjE8b77JuSuYUJIkcNyB7W/fCard63Ud7Xzu3zhdZAeC4AKRKUgGQRpaIbuRyOS4qvwid/E7OaznJkgSzxoze3l7Oi5mmyC/gbltmtBpR21ULnVnHbUO2ZdGDS1evQdrTsgzngi9frLdY2MC/29gNk80U1nERvhF0IPv4449Dp9N5LO/u7kZBQeja2K1fvx4FBQWQSCSYNm0a9uzZ0++2bW1t+MlPfoJx48aBz+dj1apVXrf7+OOPMWHCBMTFxWHChAnYvHlzyMYbrbgUerkFsiK+CHNHzwUAaM1aVCmrvO6DlRUAvgeywIULYbehe9hNTRHDi1amFbUptTiVcgotiS1ol7ajMb4RE6ZPQEVFBQWxbrjblu1o3oGdzTuxpX4L2ZZFIYFkZIdznYM/xcsuTRH01BQhGgg6kHW+SDmj0+kgkUiC3T0AYNOmTVi1ahUeeughVFVVYf78+Vi6dCmX8XXHZDIhIyMDDz30EMrLy71us3//fixfvhwrVqzAkSNHsGLFCtx4442orKwMyZijlYECWQBYmOtkw9Xi3YbL5aSXDe5YwMLqZK2MFRqTxufnEcRQc1R1FAyPQa+4F0wmg8akRrQktKBH3ENyAi8425bZGTuX4eoydHFaTBayLYs87X0XKu4Ha4bAMlIC2ZzEgTOyzp+X8+dIRI6AXQtWr14NwDFd9OijjyI+Pp5bZ7PZUFlZ6SI1CIYXX3wRt99+O+644w4AwLp16/DVV1/htddew9q1az22HzNmDF5++WUAwNtvv+11n+vWrcPll1+ONWvWAADWrFmDXbt2Yd26dfjggw9CMu5ohJUWCPlCFCYXeqyfN2oe+Dw+7IwdO5t34v7p93ts4+Ih60dG1t1LNkWS4vvACWIIOa46zj3+QdEP8NqR1wAA53rOYc6oOZEaVtTibFvWbex2kSW169uRJL5QM0G2ZZHHRVrgq0Z2GBfssoGsXCpHvCh+wG2pKUL0EXBqoaqqClVVVWAYBkePHuX+X1VVhZMnT6K8vBwbNmwIeoBmsxmHDh3C4sWLXZYvXrwY+/btC3i/+/fv99jnkiVL+t2nyWSCRqNx+Ys1DFYD17WrOKUYIoHIY5sUSQomZ0wGADRoGlyCVhZ/rbdYyEuWiAUYhsGxrmMAgDRJmkvgerb3bKSGFdU425a5++86+22SbVl04JxJ9FUjO1yb2vRZ+rjfI1880Z0/L/KSjQ4Czsju2LEDAPCzn/0ML7/8MmQyWcgG5QyrvcrMdD3ZMjMz0d4e+Jeovb3dr32uXbsWTzzxRMCvFw3Uqes4bSrrH+uNhbkLcVh5GIBDXrBiwgqX9c0ax92rmC/2+SIIAHLJ8J2aIoYPLdoW9Jp6AQCl8lIUplyYuTjXcy5Sw4pqWNsylUoFpdFVN8hmrVjbMrlcToFshGEzsiK+CKlxqT49x6XYaxglIvxt7uOSkSUv2aggaLHXO++8E7Yg1hl3iyeGYXyyfQrVPtesWYPe3l7ur7m52et20cxJ9cD6WBYXG65mVxsuO2PnTvycpBzweb5/hYZz1SsxfGCzsYAjkJWJZVBIHV7JZ3vP9lsXMJJxti3r7el1sS1TGVToM/aRbVkUwd5cZMZn+vw7Olw1sv44FgBuTRFIWhAVBJSRXb16NZ566ikkJCRwWtn+ePHFFwMaGAs7ZeWeKVUqlR4ZVX/Iysrya59xcXGIi4sL+PWigZNdvgWyhcmFyEnMQYuuBYc6DkFr1nIaN2WfEma7o1AjT+a7rABwm5oyDp8LITG8OKZyCmTTSwEAhSmFUBqU6DX1otvY7fJdJhzI5XJMnTEV/6z7J+Jt8eBb+WB4DHgMD82dzSgeXUydvaKAPksftGYtAN8LvQAgUZSIOEEcTDbTsApknTOyvnapZOtIKJCNDgK6La6qqoLFYuEe9/dXXV0d9ADFYjGmTZuGbdu2uSzftm0b5swJvOhi9uzZHvvcunVrUPuMdpwzsuNS+5cW8Hg8zr3Ayljx7flvuXWBWm8BlJElYgOXQFbuCGSLUoq4Zed6SV7QH138LhxPPo5TKafQmdyJdmk7WhJbYB1jJduyKMHFessPaRiPx+MKvobT9dtfaYGQL+R+y0haEB0ElJFl9bHuj8PF6tWrsWLFCkyfPh2zZ8/GG2+8gaamJqxcuRKAY9q/tbUV7777LvccNojW6XTo7OxEdXU1xGIxJkyYAMDRyGHBggV47rnnsGzZMnz22Wf4+uuvsXfvwK1ZYxWb3YYz6jMAHCdrojhxwO0X5CzAv2r/BQDY3bwbV4y5AkDghV7A8K56JYYHVruVa+E8OnE018TD2eHjbM9ZzMiaEZHxRTvHVcc527KrS67mriHHTcdJThAlOBco+epYwCKXynFefx5qkxoWuwUivmfBcKzhbyALAFnxWVD2KdFl7ILZZoZYQC4ckSTgYi8Wg8EAhmE4+63GxkZs3rwZEyZM8HAFCJTly5ejq6sLTz75JNra2lBaWootW7YgPz8fgKMBgrun7JQpU7jHhw4dwvvvv4/8/Hw0NDQAAObMmYONGzfi4YcfxiOPPIKioiJs2rQJM2fODMmYo41GbSMMVgOAgWUFLDMyZyBeGI8+ax/2tO6BzW6DgC9wCWT98ZAFAFmcDEK+EFa7dVgVCxDDh7M9Z7nzhM3GAp6BLOGd410XbMuuGHMFvqj/At3GbhzpPAI7Y/dLU0+Eh0CaIbA4S2rURjUU8YqQjStSsIFsoigRKXEpPj0nMyET+J+6Qtmn9ElbS4SPoK8qy5Yt4zKhPT09uPjii/HCCy9g2bJleO2114IeIMtdd92FhoYGmEwmHDp0CAsWLODWbdiwATt37nTZnmEYjz82iGW54YYbcPLkSZjNZtTW1uL6668P2XijDefWtAPJClhEggtdvnpMPahR1QAITlrA5/GRJkkDMLyKBYjhg3MgxupjAZIW+ApbKCfgCTA+bTzKMxwNaTRmDRp6GyI4MoIlkPa0LMOt4Mtit6BN3wbAkY31tfCNvGSji6AD2cOHD2P+/PkAgI8++ghZWVlobGzEu+++i1deeSXoARKhwbmjV0l6iU/P8eZewGZkhXyhX4UCLOyFUG1Uw2a3+f18gggn3vSxAJAqSeVuwigj6x2D1cB9NmNTxkIilGCyYjK3vr+W18TQ4hx4+XsNH26BbLuuHTbG8TvkT1bVxbmAdLIRJ+hAtq+vD0lJjor2rVu34vrrrwefz8esWbPQ2Ohppk9EBudA1peMLADMGz0PPDjuUHe17ALDMJyHbE5iDoR8/5UprE7WxtjQY+rx+/kEEU7YQJbP42NC+gSXday8oMvYxfnMEhc42X2S86lmbwLY5ioAUN1ZHYFREe4EJS0YZnUOgehjAdfPjdrURp6gA9mxY8fi008/RXNzM7766itOF6tUKofEX5YYHIZhuEA2NS7VZ11TujQdkzImAQDqeupQ3VkNo80IwL+T3pnhaqpNxD4mm4kriCxMLvRoVUnygoFxbuvL3gRMSJ/A3fBWK6sjMSzCDbbYS8gXcrMMvjLcMrIBB7IJ1BQhmgg6kH300UfxwAMPYMyYMZg5cyZmz54NwJGddS64IiKHyqBCt7EbgKPQy59GEhU5Fdzj9068xz3Ol+UHNJbh2uaQiH1Odp+ElbECcJUVsFDB18C4N5IAAIlQwgW1DZoGqI3qiIyNuIBzMwR/i++GW5vxQAPZrHhqihBNBB3I3nDDDWhqasLBgwfx5ZdfcssXLVqEl156KdjdEyGAtRMCfHMscGZBzoWiuu1N27nHIcnIDoOpKWL44K0RgjPOGVkKZD1hM7IivgjFKcXccmd5QU1nzVAPi3DCYDVwshh/ZQUAZWRZ5PFyTnZHGdnIExIvlKysLEyZMsXFJ/Diiy/G+PH+BU1EeHBxLEjzTR/LclHqRciOz0ayORmjdKOQr81Hjj4HqZZU2O12v8cy3DRWxPDBJZDNGDgjS9ICV7RmLRo0DQAcN8siwQV/UeeCL9LJRhZln5J77K9jATD8ZtSadY5AVsgX+hXYi/iiC00RKCMbcYL2kQWA7du3Y/v27VAqlR7Bzdtvvx2KlyCCwMWxIM03xwKWrq4uzDPOQ2NPI/jMhZaTncc7sVO10++Wk8PtQkgMH9hAVsQX4aKUizzWy6VyJImToDVrKSPrRm3XhVkf9yI51oILIOeCSOOcPXSeHvcVqVCKBFEC9BZ9zCciGIZBi7YFgKN4WcAX+PX8zPhMdBo6oTKoYLFZXG7eiKEl6IzsE088gcWLF2P79u1QqVRQq9Uuf0TkYQNZiUDil7ZVpVKhsrISGUwGDAIDNGINtCIttHFaKNIV3HqVyveAdLhprIjhgcas6TejyMLj8VCU7JAXdPR1QGfWDeUQoxpnfezE9Iku6xTxCoxOHO3YTnUMFrtlSMdGXMC5wj6QjCxwQV4Q64mILmMX1/wkkIYGrAUXAwadhs6Qjo3wj6Azsq+//jo2bNiAFStWhGI8RIjRW/Sc92txarHPd512ux01NTXQ6/UYO3os9vbsBf6XbE8SJ0EiliAuIw6dnZ2oqalBRUWFTy0oh5vGihgenOg6wT32VujFUpRSxE2P1/fWc64eIx1nxwJvn195Rjlada0w2Uw41X1qwM94qLHb7VAqlVCpVDCbzRCLxZDL5VAoFMOura5LM4QANLKAQx7WqGmEzqKD0WqERCgJ1fCGlED1sSwuzgV9HRiVOCok4yL8J+hA1mw2Y86cOaEYCxEGTqtPc4/9KfRSKpXo7u5GamoqRAIRcpJyuM48yeJkAI4MVWpqKrq7u9HZ2YnMzMEvjEmiJIj4IljsFsrIElFDf40Q3HFxLug9S4Hs/2A7okmFUhQkF3isn6yYjC31WwA4bLiiJZBVqVSoqalBd3c3bDYb+Hw+7HY7BAIB0tLS/JZORTvBeMiyuFsostn2WCPoQDaeLLiihaBvN++44w68//77oRgLEQactWv+BLIqlQo2mw0ikWOKdYxsDLdOFnfBH1gkEsFms6Gz07epFR6Px10IY11jRQwfBnMsYHHxku2hgi/A0aWvVdcKwKHB99YoZYrighVjtBR8OUujkpOTkZmZiYyMDGRmZiI5OTkg6VS046KRDaAzIzB8ZtVCGciy3rxEZAg6I2s0GvHGG2/g66+/RllZGRf4sLz44ovBvgQRBKfUgTkWmM1ml2m1wpRCVCmroLfocVGqayEMn8+H2Wz2ed/pknS06dugNqphtVsD6hA23BhJ05vRCBvIJogSMCZ5TL/buVhw9VLBF3AhGwt4FnqxjE0Zi3hhPPqsfVHRGMFZOpWRkeHhrS0SiZCRkeEhnYr185TNyAp5/jdDYBkuBbuhlhYQkSPoCKKmpgaTJ08GABw7dsxlnT/G+0R4YDOyfB7fIwAdCLFY7OJAESeIw4/H/xg2u82jEMZut0MsFvu8b/aOngEDtVGNjPgMn587HBlp05vRRmdfJ/dDNDF94oAm8ZnxmVxARs4FDgbTxwIOe6NJGZNQ2VaJjr4OtOnakJ2YPVRD9MBZOsX+Tin7lOg19SI7IRuJ4kQP6ZRAIIj585TNHGbEZ/hdpc8yXLzAnQPZQOQRzhltCmQjS9CB7I4dO0IxDiIMWOwW1PXUAXB04pIKpT4/Vy6XQyAQwGKxcFl2Po8PvsD1R95isUAgECAjw/dg1N25YCQHsuz0pV6vd+iRnWY0LBYLt37mzJlR/yMZqzjLCibKJw6wpePmvDC5EMe6juG87jz6LH0erWxHGgM5FjgzOWMyKtsqATjkBZEMZN2lU2qjGp+e+RQ2xgbAEazly/IdLi824Ny5c+ju7o7p89RkM0FtcjgJBaqPBYZPIMtabyniFQEVrCmkF1q9k0Y2skT/XAgRMPW99ZzVzfhU/5pTKBQKpKWlQa1Wg2EYr9swDAO1Wo20tLSAA9lYnpoKFvfpTXdZDju9qdfrUVNTE1ADCmJwnAOxSfLBi7cKUxwFXwwYzrJrJHNC5XB8SBIlIU+W1+92Lo0RIiwvcJdOnVaf5oJYwHFdOtRxCJ+c+QS7mnfhi0NfoF5Vj+S05Jg9T5X64JohsAyH67feoufatgfapVIkEHENfkgjG1lCEsju2bMHN998M2bPno3WVofo/7333sPevXtDsXsiQJwbIYxP9y+Q5fP5KCsrQ0JCAjo7O2GxuHo/WiwWdHZ2IiEhAWVlZX7pw4bLHX2weJve7DH24GzPWdgZx4+h+/QmEXp8LfRicSn4GuEdvpR9SigNjgBpQvqEAWUZZRllXFvPSBd8OUunGIbhZCI8Hs9zhsgKqLVq7Ovahw3HN+DfZ/+Nms4artUr+7xoP0+dPWQDaYbAIpfEfrFXsPpYFvaGoNPQSf7IESToQPbjjz/GkiVLIJVKUVVVBZPJBADQarV49tlngx4gETgugayfGVnAIS9gp8p6e3vR0dGBzs5OdHR0oLe312W9Pzi3qY2GC6Hdbkd7ezuOHTuGw4cP49ixY2hvbw97ZsV9etNkM+HTuk+xtWErvm39ltvOX2cIwncYhuGKldIkaT5VcrNNEQByLnDWxw4my5CJZdxNwKnuU+iz9IV1bAPhLJ3qMnZxQWl2QjZuuOgG3DLxFlTkVqAgsQAiiGDj22Dj22Bn7GjRtuDb1m/xfu37LtfYaD9PXay3gsjIpkkvFImpjJG/fgdCqAJZ9oaAATOikzKRJmiN7NNPP43XX38dt9xyCzZu3MgtnzNnDp588slgd08EwanuwBwLnJHL5aioqEBnZyc6Ozu5St2MjAxkZGQEVKnr7kMYSSJZaOU+vdnQ28B1mjnRdQKTFZORJE4C4L8zBOEbLdoWLoiZJJ/kU4EqKy0AMOILvnzVx7JMVkxGXU8dbIwNx7uOY0bWjHAOr19Y6ZRKpcI564WbETbQThAlYHzaeKTb0mGWmqGxatAl6EKjphFas5bbvqazxsXWMJrPU+fp72A0siK+CClxKegx9cRs8BbqjCzg+HwDtTQjgiPojOypU6ewYMECj+UymQw9PT3B7p4IEIZhUNvtcCxQSBUuuiZ/4fP5yMzMRGlpKaZOnYrS0lJkZmYGbDcTLRqrSPtIujtD1PfWc4/tjN1FR+ivMwThG0dVR7nHg2UUWUYljIJE4CgOGenSAmfrLV+aHEzOmMw9jqRO1lk6dV55HgK7gCvkA1ylU0WFRUiXpGN+znz8tOSnWD5uOZeV7DJ0uUgMovk8denqFURGFoCLF3h/NRTRTMgC2Xiy4IoGgg5ks7OzUVdX57F87969KCws9PIMYiho07dxmYNAs7Hhwjkj223ojsgYoqHQynl602KzcK2EWWq7atFn6QvIGWIoiJQkI5Q4ZxR90ccCgIAv4Lxmm7RNMNuiMwMXbhiG4aQFqXGpyE4Y3IXAueCrSlkVrqH5hFwuh2K8Ah3ogNQmRR4vD/oevYd0qqCggDtPeTwe0qRpLlaG7M1MtJ6nLKHo6sXCJiOMNiP0Fn1Q+4oE4crIEpEhaGnBr371K9x77714++23wePxcP78eezfvx8PPPAAHn300VCMkQgAF32sHx29hoJ4YTwkAgmMNmPEMrLeCq30Fj1EfBHEAkdGJZAWvP7gPL2pEWlgszuqpoV8Iax2K2yMDdXKaowVjYVcLo+qH8jh4n3ra2tadwqTC3Gy+yTsjB0Nmga/PJqHC+f159Fj6gHgyGb7IsvIS8pDalwq1CY1jnQegZ2xD1ggFm729+5HbUotZBYZbsm/BUXyIg/plN1u585TtnlCYXIhDpw/AACo76nH5IzJUKvVUXeeOsMGsnwe3yWZEAju3b0SxYlB7W+oYa23ksRJSI5LDng/zkVzlJGNHEFfQX73u9/h2muvxSWXXAKdTocFCxbgjjvuwK9+9SvcfffdoRgjEQDRHMjyeDzujj5SGln3Qqs6dR3+eeKf2Hhyo0sRSjgLOJynNxvbGiGwOwzKF+QsgIAngMAuQGNbI4QSod/OEOEk0pKMUGG1W7mGIaMTRyNVkurzc8m5wM1/1wd9LOA498sV5QAAjVmDht6GcAzNJxiGwdbGrWB4DLRxWlw//3qv0ilvDi7JccncNUylU6GlvSUgB5ehhJUWZEgzgu6mGG0Fu75it9vRcr4F/A4+8rX5mGiZGNQskkt3L/KSjRghOeOeeeYZqFQqfPfddzhw4AA6Ozvx1FNPhWLXRIBEcyALXJia6jH1RMS2xLnQSmfWYVfLLtgZO/QWPactZglnAYdcLsfUGVNRb62H1CZFujUdKdYUjBePh9QmRY+wB82pzVGT3YwGSUaoONtzFkabEYB/2ViAnAsA//WxLC462QjacJ1Wn0ajphEAMC1z2oBZSm8OLrn8XMjMMkhtUqgF6qhthmC329F8vhnSLinytfkoMhYFLQFyycjGiHOBSqXCzp07sX3XdozWjUaWIQuZ2kzs3bsXO3fuDOjGWxHv1BSBMrIRI6DbstWrV/u87YsvvhjISxBBwjoWJIgSkJOUE+HReOLsRdht6A66+MBf2EIrhmGwo3mHi86xtqsWUxVTuanScBdwnDGfQY2sBjKLDJekXYLigmKMLhyNh6ofglqoRnNzM35u/jnnYBBJ3CUZfZY+HGg7AJlYhmmZ08Dj8cIuyQgVzhlFXxohOEPOBRcaIQC+Z2QBYIpiCve4WlmN64uv9+l5drsdSqUSKpWKc0+Ry+VQKBQBZUG/aviKe7w4f/Gg27s7uCT3JGN3zW5oRVrYk+z4jfw3fo8h3LASoBZlC3J0OWB4DDKQgb179wYlAYo1L3DnDor2ODs0Yg0AYGzaWJdZJH9vRuIEcUiTpKHb2E0a2QgSUCBbVeUq0j906BBsNhvGjXMUFZ0+fRoCgQDTpk0LfoSEz7AX+qb2JojaRcjh5yAnMwdgAAwuXxtSXJwLjKohD2TZQqujHUc5vRSL1qxFs7YZebK8ISng2Na4DQyPQa+4F4suXoSpuVMBABXmCnxy5hNoLVpsPLkRvyj7RdjG4CvOkgz2JqBJ4yhSk0vlXBGUsyQjagNZP62jnMlNyuW0zCNRWmBn7FxGVhGv8KvN9IT0Cdxn52tGNtSabFZWAAA88HBZ/mU+PY91cMnMzMREZiL+2vlX9Gp6cbjzMLoMXUG5w4Qa5+CNJ+FxwduY1DFBBW+AW5vxKA9k3WeROrouZE6TxcncLFJnZydqampQUVHh141RZnwmuo3dUBlUsNqtQcs2CP8JSFqwY8cO7u+aa65BRUUFWlpacPjwYRw+fBjNzc245JJLcNVVV4V6vEQ/sNMme/fuxeEjh5FlyEKOLge5qtyAp03CSaTv6BUKBYQJQhxvOe4I9OFqv1TbVRtwC15/sNqt2NG8A4CjCG72qNncuttLb+cKYd478V5EDeRZnCUZDZoGLogFHN63zkSzpyZwwcyfz+NjQvoEv54r5AsxRjYGgONzGGldfZo0TdBZdAD8vwmQCCWYkOb4vOt769Fj7Blw+3Bosp1lBdOzpgdU/MTjXQiA7YydO4+jAffgzcgYuXWJosSgJUDuxV6+jCdSDifus0gak4ZbJ4uTAQiuMxubhLExtqgP6ocrQWtkX3jhBaxduxapqRcKJVJTU/H000/jhRdeCHb3hA+4X+hNUhO0Ii00Yg3SU9KjsvjGuVggEic/Awb/Nvwbffw+JFmTMCF1AuaOnot4UTwAoKmnCa3trWEv4DjYcZDzoVyQswBxgjhuXZ4sD1eMuQIAoDap8dHpj8IyBn9gJRkWu8Wl+xjgsKLSmXXc/6PZU9NoNeK0+jQAhwMBe9z9gfUctdqtLnY+I4FgstkAuIIvADjSeaTf7cKlyfZXVtAfl+VdyOR+3fh1wPsJNe7Bm3MTB9ZhIJjgzZ9iL+cky/Hjx3H27FkcP348KG2qPzjPItkYm4vNYbL4gmNBoIW95CUbeYL+ddZoNOjo8Dx4SqUSWq3WyzOIUOLtQu98YVEkKaKy+CbS3b3eO/EevtN+hzpZHXgJPIyXjodKqUKxqBgyswwSqwQdvI6wF3A4//gtyl/ksf4Xky7ICTYc3wCTzRS2sfgCK8k4fP4w9+Mo4DvcFpybcES7p+bJ7pOwMQ67M38LvVhcnAtGWMGXc2vaQD4/Xwu+vNnkacwaGK0XMoz+BmQMw2Bb4zbHc/2QFXhjQvoEzj+3sq0SGrNmkGcMDc7Bm9FqdNGDy8Qy7nGgwVtKXAoEPMd5P1AgGw0OJ86zSLVdtdwMQFZClodtWCCzSM7dvCiQjQxBB7LXXXcdfvazn+Gjjz5CS0sLWlpa8NFHH+H222/H9df7JuL3hfXr16OgoAASiQTTpk3Dnj17Btx+165dmDZtGiQSCQoLC/H666+7rN+wYQNXmOL8ZzQa+9ljdOLtQs9WkfJ5fKRJ0oK68w4XkezuVaeuwytVrwAA9CI9fnXdr1CxsAITJ07EzNKZaE1sxamUU9gm3Ia09LRB9hY4dsaOb5q+AQCI+WIsGO3ZIW9s6lgu69Np6MSnZz4N23h8gZVknG0/CzCO79iVBVdy373arlrY7LawSzKCJZhCLxbngq+RppN1dizwV5YBuDZGGKjDl7smu7KtEv868S9sPLnRJcvoT0B2Wn0aDZoGAIO7FQwGj8fDojzHDaiVsWJX866A9xVK2OCNYRjsadnDNS0YnTgaGVLXczKQ4E3AFyBN8r/uZv0kIqLF4YSdRTLZTPi+/XtuubOMy3nM/s4iOWdkqeArMgQdyL7++uu46qqrcPPNNyM/Px/5+fn46U9/iqVLl2L9+vWhGCM2bdqEVatW4aGHHkJVVRXmz5+PpUuXoqmpyev29fX1uPLKKzF//nxUVVXhD3/4A37zm9/g448/dtlOJpOhra3N5U8ikYRkzEOFux+q1W7l7jhTJalctiycfqiBEKliAYvdgoe+fYjTNN468VZMz57OteBdNGcR8orz0CvuRau+lTM9Dwc1nTXoNDiOx5zRc/qd3nYu8nr72NsR1WPyeDx8bfkaBr4BSdYkTEqbhJykHOTL8gEARpMRJ5tPRr2npsvUuI+tad1xtuAaSc4FVruVs/fz13+XRRGvwOjE0QAcNxX9fafZgMxmt2FH8w4c7jgMADBYDdjbutdlW18DMmdZwZIxS/weuzuX51/OPY4WeQEbvJ1Wn0Zdj6PzplggxqV5l3o0rghUAsTeAHQbumFnPINQ9yQLwzA4cP4APj3zKTr7HNe9oUiysLNIh84f4jL5Y1PHumRSgcBnkVwyssPUSzbauzgGXV4XHx+P9evX409/+hPOnj0LhmEwduxYJCQkhGJ8ABwWXrfffjvuuOMOAMC6devw1Vdf4bXXXsPatWs9tn/99deRl5eHdevWAQBKSkpw8OBB/PnPf8YPf/hDbjsej4esrCyP53vDZDLBZLowravRRMcUkvO0CQB0Gy9cVNwzDdFUfBMpQ+03a97kipIKkwtx9xTPph03XHQDvj3v0H9+dOYjzBk9JyxjYac3AdcfQ3cmpE/AvNHzsLd1L87rz+O/5/6La8deG5YxDcY3Td9gl3oXEmWJKDGVoCiuCB0dHcjn56Pb3A07z45GWyOWz1wedZ6azvZN7afbkWPKgUFswFjZ2ID2ly/Lh4AngI2xRUVGNtT2VP1xrvccDFYDgMD0sSzlGeVo1bXCaDPidPdprzcUYrEYZqsZW+q3eLiLNPQ2oKG3gXPK8CUgC6WswPl9pEvS0WXswrfnv0WfpS8gzXUoj59cLoeZMePb5gs69oW5Cz2m0oORALHJCCtjRa+p1+OGxj3JcqzrGNeW+KuGr7B83HKIBKKwO5woFAqIEkVoaGgABI5s8qzsWS7bsIW9gXRmixaNbLjO/1jo4hgynwg2AxNqzGYzDh06hAcffNBl+eLFi7Fv3z6vz9m/fz8WL3YV8C9ZsgRvvfUWLBYLd2LpdDrk5+fDZrNh8uTJeOqppzBlyhRvu8TatWvxxBNPhOAdhRb2zpvFOSh0DhaB6Cq+iRfFI14Yjz5r35AFsse7juONmjcAAAKeAM/Oe9aluIplYe5C7odpR9MOqAyqoFs6usMwDLY3bQcACHlCLMxZOOD2vyr7FZeBevPom7im8Bou2z5U9Fn68Nz3zwEAdCIdfrzoxyiPL0dnZyeMJiP2WPeg2d4MnUCH1VLfvaaHAueLscligrBbiBwmBzKJDN/u+Tagi7FYIEZuUi4aNA2o762HzW4b8mPCMpQ/NsHqY1kmKyZjS/0WAECVssprIMtL4OGg8iA6bB0A3xGEjEsdx92M7m3di9FJowEbfArIQikrYBHwBViUtwj/d/r/YLKZsLd1LxaP8a+ALNTHL12ejkPaQxCbxTAJTRiXPg5jU1xv2IIJ3gDPZIR7IOucZOkydGF/635undasxYG2A5ifMx9AeJMsfD4fe5m93CxSUXaRiye3xWKBWq0OeBYpGpoihOv8d7ZwS01NdZGHWCyWoCzcQkl0zvs5wd7Vud+pZWZmor3dux6lvb3d6/ZWq5UTlY8fPx4bNmzA559/jg8++AASiQRz587FmTNnvO5zzZo16O3t5f6am6OjSpmdNrFYLLAxNhftn7O3YzQW3wxlm1qTzYSH9z4MK2MF4Jiu729KWcQX4bri6wA4sg2f1n0a8vHUdteiVdcKALg4++JB+31PVkzGxVkXAwAaNY2cB+ZQ8ubRN9GmbwMAzBk1B5ePuZyTZEyfNh0Lpi9Ar7gXNtjwyZlPAn6dUE9juRec2BPtnKtHsAUnbMGXyWbCed35gMYXLENdUOOsjw0mIztYwdcZ9Rnc+/29OM+cR7wtHnGCOPyg6AdYkLPAEbzCERAdaj/ksybbxa3Az2BzIJwLNf2VF4Tj+G04sQGVvEqYBCYooMBMxUyX9RaLBZ2dnUFJgAaz4GKTLFa7FV83fs0VV7IcUx1Dm85xPQlnkqVaWY0vlV+iTlYHq9SKAnEBOjo60NnZiY6ODvT29rp0bvMXiVCClLgUAJHRyIbr/I8WjbMvRH0gy+Ku62EYxmPZYNs7L581axZuvvlmlJeXY/78+fi///s/XHTRRfjLX/7idX9xcXGQyWQuf9GAQqFAWloa1Go1jiiPcHpTuVTOaXeGwg81ENgLodasDXk1vnswtG7LOnQqO8FjeChJK8Evy3454POduw19fPpjrxqwYHBxK8jzdCvwhvOY36h5I+RjGoiG3ga8c/wdAA4P1TUXr/E4x64fez3ne/vxmY9htVv9fp1QW/V4uxiz+jwAyEzKDOpizFpwAcDZ3qHXyUbix8Y5IxtIoRdLcWox4gXxSDYno+VMi8tNy4HWA7j1i1vRYehAU2IThBIhLk2/FOnidPB4PMwfPR98Hh8CuwDnzp+DTWQbNCBzlxUMJOfxlxlZMzg3gF0tu3y+noXj+B1XHcf66vXQiXQ4JzuH2WNnw6AzhDR4AwYPZNkky/6W/eg2dgMA0iRpmJl9Iaje2bwTBpMhbEkWO2PH898/D8Axi7R00VJcsvASTJw4EUVFRZg4cSLmz5+PioqKoDKKrLygs68TNrttkK1DRzjPf28a52ZtMxdLAUOjcfaFqG9BwZ4M7tlXpVLZr54mKyvL6/ZCoRDp6d47r/D5fMyYMaPfjGy0wufzUVZWhm/2foNTdacg4Atg49uwMHch+Dx+0NMm4cR5aqrb0I3sxOyQ7Nd9mkVj1qCurQ7jeONgEBtw/4L7IeKLBtxHblIuZmfPxv62/WjRtaCyrdJrlWugfN3kCGR54OHSvEt9es7FWRejPKMcNcoadCo78eGuD1EsKw6bFpKFYRis/W4tF5j+bOLPOF2iM5kJmViQswA7m3dC2afE3ta9qMit8Pl1wjGN5c3VQ9mn5NYr4hVBtdR1b1Xrz/sNBd7en51xtF5mZQ6hbBlssVlwSu1ofz1GNsZDc+kPPd09mGuYi96eXvAZPo6fOg4xX4wOQwf29+4Hk8AAIiAvKw/3T74fzaebXaZOSyWlOKc5h15RL3bxduHH6T8e8PXCIStgEfFFqMitwOdnP0eftQ8Hzh/AwtyB5UKA9+Pnjj/Hr8/Shwf3PMjNPC2fuhw/nvxjrq0uq53MyMhARkZGUNcL58+PDVSdUSgU0Il0aOxoBIQOCcZl+ZchVZKKBk0DOvQd6DH24FDDIcwpnhOWQPbL+i9xVHUUADA2ZSx+OO6HEPKFIdfiZiVk4ZT6FKyMFd3Gbr863QWDt++P2qhGfW89xqeNR7woPuDz313jfKbnDLY3bkeeLA8Lcy7oraOhi2P0RDX9IBaLMW3aNGzbts1l+bZt2zBnjvcinNmzZ3tsv3XrVkyfPt3jjoWFYRhUV1cjOzs0wdRQkp6ejr2CvegR9kBqk2Ji3ETw9LyQ3XmHi3BYcLlPs6TJ0/C97ntoxBoYBAZMTpiM9tp2nzJ7N1x0A/f4w9MfhmR8gCPgqe+tB+DoO+/rDyqPx8PNeTejpKcE43rG4bsj36Guri7s5uJfN32NfecdevTshGzcMemOfrf90UU/4h7708AhXJkF94uxxWbhpv/EAjE3JRioq4ezc0EkCr7c31+vqRebTm7ChuMbXDqthcq15HTPac5hIBh9LHueyhk5DAIDNGINjBIjWtGKA90HkGBOwFjNWFSkVuCdJe+gOKcYFRUVmD9/PpdNWzp7KdSj1KhNqcW3vd9yetv+CJesgMU5w+tcyDkQ7sdPb9HjcMdhjylqX4/fnw/+mQvWS9NLcefkO7m2uqWlpZg6dSpKS0uRmZkZ9E3vYNfvblM3NvVugklgQpI1CTMzZyJdmg4+j4+K3AqIGBGSrEk4rT8Naa405DfhRqsR6w6v4/7/wPQHwtY+NlIFX+7fH61Zi0/OfILKtkr8++y/uexwIOe/s8a5z9LHNcBp0jRBaVC6bBvpQvKoD2QBYPXq1XjzzTfx9ttvo7a2Fvfddx+ampqwcuVKAA796i233MJtv3LlSjQ2NmL16tWora3F22+/jbfeegsPPPAAt80TTzyBr776CufOnUN1dTVuv/12VFdXc/uMJb5u+ho7unegNqUWykwlrpx9ZUinTcJFqJsieAuGDrQd4DpnyZPkmFY4zedg6JK8S7isMVv0FQqcZQX+TG+qVCrYGm0YxRsFg8CAFqYFRokxrObifZY+PPfdc9z/fz/j9wNWZM8dNZeTtOxp3eOzZsxbZqHH2OPy/ECmsdxdPQ60HeAq7kcljnLJggVyMR6TPAY8OPYRiaYIzu/PaDViy7kt6DH1wGwzY1fzLhxoO8BNBYbix8ZZVhCoPtb5PB2dORo2vuPHdt/5fahsq4SNb4NWqEWRtAjLEpZBIpBw43cOyKaWTcW9C+4Fw3O8vz99/ycXb1lnwikrYJk9ajbihY5zY2fLTp9s8pyPn8lmwqdnPkVlWyU2n9mMrQ1bXdqpDnb8djbv5G64pUIp1s5fO+jMUzAMFMjaGTse/vZhtDAtqJPVIS09DaOFozl5g6XXgklJk6AVaXFGdgbPn3geFltobQX/WftPTtM/d/RczB09N6T7d4ZtUwsMrU7W+ftjY2zY1rgNZpvjO9Jt7Mb3HRd8c/09/50Lyfe27uWsy4pSilwkVUDkC8ljIpBdvnw51q1bhyeffBKTJ0/G7t27sWXLFuTnO7wr29raXDxlCwoKsGXLFuzcuZNzI3jllVdcrLd6enrwy1/+EiUlJVi8eDFaW1uxe/duXHzxxUP+/oJBZ9bhj5V/BAAwPAb3LLgH0ydPD+mdd7jwNyM7WBGQczBksBpwsP0gV/wm5Atxad6lEPAFPgdDIr6Is7myMlZ8VvdZgO/UFVZWAMBn+x/nH/+JeRO5H3/WVzNUWkj3z/jVL1+FsccIHsPD3NFzB5VBCPgCTl9sZ+w+F325Zxba9G3YdGoTNp/ZzL1H9n36k1lwvhi3altdvg/uUpFALsZSoZTzQz3be9ZFPzYUOBfUfFn/JXpMPS7rqzqq8HXT17DZbSH5sXEu9Ao0I+t8nmYlXrA/7LP0cY8vHnUx5hTNQY+6Z8BjvTB3IS7NdXwnu4xdeLXqVa/bhVNWwBIniMOCHEdTk15TLw62Hxz0OezxYxgGO5t3unQGO9tzFhtPbsSB8wdgtpkHPH4qgwqP7XuM+/9vZ/zWq/wnlAykkX2/9n0ugyeRSfC7H//OJZs+ceJE3HzVzbAX2qET6VDXU4e/H/17yMamMqjw5tE3ATiatjww7YFBnhEckcrIOl/fDrYf9PCxrVZWc1Iqf89/VtZ5pusM55MtEUowb/Q8l+2ioZA86jWyLHfddRfuuusur+s2bNjgsWzhwoU4fPiw58b/46WXXsJLL70UquFFjFerX+XS/PNHzw9LpiFcyCVOGdlBmiL4Yi+i7FRCqVfikPYQGjQNLsVQs7JneZ1GHkzT88PiH+KtY28BcBQw/az0Z1xBUyA0a5s5M/nS9FIPU+7+cP7xzxBm4GDHQaiNarTp23Bed57LLgajhXT/jPusfTh7/izGwaEtvqvirgELLFmuH3s9Xj/yOuyMHR+f+Ri/LPvloFN67tNY2xq2ccfvu/bvoIhXICcpB4B/mQX2Yqw36rGjeQe3fGb2TO77AAR3MS5KKUKLrgUGqwHt+vaQab19QS6Xgy/gY0f9Di77JBVKMVE+EYc6DoFhGNSp69Bn6MPFaRcH9P6c/SlbT7Uix5ADvUiP4pTigMbsftOSJknjNJbstPO4tHEA4NN5+uDFD2J/234YrAZsPLURy8Yu8yhCc3b5CIesgOWy/MvwZcOXAIDtTdsH1dWz38+jHUe5jL5YIIaAJ4DBaoCNsaFKWYXTqtOYlDQJ89MddlXunqHvnXoPNp0NPBEPC/MW4obiGwZ62ZCQJEqCmC+G2W52CWRPdZ/Ci4de5P7/zNxnII+XA/HwOI5PzXsKN/3nJlgZK/5e83csylvEHftgWF+9nutmdkPxDRibGphXtK9EqikC+/1pVDdyN/x8Hh+FKYWoU9eBYRh80/QNri241u/rm0KhQEJKAnbU7AB4AHiOzLbzjFywFm6hIjpTdYRPHFcdx/u17wMAJAIJHpr1kE+BRrTga0Z2MHuR1o5WvL3lbby05yUcVh7Gud5zLkFsSXqJR/bI12AoV5bLmWc3a5vxXft3/r5NF7Y3buce+2PG7vzjz+PxMDVzKrdub+tebjopUC2k+2esUChw1HgUPaIeGAQGlEpL0Xy82SfZAlv0BYAr+hoMNrNgZ+z4uvFr7kcIcFwsnZf5k1lgXT0O1h+E1uSYds5OzHZpSxusq4dLwdcQOxcoFAqcNZ9FR3cHwDgyzVcWXokZWTOwZMwSxw0EA2i1Wuzs2gmjxL8W3M4uEjXHasBT8ZCjy8G0vmmo3BuYjMVd7sF+fiKBCFcWXukSyPhynmYnZmNluUMSZmfseGr/Uy6V4wzDYGuDI5ANl6yAZf7o+Zw39fam7YM6iygUCjDxDI61HAP+l8y/JO8S3FRyEyYrJjtumhmAb+LjQO8B3PPdPdheu93F2WNH1Q7omnUY1zMOU3VTsWrcqiH5HeDxeBe6e/3vRsRoNeL3u3/PySpumXDLgA1lxqeNx89KfwbAMev16L5HA3I7ceaM+gw+PuPo4pkgSsBdk70nwEKJS5vavqGTFigUCkhlUnxX/x33/bk4+2Jcmncpd2zUBjUONx72+/rG5/Ox374fGmiQZE1CfkK+y81rKCzcQgUFsjGK1W7FE/ufAPO/b+/K8pXcFGes4ItGtr8iIDtjR0NvA75u/hr/7fgvTnechlAnBI9xXMDjRfGYmjkVPyn5CSpyK4Jqy+hc9OVPAZM3ApEVAJ4//mNTxnIZxS5DF76s/5L7AfBXC+XtMz7bexatWofPbbwkHtOLpvslW/C36IvNLFS2VnL+uvGieO47bbAasK1hG0xmk1+ZBT6fD1uWDXWGOiRZkyCGGJfkXsJ9H0JxMXax4BriVrUf132Mz/o+g0lggswqw6WjL+UM2guSC3BV/lVIZ9JhEphQI6rBLV/egprOGp+8et1vbvhJfGhEGmjEGshksoA12e5NXKZlTsM1RdfgJ+N/gtykXJdtfT1PV5Ss4ArvjnUd4wIZwFVWMDVzalhkBSzxonjMGeUI3FQGFY50Hhlwe4PNgE29mziz/tK0UhQmFyJOEIfZo2bjhqIbMFY8FiaBCU2JTTjfeR4bvtiAbbXbAAkgThbjkP4QV8x6cdLFOFl9MixFn+7Y7XaMYkYhR58DWacMR44ewZ+++ROXWR6fNh73Tr130P2sLF/JnUMnuk7gH8f/EdS4Xjj0AncDccekO1wSJuFCLpEj2ZyMHH0O9PX6Ab2vQ+qTzQO+MH7BBZu58bmYnDEZAp4Al+ZdyhXUndSd9Lugbt/5fdjcthl1sjoY44woSyqDUqkMqYVbqIgZaQHhysaTG1HbXQvAEdTcMvGWQZ4RfThfYPqTFrgXARmtRtSoanCy66RL1q5P0IdkSzJSJam4OOdiFKYVQsDz3mXJ32nkS3Mv5aY/tzdtR5ehK6CLY4e+g/thK04tRr4s3+fnuv/483l8XFFwBTbXbYbJakKrrhXbG7fj8jGX+62Fcv+MzTYz9rVe6Jo3d/RciAViv2QLbNFXu76dK/oaSEahUCigFWpxtu0sIAR4fB4W5y9GiiQFH576EHqLHm26Nnxf/71fVj06sw7Pn3geOpkOebo8zJTNhLHHCDPfzElT5HJ5UJ2vnJ0LWDeKoWBPyx48c+AZ2EQ21MnqcJPsJiQzyejo6OCkN2KBGEsmLMG/ev4FnUkHGIHf/Ps3uCX1Fshssn5lOmlpaS43NzweD8oeJ9uyJAUy0jPQ2dmJmpoaVFRU+Pwj6dzERSQSgc/jc7IRZ/w5T0UCER6a9RB+/tXPAQAvH34Zi/IWIV2a7iIrWDJmiU9jDIbL8i/jZCzbGrdhisJ7t0iGYfDk/idxynwKibJETLNNwzjpOJfjJxAIsKhkEfij+Fh/ej1453iIs8XhnPkcGs42QCqUctnn8YrxKBldEtAx8RdWhpStzIZQLwTDY/B15ddoUDegRFSCDlkHnpv/HMSCwa9DYoEYT819Ciu+WAE7Y8drVa9hsnQy4oxxPrVadZZZHFceR+PpRiSLkpGQkoAVE1aE4+27wH4WpZpSx/lk4uP48eNeu2qFugPXeyfe41qGjzOOw5TkKVAqldx+S5NKUaWrQlNiE547/hw2FW7y2s3SnT5LH57c/yQAh//uNZdfg4q0ipBbuIUKCmRjkHZ9O/5SdaFxw2OzHwtrdWq4iBPEIUmUBK1F229G1nlKvdfUi/+c+49LJS/gmD4qSS9BhjUDUpEUPBsP/H4mGwLR9IgEIiwbuwzvHHsHVrsVn5/9nJsO84dvmr/hHl+W51+Pd/cffwBIlaTiqoKr8PnZz2G1W3Gu9xx2N+5GaWKpX1NIzp+x2WbG9sbt3E1CviwfY2RjAPinLWaLvtZXr+eKvgaa4mvVt+JfPf9CtiAbSdYkTBw9kdOaLh6zGP85/R9IrBKc0p/C5IzJPl88/3zwz44qYhGQND4JN02+CV2qrpBejN29ZIeCk90n8cCuB7huSdeXX4+7p93dr19ohaUC9+28D7XNtcjV5GJf1z5MzJmIKdkXgixnr96ioiIPFwnnRhIZ8RkBa7JZuYdKpeKCZHcCOU9nZM3ANYXX4N/n/g2tSYuXdr6EH+f+GIcOH0KOKQc6kQ6Lcn1rPhIMC3MWQsgTwspYsb1xO347/bde3+Pmus0XLMPigd9e+VtITJJ+g4WLki/Ch90fokZbA9gcs1LseZoqScXsUbND6hncH85+z3EJcdBYHNfjg/qD4Al4SLIkYU7cHMisvjcNKssow80lN+OTI58gT5eHD7Z8gOmZ0yHgCwYM9JwDQ6vNigNtB5BjzoGdZ8es9FnQqrWIkw8euAWK82chiBdAbVJDx9NBoVBwnURZ72sAIfXJPqY6hnWH1gFwBJt3XHEHikXFLt+feenzcPj7w9CpddD16vBa9WtYNW3VoPt+peoVbmZsRtYM/Gj8j8Dn8SPmEzsYkQ+lCb/543d/RJ/VUeF7w0U3YLJicmQHFARsZrM/jSw7pd7Z14nNZzZzQSyPx8OY5DG4svBK3DzhZszImoGEuARkZ2cjISHBYfFicbVzCWYa+YfFFxwvPjr9UUDV6c62W/7ICgDXDm7Or52ZkIklY5ZwWrqWzhacNZ/1K5BlP+NeUy82n9nMTcMK+ALMHT03YIsqXzt9Ga1G3L/zfnTwOlAnq0OGPAO54lzOqoen42FK8hRoRVrUyerw7NFn0awdvEX03ta93BRzvDAeT8x7AtlZ2SH300wQJXDZZl+cC/yZWvS27fH64/j1tl9z14DL8y/H/dPvH9AvNDkuGesvXY9FokWIs8VBK9TiQMcB7G3dy03DikQiyOVy9Gh7sKtyF5p6mnCw8yC+rP8SG09uxJkeR7MYPo/P2dIFoslmm7iE4zxdPX01MpGJkp4StB1rw5cHvoSwW4gcXQ5mGWfhWOWxsE+7J8cl4+Jsh/vNef15nOg+4bHNGfUZrK1cy/3/8TmPIz8lf0C/1+6ubmRJs/DjCT/GtMxpXMMLPo+PRXmLuGRGqDyDveEuQ5JKpBfWMXbY+DbI0+XIFmX77Z5yU95NmGyYjCRLEs5bz0PJVw7YatVd+tIl6EIb2qARa5AoS0SyNTnkdoTOuH8W8XHx3OdgsBpcnGSOHDmCI0eOhMwnW2fW4be7fss1vvh56c8xL2eex/dndPZoPD3/aa7Y9p3j7+Bo59EB912lrHKpvXl89uNBFTgPBZSRjXLcq1PrtHU4WHcQPBEPqdJUrJq6KtJDDIp0aToaNA3QW/QwWA2QCqUu68ViMVR9Knzb9i1XQJAmScPSgqWQxbne8dvtdqSlpWHChAn9Tt8EOo2cL8vHzKyZ+K7tO/R29eKzbz9DXnyez1211EY1DnY47HjykvL8rvhmf/wrKyvR2dnpckefJ8vDwlELcbDhIEwCEz7t+xSjT47GzRNu9mnf7Ge8v30/11pTLBDj8vzLkRyX7LKtP7IFXzt9rf1uLSeTkafLsWbpGhh6DS6ZhYXyhThfex4nmk4AFuD+nffjvSvf63eaTGPWuNgRPTDjgbBqyIuSi9Cub4fWrIXKoOq3s48/U4vetjVbzfhe+T3kjBx9iX0oGlWEZ+c969MPTU9XDyYnTMbZ7LM4rHJUOB/tPAq1UY14YTx6TD3oMfXAZrFBbpTDIrCgW+fZsSkzPpMLooDA/GlZbV2oz1PogWsE1+Co5Sj6BH34Xvc98L+YoVReGlB3uEC4LP8yronI9sbtLp67fZY+PLDrARhtjsK75eOW+yR5YG84RQIRLs6+GCXpJTjbcxajEkd5fN/CZVDvLkNifXNZEkQJqMirgIAR+JUVttvtOH38NCanTMY3qm8AHlDZVol8WT6S45K5QI+VTSxYsMAliLTYLfi+/YJn6uyc2ciID0z6EuhnkSi60OWuRdeC1Lj/tXaVMDjbfBY88JAmT4PWrAWPxwMPPEiEEi7I9DWbzkpSWnQtAIAyeRnunnJ3v+O8KPUi3Fl+J/5S9RfO3/f/rvk/r9dOk82ER799lKu9uXvK3ciT5QX8GQ0VFMhGMe4/ZHbYsa91H8bZxkEn0uHG8hs9Ao1Yw7lNbZehy0Mrd8p0Coc7D8POtwN8R2epKwqugEQocdnOWU8nl8tRUVER8raMV2VdBW2tFomWRBw8chAWhcVnfdOO5h1c5uuy/MsCqioe6MdfLpCjLL8MH2g+gE6kw3PfP4cUSQquLrx6wH0yDIP9vftxSHkIVoEV4AMpkhQsHbMUKZIUl20Dsaj60UU/ws7mnQAcmWz3QHbzmc2c16xUKMWLFS9CJpFBJpF5XMifSHsCp3pOoVHTiNruWjz33XN4dPajXl/3+e+e5/wTZ2fPDrsdUYGsAMcajiHJkoRdlbswPmO8xw2OPy14Ac9pSBtjw5ZzW6C0KZFkS8Jkw2Q8UP6Ax7nQH6yEZGbOTMikMuxu2Q07Y0eLtsV1w/+dHiL7hfEJeAIkxyUjTZKGaZnTXDYP1J821OcpmyHLFmfjjOwMtAbX5ghj5WMRL4wfEg3pJbmX4Kn9T4GBoxHDPVPu4c75Zyuf5brAjUsdh9/O+K1P+3TXySeJk/qdjQuXQb27dZp7IHtp3qXc99GftqVsUFiYVYgOXgeOq47DardiV/MuXFN0DUw2E/QWPfqEfahpqsGxrcegblbDIDCgr6cPGrOGa3RSlFLEzZCEU2bh/lkkiBK4dc7uNACQ2ZcJ8ICOHldrLj6Pj7EpYzEpYxIU8QoP+ZZ7IkssFqOmrwZf1n8J8BwWaM8teG5QaeHPS3+O7U3bcaLrBM71nsP66vW4b9p9Htv97cjfuBm5SfJJuLnEt2RIpKFANkrx9qO3r3UflHwlBBBgjHAMJOclUOWqIl4xGAzuzgXOgew/T/wTzx99HiXCEiRZkpCeko7Lx1zu4UnqTU/HTrOG6uKlUqkgbBYi3Z6OHkEPzlrPYm7qXEiF0n71Tc4XoT3Ve5Cjz4FWpMWlOQM3FRiIwX78BTUCvH7kdQDAI3sfQbI4GXNHzfW4GMrlcsjSZHi68mn85+x/UCL632ecnI5FYxZ5FGkE6hc4UNHXye6TeKbyGW7bR2c/iuLU/jPVieJEvLDwBfx0y09hspnw4ekPMUUxBdcUXeOy3a7mXfjsrKN5RaIoEU/OfTKsdkQqlQpJzUkY1zMOfIaPhnMNsCltgxZPOeOccTpyxFEQ6LwtwzDY3bzbEXTyAYvIgvnp89F4qhEF2QU+BWTOzhcl6SVIFCdia8NWzroNcARHyXHJkAlkEDNiTMmZgvTEdCSKEr1mfYM1Qw/leeqcIVuQuAAfn77gXJCdmM0FGuHWkAKO69pUxVTUtdTB2mbFV99+hZyUHBwzHsPndZ8DPMeN258X/tmn4hvAu07eG+E0qHd3T1HEK8Dn8WFn7JismOxy/fYnK+wcFM7KnoVGTSN0Zh1ada14o+YNFxszmVkGQ7cBUqsUGrFrvQSfx+fsEgH/dP3+4v5Z9DcLMxB2xo7T6tM4rT6NzIRMlMpLkYxkmM1mrzMyWpNDElQiKEFTYhMeW/iY10JJd4R8IZ6e+zSW/2c5LHYLNhzfgEV5i1CWUcZtU9tVi7ePvc1t/+ScJ11mXqIZCmSjEHftDY/Hg8qgQo2qxrGBAJg9djb0Gn3YMwvhxG63Q2aWIUefA4FdgNrjtcgc7/CIfaX6FcdJxQOaEptwBe8KjE8cD8bGuCi7LRYL1Gp1WL3s2ONh6DMgJzMHXZ1dAOMw/p6smOwx7VVRUYHu7m7uImSymKBv0yOHyYFYJEbX8S6oBIHfgAz0439X+V3oNnTj/07/H6yMFY9sfQS/UvwKIqPIJYNrYSw40HsAhwSHwIgYNCU2YZloGQqlheDZeYDT9SuYz5gt+nqt6jUkmZPw/s73UZFdARvfhj8e+yPMVjPAc0yvDpY9BoBxaePw8KyH8ci3jwAAnt7/NLJsWZCapTCbzbDyrfhzzZ/BY3hgeAx+O+O3PjedCAT2BkZoEMIgMMDGt0Ev1iMzM9OjeEqpUsIitqBGVQNVnwoqgwp2xg6RQAQRXwQxXwwhhBB3iMHn8xGXEofznechEojQbejmGmkIeAJcUXgF5GK5XwGZe0YvNykXy8cth8qg4gJY9iaxvb3dMf1p5SFJlBSygqxw4hwMKUQKTJRP5FrqFqVccJYIZ3DjPJYp2ikQ9AjAZ/iorq3Geel5lyDkofkP+dV9K1xFcv7g/h1KFCfiuuLr0Gfp83Bh8Scr7BwUigViLMxZiP+e+69jP25evAyPgdAu5FoTA46bggRRAsoV5R6Ss3DJLNw/i7ykPFySdwlUBhUYhgED5sK/dsdYZakyMAwDOxye2W26Nk7O1aHvQIe+Axm2DDQLm1HQXACbycYlsqx2K3ac2QEdT4ckSxKu4F2BaYnTvI7NG8Wpxbiz/E68UvWKQ2Kw92G8OvNVaLo1MJgMeP3Y60g0J0Ij0uCXZb8MexOJUEKBbBTirr2xM3bsbt7NFZFMzZyKFEmKQ8MW5sxCuGDvNi2NFuTocsDwGLTWtWJ3524c7TuKry1fc9q2m6ffjBtH34ijR4+GVk/nI87HY4JtAmehdaLrBMamjEW8KB58Hp/L9Jw5cwZ1dXVcNr1eV49eUS8AoDQtvDo9Ho+HP8z8A3pMPdhXtw+5mlzsVu/GJcWXIFPm+I6069vxzdlvwDfxMVYwFi2pLXjwsgcxLXFa6DWLAC5JuwS7enchwZyAc5pzGK0fjSPKI0gxpKBEVAJJjgS/m/E7n/d37dhrcbjjMLbVbkOeOg/vbXkPMzNnQiwUo0ZZA0WfAvGieMgL5bhu7HV+j9dXnG84c7NyYetyOAj0mHpgspmgMqqgZJTobuzG1tNbYbAY0CvuHXS/3DSkxXuHoEvzL0V2gsPRwZ+AzFtGL1GciERxost2FosFQqEQkyZNQl1dnYcmm90m3DeQ/uKeIZudfaGrlnunr3AFN8CFm5s0Wxp3c9Noa0SjvpELQhbzFmOWbNbgO3Mbc386eWBojom37xDrW+yMv1lhj6BQlofpWdNR21WLOEEc4kXxSBAlIF4UD6FeCJlMBhiBUVmjIBVKB8wchktm4f5Z8Hg8jE8b77GdxWJBB89xLmdmZroeM7sFZ9RncFR1FN2GbgjsAhhsBhxtOIrTzGko5ApMSpiETFEm9p3f57Cp5AMiqQjjEsf5ncj6WenPsL1pOxrbGyFtlOK9zvcwNnksGjQN4Kv5GMcbB3GSGNdlh++6GQ4okI1C3LU3J7pOcP2bUyQpnC/hUGQWwoGzbCJJlgRNr2N6yBxvxvc930Pdo8ZYwViclZ3FqvmrcOO4GwEgLLpXX8fLHo8UUQpGJ45Gq64VvaZevHfiPfB5fCSKE5EkToLMJEPdrjpHIJUhh4kxcQbhAFCUVoSMhPAWIQj4Ajwz9xk8VPcQem296BZ248vmL3Fd8XVo1jZjT8seR5ZDCCigwLLMZbg873Lw+fyQf8YqlQpna86iQFiARlsjdHwdvtd9j2Zrs2Pq3ZaGS4SXQKPW+BUk/2rsr6CuVsNgMUAlUOGE6QSK4otw2nIaAoEAqdZUVNgr0NXVNSQ3OCKRCPGiePRZ+nBedx5vH32b205gF0BudPzoOcPn8SHkC2GxW3x2wZg1ahbGplzIlPgTkPmb0SsuLkZ6enpYbm7CgXswJBKIuA5z7oQruHG+ucnJykG6Nh3KPiXX+Qp8QCgVoiSxJKDzP2xFcj4SrqywtwB5RtYMzMia4bKdxWJBr6gXJSUlqK2tRRwvbsAgNpwyC38+i+xsx41nV1eXy7YivggT0iegJK0ErbpW1DbVogUtENlE0Al06O3pxZmeMy5tnAV8AS4bcxlkQpnfiSwhX4jfTfgdXj7zMkRWEU7oTyBdno7qvmrYxXYIGSFmJ87Goe8PRUWjA1+hQDYKcc4sWGwWfNd2oS3qgpwFQVcMRxJ32QQMF9ZVK6sdD4RAsi0Zt6ff7lKkE2rdq6+4Z3pK5aWcxx7gmPrSmDTQmBxTNCK7CKo4FWy9Npf9SIVSZCVkDYnXY09XD2bIZmCfdR+0Ri30Fj0+PPUhN40FAKOTRqNidAXMejM3jlB+xs7HelzOOJyrdwT0zRqHdZaNb8OsglmACX79qNvtdpw6fgrTU6fja9vXsNltqOupQ72mnttveX45GDMTVumN+w1nalwq+ix9HtvZ+DbweDzI+DJkpWchIz4DGdIMpEnSIOALwDAMbIwNZpsZFrsFjecawTAMpudMh9luhsVmgcVuQXJcMvKSXCuI/QnIAsnohatwMhxEg4bUfTatILmAKzoEHIHE4jGLkSRMCvj8j+QxCVdW2N8Aedw4R+OISMos/PksysvLAaDfba1WK8QGMeaMmQNhghAHTx3Eactp2KyO3xDuRgiOugPWttLfRJbdbkdPQw8mJE7AYd1hgAfsaNrBrS/NLEVRdtGQFESGEgpkoxDnzIJIIMJVhVdhV8suZEgzPCyEwpVZCBeD2bcAgFgoxryCeYi3xkdFttk901OQXIDL8y9He5/Dbklr1kJj1sBis0BkEwE8R/DiTkFyAVcwE+5sukqlAo/hYenYpfj0zKfcdDfLpIxJmD1qNgQ8ATo0HWEZh/OxlgvlSBQnQmfWceunZ01HfnI+LBb/JDLsfkdljMIl8Zfgq4avAIDrcJQvy8f4tPGwWq1hvVlwv8GZlDEJ7X3t4IGHdGk65FI5MqQZyIjPgL5TD7PJjDFZYzyCLB6PByFP6MjOWixIS0oDAGRKM0MekAWS0YvUDaS/RIOG1P3mpjClEJVtldz6eaPnIU3qOL7BnP+RPCbhyAr7GyALhcKIyywA/z8LX7ZtamrCRWkXYWb6TJxRn8Ex1THOZ70opchFJuNvIou9dk7On4zmhmaXJifJccmYkTVjSBItoYYC2SjEPbOQmZCJGy66wcNQPpyZhXDhfqF3942NF8XjqsKrIJfKOUP8SJ9I3rRQY1PHuojhGYaBzqhDfUM9GAGDopQiaC0Xgtw4QZyHbVE4s+lskCUVSnF10dXYfGYz9BY9+Dw+FuQsQEl6SdjH4X6sx6eNx8F2h5dublIu93n4G9Q777cwpRBlGWWo6XQUQsYJ4rAwdyF4PF7Ybxa83eDcPul28MDzqPC3iq2QxEmgVqsDnob0tm0gAVksZVn9IRo0pO43NylxKShILkB9bz0myie6aChjbTbNmXB8h/wNCiMts3Aet6+fhS/bss1RhHwhStJLMD5tPDr6OqCz6FCYXOhyPfA3kcVeO+PEcbg091J8ePpDrpiuIreCK/aMNdkiBbJRiLfMAp/Hd7FEiraKYV9xv9AL+AJkxmeio68DKXEpuKroKsjEjqrTaLnQ+5LpAQCD1oDMNMdJn6nwzQQ8XNl05yArSZyEH170Q5xRn0FuUi43LRXucbgf68kZk7kpsoU5C12CPX+Otft+Z42aBb1FjzZ9GypyK1z8HMP5HfI2lS3geer1/C2eGmwaMhQBWaxkWf0l0sGN+80N4Gix3Gfp8yiqi7XZNHfC8R3yN0COlpsyfz6Lwbb1ljjx5rwSSCLL+dqZJk3DJXmX4FD7IUxIn4BRiaM8xhkNv7++QIFsFBINmYVw4e1Cv7RwKdp0bchNyoVIcOF9RsuF3p/jUVRUhGPHjkVUpwd4XgwTRAlezdPDOQ5vxTf9dTDy51i771fAE2DxmMVB79dfwl08FQ3ZplgkksGNt5sbthjUmVicTRsq/A2Qh9tNWTglMu7XzotSL8JFqRd53TZafn99gQLZKCXSmYVw4e1CLxVKUZhS6LJdtF3ofT0eaWlpOH/+fER1ekB06AXDVXwTDUU9QPiLp6Il2xSLRCq4iYbzjohtwpnIipZrZ6ihQDaKGY4/ZLF8off1eERDNj0asvrhOtbR9B0Kd/HUcMs2DXei4bwjYp9wJbKi6doZSniMrwaGhAsajQbJycno7e11mDMTPjNYz3n2Qh9LPnbueGsvyF6E2LalQ/HeIj2OcB3raPsO2e32YXXDSQRHpM87YngQjutKtF07+8OfGIsC2QChQDY4RsKFPlqCm0iPI1zHeiR8h4jYJdLnHUH0RyxcOymQHQIokA0eutCPHMJ1rOk7RBAE4T/Rfu2kQHYIoECWIAiCIAgi9PgTY0U+7CYIgiAIgiCIAKBAliAIgiAIgohJKJAlCIIgCIIgYhIKZAmCIAiCIIiYhAJZgiAIgiAIIiaJmUB2/fr1KCgogEQiwbRp07Bnz54Bt9+1axemTZsGiUSCwsJCvP766x7bfPzxx5gwYQLi4uIwYcIEbN68OVzDJwiCIAiCIEJMTASymzZtwqpVq/DQQw+hqqoK8+fPx9KlS9HU1OR1+/r6elx55ZWYP38+qqqq8Ic//AG/+c1v8PHHH3Pb7N+/H8uXL8eKFStw5MgRrFixAjfeeCMqKyuH6m0RBEEQBEEQQRATPrIzZ87E1KlT8dprr3HLSkpKcO2112Lt2rUe2//+97/H559/jtraWm7ZypUrceTIEezfvx8AsHz5cmg0GnzxxRfcNldccQVSU1PxwQcfDDom8pElCIIgCIIIPf7EWMIhGlPAmM1mHDp0CA8++KDL8sWLF2Pfvn1en7N//34sXrzYZdmSJUvw1ltvwWKxQCQSYf/+/bjvvvs8tlm3bp3XfZpMJphMJu7/vb29ABwfNkEQBEEQBBEa2NjKl1xr1AeyKpUKNpsNmZmZLsszMzPR3t7u9Tnt7e1et7darVCpVMjOzu53m/72uXbtWjzxxBMey3Nzc/15OwRBEARBEIQPaLVaJCcnD7hN1AeyLDwez+X/DMN4LBtse/fl/uxzzZo1WL16Nfd/u92O7u5upKenDziOgdBoNMjNzUVzczPJE2IMOnaxCx272IaOX+xCxy62GcrjxzAMtFotRo0aNei2UR/IyuVyCAQCj0ypUqn0yKiyZGVled1eKBQiPT19wG3622dcXBzi4uJclqWkpPjzVvpFJpPRSR2j0LGLXejYxTZ0/GIXOnaxzVAdv8EysSxR71ogFosxbdo0bNu2zWX5tm3bMGfOHK/PmT17tsf2W7duxfTp0yESiQbcpr99EgRBEARBENFF1GdkAWD16tVYsWIFpk+fjtmzZ+ONN95AU1MTVq5cCcAx7d/a2op3330XgMOh4NVXX8Xq1avxi1/8Avv378dbb73l4kZw7733YsGCBXjuueewbNkyfPbZZ/j666+xd+/eiLxHgiAIgiAIwj9iIpBdvnw5urq68OSTT6KtrQ2lpaXYsmUL8vPzAQBtbW0unrIFBQXYsmUL7rvvPvz1r3/FqFGj8Morr+CHP/wht82cOXOwceNGPPzww3jkkUdQVFSETZs2YebMmUP2vuLi4vDYY495SBaI6IeOXexCxy62oeMXu9Cxi22i9fjFhI8sQRAEQRAEQbgT9RpZgiAIgiAIgvAGBbIEQRAEQRBETEKBLEEQBEEQBBGTUCBLEARBEARBxCQUyEaI9evXo6CgABKJBNOmTcOePXsiPSTCC7t378Y111yDUaNGgcfj4dNPP3VZzzAMHn/8cYwaNQpSqRQVFRU4fvx4ZAZLuLB27VrMmDEDSUlJUCgUuPbaa3Hq1CmXbej4RSevvfYaysrKOOP12bNn44svvuDW03GLHdauXQsej4dVq1Zxy+j4RS+PP/44eDyey19WVha3PhqPHQWyEWDTpk1YtWoVHnroIVRVVWH+/PlYunSpi4UYER3o9XqUl5fj1Vdf9br++eefx4svvohXX30V33//PbKysnD55ZdDq9UO8UgJd3bt2oVf//rXOHDgALZt2war1YrFixdDr9dz29Dxi05ycnLwxz/+EQcPHsTBgwdx6aWXYtmyZdwPJh232OD777/HG2+8gbKyMpfldPyim4kTJ6KtrY37O3r0KLcuKo8dQww5F198MbNy5UqXZePHj2cefPDBCI2I8AUAzObNm7n/2+12Jisri/njH//ILTMajUxycjLz+uuvR2CExEAolUoGALNr1y6GYej4xRqpqanMm2++ScctRtBqtUxxcTGzbds2ZuHChcy9997LMAydd9HOY489xpSXl3tdF63HjjKyQ4zZbMahQ4ewePFil+WLFy/Gvn37IjQqIhDq6+vR3t7ucizj4uKwcOFCOpZRSG9vLwAgLS0NAB2/WMFms2Hjxo3Q6/WYPXs2HbcY4de//jWuuuoqXHbZZS7L6fhFP2fOnMGoUaNQUFCAH//4xzh37hyA6D12MdHZazihUqlgs9mQmZnpsjwzMxPt7e0RGhURCOzx8nYsGxsbIzEkoh8YhsHq1asxb948lJaWAqDjF+0cPXoUs2fPhtFoRGJiIjZv3owJEyZwP5h03KKXjRs34vDhw/j+++891tF5F93MnDkT7777Li666CJ0dHTg6aefxpw5c3D8+PGoPXYUyEYIHo/n8n+GYTyWEbEBHcvo5+6770ZNTQ327t3rsY6OX3Qybtw4VFdXo6enBx9//DFuvfVW7Nq1i1tPxy06aW5uxr333outW7dCIpH0ux0dv+hk6dKl3ONJkyZh9uzZKCoqwj/+8Q/MmjULQPQdO5IWDDFyuRwCgcAj+6pUKj3ucojohq3kpGMZ3dxzzz34/PPPsWPHDuTk5HDL6fhFN2KxGGPHjsX06dOxdu1alJeX4+WXX6bjFuUcOnQISqUS06ZNg1AohFAoxK5du/DKK69AKBRyx4iOX2yQkJCASZMm4cyZM1F77lEgO8SIxWJMmzYN27Ztc1m+bds2zJkzJ0KjIgKhoKAAWVlZLsfSbDZj165ddCyjAIZhcPfdd+OTTz7BN998g4KCApf1dPxiC4ZhYDKZ6LhFOYsWLcLRo0dRXV3N/U2fPh0//elPUV1djcLCQjp+MYTJZEJtbS2ys7Oj99yLWJnZCGbjxo2MSCRi3nrrLebEiRPMqlWrmISEBKahoSHSQyPc0Gq1TFVVFVNVVcUAYF588UWmqqqKaWxsZBiGYf74xz8yycnJzCeffMIcPXqUuemmm5js7GxGo9FEeOTEnXfeySQnJzM7d+5k2trauL++vj5uGzp+0cmaNWuY3bt3M/X19UxNTQ3zhz/8geHz+czWrVsZhqHjFms4uxYwDB2/aOb+++9ndu7cyZw7d445cOAAc/XVVzNJSUlcfBKNx44C2Qjx17/+lcnPz2fEYjEzdepUzhKIiC527NjBAPD4u/XWWxmGcdiRPPbYY0xWVhYTFxfHLFiwgDl69GhkB00wDMN4PW4AmHfeeYfbho5fdPLzn/+cuz5mZGQwixYt4oJYhqHjFmu4B7J0/KKX5cuXM9nZ2YxIJGJGjRrFXH/99czx48e59dF47HgMwzCRyQUTBEEQBEEQROCQRpYgCIIgCIKISSiQJQiCIAiCIGISCmQJgiAIgiCImIQCWYIgCIIgCCImoUCWIAiCIAiCiEkokCUIgiAIgiBiEgpkCYIgCIIgiJiEAlmCIAiCIAgiJqFAliAIgiAIgohJKJAlCIIIERUVFVi1alXM7TvSr/2rX/0KP/nJT8K2f4Ighi/CSA+AIAhipFJRUYHJkydj3bp1Ay4DgE8++QQikWhoB9jPa/c3xkBZu3Yt4uLiQrIvgiBGFhTIEgRBxABpaWnD9rUj+d4IgohtSFpAEAQRBr788kvMmzcPKSkpSE9Px9VXX42zZ89y62+77Tbs2rULL7/8Mng8Hng8ntdlDQ0NADyn9+12O5577jmMHTsWcXFxyMvLwzPPPAMAYBgGzz//PAoLCyGVSlFeXo6PPvpowPF+9NFHmDRpEqRSKdLT03HZZZdBr9d7vPZAYwzkdRsaGsDj8dDY2OjHp0sQBOGAMrIEQRBhQK/XY/Xq1Zg0aRL0ej0effRRXHfddaiurgafz8fLL7+M06dPo7S0FE8++SQAQCqVeizLyMjwuv81a9bg73//O1566SXMmzcPbW1tOHnyJADg4YcfxieffILXXnsNxcXF2L17N26++WZkZGRg4cKFHvtqa2vDTTfdhOeffx7XXXcdtFot9uzZA4ZhPLb1Nm52jP6+LgBUV1cjJSUF+fn5fn7CBEEQFMgSBEGEhR/+8Icu/3/rrbegUChw4sQJlJaWIjk5GWKxGPHx8cjKyuK287bMHa1Wi5dffhmvvvoqbr31VgBAUVER5s2bB71ejxdffBHffPMNZs+eDQAoLCzE3r178be//a3fQNZqteL666/nAspJkyZ5fe3+xh3I6wLAkSNHUF5e3u97JQiCGAgKZAmCIMLA2bNn8cgjj+DAgQNQqVSw2+0AgKamJpSWlga179raWphMJixatMhj3YkTJ2A0GnH55Ze7LDebzZgyZYrX/ZWXl2PRokWYNGkSlixZgsWLF+OGG25Aamqqz2MK5HUBR0aWAlmCIAKFAlmCIIgwcM011yA3Nxd///vfMWrUKNjtdpSWlsJsNge9b6lU2u86NmD+73//i9GjR7us688ZQCAQYNu2bdi3bx+2bt2Kv/zlL3jooYdQWVmJgoICn8YUyOsCjozsD37wA59egyAIwh0q9iIIgggxXV1dqK2txcMPP4xFixahpKQEarXaYzuxWAybzTboMneKi4shlUqxfft2j3UTJkxAXFwcmpqaMHbsWJe/3NzcfvfJ4/Ewd+5cPPHEE6iqqoJYLMbmzZu9buttjIG8rkajQUNDA2VkCYIIGMrIEgRBhJjU1FSkp6fjjTfeQHZ2NpqamvDggw96bDdmzBhUVlaioaEBiYmJSEtL87qMz3fNOUgkEvz+97/H7373O4jFYsydOxednZ04fvw4br/9djzwwAO47777YLfbMW/ePGg0Guzbtw+JiYmcptaZyspKbN++HYsXL4ZCoUBlZSU6OztRUlLi9f15G2NSUpLfr3vkyBEIBAJMnDgxwE+aIIiRDgWyBEEQIYbP52Pjxo34zW9+g9LSUowbNw6vvPIKKioqXLZ74IEHcOutt2LChAkwGAyor6/3umzMmDEer/HII49AKBTi0Ucfxfnz55GdnY2VK1cCAJ566ikoFAqsXbsW586dQ0pKCqZOnYo//OEPXscrk8mwe/durFu3DhqNBvn5+XjhhRewdOlSr9v3N0Z/X/fIkSMYP348NUMgCCJgeIw3fxWCIAiCIAiCiHJII0sQBEEQBEHEJBTIEgRBEARBEDEJBbIEQRAEQRBETEKBLEEQBEEQBBGTUCBLEARBEARBxCQUyBIEQRAEQRAxCQWyBEEQBEEQRExCgSxBEARBEAQRk1AgSxAEQRAEQcQkFMgSBEEQBEEQMQkFsgRBEARBEERM8v+C7KtrCOIP0gAAAABJRU5ErkJggg==",
+ "text/plain": [
+ "<Figure size 700x233.333 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib.ticker as ticker\n",
+ "\n",
+ "maxrho = max([max(x) for x in profile_TASEPy]) # maximum density need to set the y-axis range\n",
+ "\n",
+ "plt.figure(figsize=(7,7/3))\n",
+ "\n",
+ "sites = [x+1 for x in range(L)]\n",
+ "\n",
+ "plt.plot(sites, profile_TASEPy[-1], linewidth=2, label='n='+str(K) , color='C{}'.format(K-1), linestyle='-')\n",
+ "plt.plot(sites, profile_simulations, 'o', label='sims' , color='gray', ms = 8, alpha=0.5)\n",
+ "\n",
+ "plt.ylim(0,1.1*maxrho)\n",
+ "\n",
+ "plt.xlabel(r'lattice site $i$', fontsize=10)\n",
+ "plt.ylabel(r'density $\\rho_{i}^{(K)}$', fontsize=10)\n",
+ "\n",
+ "# Set the title\n",
+ "#plt.title(r'Density profile, $\\alpha = $'+str(alpha), fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='upper right')\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "b8c3f596",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 700x700 with 3 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_values = range(1,K+1)\n",
+ "\n",
+ "maxrho = max([max(x) for x in profile_TASEPy]) # maximum density need to set the y-axis range\n",
+ "\n",
+ "# Create a figure with K subplots, arranged in K rows and 1 columns\n",
+ "fig, axs = plt.subplots(K, 1, figsize=(7,K*7/3), sharex=False, sharey=True)\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "\n",
+ "for i, n in enumerate(n_values):\n",
+ " ax = axs[i] # Select the current subplot\n",
+ " \n",
+ " ax.plot(sites, profile_TASEPy[n], linewidth=2, label=f'n={n}', color='C{}'.format(i), linestyle='-') \n",
+ " ax.plot(sites, profile_simulations, 'o', label='sims' , color='gray', ms = 8, alpha=0.5)\n",
+ " \n",
+ " ax.set_ylim(0,1.1*maxrho)\n",
+ "\n",
+ " ax.set_xlabel(r'lattice site $i$', fontsize=10)\n",
+ " ax.set_ylabel(r'density $\\rho_i$', fontsize=10)\n",
+ " ax.set_title(r'Density profile, $\\alpha = $' + str(alpha) + f', n={n}', fontsize=12)\n",
+ " \n",
+ " ax.legend(loc='upper right')\n",
+ "\n",
+ "# Adjust the space between subplots to prevent labels from overlapping\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "3d5a6073",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J TASEPy = [0.2, 0.19550056242969632, 0.1953555575128311, 0.1949659459731425]\n",
+ "J simulations = 0.19483457053285302\n",
+ "\n",
+ "TASEPy results (current):\n",
+ " order 0 order 1 order 2 order 3\n",
+ "--------- --------- --------- ---------\n",
+ " 2.65119 0.341824 0.2674 0.0674292\n"
+ ]
+ }
+ ],
+ "source": [
+ "J_TASEPy = current(Jcoeff, alpha)\n",
+ "\n",
+ "print('J TASEPy = ', J_TASEPy)\n",
+ "print('J simulations = ', J_simulations)\n",
+ "\n",
+ "per_err = [100*abs(j-J_simulations)/J_simulations for j in J_TASEPy]\n",
+ "headers = ['order ' + str(x) for x in range(K+1)]\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (% error of the current):')\n",
+ "print(tabulate([per_err], headers = headers))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "65ca43d7",
+ "metadata": {},
+ "source": [
+ "### Example 2: L = 50, $\\ell = 5$ and $K=4$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "ccb2767e",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# imports hopping rates (example L=50 and ll=5)\n",
+ "\n",
+ "file = open('simulations/rates_L50.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "rates = []\n",
+ "for lines in reader:\n",
+ " rates.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports simulated density profile (example L=50 and ll=5)\n",
+ "\n",
+ "file = open('simulations/rho_a02_L50_ll5_iter1e6.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "profile_simulations = []\n",
+ "for lines in reader:\n",
+ " profile_simulations.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "# imports simulated current and average (example L=50 and ll=5)\n",
+ "\n",
+ "file = open('simulations/current_a02_L50_ll5_iter1e6.dat','r')\n",
+ "reader=csv.reader(file)\n",
+ "\n",
+ "currents_sim = []\n",
+ "for lines in reader:\n",
+ " currents_sim.append(float(lines[0]))\n",
+ "file.close()\n",
+ "\n",
+ "J_simulations = sum(currents_sim)/len(currents_sim)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "id": "bc98c5e1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes the PSA for order K = 4\n",
+ "\n",
+ "L = len(rates) # lattice size\n",
+ "ll = 5 # particle size\n",
+ "K = 4 # maximum PSA order\n",
+ "\n",
+ "rhocoeff, Jcoeff = psa_compute(rates, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "3daedb3e",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# initiation rate\n",
+ "\n",
+ "alpha = 0.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "5fe44740",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# computes local density profiles\n",
+ "\n",
+ "profile_TASEPy = local_density(rhocoeff, alpha)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "id": "f0390aa2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 700x233.333 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib.ticker as ticker\n",
+ "\n",
+ "maxrho = max([max(x) for x in profile_TASEPy]) # maximum density need to set the y-axis range\n",
+ "\n",
+ "plt.figure(figsize=(7,7/3))\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "\n",
+ "plt.plot(sites, profile_TASEPy[-1], linewidth=2, label='n='+str(K) , color='C{}'.format(K-1), linestyle='-')\n",
+ "plt.plot(sites, profile_simulations, 'o', label='sims' , color='gray', ms = 8, alpha=0.5)\n",
+ "\n",
+ "plt.ylim(0,1.1*maxrho)\n",
+ "\n",
+ "plt.xlabel(r'lattice site $i$', fontsize=10)\n",
+ "plt.ylabel(r'density $\\rho_{i}^{(K)}$', fontsize=10)\n",
+ "\n",
+ "# Set the title\n",
+ "#plt.title(r'Density profile, $\\alpha = $'+str(alpha), fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='upper right')\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "#plt.savefig('figure_benchmark1.pdf', dpi=300)\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "id": "20d0ee90",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<Figure size 700x933.333 with 4 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_values = range(1,K+1)\n",
+ "\n",
+ "maxrho = max([max(x) for x in profile_TASEPy]) # maximum density need to set the y-axis range\n",
+ "\n",
+ "# Create a figure with K subplots, arranged in K rows and 1 columns\n",
+ "fig, axs = plt.subplots(K, 1, figsize=(7, K*(7/3)), sharex=False, sharey=True)\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "\n",
+ "for i, n in enumerate(n_values):\n",
+ " ax = axs[i] # Select the current subplot\n",
+ " \n",
+ " ax.plot(sites, profile_TASEPy[n], linewidth=2, label=f'n={n}', color='C{}'.format(i), linestyle='-') \n",
+ " ax.plot(sites, profile_simulations, 'o', label='sims' , color='gray', ms = 8, alpha=0.5)\n",
+ " \n",
+ " ax.set_ylim(0,1.1*maxrho)\n",
+ "\n",
+ " ax.set_xlabel(r'lattice site $i$', fontsize=10)\n",
+ " ax.set_ylabel(r'density $\\rho_{i}^{(n)}$', fontsize=10)\n",
+ " ax.set_title(r'Density profile, $\\alpha = $' + str(alpha) + f', n={n}', fontsize=12)\n",
+ " \n",
+ " ax.legend(loc='upper right')\n",
+ "\n",
+ "# Adjust the space between subplots to prevent labels from overlapping\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "id": "fbea1795",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J TASEPy = [0.2, 0.12055656300314212, 0.15098896261086323, 0.139363115500763, 0.14380788008156592]\n",
+ "J simulations = 0.14261978443738338\n",
+ "\n",
+ "TASEPy results (% error of the current):\n",
+ " order 0 order 1 order 2 order 3 order 4\n",
+ "--------- --------- --------- --------- ---------\n",
+ " 40.233 -15.47 5.86817 -2.28346 0.833051\n"
+ ]
+ }
+ ],
+ "source": [
+ "J_TASEPy = current(Jcoeff, alpha)\n",
+ "\n",
+ "print('J TASEPy = ', J_TASEPy)\n",
+ "print('J simulations = ', J_simulations)\n",
+ "\n",
+ "per_err = [100*abs(j-J_simulations)/J_simulations for j in J_TASEPy]\n",
+ "headers = ['order ' + str(x) for x in range(K+1)]\n",
+ "\n",
+ "print()\n",
+ "print('TASEPy results (% error of the current):')\n",
+ "print(tabulate([per_err], headers = headers))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fbd05f02",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/TASEPy-1.1/exact/current-coeff_L4_ll1.csv b/TASEPy-1.1/exact/current-coeff_L4_ll1.csv
new file mode 100644
index 0000000..959fb36
--- /dev/null
+++ b/TASEPy-1.1/exact/current-coeff_L4_ll1.csv
@@ -0,0 +1 @@
+1.,-0.5319148936170212,-0.14989203071293566,-0.8464620311607027,1.085377548111617,4.669583456509007
diff --git a/TASEPy-1.1/exact/current-coeff_L4_ll2.csv b/TASEPy-1.1/exact/current-coeff_L4_ll2.csv
new file mode 100644
index 0000000..8d3f3fe
--- /dev/null
+++ b/TASEPy-1.1/exact/current-coeff_L4_ll2.csv
@@ -0,0 +1 @@
+1.,-1.1898096304591266,-0.11223590902850811,3.5725900433179367,-7.654405013874012,7.0512365378538275
diff --git a/TASEPy-1.1/exact/current-coeff_L4_ll3.csv b/TASEPy-1.1/exact/current-coeff_L4_ll3.csv
new file mode 100644
index 0000000..1617661
--- /dev/null
+++ b/TASEPy-1.1/exact/current-coeff_L4_ll3.csv
@@ -0,0 +1 @@
+1.,-2.107240823119677,3.9153641176659923,-6.763596357815028,11.119019745110963,-17.60823247054707
diff --git a/TASEPy-1.1/exact/exact-small-system.nb b/TASEPy-1.1/exact/exact-small-system.nb
new file mode 100644
index 0000000..69f6549
--- /dev/null
+++ b/TASEPy-1.1/exact/exact-small-system.nb
@@ -0,0 +1,795 @@
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+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
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+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
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diff --git a/TASEPy-1.1/simulations/current_a02_L50_ll5_iter1e6.dat b/TASEPy-1.1/simulations/current_a02_L50_ll5_iter1e6.dat
new file mode 100644
index 0000000..027f047
--- /dev/null
+++ b/TASEPy-1.1/simulations/current_a02_L50_ll5_iter1e6.dat
@@ -0,0 +1,51 @@
+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
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+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
+ 0.14261990709039787
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+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261976161821777
+ 0.14261961614603763
+ 0.14261961614603763
+ 0.14261961614603763
+ 0.14261961614603763
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diff --git a/TASEPy-1.1/simulations/dTASEPe.dat b/TASEPy-1.1/simulations/dTASEPe.dat
new file mode 100644
index 0000000..a1b4e0c
--- /dev/null
+++ b/TASEPy-1.1/simulations/dTASEPe.dat
@@ -0,0 +1,7 @@
+5
+0.2
+1000000
+rates_L50.dat
+rho_a02_L50_ll5_iter1e6.dat
+current_a02_L50_ll5_iter1e6.dat
+info_a02_L50_ll5_iter1e6.log
\ No newline at end of file
diff --git a/TASEPy-1.1/simulations/dTASEPe.f90 b/TASEPy-1.1/simulations/dTASEPe.f90
new file mode 100644
index 0000000..e12a987
--- /dev/null
+++ b/TASEPy-1.1/simulations/dTASEPe.f90
@@ -0,0 +1,264 @@
+!==============================================================================
+!
+! MODEL
+! -----
+! Totally asymmetric simple exclusion process with open boundary conditions,
+! elongated particles and site-dependent hopping rates.
+!
+! PROGRAM
+! -------
+! The program computes elongation rates relative to the initiation rate from
+! the Ribo-seq A-site density profile using NLOPT package and the third order
+! of the power series method.
+!
+!==============================================================================
+
+program dTASEPe
+
+ use mt19937
+ implicit none
+
+ interface
+ subroutine mc(L,ll,alpha,omega,tau,iter,rho,current)
+ integer(kind=4),intent(in) :: L,ll
+ real(kind=8),intent(in) :: alpha,omega(1:L)
+ integer(kind=4),intent(inout) :: tau(1:L)
+ integer(kind=8),intent(in) :: iter
+ real(kind=8),intent(out) :: rho(1:L),current(0:L)
+ end subroutine mc
+ end interface
+
+ ! program parameters
+ integer(kind=4) :: err11,err22,err33,err44,err55,stat22,i,L,ll
+ integer(kind=8) :: iter
+ integer(kind=4),allocatable :: tau(:)
+ character(len=80) :: inputfile_rates, outputfile_current, &
+ & outputfile_density, outputfile_log
+ logical :: eof,found
+ real(kind=8),allocatable :: rho(:),current(:),omega(:)
+ real(kind=8) :: t1,t2,omegai,tden1,tden2,rel,alpha
+ external fnc3
+
+!======================================================================
+! INPUT
+!======================================================================
+
+ call cpu_time(t1)
+
+ open(unit=11,file='dTASEPe.dat',status='OLD',iostat=err11)
+ read(11,*) ll ! particle size
+ read(11,*) alpha ! initiation rate
+ read(11,*) iter ! number of iterations for MC (Gillespie algorithm)
+ read(11,*) inputfile_rates ! file with hopping rates omega(1), ... , omega(L)
+ read(11,*) outputfile_density ! file with local density rho(1), ... , rho(L)
+ read(11,*) outputfile_current ! file with current current(0), ... , current(L)
+ read(11,*) outputfile_log ! log file
+ close (11)
+
+!======================================================================
+! MAIN PROGRAM
+!======================================================================
+
+ ! begin measuring time
+ call cpu_time(t1)
+
+ ! write to log file
+ open(55,file=outputfile_log,status='REPLACE',iostat=err55)
+ write(55,'(A22)') 'INFO: Program started.'
+ close(55)
+
+ ! initial seed for random number generator
+ call init_genrand(4357)
+
+ ! read file with hopping rates (to get lattice size)
+ !---------------------------------------------------
+ open(22,file=inputfile_rates,status='OLD',iostat=err22)
+ i=0
+ eof=.FALSE.
+ do while (eof.EQV..FALSE.)
+ read(22,*,iostat=stat22) omegai
+ if (stat22.EQ.0) then
+ i=i+1
+ else
+ eof=.TRUE.
+ endif
+ enddo
+ close(22)
+
+ ! set lattice size
+ !--------------
+ L=i
+
+ ! read file with hopping rates (to get hopping rates)
+ !----------------------------------------------------
+ allocate(omega(1:L))
+ open(22,file=inputfile_rates,status='OLD',iostat=err22)
+ do i=1,L
+ read(22,*) omega(i)
+ enddo
+ close(22)
+
+ ! run Monte Carlo simulation (to reach the steady state)
+ !-------------------------------------------------------
+ allocate(tau(1:L))
+ tau=0
+ allocate(rho(1:L),current(0:L))
+ rho=0.0d0
+ current=0.0d0
+ found=.FALSE.
+ do while (found.EQV..FALSE.)
+ tden1=sum(rho)/dble(L)
+ call mc(L,ll,alpha,omega,tau,100_8,rho,current)
+ tden2=sum(rho)/dble(L)
+ if (tden2.gt.epsilon(1.0d0)) then
+ rel=abs(tden2-tden1)/tden2
+ if (rel.lt.1.d-3) then
+ found=.TRUE.
+ endif
+ endif
+ enddo
+
+ ! run Monte Carlo simulation (in the steady state)
+ !--------------------------------------------------
+ rho=0.0d0
+ current=0.0d0
+ call mc(L,ll,alpha,omega,tau,iter,rho,current)
+ deallocate(tau)
+
+ ! write output
+ !--------------
+ open(33,file=outputfile_density,status='REPLACE',iostat=err33)
+ open(44,file=outputfile_current,status='REPLACE',iostat=err44)
+ write(44,*) current(0)
+ do i=1,L
+ write(33,*) rho(i)
+ write(44,*) current(i)
+ enddo
+ close(33)
+ close(44)
+ deallocate(rho,current)
+
+ ! stop measuring time
+ call cpu_time(t2)
+
+ ! write to log file
+ open(55,file=outputfile_log,status='OLD',position='APPEND',iostat=err55)
+ write(55,'(A39,F9.3,A9)') 'INFO: Program finished successfully in ',t2-t1,' seconds.'
+ close(55)
+
+end program dTASEPe
+
+!======================================================================
+! SUBROUTINES
+!======================================================================
+
+subroutine mc(L,ll,alpha,omega,tau,iter,rho,current)
+
+ use mt19937
+ implicit none
+
+ integer(kind=4),intent(in) :: L,ll
+ real(kind=8),intent(in) :: alpha,omega(1:L)
+ integer(kind=4),intent(inout) :: tau(1:L)
+ integer(kind=8),intent(in) :: iter
+ real(kind=8),intent(out) :: rho(1:L),current(0:L)
+
+ ! local variables
+ integer(kind=8) :: i,k
+ real(kind=8) :: r1,r2,a0,atest,t,dt
+ real(kind=8),allocatable :: a(:)
+
+ ! initial propensity function
+ allocate(a(0:L))
+ if (sum(tau(1:min(ll,L))).EQ.0) then
+ a(0)=alpha
+ else
+ a(0)=0.0d0
+ endif
+ do i=1,L
+ if (i+ll.le.L) then
+ a(i)=omega(i)*dble(tau(i))*dble(1-tau(i+ll))
+ else
+ a(i)=omega(i)*dble(tau(i))
+ endif
+ enddo
+
+ t=0.0d0
+ rho=0.0d0
+ current=0.0d0
+
+ do k=1,iter*L
+
+ a0=sum(a)
+
+ r1=grnd()
+ r2=grnd()
+
+ ! chooses time until the next event
+ dt=-dlog(dble(r1))/a0
+ t=t+dt
+
+ ! density profile
+ rho=rho+dble(tau)*dt
+
+ ! chooses which event happens next
+ i=0
+ atest=a(0)
+ do while (r2.GT.atest/a0)
+ i=i+1
+ atest=atest+a(i)
+ enddo
+
+ ! updates the propensity function
+ a(i)=0.0d0
+
+ ! new particles is placed at site 1
+ if (i.EQ.0) then
+
+ if (1+ll.le.L) then
+ a(1)=omega(1)*dble(1-tau(1+ll))
+ else
+ a(1)=omega(1)
+ endif
+ tau(1)=1
+
+ ! moves particle to the right
+ elseif ((i.ge.1).and.(i.le.L-1)) then
+
+ ! checks if the moved particle can move again
+ if (i+ll+1.le.L) then
+ a(i+1)=omega(i+1)*dble(1-tau(i+1+ll))
+ else
+ a(i+1)=omega(i+1)
+ endif
+
+ ! checks if new particle can come onto the lattice
+ if (i.eq.ll) then
+ a(0)=alpha
+ endif
+
+ ! checks if the trailing particle can move
+ if (i.ge.ll+1) then
+ a(i-ll)=omega(i-ll)*dble(tau(i-ll))
+ endif
+
+ tau(i)=0
+ tau(i+1)=1
+
+ ! removes particle from the lattice
+ else
+
+ ! checks if the trailing particle can move
+ if (i.ge.ll+1) then
+ a(i-ll)=omega(i-ll)*dble(tau(i-ll))
+ endif
+ tau(L)=0
+
+ endif
+ current(i)=current(i)+1.0d0
+ enddo
+ deallocate(a)
+ rho=rho/t
+ current=current/t
+ return
+end subroutine mc
\ No newline at end of file
diff --git a/TASEPy-1.1/simulations/mt19937.f90 b/TASEPy-1.1/simulations/mt19937.f90
new file mode 100644
index 0000000..7c55b60
--- /dev/null
+++ b/TASEPy-1.1/simulations/mt19937.f90
@@ -0,0 +1,200 @@
+! A Fortran-program for MT19937: Real number version
+
+! Code converted using TO_F90 by Alan Miller
+! Date: 1999-11-26 Time: 17:09:23
+! Latest revision - 5 February 2002
+! A new seed initialization routine has been added based upon the new
+! C version dated 26 January 2002.
+! This version assumes that integer overflows do NOT cause crashes.
+! This version is compatible with Lahey's ELF90 compiler,
+! and should be compatible with most full Fortran 90 or 95 compilers.
+! Notice the strange way in which umask is specified for ELF90.
+
+! genrand() generates one pseudorandom real number (double) which is
+! uniformly distributed on [0,1]-interval, for each call.
+! sgenrand(seed) set initial values to the working area of 624 words.
+! Before genrand(), sgenrand(seed) must be called once. (seed is any 32-bit
+! integer except for 0).
+! Integer generator is obtained by modifying two lines.
+! Coded by Takuji Nishimura, considering the suggestions by
+! Topher Cooper and Marc Rieffel in July-Aug. 1997.
+
+! This library is free software; you can redistribute it and/or modify it
+! under the terms of the GNU Library General Public License as published by
+! the Free Software Foundation; either version 2 of the License, or (at your
+! option) any later version. This library is distributed in the hope that
+! it will be useful, but WITHOUT ANY WARRANTY; without even the implied
+! warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+! See the GNU Library General Public License for more details.
+! You should have received a copy of the GNU Library General Public License
+! along with this library; if not, write to the Free Foundation, Inc.,
+! 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+! Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura.
+! When you use this, send an email to: matumoto@math.keio.ac.jp
+! with an appropriate reference to your work.
+
+!***********************************************************************
+! Fortran translation by Hiroshi Takano. Jan. 13, 1999.
+
+! genrand() -> double precision function grnd()
+! sgenrand(seed) -> subroutine sgrnd(seed)
+! integer seed
+
+! This program uses the following standard intrinsics.
+! ishft(i,n): If n > 0, shifts bits in i by n positions to left.
+! If n < 0, shifts bits in i by n positions to right.
+! iand (i,j): Performs logical AND on corresponding bits of i and j.
+! ior (i,j): Performs inclusive OR on corresponding bits of i and j.
+! ieor (i,j): Performs exclusive OR on corresponding bits of i and j.
+
+!***********************************************************************
+
+MODULE mt19937
+IMPLICIT NONE
+INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(12, 60)
+
+! Period parameters
+INTEGER, PARAMETER :: n = 624, n1 = n+1, m = 397, mata = -1727483681
+! constant vector a
+INTEGER, PARAMETER :: umask = -2147483647 - 1
+! most significant w-r bits
+INTEGER, PARAMETER :: lmask = 2147483647
+! least significant r bits
+! Tempering parameters
+INTEGER, PARAMETER :: tmaskb= -1658038656, tmaskc= -272236544
+
+! the array for the state vector
+INTEGER, SAVE :: mt(0:n-1), mti = n1
+! mti==N+1 means mt[N] is not initialized
+
+PRIVATE
+PUBLIC :: dp, sgrnd, grnd, init_genrand
+
+CONTAINS
+
+
+SUBROUTINE sgrnd(seed)
+! This is the original version of the seeding routine.
+! It was replaced in the Japanese version in C on 26 January 2002
+! It is recommended that routine init_genrand is used instead.
+
+INTEGER, INTENT(IN) :: seed
+
+! setting initial seeds to mt[N] using the generator Line 25 of Table 1 in
+! [KNUTH 1981, The Art of Computer Programming Vol. 2 (2nd Ed.), pp102]
+
+mt(0)= IAND(seed, -1)
+DO mti=1,n-1
+ mt(mti) = IAND(69069 * mt(mti-1), -1)
+END DO
+
+RETURN
+END SUBROUTINE sgrnd
+!***********************************************************************
+
+SUBROUTINE init_genrand(seed)
+! This initialization is based upon the multiplier given on p.106 of the
+! 3rd edition of Knuth, The Art of Computer Programming Vol. 2.
+
+! This version assumes that integer overflow does NOT cause a crash.
+
+INTEGER, INTENT(IN) :: seed
+
+INTEGER :: latest
+
+mt(0) = seed
+latest = seed
+DO mti = 1, n-1
+ latest = IEOR( latest, ISHFT( latest, -30 ) )
+ latest = latest * 1812433253 + mti
+ mt(mti) = latest
+END DO
+
+RETURN
+END SUBROUTINE init_genrand
+!***********************************************************************
+
+FUNCTION grnd() RESULT(fn_val)
+REAL (dp) :: fn_val
+
+INTEGER, SAVE :: mag01(0:1) = (/ 0, mata /)
+! mag01(x) = x * MATA for x=0,1
+INTEGER :: kk, y
+
+! These statement functions have been replaced with separate functions
+! tshftu(y) = ISHFT(y,-11)
+! tshfts(y) = ISHFT(y,7)
+! tshftt(y) = ISHFT(y,15)
+! tshftl(y) = ISHFT(y,-18)
+
+IF(mti >= n) THEN
+! generate N words at one time
+ IF(mti == n+1) THEN
+! if sgrnd() has not been called,
+ CALL sgrnd(4357)
+! a default initial seed is used
+ END IF
+
+ DO kk = 0, n-m-1
+ y = IOR(IAND(mt(kk),umask), IAND(mt(kk+1),lmask))
+ mt(kk) = IEOR(IEOR(mt(kk+m), ISHFT(y,-1)),mag01(IAND(y,1)))
+ END DO
+ DO kk = n-m, n-2
+ y = IOR(IAND(mt(kk),umask), IAND(mt(kk+1),lmask))
+ mt(kk) = IEOR(IEOR(mt(kk+(m-n)), ISHFT(y,-1)),mag01(IAND(y,1)))
+ END DO
+ y = IOR(IAND(mt(n-1),umask), IAND(mt(0),lmask))
+ mt(n-1) = IEOR(IEOR(mt(m-1), ISHFT(y,-1)),mag01(IAND(y,1)))
+ mti = 0
+END IF
+
+y = mt(mti)
+mti = mti + 1
+y = IEOR(y, tshftu(y))
+y = IEOR(y, IAND(tshfts(y),tmaskb))
+y = IEOR(y, IAND(tshftt(y),tmaskc))
+y = IEOR(y, tshftl(y))
+
+IF(y < 0) THEN
+ fn_val = (DBLE(y) + 2.0D0**32) / (2.0D0**32 - 1.0D0)
+ELSE
+ fn_val = DBLE(y) / (2.0D0**32 - 1.0D0)
+END IF
+
+RETURN
+END FUNCTION grnd
+
+FUNCTION tshftu(y) RESULT(fn_val)
+INTEGER, INTENT(IN) :: y
+INTEGER :: fn_val
+
+fn_val = ISHFT(y,-11)
+RETURN
+END FUNCTION tshftu
+
+FUNCTION tshfts(y) RESULT(fn_val)
+INTEGER, INTENT(IN) :: y
+INTEGER :: fn_val
+
+fn_val = ISHFT(y,7)
+RETURN
+END FUNCTION tshfts
+
+FUNCTION tshftt(y) RESULT(fn_val)
+INTEGER, INTENT(IN) :: y
+INTEGER :: fn_val
+
+fn_val = ISHFT(y,15)
+RETURN
+END FUNCTION tshftt
+
+FUNCTION tshftl(y) RESULT(fn_val)
+INTEGER, INTENT(IN) :: y
+INTEGER :: fn_val
+
+fn_val = ISHFT(y,-18)
+RETURN
+END FUNCTION tshftl
+
+END MODULE mt19937
diff --git a/TASEPy-1.1/simulations/rates_L50.dat b/TASEPy-1.1/simulations/rates_L50.dat
new file mode 100644
index 0000000..b54030f
--- /dev/null
+++ b/TASEPy-1.1/simulations/rates_L50.dat
@@ -0,0 +1,50 @@
+8.89
+5.70
+1.78
+4.40
+1.10
+9.35
+5.89
+5.31
+3.21
+7.84
+9.86
+2.95
+5.13
+8.96
+6.25
+3.38
+9.28
+4.81
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+6.29
+1.75
+8.11
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+4.61
+6.69
+8.42
+1.95
+5.24
+3.79
+8.04
+2.95
+2.90
+8.91
+4.67
+7.11
+8.70
+1.07
+6.87
+3.92
+6.92
+7.90
+6.45
+1.23
+6.55
+6.54
+8.62
+4.51
+9.44
+4.39
\ No newline at end of file
diff --git a/TASEPy-1.1/simulations/rho_a02_L50_ll1_iter1e6.dat b/TASEPy-1.1/simulations/rho_a02_L50_ll1_iter1e6.dat
new file mode 100644
index 0000000..ae9158c
--- /dev/null
+++ b/TASEPy-1.1/simulations/rho_a02_L50_ll1_iter1e6.dat
@@ -0,0 +1,50 @@
+ 2.5629929222932168E-002
+ 5.0972556068833184E-002
+ 0.12258054950317478
+ 7.6098890633674129E-002
+ 0.17856950880113151
+ 2.1643832463879100E-002
+ 3.4624105826849959E-002
+ 4.0289759503642886E-002
+ 6.1566188520552644E-002
+ 2.5360330945836954E-002
+ 2.3478936100501367E-002
+ 6.8265321170689286E-002
+ 3.8474627886206605E-002
+ 2.2705687232558443E-002
+ 3.4363669676981679E-002
+ 5.8383206047330390E-002
+ 2.2312166803095109E-002
+ 4.1195564389257325E-002
+ 2.1951115185922732E-002
+ 4.3405356474834268E-002
+ 0.11259420957513686
+ 2.4564056288538742E-002
+ 2.7388036837511974E-002
+ 2.6700452993988422E-002
+ 4.3460527818137966E-002
+ 3.0669130155292813E-002
+ 3.2861255062738876E-002
+ 0.10312696064947854
+ 3.9788269897305682E-002
+ 5.2569967401983352E-002
+ 2.8721811009999446E-002
+ 7.2155363106396989E-002
+ 6.8004114344836983E-002
+ 2.3390623258829148E-002
+ 4.3759448054227774E-002
+ 3.3978158081749692E-002
+ 5.4606712203298650E-002
+ 0.18557613627853026
+ 3.0541997461170461E-002
+ 5.0889836819430614E-002
+ 2.9447087354547437E-002
+ 2.9943480591977590E-002
+ 5.5729626852053030E-002
+ 0.16124076039158949
+ 3.0453637716482851E-002
+ 3.0276039053491310E-002
+ 2.4168378039703182E-002
+ 4.3840339447343876E-002
+ 2.2238647286365227E-002
+ 4.4430970344825377E-002
diff --git a/TASEPy-1.1/simulations/rho_a02_L50_ll5_iter1e6.dat b/TASEPy-1.1/simulations/rho_a02_L50_ll5_iter1e6.dat
new file mode 100644
index 0000000..7c9d451
--- /dev/null
+++ b/TASEPy-1.1/simulations/rho_a02_L50_ll5_iter1e6.dat
@@ -0,0 +1,50 @@
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diff --git a/TASEPy-1.1/tutorial_TASEPy.ipynb b/TASEPy-1.1/tutorial_TASEPy.ipynb
new file mode 100644
index 0000000..843dedd
--- /dev/null
+++ b/TASEPy-1.1/tutorial_TASEPy.ipynb
@@ -0,0 +1,589 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# TASEPy tutorial\n",
+ "\n",
+ "In this notebook we run a short tutorial explaining how to compute particle densities and current using TASEPy. \n",
+ "\n",
+ "We consider a system with the following parameters:\n",
+ "- the lattice size $L = 100$,\n",
+ "- the hopping rates for each lattice site $\\omega_i$ are selected randomly between $1$ and $10$\n",
+ "- the particle size $\\ell = 1$ and\n",
+ "- the maximum order of the power-series approximation (PSA) $K=4$. \n",
+ "\n",
+ "This combination of parameters above takes less than a minute on Intel(R) Core(TM) i7-8565U CPU @ 1.80GHz with 16 GB of RAM. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Parameter declaration\n",
+ "We start by importing the necessary libraries and declaring the parameters explained above."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import methods from TASEPy\n",
+ "\n",
+ "from TASEPy import psa_compute\n",
+ "from TASEPy import total_coeffs\n",
+ "from TASEPy import local_density\n",
+ "from TASEPy import mean_density\n",
+ "from TASEPy import current\n",
+ "\n",
+ "# import random number generator\n",
+ "from statistics import random"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# declare parameters\n",
+ "\n",
+ "# lattice size\n",
+ "L = 100\n",
+ "\n",
+ "# particle size (in lattice sites)\n",
+ "ll = 1\n",
+ "\n",
+ "# list of particle hopping rates selected randomly from interval [1,10]\n",
+ "random_seed = random.seed(1234)\n",
+ "wlist = [random.uniform(1,10) for site in range(L)] \n",
+ " \n",
+ "# maximum order of the PSA\n",
+ "K = 4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Compute the PSA coefficients\n",
+ "\n",
+ "The core of TASEPy resides in the function `psa_compute(wlist, K, ll, save_coeffs, coeffs_file)`. This function takes the following inputs: `wlist` is the list of rates, `K` is the maximum order computed by the algorithm, `ll` is the particle size (default value is 1 if omitted), `save_coeffs` is a boolean variable specifying if the method should save probability coefficients in a file or not (default value is False if omitted), and `coeffs_file` is a string containing the name of that file (default value is 'Pcoeff.csv' if omitted). The lattice size $L$ is inferred from the size of `wlist`. The function computes all the coefficients $c_n(X)$ and returns 2 elements: (1) a 2d list containing the density coefficients $\\rho_{i,n}$ for all sites $i$ and orders $n$, and (2) a list containing the values of the current coefficients $J_n$. The coefficients $c_n(X)$ for $n=0,\\dots,K$ are computed using Eqs.(29)-(31) of the affiliated paper. The $\\rho_{i,n}$ and $J_n$ are computed using Eqs.(25). If `save_coeffs` is True, then the output file `coeffs_file` contains one row for each coefficient with the following structure: $n$, $X$, $c_n(X)$, where $X$ is a list of particle positions.\n",
+ "\n",
+ "In the following example the density and current coefficients are stored in the lists `rhocoeff` and `Jcoeff` respectively, which are defined as follows:\n",
+ "- `rhocoeff[i]` is the list $[\\rho_{i+1, 0},\\ldots\\rho_{i+1, n}, \\ldots, \\rho_{i+1, K}]$ of density coefficients of the i-th order of the PSA (note that `rhocoeff[i]` corresponds to the lattice site $i+1$) and \n",
+ "- `Jcoeff[i]` is the particle current coefficient of the i-th order of the PSA."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rhocoeff, Jcoeff = psa_compute(wlist, K, ll)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Density coefficients of lattice site 2 are: [0.0, 0.20134525236037026, 0.9398020417237882, -0.14961445438660803, -1.1931351947862368]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Density coefficients of lattice site 2 are:',rhocoeff[1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Jcoeff = [1.0, -0.10311317417543009, -0.029907583959470685, -1.0778682000745903, 1.3340057691566471]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Jcoeff = ', Jcoeff)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If `save_coeffs` is set to `True`, the resulting file `coeffs_file` will store all non-zero $c_n(X)$ for all orders $n\\leq K$. For large lattice sizes this file may become very large. Hence, we advise using this option with caution, e.g. only for small lattice sizes or for small values of $K$. The number of coefficients that will be stored can be obtained by calling the function `total_coeffs(K, L, ll)`. For the example above, we get:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "4259880"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "total_coeffs(K, L, ll)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this case, the file will have circa 4,300,000 lines (one line for each coefficient). Each line contains the order of the PSA $n$, the list of positions of all particles in the configuration $X$, and the coefficient for that configuration $c_n(X)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rhocoeff, Jcoeff = psa_compute(wlist, K, ll, True, 'test.csv')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The size of the resulting file 'test.csv' is circa 173 MB, or about 43 bytes per line. Hence, a caution is need when setting the option to save coefficients, as the file size may be very large. We advise using this option only for small lattice sizes or for small values of $K$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 3. Plot density profile for a given value of $\\alpha$\n",
+ "\n",
+ "Here we chose a value of the initiation rate $\\alpha$ and use the coefficients in the list `rhocoeff` to compute density profiles for different orders of the PSA. We use the method `local_density(rhocoeff, alpha)` and write the output in `rho`. `rho` is a list, whose elements are density profiles computed for different orders. According to Eq. (25b) in the affiliated paper, \n",
+ "\n",
+ "\\begin{equation}\n",
+ " \\rho_i=\\sum_{n=0}^{\\infty}\\rho_{i,n}\\alpha^n,\\quad \\rho_{i,0}=0,\\quad \\rho_{i,n}=\\sum_{\\substack{C\\\\\\tau_i=1}}c_n(C),\\quad n\\geq 1. \\tag{25b}\n",
+ "\\end{equation}\n",
+ "\n",
+ "Let us we denote by $\\rho_{i}^{(k)}=\\sum_{n=0}^{k}\\rho_{i,n}\\alpha^n$ the particle density at site $i$ truncated at $k$th order. Then `rho` is the list $[[\\rho_{1}^{(0)},\\ldots,\\rho_{L}^{(0)}],\\ldots,[\\rho_{1}^{(K)},\\ldots,\\rho_{L}^{(K)}]]$, where $K$ is the maximum order of the PSA. For instance, `rho[2]` contains the density profile computed up to and including the order $n=2$. Note that `rho[0]` should always return $[0,...,0]$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "alpha = 0.2\n",
+ "rho = local_density(rhocoeff, alpha)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The cell below plots density profile $\\rho_{i}^{(K)}$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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D4y0iU7EYw6++CkDNAfu7z2tP0gw0sdElfdpA++u89SQyfeOjc+BWb29B+Vpda11pSmtv/hvKX4vtvxEyBtwwGtGNGxl46qmMryU8IXQ1MpI2cMj1wCs4B+6ilIorpV5SSt2ilLpYKfWOUi1ssuF6383NAB4PvDwG3BocJNHTg0QiRPZYZK9p1/ga8OHXX0dFo0T22MP9vSFZRpZPBGDn73/Pli9/GZVIjNcyJ5xEVgPuF7E5ZWTV1UhVFSoWy7uKwRoeTtY6V1iIWBtwHRlKdJd3fX4DHq+w82OoLLZ86RI2ffRjRNu2pL2m68Clqgqwa8E1KholsWMHBIOEZs4sy1rLU6C8G6BVrlqgVG4PXHdgC8+ZkxxHOc4e+LDTV7r6wANTntdirHxC6F0338yue/7M8OrVpV9gheDmwB3POtjsz4E7rzsGHDxCtjzD6F5BzUSIxEZDG/Cqfew+Ad5SnHLg97iNB24Yjej69c73dSnPK6XcELr+LMc9efCYo/MItbQgwWA5lmoMeKlw85yOdxWoK7MBd8LnoblzkiHscc6BD734EgA1aQbcLqFL5HEDofOhE1EbXC50PbebA8/mgTuRC/AONMlPyBbzGPBK8zB1aL9qyVIIh+1+6CMjZTt+mgGvsBSDoXJI9Pe7egk9GEpjDQyihoeRmhqqFi+xt9merAV3a8DL2D66qEYuTmtVgwfLVaA3A5S9Dlx/2MJz57qh2PFupzr0sjbgqcMh3BB6jk5sVjTqeunxMntl5STRmxpCDzT5y8icHLjzOhTezMVbk1ppBkor0EOtswhNsy8d5bxhMzlwQ754I1mxLakh9MQO53M8c6abDvL+32ljXq78NxTngc8GnhORO0TkJHEaku/uxHUTlyZ/CL08KnQ3hD53rhuKHc867ER/P9E319kd2PbZJ+U1ffxcIXRvrrbcyuRy4ubAm9M9cJVI2Dd5IimTiwoOoafUWVeWB+7tDx2cPt1+rpwG3Pnf1BfWSjs/hsohxYD7ynJ1+Nw24LPSto87TVzKpUCH4srIrgCWAT8D/gN4Q0S+KyJLS7y2SYXlqQGH0orY8lEi6w9beE55PPDhVa+AUlTvvTcBR9ChyXeYidcLq7S8bSnRRjjgitiaAbB6et2bnEBdXUrP/KQBLzyEnujurqhuY14RW2j6BHjgjgGPLFqU8thg8KM7qUEmA25HCUMzZ7itUr214Lq1arlqwKH4MjIFbHe+4sA04E4R+UEJ1zapcPugOwZcSuSBx9o7eOPIo+j88f+Mvt3WZAg90OBc/MfRA0+Gzw9Mey1QWwsiWIODo6rLvV7YRLTXLBcJfw7cI2Lz90HXuNvkeRPmDeWpWKxs1Q/54BrwWbMITp8BlNuA2+c/4vTqNx64IRsporQsHnhw5kxCs5wQ+vZJ5oGLyOdF5HngB8CT2H3RPwUcBpxV4vVNGpJlZKVVoQ+98AKJ7m76//73UbfTbVTD8+a6rUzHs2Xk8Eu2Aa/25b8BJBBIagBGaWTjLSeKd0/dHLjbB12r0D2tUt0acY+ADTwTyZw8eS78bR0TPZVhpJRSxDqT6tyg44HHy1hKpj3uKuOBG3KQIgbt6EBFo8nHnhx4OEMI3fXAKzwHPhN4r1LqRKXU75VSMQCllAWcVtLVTSIS2ULoYzTg2nvxdgDyo+Jx2wMTIdzamsyBj6MBH3rJLiHL5IFDft3YvGHzYmuDt1z6ZbZ88YsVFTL2468Dl1DIvsGxLFf44hWw2ds63dry9MB1KM8VyFWIl5no6YFYjEBTE4HqakJODjxRxhs2/b8Z3mMPwNarVPLnxTBxeD1qlEpNTTlC29CMmQRnzIBQiERPj1tR4XrglaxCB6qUUhu9T4jI9wGUUq+VZFWTkPRGLrYHqsYYyvQacGVZ2bdJJOz6w0jEowLvH5cLVay9nXh7O4GGBjev6CefgSbeEHoxtcHWwAC7/vxndt3317K2rC0UbcB1i1RI3ujF2trsxz4PPBlmz23AlWW5Su9qZ6hMpZTl6c9veFYLYI/ahYkRsYVbW+3UVoWlGAyVg/aopaYGSC0l04NMQi0zkUCAkPOZjnd02E5UZyeIEGppKdt6izHgx2d47uSxLmSyk+aBl6iMzM3JxONZFcne/DeARCL2PPJEAjUOZWy6gUvNAfunCK+8uANNRvPAvSH0IjxGf7irElFKeQSOSS9bN/yJOgY8LQdegAo90d0N8TjBpiZCc+zwXaXUgrv57xY75BiaoT3w8ofQg01NyRujCkkxGCoLfU2pOcBODXpLyVwV+gxbxxF28+Db7dcsi+DMGe5Y5XKQtwEXkU+JyMvAPiLykoi87HxtAF4u5uBOGdoaEVkrIpdleH0fEfmniIyIyCWF7FtuXKVxiUPoMe8cZc9Ep5RtXAM+x30uOI5hdN3ApfqAzOFzyK+UzBtCV0NDBZ8rXToHFWzAh4dRsRhSVUWgutp93vXAN2sDniUHnkcIPTkBqTVZZ10hteBeARvglpFNRB14sLnZjZBVyvkxVA4qGrUjgYEANQfZ1zavkE33qgjOtD1sXQsea+9IDjEpowIdIFTAtrcCfwW+C1wGCKCAPqVUwbezIhIErsP26Nuwa8vvUUq96tmsG/g8cGYR+5YNpVQGD7w008hSxjDu6ATP2E5NbGuyBlwTaGiAzk5byFZiUcWQ9sAzCNjc4+tubKPcQPiFTPHubiLOjU8+pChAK9SA+/PfGl1KlgyhN2R83T8sIRNagR5qbSU4AY1SRsO9udAGfJoWsZVnfdbQEGpkxI5K1dQQap7GCEbIZkgn7hFbhucvAJIG3NtGNTTT9sC9teASsk1pqIwKdCgshH6fUmoD8G5gFbbXvQrYJCLFFBwfDqxVSq1TSkWB24EzvBsopTqUUs8BsUL3LSfWwCDEYkhNjVsTXTIRm1dEkUXIlmyj6jXg49NOVVlWsgf6AdkNeD7d2LSR0fmmQo1ObHvle+Buj/wmvwF3QuhOiC7Q6Dfg+YfQdZolPLuVYLNjwCskROz3wHX4sVw3GN7wuYgkPfAKOT+lYuDpp+l/4smJXsakxhvJ0s6QvrZavb22GLO+3o2kaW873tHuaaNaXg88bwOulDrK+V6vlGr0fDUopRpz7Z+BecBmz+M257mS7SsiF4jIShFZ2dmZOfxcCixfH3SAgGOUrMHBooVk1sBASgg6nuV3SDZx8YbQnYEmfWNr5hJr76DrZz9jcOVKlGURXb8ea2CA0Jw5hJ2LcibyGWiiL+JVS+0eQIW2U03xwMfx7zsW/H3QNfqzojUKwWw58L6+nJ+fpJfbmizTqpgceLKNKjiRoXDY/myXoR+6X1warLAUQymwhobY/MkL2fzJT45arWIYHbdjYOsswvNSDbi+NnmnjLkh9O3txLbpErLyeuCFhNBLTaYWrPlaurz2VUrdCNwIsGLFinGrG/GHz8EuFZKqKtTIiNsAv1Bi/jnKnVk8cLeNavIeplQeeNcNN7Dzt78F7PrGqiWLgaTIIxu5BpooLcoTIbJ4McOrVhUsbNJ1l5B+riqF7CH0VIMe8IXQJRwmUFtrD/4YGEhTqXtJhtBnTXgOXCmFt7tyUoVuG3ARIdTcTLyzk0R3NwHPTed44Hrg2oBPQQ98+NVXUc7NUN+jjzLtnHNy7jPy5psEGhpGvQnf3dBd2EKts11nKLZ9u13l0Zlso6pJqQUP2J/5cBlrwKG4Ri7vE5EG5+evi8hdInJoEcduAxZ4Hs8HtmbZtpT7lpxMBhzGHkb3i9YyeZlKqSwittJ44CPOSL1AQwPx7dsZeOqfwOj5b8gdQvdeWPU/RaHNXOLbPJOAsgj8JpqEr4mLRquh3ccN6QbarenuGT2MnvQcJi4HrpRiw7nnseHc81K67/lD6IBdQ0t58uDJz5nTBU+fnymUA9eiUoC+hx/OuX2ip4f17z2LzZ+4YDyXNemIuyH0WQRqamzBZSxGvLOTeFeyC5sm5GmnGt+eDL+Xk2LKyL6ulOoTkaOAE4BbgJ8W8T7PActEZLGIRIDzgHvKsG/J8YfpNGMtJdMXP/2+mcJjiZ4e1NAQgYaGlDBsqTxwXQe56Lbfssdtv2Xahz5E3bHH0HTG6JKDXCF0ffEOTp+eLC0qsJ3qZCgj021UA74Qur9xi7+MDJJee66JZDoHniJiK3MIPbFzJ0MvvsjwSy8x+MwzAKhEImUAhCbZD3381+i2OPZ54JWSYigFQy8lDfjAP5/OWXkyvHoNamSEkTfeQMX88qLdl6SWxDbM4Xl2RDO2ZYurP0r5HDs3pfGOzmQUdJwjSn6KMeD69vpU4KdKqT8BBRe+KaXiwGeBB4DXgDuUUq+IyIUiciGAiMwWkTbgi8AVItImIo3Z9i3idykJ/j7omrF74PYHqnr5cvtxBgPurwHXuANNxlBGphKJ5Adz/nxqDzmE2V+7nIU33JCzWUGyE1vm4+uLd2jatGR/7AIGmlgDA3aXMkf9Ge/oqMjuWlaeIXR/Dty7Ta5SsphXhd7UBCLupLNyoSshAHr/ZN9Lx7u67NrYGTOQcNh9XTdzKUc3toRvSmAyhN4z7scuF0MvvQg4HmEsRv/jfxt1+5F1b9o/WFbKTfDujhtCd+q7XSHblq0Zb0QDVVX25yked8vIQmVOSRRjwLeIyA3AucB9IlJV5PuglLpPKbWXUmqpUuoq57nrlVLXOz9vV0rNd8Ryzc7Pu7LtO1H4+6BrkhPJiisl016la8AzhNAzCdgATzvV4kPo8fZ2iMUItsxMqWHOh1yd2LSxDk6fnhReFeCB6wtPeN5cAnV1qJGRcZ9/XgzJELpfxNac8jijB66V6KOE0K2hIaxdu+wOfM3NSChk3ywolfcglFIQ91QE9D30ENbgYFLA5ruoJUeKlsEDTxOx2d+niogt1tFBfOs2AnV1TP+PjwC5w+jRN9cl92/bMsqWuxdeERuQokT3TiLz4g2ZB6dPT5vMON4UY3jPwfZ8T1RK9WBPIru0lIuabOTMgRfZtlELs6qWLbOVu319WMPDqds4jUDCCxakPJ/0wIsPoesuYZF58wveNzlSNFcIfZpbWlRIDtyNDLTOToayKlCJ7orYcuTA/SI28DZzyW7A4546ay0eKzYPrpQqOqTq9cCtwUH6Hnk0GdqflRqtSXZjK20OPNHTg4rH056DpAEPTTEP3B0qdMABNJ5wAgD9f/972nXCi+uBk9ppbHfGbkecjGSB34Cn58AhVXVebgU6FB9CrwbeJyLfAC4A3lrSVU0y9MUg4DfgdWMMoXvVxVrotSPVyEU32W3pIz4Drg1CNhV4Pui78/D8MRjwbB64DqFPn+4ZcJG/R+YODpgz2w3nV2IeXE8TSxtW4v2sBALuZ8VLyOn4pMNzmfCGz9331uezwDzv1i9dwhvHvaOoMbR6KIu+6PX++Z40Bbq7Pt0PvYQz4Idfe43XjziSzuuuS3ne/785URqB8UIL2GoOPJDw3LlUL1+OGhpi4Kmnsu6T4oEbAw7Ynwelh+44FUPeUrJkCD31ZlS3U4Xy14BDcQb8T9jNXOLAgOdrt2X8VOjOBbC1NWnAO1ONVGyTXQ4fXujzwJ3GINausRhwx7ufn295fhJtwBMDOULo06YnDU5XV955bHd0n8cDr8RSMitLCD1QXY3opj/19SmlV5qqPe36+JG1b6a9pnGFN60elbfudlaAkVKWRd/jj5PYsYOR11/Pez93HU4IffpHPgyhEANPPsXwq/ZsI90H3V2fFrGNkjJJ9Pez7sz38Mbbj2P9uefS9rnPsf07VzG8Zk3G7Qefew4si4G/pY7d1f+b2vOWmhokErFTLkNDBf+elYYWsNUcfBAADcfboyr6Hnwo4/aJvr6UG91KNOAqkWB49eq8NRzW4CD9/3hiTBoYbyWHxuuBJ3xd2DTeG+fJ4oHPV0qdp5T6gVLqv/RXyVc2iUi4jVyaU54X14AXfn+jlPIMgmjxeOCpQrboZtuARxYuTHk+2Yt8DAbc+efWasxCCOYKoXclQ+iBmhqkthYVi+WtF9AlZOE5s1PUoJVGtjpw8AirMuS/IdngZmTt2qzvH29PFd6AJ8/ri2j0P/Ek7d/7flqYGSC+bZvbVMY7gSlfdAi9er/9qD/6aEgk6P3Tn+y1+Upr8unGNvR//8fI6tXEt29n+MWX6HvoYXb+5je0f/fqjNvrdM/Im2+mXPj9HriITBkvXCUSycFCzljfhuPfBUDfY49lTIdE161LeVyJBnznbbez/sz30HPnH/LafuvlX2PzJz5B/2OPFX3MWIYysKSIbYub8tPRQneb2ZPPA39KREYvAt7NsHKJ2IrwwBM9PaholEBDA4Ha2mSY2JPnVbGYLWITSQtzu8NMxuCBR7c4OfAiQuhSUwPBoDvMw0/C9w/hNiDJsxtbqgdewSF0d5RodgOeScAGEFmyBAIBohs3YkWjGbfJFEIPZTFQHddcQ/cvf8nAk+ktN0fe9ORFtxZhwLUKd84cms54N4DbXMSfA88nQhDduAmAxlNOYY/f3srsb3/Lft5ngNzjO+keNTJCbHOySaM/B+79ebLnwUfWvok1OEh47lz3Br9q6VIiS5Zg9fYyuHJl+j5O+Lx6//0BiG6tPAOuVfXDq1bl3Da6eTN9Dzxgb/9a8dOsk6WYnkhWYyOB+nrU8DAkErZI1DdpbDJ64EcB/+dMAtNTyV7KudcUJmsZ2RjqwP0tKPU/qLcfemzrVnsO+JzZBHwfrEAJysjGkgMXkWQYPUNONe6q0G1vzG3ukacS3fXAZ7e6OdZKM+DKowT3fza8z2Xrshaoria8YD4kEkQ3bMi4jV85C54yLY+BVLEYI47xG16dHob2hulj2woz4Coet8+9COFZs6h/+9vdvz2kq9BDnpRJNqKbbANevXw5tYceSvNZZ0E4TLyzM2PoW6d7AIadFEDKkCGvAZ8izVy0oas+KHUqYMO7HC/8ofQwetQRsNUdeSSIEN/eXnG14NGNtq4nunlzji2h+9e/Bid0PhZFvVvV4vOiveW5QV/4HFIjX+XuwgbFGfCTgT2xm7icDpzmfN8tyXaRgLGVkbm5TT0EQnuZnnaqUSf/HVmwED+BujoQsXuxZwiZ5sKKRp0WgYGiP5hBfQOT4fdPitimOd+10cnPgLv9v+fM8YTQK8yADw3ZQ26qqzOWl+iZ4Nk8cICqpXsCEM0SRo+3p4f+kgYqacCjGzeCc6EeWbM67X1G3ky+f6EeeLyjAyyL0MyZSCRCoLqahpNOdF/3i9gCjY0QCtm1/FkiC9GNGwCILNoDAAkGiTgXU/+FXSmVYsBH3ngDcASUiQRSW5tygztVmrloBXrNQQelPO/mwR9+JC0v7Hrg++xtf2Ysy42eVArRDbYBj+Uw4Im+Pno9YfZc249GspNa6mfVmz70C9gg9ca53F3YoDgDvgk4GviIUmojdg/y8q+8QnBD3bW1abXSYwmhJ/PfqR64N4Qe3Wx7Kf78N4AEAjmV4KMef+tWUIrw7NkpTTgKIdtMcGVZ6T2qdW1wHiF03cRFnEYKlVpGNlr+235eG/Dsfc6r9rQNeLY8eKwjgwrdyYF766y1UQMYXpMuUouuLT6E7g2fa5pOf7ezmKD7t9WISDLMnyUPHtuY/tkOOz/7L9SJnp6U/7GRN9a6z0OGtrXNTSmvT1aGXrA98JoDUw149f7LCbW0EO/oYOT1N1Je0yVkkSVLUzqNVQrxnTvdlGRs2zZUlhs8gJ7f34k1OEhkD/smLzqG38ONZM3O7oGHfCVkYGsrgs3NSFXVpPHAfwK8DXi/87gPezb3bknUyR1GHMGRl0Ct7YGqsRhw58KcScSmL3J+Bbp7/BzNVEYjOobwuXt8V8iWGsZP9PaCZRFoanJvDpK1wbm9Itf7nt1qGwNPGVkldWPL1gddkxSxZR/mV7VMG/B0Jbo9ZCG9WUqmHLjXgEfXr0+pE1ZKpeTA41u3FXQe3Xn0HgNe+5YVNL33vcz42MeQYDBtH7fyIIMBV/G4ezH29jfQpZI68uQe3/G+tapf/67+NqrusafARLJE/4B9UxcKUb3fvimviYgdIocUvYM1MmL3jQgEiCxeRGR+5RnwlFSRZbn9HvyoeJzu3/wagJZLvgSBAPHt27NGdHIRyxDJAp8Bn5EeQhcRFtx0IwtvvsktPysnxRjwf1NKfQYYBlBK7aSIVqpTBe0ZaU/Jy1gaucQ8DTqApJHyGHBXgZ4hhA7egSaF58FdBfqYDLieSJZ6A+EK2JwLKSRz4fk0c9F10TpfFaipIdDQgIrFKsqrStaAp+e/IVme52+D62U0DzzR1QXxOMFp01JDxBnqwL0GHMtKuSGId3Rg9fcTbGpKTkDLYw65u79TQub1QCQQYO53r2LWFy/OuM9o3fdi27ZBPE5o9uyUqJa+UfV74NqA1x5+uC3627ABKxpNa6OqmQrNXIZXrQKlqN5774xdEjMZ8OiGjWBZhBfMJxCJVKQHrvPf7uNNmcPifQ89RHzrNiKLFtHwznfanz2l7MhhEcR911uNrgUHCLWke+BgT2asfctbijruWCnGgMdEJIgzvlNEWgCrpKuaROgLoa7Z9TK2EHqqiC3o8cCVZZ/umBtCz+GBF6FEd2vA52U3LrkIZhlokvAMMtGE8qgNdteWYfZuJZaSZeuDrmk++2wW3HA90/79A1nfI7J4cVYleiYFOmRuVqJDqRFdW+7Jg+ubg8iyPdPmIOeD64F7puHlIjRK//tohvC597E/B65LyKqWLLHDqYkE0XXrMirQYWo0cxnKkv/W1B3xNgAGV650565rAVvVEvszMBkMeKwtswHv/uUtgN13QAIB19GIbm7LuP1oJPoHsPr73ZScl1QRW2YDPpEUY8B/DPwRaBWRq4AngO+WdFWTCC3+yRhCH0MnNjcn4ximQFWVXcvqzNFWluXenYYz5MDBa0CL8cCLLyHTZMvB69ys9sLsn/MfaKJLyMKzkwajEkvJ3HaxWQx4oKqK+mOPHbXP/GhK9EylL+AIGMNh25MeGcEaHrZV3aEQjSedDJDSEEWngaqW7klI175mCV1mws2Bz87fgCf7oWcw4Lq7oJPb1OgQesxRqLvH96R7qpYtA+yIQ7YGS1OhjGzoRSf/7VOga0IzZlC1776okRGGnn8eSArYqpYuAZIGfCy541KjP+ORJfYaM3ngg//6F0MvvkiwqcmdihheYF+n9HWrELzT/PwNlVJD6FPAgCulbgW+jG20twJnKqV+X+qFTRaSIfRlaa+NrYwsfY6ymwfv6CTe2YkaGbGHgWQrQ2osvha8FDnwbANNtJEOTUt64IUMNIln8MArsZSs3+kKVrXvPmN6H/3Z8ivRkzd5qR64iCTDxDt32vltpYgs2oOaA+z63xFPKZkbRVq61M1jF9LMJTlKMX8Rz2gRl9hGbcBTb0x1Pjy6dWtKsxZvx0DXgL/++pT1wJVSyRKyAzMbcID6I48AoN8Jo0c9AjbweuDFhZ3HA+2B1x99FJDZA++9224Q1HzOOW6UUzsa3mqEfMnUhU0TnDHD1VZkC6FPJHkbcBH5ov4CTgGqnK+Tned2OxI9PSQ6dyA1NRnDh8WWkal43FZji6TOn3XD6J2uF+Lvge7F9cCLyYG7F8VSiNj8HniGEHoe3bnctbkeeNJglEuJPvTii3l5bvGdO+n/+98hEKDxlFPGdMxsHdmyCW8gNQ+u899Vy5ZRtffe9nutWeMK1bSArWrPpYTnOhf1AkLo8SJmIbuah1FC6P7IUqC62v47x2JuGgWSn9XI/PlU7bUXYKcMspV3TnYPPN7eTqJzB4HGRiKLFmXdLpkHt/uip3ngra22+Ku9fVS1d7lQShFzSsjqjjoayOyB6wYv9ccc7T4Xnu/c3BURQs/UhU0jItSuWEFw2rRRr7UTRSEeeIPztQL4FDDP+boQ2K/0S6t8dGOMqiVLkED6qSw2B55tjrIWsiV27HAbXWQLn4NnpGiBIXRrcJBEdzcSieSc+z0agbrMIXR/DTh4Qqo7d7o5/my4g0y8BrwMA0123n47G849j21Xfivntrv++leIxag74oi0OuhCyaZE133w/SF08HQ76+52899Vy5a5M8MTvb32hVupZA586Z7J9pF5htCtoSHbEIbDbjOefHD7oWeoOtCfbX8IHbxCNnsbZVnJkbrz5qWG0F0RW3PqsXUd+CQ14G7+e//9M/bQ19QceihSXc3I6tXE2juIrl8PJMPTEokka8ErYC54vLMTa3CQYFOTGymKbd6cUhGhYjG3V3/Vvkn1vRaEjsUDz/R/BLDghuvZ85GH3YhqJZG3AVdKfUsp9S1gJnCoUupLSqkvAYcBxbtpkxhdb5pJwAa4ZQXW4GBBZTnJ8LlvDKOnFtxt4jKKAS92oImrQJ87N+ONSb5oEZ01kFvEFohEbI89Hs851zuZc83kgScNuDUywrozzmTzJy8s+nfQDK9Z4/bhHnz22Zx/z133/BnAbSs6FjIp0RP9/fQ5vZ/rMihgvXOvvR64iKR44YmuLqzeXgINDYRmtbiRpHw98Ni2ZDSkkM9Ktm5sKpFwVeaZPJ6I9rScz3+8owMVixGcMYNAbS2RhQuQSITY1q3uxTx9dGs9hEIoRyMw2Rh+2fZAqw8YvaN1oKrKVUf33Pl7VDRKaNaslN77kXnFG75So1Mn4UV72FPBGhpcZ0Iz8uabqFiM8B4LU1KHbolhMQbcHQiUOQUkoZDrjFUaxVydFwLeeEsUWFSS1UwyXAFbhhIyAAmH7d65luX2hc6H5BhG3xCIFm3Ad+RUoEPxI0WjJQifQ7JFaMIfQvdMIkvZfoYWNmXPTbpNXCIR18sEMk4kG3jyKUbWrKH/b3/L2oo0H6zBQbZc/EU3zJjo7nbDxpmIbtzI0AsvILW1NLzznUUfV5NJib7rvvtQQ0PUrliRMYzqrQXXBrza8U6r9rEN+PDqNSn5bxEp2APPVEKWD/rmzT9BLr59OyoWI9TSkvGi6ffA/RPzJBRyBaVDTqjVH0IXkUkdRh9yB5jkHklR5+TBd95+OwARJ3yuqSQlenRjUrwoIknRoqfqQE+4q943NegbnDEDqanB6u11Gyjly2gh9EqnGAP+a+BZEblSRL4JPAPcUszBReQkp6f6WhG5LMPrIiI/dl5/SUQO9by2wenD/oKIpHftLwNR9+KX2YBDcWF0fw24xlsL7irQs9SAg8cDzzIRLOvxXQFb4VPIvASylpGlh9DtxzoPnr0WPNnEZXZK+DBTGZm3F3TfI48WvH7N9quuIrpuHZGlS6lZcRgAQy9nH7TQ63jfjce/qyR37pmU6HpSU/P7zs64j745im7aRHz7drtTlHNBrHY98NWeKgr7wh5qaYFQiMSOHXl5p9rQhwoQsIEdOQo0NhLfts0NmUPqRTzjfs7nXX/+9c1mZF7yZrN6L0dQ6rSO9YfQAUI6QjHJDLiyLDcHXL1/Hgb8CNuAJ5wWzLqETFNJSnRXge7ckLqiRa8Bf00b8PTmNZEiw+i66qEQEWalUIwK/SrgfGAn0AOcr5TKPONvFJxa8uuwe6vvB7xfRPy59JOBZc7XBcBPfa8fp5Q6WCm1otDjlwKv+CcbxRjwTAp08IfQdZ5wlBy4K2Ir8I7UrQEfqwHXKnRfJ7YMIXTv49GU6MkmLv7oRHJam7IsVCxG/6NJo933aHEGvPfPf6H3D3chVVXM+3/XUrvC/qhlm5SklKL3z44Bf/fYw+carxJ9eM0ahl96iUBDAw0nnJBxex2dGHz2WXv/pUvdjmhVe9uq+OE1r6eUkIHdc1yf23zC6G4IfU5h/QIkGKTubXatckqzEa3tyPK51hGnqKNOzjRwR+fBNTqdkPKcY9QnWze26IaNWP39hFpbU/pwZ6Nq2bIUHctk8cDB87dO8cBfBeyxtX7Czk1cIWH0WHsH0bVvIjU1VO0ztmqRiaCoBKdS6v+UUj9yvv5V5LEPB9YqpdYppaLA7cAZvm3OAH6lbJ4GmkUkf6nrOJLYtYt4eztSXT2qoXNrwQvoxhZ3G3Rk9sBH3nwTa9cuArW1aUbQi1vGVaAHPpYxoinHdzqxWf1JFb5SyhUP+deez0ATN9zlu1sOVFXZ9b7xOImeHgafe45Eb699Fx8OM/Svf2WsOR6N6ObNbL/ySgBaL7+c6r32osbJOw6/ktmAD73wArFNmwi1tFD31rcWdLzR8ObBtffddPppWds3aqM14tR7e41a1bI97ZD8+vUMv/Kq8/7Jm1AdRh8tTaDRk8uK8V7qjrJV0v1eA+42ccnsgbv90DdtThli4o0WpRnwDMNi/ANfops30/2rX9Fz1x8Z+Oc/GVm/PuPUs4lm+GVbwFbtiLxy4W2rCtk98EooJcvmgWuxprIsRrQH7msfm7J9AUp0ffNYd/jhaRMdJwPFK5TGzjzAWyPQ5jyX7zYKeFBEnheRCzIdQEQuEJGVIrKys8TlRdr7jixZnLHXs0b3Qy+klCyZA0814LoTkBb+hBcuHFWFqmdQe0VhA089xZpDD2PXffdl3U//M481B55pmInV1wexGIG6urR/mHwGmsR0zjWD4MQ7lWyXEz5vPO1U6g4/HCyL/sf/lvfaVSLB1su+ijUwQMOJJ9J8zvuA5BzloVWvZBSy9d5zj3Pc00b9XBSKNrDDr7zqHqPprLOybh/y3Rzp8iqwb3YiixeDZbkNQaqWphvwfDxwd6xrASVkmnrHsAz+82l3pGWuyFKwuZlAfT1Wfz+Jnp6UEjJNyu/a2IiEQhnfB2Dw2edou+hi3jzxJNq/ezXbLr+cTed/lHUnn8Kaw//NLgWsIHTqpuaA7PXfflIMuN8DL0M/9KGXV/HGsW+n5493Z93G25gqssci+/uC1GhLdONGrMFBQq2tGfuSJ3u7F2DAn3gCgLqjjsp7n0piIg14JsvjvyKOts2RSqlDscPsnxGRY9I2VOpGpdQKpdSKljGUQ2XCH3rMRjHd2PyDTDTB5mbwlJXlqkvMNI+765ZbsAYH6fjvH6U0w/BSihpw7/G9dejZwueQ30CTeBYPHJIRitj27fQ9/DAAjccfT/073wFA36OP5L327l/+kqHnnyfYMpPZV37TvVEKzZpFsGUm1q5daT25VTRK331/BUqjPveiPfD+v/8dq7eXqv32pWb58qzbewV+AFV7pXqlOg8OILW1KZPEQgUo0YvpwqYJz51LZMkSrIEBtzQqpruwZamuEJGkkG3TpuTQE89nNTR7tvvZ8wvYNPr87Pztb+m7/34IBmk85WQaTz+d2re8xf7fi8XYeccdBf9e48mQ44HX5OmBg91WVaqqCM2endYOtBy14Duuu454ezs7rv9p1uqN+PbtdmOqmTPdyJ3W92gPfCRL/luTzJnnZ8BVIsHAU3aNvI4GTTYm0oC3AV4LNB+7s1te2yil9PcO7Nauh4/bSjOQLCEb3YCLmwPP3wOPZcmBi6+xy2j5b0i28NQGNNHT4zZ1iG3aRP/jj6ftk+jtxerrs8PzWS5++SKRCITDqFjMVU9naqPqrjePgSaxUVTP+nz1PfQQic4ddl3wvvvS8A7bgA88+VTKFK5sDL/+Op3//SMA5n7nOylDV0SEmuWOF+6ogTX9//gHid5eqvbai+oS59O0Eh3nAth8dmbxmibNgPvCylUeA+7vY5D0wEcPoSuliurC5kV7h/1PPOFrD5w5hA5JIdvIm+tsTUQgkBIBEBH39/W3UXXfw7kJCNTXM/1jH2XPhx9i3rXXMu+aH7DHr3/FIsdwD/zjiaI6KY4HKhpl5DW7h72OBOVDaMYM9rj1Vhb+/GdpETsJh91BIOMxF3xk/Xr3OhPbuImhf72Qcbtk+Dz5dw/PboVQyB62MzycFLBlCJ9DMgeer4ht+NVXSfT0EJ43b9SGOJXMRBrw54BlIrJYRCLAecA9vm3uAT7sqNHfCvQqpbaJSJ2INACISB1wApBdFjwO5CNgg8JFbNbwsD0JKhzOaEC9Bnw0BTo44xXDYVQ0ijUyQt8jj0A8bhtWkgMBvHhLyEYLz+eDiLilZO5NRIY2qppcA01UPO56hZlKPrQB3/WXewFoOP5422ObPZvq5ctRQ0MMPPXPUdesolG2fuUyVCxG8znnUH/ssWnb6Ivn8KpXUp7v/ctfAGg8/bRRj1EMrhId++/adNrox/Aa8EBDQ9r5qt7HY8B9ffy1IC2XB2719qKGhux0SIY8cz7UH5XsFhZvb0/zwjKhje/gM8+AUvZYWd/Meh1Gz3YT2vSe97Dwl79gz8cepfXSS9NEkeHWWdQcfDBqZIT+fzxR1O9WaobfeAMVjRJZtChrf/1s1Oy/nKolSzK+Np5Ctp2//g0A4vT777377ozbZao+kFAoOVynrc3Va2QSsAEpKvRczaAgNXw+1mvdRDFhBlwpFQc+CzwAvAbcoZR6RUQuFBHdeeM+YB2wFrgJ+LTzfCvwhIi8CDwL3KuUur+c63cNeIYhJl4KNeBuX96WloyNMVIUpaPUgEO6Ad3lhHdbvngxgfp6Bp97jqFXUo1QJlXvWPAPNMnURlWjO3l5RWx9jz7G1q99jfVnnc2aw1a4pXuZcq7agOua+4YTjndfyzeM3vmTnzDy2muEFyyg9StfzrhN9f526NqrRE/0D9D/qN1YpenUU0c9RrFoJXrDiSfkvIAHIhG3c5Ru4JLyXh4PPOK7Cc03B+4tISv2Alj7lrdAOMzwyy8z9KIdHh6tOREkQ6UD/7RvxrwlZBqdMvBrATQSDFL31rdmFLhpGo63Pz/ecsTxovfee2m/+upRw9jDTsQnVwOXQhkvA57o7aXnj38EYO53rwLsDoWZomDRDdqAL0p53tu4J1sJmSZQV0dw+nRULJZXS+X+JxwB2yQNn8PEeuAope5TSu2llFrqlKehlLpeKXW987NSSn3Gef0ApdRK5/l1SqmDnK/let9ykejvJ75tGxKJuBeTbGgRm8rDgEfbttB2kT0/ObJ4ccZtCvHAITnQJLppEwNPPw2hEM1nnumGYLtvSfXC9Z3wWEvI3OP7lPDZasDt55JlZPEdO2j7/Bdo+/Sn6f3DXQy/8gpqZITw3LlMP//8jBdmb+e6YMtMag4+2H2sG6r0P/Z41tx//5NP0nXjTSDC3Ku/m7V1Yo32wF95xb3T73/kYdTICDUrDht1vvdYaD77LKr225eZF2TUbKahvXB/+BxwW6pCuo7D7cbW3p71XEHxJWReArW11B56KChFzx2/A3IbcP26K/bMcLPZdPrpTPvA+5n+Hx8pem0Nx78LgP7HH08b5RrfuZPev9yLiscz7ju8ejU7brwpbb9MJHp62HbF1+m+5Vfs/H32uVBuA5dxMuCjlV+paDQvr9ZLz513ooaGqDvibTSecgrVy5dj9fWllHdqMoXQIdm4Z3DlShI7dxJoanIn5mX8XfRUMp8+xU+ir4+hF14A50ZusjKhBnyyEnUV6EtyKo3z9cAHnnmWDe97n+397bGQ1q9dnnE714CHw3nlHfVAk5677oJEgroj3kawuZlpH/wgBALsuu+vbnOU/r/9jR0/+QmQ/S63ULRafNvllzOybl1SxJYhhB70TNBad+pp9D34IIHaWlouuog9fv0r9nr2GfZ89JGsnrFXtd/wrnelRDCq9tqL8Lx5JLq6XE/Py8jatWz5wkVgWcy48JNuvXcmQjNnEpozB2tw0L3w9Dph+1yh7bHQcNxxLLnrrpy6C81oBlxEaDz9dMJz51J76CEprwWqq+0ISSxGfMeOrO/vlpAV2IXNj/aAdHojl7ZDD65IPk6/2Qw2NjL7G98Y0+c4snAhVfvsg9Xfz+DTT7vPK6XYctHFbL3kEjp/9OO0/ayBATZ/6tN0Xnst3T/7Wc7j7Lz9dpRTstZ1/Q1ZdRrDL2kPPP/8dz7kKiUbeeMNXj/iSLZecmne76nicbp/cysA0z9i30Q1nXkmAD0ZwujJEPqilOe1B973wAOAnf8eLdoTybMWfODppyGRoObgg0eNwlQ6xoAXgbf9ZC7ckaKjlJF133ormz76URI7d1J31FEsvuOOrPkq7WVG5s3Lq0xJ5yZ33WuXjTWebE/GisyfZzcBicfZeetv6bn7bjZ/+jOo4WGaznovTe8+Ped758OsSy8hsmgRI6+/zvqz3+eW5WQKoUs4bHuFSpHo7aXuyCNZ8ud7mHnhJ6l9y1tyho29or/G449PeU1E3DB6vy+MHu/qYvMnL8Tq76fhxBNp+dzncv5eNTqM/vLLxLu6bDVrKETDiSfm3Ldc6M+Q30BrZl/xNfZ89JGMeeJ8wui6qU6hXdj81B+ZGsIcbUAPOII5bzVGidI9mdBeeEpXvwcetPPvQNcvfpEyWx2g83+vc2vou266edSbIGtkxDV0wenTiXd2svO229O3Gxy003ahUMlurjWuAc/gtSql2P6tb2P197Prvvvc/vu56HvoIeLbthFZvJi6o+2pYY2nnQrhMANPPJkS4lbxeLKjni8t6FYcOOF9fwvVtN9F14K3jZ4OGHDC5/WTOHwOxoAXRb4CNsjtgfc9+ijt//kdSCSY8fGPseCG67MqZyF5YY3kcfMAySYWamgICYdpcIwYwPSPfBiww+jbLvuqvYYLLmDOd76TsXa2GKqWLGHRnXfSePrpqMFBdyJSphA6QO3hhxNoamLOVVex4OabCgrlh1paCLbMtL3KDAM+Gt5hh9G7f/Vrtn71coZWvYI1PEzbpz9DbMsWqg88kLnf/15eQzmqtRJ91Svsuv9+SCSoP/LIFMX6RDP7W1ey5N6/ZBX9jEY+BrwUIXSAqn32SZlk5vfC/EgwSMQTRi2VXiMTbh784UdQiQTW0BDtP/i+vc4lSyAeZ9s3vuGmGoZXr6b7V7+CQICq/fbFGhyk87rrsr5/7z33kNixg6p992WOkyfuuvHGtBv+4VdfBcuiaq9lBBxBWKmo2nMpBIMMvfACfb7KlF1/uZfBlSvtCgig/btX59ViVwtkp3/4Q+7/U2jaNOqPPQYsi94//8XdNrZlC8TjhObMSWtM5C+VzfVZduvaRwmhK6Umff23xhjwIhhZaw+HyDbExEtyJni6AU/09bHdGU0565IvMeuSS3J61XVHHEHrFVcw65Iv5bVWrzq47qijUrzY2kMOoeagg1zRV+vlX2XWFy8uuSIzWF/H3B98nznf+U9XjZrtojvvR//NXk8+QfNZ7y14HRIOs/gPf2DRHb9LUyUD1L5lBU1nnomKRun94x/ZcPbZrD3+eIZefJHQ3DksuO5/8744JpXoq1zVe+M4hs+LIVBdnVeUKBNaJDi6AR9bCZlGAgG3ZzfkFmdCqpc+nga8atkyInvsQWLnTgaff56um39GfOs2qvbdl0W3/ZZQayvDL77EzttuR1kW2795JSQSTPvAB5j3gx9AIEDPHb9nZN36tPdWlkX3z38BwIyPnk/9scdSc9BBJHbupNtRb2uGnPB5TR79zwslNGMGLRd9AYBtX7nM/Zsn+vvp+MEPAJj9jW9QtWxPYps305UhLZDo6aHv8cfp+H//zcYPfZihF18k0NRE0xmpzTWbnTB67913uzXho/W/96dLspWQadzmL6M0c4lu2EBsyxaCzc1F3dxWEsaAF0E+Q0w0ozVy6bjmh8Q7Oqg56CCmn39+XseWUIjpH/x3qrKI3Px48zuNp5yc9vqsy75CzUEHMe/a/2L6hz+c13sWg4jQfPbZLLnnTyy46aashkUCgTF5/+FZs1KEfinvHQwy93tXs/SB+5n+H/9BoLGRROcOAnV1LPjp9QXNPq9ebv/jD61axdC//oXU1NDwjuOKXneloct3srVTjW7a5BkCMfbuxjqUGZw2La8SKX2hHuvM+lyIiFvN0H3Lr+i6+WbATj8Em5qY/fUrAOi89lo6/+d/7JvBlhZaLvoCVXvuSfNZZ0EiQce1/5X23v2P/43o+vWE5syh8aSTEBHXkHb9/OcpU7WGV+U/gawYZnzsY9QdewyJ3l62fPFLqFiMHdf9hHhnJ9UHHUjzOe+j9etft9d2w41EnRC1ikbp/J//5fWjj6Htwk/RdcMNDD73HAAtX/h82jCf+mOOIdjczMjrr7P9299m4/nns+WLtjOSyYAH6+vcdJvU1GQdcqPRN3OZ2qmqWMy+0XjQTofUHXFESbslTgSliZPuRlgDA8S2bkXC4bw8hWwh9IFnnqXnjjsgHLY903H6IGkPXKqqqD/uHWmv1x5yCIt+l55zGy8iCxfmVBmP+xr22IPWy75Cy+c/R9+jj1G1bE+q994r944eQtOmEZ4/320a0fCOd2RVrU9G3BC6R9gU7+pi17330nvvvQw7QkDd4Wus1B97LOH581Pafo66Pud/b6wz6/Oh4fjj6brpZvofsbUTjaeeSu1h9lS6hne9i4bj30XfQw/T9dPrAWj92uVu+ebMz32W3r/8hf6HH2Hw+efd/QC6fm57stM/8mE3YlT71rdSe/jhDD77LB3XXkt49mz6HnvMPd+lLiHTSCDA3O99j/XveS9DL7zA1q98hV0PPgQizP76N+woyeGH03jqqey6917av3c1Mz/1KbZd/jW3337NYYdRe+gh1BxyCDUHH5yxUkQiERpPPZWdt95KjyfXH547N2v3wsiCBQx1d1O9zz45r5Ph2bMhGLSbv4yMMPzKq3TdfDMDTz2F8okDJ3v4HIwBLxipqWHpww8R27I1L08xkwG3hofZ9g37bnbmhZ/MqBIuFbo9af0xx4zaHGN3JFBbS9NpxddsVx+wv2vAG8fwPpVIyBNCtwYH6frFL+j62c/dckg963za+88jUFU15uMFm5vZ8+H86611BCeSRexZSqr335/Q7Nn2WNaaGmZdeknK661XXMHAP5/G6u+n7pijU4SM4VmzmHH++ez4yU9ov/p7tFx0EaGZM4h3djK08nkCDQ00n/0+d3sRoeULn2fjv3+Qntt/l3w+EqHx5JPH91oxbRrzrr2WjR/6kNszovm8c13BJsCsL3+Z/sceo//hR+y+B5ZFeMEC5nznO9T9W37NMGd88gKsgQFCra3UHHgA1QcckDb3wUt44UKGXnwxL/GehEKE58wh1tbGhnPPY2T16uSLwaDddKiujsjCha5AcTJjDHiBSCBAZP78vJWv2oAnursZePZZsCx2/fV+Yhs3UbVsGTM/8YnxXC6Np7+bWHs70849d1yPsztSs//+9P31foJNTWlK6smO9sCjGzfy5kknuzXXdUcfTfN7zqT+uOOyTkIrB3VHHMHsK6+k7m3jX8MrgQBNp51K180/Y+anPpVWNhdubWXO1d+l53d3MOfKK9O0G9M/+lF23nEHw6tWsfnjH095bdp556bdWNcedhhNZ5/FwFNPUXfEETQcdxx1b3tbSWbL56L20EOY9cWL6bjmhwSbm5l10UUpr4dbZzHzM5+h45prQCmmffhDzLroooLWFp41i7nfy38CdcM7jqPvgQdoOCm/Co/wAjsyNrJ6NYHGRqZ94P1M+8AHCLW0TNqOa9mQbM3lpxorVqxQK1euLPtxY9u3s/btGXKjgQCLbr+NmgPznypkqCxG1q1nw9lnM+MTH2fmpz410cspKUop1hy2wvW4q5cvZ9ZXvmxPdtsNsUZGGH71VWoOPrgoIzDw7LP03P474t3dJLq6iHd1EWxoYI/f/Hpcc/jFoCyL3j/+kSrP+NyU1+Nxeu66i+q996bmoIMmYIWjs+uBB+n++c+dKYLnTInIo4g8r5RKa05hDPg4o5Si/TtX2WUgwQASCEIwQOOJJzLtvPPKvh5DadH/P1Ptzh5g6+VfY+j555n5mU/b41HHOddsMBgyYwz4BBlwg8FgMBjGQjYDbm6pDQaDwWCYhBgDbjAYDAbDJMQYcIPBYDAYJiHGgBsMBoPBMAkxBtxgMBgMhkmIMeAGg8FgMExCJtSAi8hJIrJGRNaKyGUZXhcR+bHz+ksicmi++xoMBoPBMJWZMAMuIkHgOuBkYD/g/SLin+12MrDM+boA+GkB+xoMBoPBMGWZSA/8cGCtUmqdUioK3A6c4dvmDOBXyuZpoFlE5uS5r8FgMBgMU5aJHGYyD9jsedwG/Fse28zLc19E5AJszx2gX0TWjGG9M4EdY9h/d8acu+Ix525smPNXPObcFU+pz13GQegTacAzNY/293XNtk0++6KUuhG4sfClpSMiKzO1sjPkxpy74jHnbmyY81c85twVT7nO3UQa8DZggefxfGBrnttE8tjXYDAYDIYpy0TmwJ8DlonIYhGJAOcB9/i2uQf4sKNGfyvQq5Talue+BoPBYDBMWSbMA1dKxUXks8ADQBD4uVLqFRG50Hn9euA+4BRgLTAInD/avuO85JKE4ndTzLkrHnPuxoY5f8Vjzl3xlOXc7TbjRA0Gg8FgmEqYTmwGg8FgMExCjAE3GAwGg2ESYgx4Hpi2rfkjIgtE5DEReU1EXhGRLzjPTxeRh0TkDef7tIlea6UiIkER+ZeI/MV5bM5dHohIs4jcKSKrnc/f28y5yw8Rudj5f10lIreJSLU5d9kRkZ+LSIeIrPI8l/V8ichXHfuxRkROLNU6jAHPgWnbWjBx4EtKqX2BtwKfcc7XZcAjSqllwCPOY0NmvgC85nlszl1+/Ai4Xym1D3AQ9jk05y4HIjIP+DywQim1P7Yw+DzMuRuNXwIn+Z7LeL6c6995wHJnn584dmXMGAOeG9O2tQCUUtuUUv/n/NyHfRGdh33ObnE2uwU4c0IWWOGIyHzgVOBmz9Pm3OVARBqBY4CfASilokqpHsy5y5cQUCMiIaAWu6+GOXdZUEr9Hej2PZ3tfJ0B3K6UGlFKrceuqjq8FOswBjw32dq5GnIgIouAQ4BngFanhh/n+6wJXFol89/AlwHL85w5d7lZAnQCv3DSDzeLSB3m3OVEKbUF+CGwCdiG3W/jQcy5K5Rs52vcbIgx4LnJq22rIRURqQf+AFyklNo10euZDIjIaUCHUur5iV7LJCQEHAr8VCl1CDCACfnmhZOrPQNYDMwF6kTkgxO7qinFuNkQY8Bzk0/LV4MHEQljG+9blVJ3OU+3O5PkcL53TNT6KpgjgXeLyAbsVM07ROQ3mHOXD21Am1LqGefxndgG3Zy73LwLWK+U6lRKxYC7gCMw565Qsp2vcbMhxoDnxrRtLQAREew85GtKqWs9L90DfMT5+SPAn8q9tkpHKfVVpdR8pdQi7M/Zo0qpD2LOXU6UUtuBzSKyt/PUO4FXMecuHzYBbxWRWuf/953Y2hVz7goj2/m6BzhPRKpEZDGwDHi2FAc0ndjyQEROwc5N6ratV03siioXETkK+AfwMsk87uXYefA7gIXYF4z3KaX8IhCDg4i8HbhEKXWaiMzAnLuciMjB2OK/CLAOu/VyAHPuciIi3wLOxa4i+RfwcaAec+4yIiK3AW/HHhvaDnwTuJss50tEvgZ8FPv8XqSU+mtJ1mEMuMFgMBgMkw8TQjcYDAaDYRJiDLjBYDAYDJMQY8ANBoPBYJiEGANuMBgMBsMkxBhwg8FgMBgmIcaAGwwGg8EwCTEG3GAwGAyGSYgx4AbDFERE+kd5rVlEPp3tsfPcU+O4tqeyHTfP/Y9wGo8YDLs1ppGLwTAFEZF+pVR9ltcWAX9xZj+nPS4XE3Vcg2GqYDxwg2EKIyJ3i8jzIvKKiFzgPP09YKmIvCAi12R4nOLBi8iHReQlEXlRRH7tef6DIvKss98NIhL0HbtORO519lslIuf63jvTcUd9T2eb3zstew2G3ZrQRC/AYDCMKx9VSnWLSA3wnIj8AXvM5v5KqYPB9YTdx15EZDnwNeBIpdQOEZnuPL8vdu/sI5VSMRH5CfDvwK88u58EbFVKners0+R7e/868nlPgP2xe+0bDLs1xoAbDFObz4vIe5yfF2BPQtpewP7vAO5USu0A8AyzeCdwGPZNAUAN6eMmXwZ+KCLfxw6V/yPHsXK+p4hUA2GlVG8Bv4PBMCUxBtxgmKI4E83eBbxNKTUoIo8D1YW+DZBJKCPALUqpr2bbUSn1uogcBpwCXC0iDyqlvp3jWKO+J7Ace0yowbDbY3LgBsPUpQnY6RjvfYC3Os/3AQ2e7fyPvTwCnOOMNEWH0J3nzxaRWfp5EdnDu6OIzAUGlVK/AX4IHOp7b/9xc74ncADw0ii/s8Gw22AMuMEwdbkfCInIS8B/Ak8DKKW6gCcdYdk1/sfeN1BKvQJcBfxNRF4ErnWefxW4AnjQef+HgDm+4x8APCsiL2Dn0b/je2//OvJ9T2PADQZMGZnBYDAYDJMS44EbDAaDwTAJMQbcYDAYDIZJiDHgBoPBYDBMQowBNxgMBoNhEmIMuMFgMBgMkxBjwA0Gg8FgmIQYA24wGAwGwyTk/wPtp5JWCwqPcAAAAABJRU5ErkJggg==",
+ "text/plain": [
+ "<Figure size 504x168 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "# Create a figure \n",
+ "plt.figure(figsize=(7,7/3))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "plt.plot(sites, rho[-1], linewidth=2, label='n=4' , color='C{}'.format(K-1))\n",
+ "\n",
+ "maxrho = max(rho[-1]) # maximum density needed to set the y-axis range\n",
+ "plt.ylim(0,1.1*maxrho)\n",
+ "\n",
+ "plt.xlabel(r'lattice site $i$', fontsize=10)\n",
+ "plt.ylabel(r'density $\\rho_{i}^{(K)}$', fontsize=10)\n",
+ "\n",
+ "# Set the title\n",
+ "#plt.title(r'Density profile, $\\alpha = $'+str(alpha), fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='best')\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The cell below plots density profiles for all orders up to `K`, the maximum order of the PSA. This can be useful to see how the subsequent orders improve the estimate of the local density."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 504x168 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "# Create a figure \n",
+ "plt.figure(figsize=(7,7/3))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "sites = [x + 1 for x in range(L)]\n",
+ "\n",
+ "for n in range(1,K+1):\n",
+ " plt.plot(sites, rho[n], label='n='+str(n), color='C{}'.format(n-1))\n",
+ "\n",
+ "maxrho = max([max(x) for x in rho]) # maximum density needed to set the y-axis range\n",
+ "plt.ylim(0,1.1*maxrho)\n",
+ "\n",
+ "plt.xlabel(r'lattice site $i$', fontsize=10)\n",
+ "plt.ylabel(r'density $\\rho_{i}^{(n)}$', fontsize=10)\n",
+ "\n",
+ "# Set the title\n",
+ "#plt.title(r'Density profile, $\\alpha = $'+str(alpha), fontsize=12)\n",
+ "\n",
+ "plt.legend(loc='best', ncol=2)\n",
+ "\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "plt.savefig('figure_tutorial1.pdf', dpi=300)\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we see, for this particular set of hopping rates and this value of $\\alpha$, the improvements are visible but not huge."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 4. Plot mean density and current vs $\\alpha$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The advantage of the PSA is that once the coefficients for given order `K` are computed, one can generate density and current for any value of $\\alpha$. First, we define a list of values of $\\alpha$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# define a list with values of alpha to be computed\n",
+ "\n",
+ "alpha_list = [round(0.05*x,2) for x in range(21)]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We then iterate over `alpha_list` and compute the mean density and current for each $\\alpha$ in `alpha_list`. To compute the mean density we use function `mean_density()` and to compute particle current we use function `current()`, which are defined as follows:\n",
+ "\n",
+ "- `mean_density()` takes the list `rho` of density profiles for each order and returns the list $[\\rho^{(0)},\\dots,\\rho^{(K)}]$, where $\\rho^{(k)}=\\sum_{i=1}^{L}\\rho_{i}^{(k)}/L$.\n",
+ "- `current()` takes the list `Jcoeff` and the value of $\\alpha$, and returns the list $[J^{(0)},\\ldots,J^{(K)}]$, where $J^{(k)}=\\sum_{n=0}^{k} J_{n}\\alpha^{n+1}$.\n",
+ "\n",
+ "Below, we iterate over `alpha_list` and append the mean density and current for each value of $\\alpha$ and for each order of the PSA to the lists `rho_alpha` and `J_alpha`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# define empty lists where values of rho and J will be saved\n",
+ "# for example, rho_alpha[n] will contain rho(alpha) for the order n,...\n",
+ "rho_alpha = [[] for k in range(K+1)]\n",
+ "J_alpha = [[] for k in range(K+1)]\n",
+ "\n",
+ "for alpha in alpha_list:\n",
+ "\n",
+ " rho = local_density(rhocoeff, alpha)\n",
+ " mean_rho = mean_density(rho)\n",
+ " J = current(Jcoeff, alpha)\n",
+ "\n",
+ " for k in range(K+1):\n",
+ " rho_alpha[k].append(mean_rho[k])\n",
+ " J_alpha[k].append(J[k])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, we plot $\\rho(\\alpha)$ and $J(\\alpha)$ using different colors and styles for each order."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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opLTMSNSHDkJ25qlu5LAIVJ/BqH5DUd36nXUub/matEvwDAwTkaNKqbuAzRhX314REadS6kGMUeFm4F0R2aGUutfz/AXvYwerB+bu8mn/trE2fjPq1ILoJ1//+vXdfDpObZfo++yzz+jXr5/fG25Yvwf9eryTyje9dtF9avKelJaW8uKLL7Jw4cKqLrJIWwjhFjPR4RZMNVxnN6OgnNmbjpJVVAlAy6hQHC4hNESXOG0MnPf7uKhN206EPH6qDZ58fcgb3/p0mGBt9/eqaL8e76S35MRF9/FXuz/J7XKRdzCd8qIiQHHzG39lxH13IxUluA/vQo7uh/ISVIfeqE59jRfFt4VF3yMuz5iX6om6az+UH6aE+Zq03wTmKKV+LSL7gXYY1Yt8IiLfYVRAqr7tnMlaRO7w9fhNSW2W6NuxYwe//vWvWbBgQR1HWb9q8p48/fTTPPzww4SFh58sq4nZpOjYPLJGCbvS6ebbXbks2X8cAeLDLdzcrwXdkiJr8i1p2ml0uz9bbdp9ZOTp7dJRWUnu/oM4yssxmUOITkqkZ98uuDYuhOPGwnPidsOhDGTLFtT/9UKZzZiiYpD+Q0GZUCnD/Jaoq/MpaYvIG0qpbOBtpVRvjKU6ZyulpgCbRWSfX6NrQHy9QvbX62u6HF1mZibXX3897733Hp06dapZ0BfgzRVxXanJe7JmzRrmfPopD//yUUpOFGE2m7DZbDz4oO89Btuzi/loczYF5U4UMLpzMyZ2SyQ0RE8Pa2x8vUL21+uDtd17c0VcV2ra7j/99FMee+wxCgsLMZlMmFFMHjMWt9NBiM1GUueOFO/djWxfjjgcqNBQVGI7VMuOuFc+A7lHkX3bUF37GueeXrcrrfk8BFZEPgc+94wg7w70A4YA9wFX+Dc8rSYuthxdYWEhEydO5Pnnn+fyyy+vx8gC52LvyfLlyympcJCWW8asV1+gXfNmPifswnIHn27NYdORYsC4BXJz3xa0j2t4yzxqDY9u92fzpt2f9PTTT2NVihtGjcbtdGCLiiKhUwdMJhO4XMian+BoFup3b2JK8sxSvuZW46q6Q9e6/laq1Hjeiog4ga2ef//1W0RanXvttdfYv38/zz33HM899xwACxYsICmpaS92EWmzkJwQTlyE9az1li/ELcKKtAK+3JFLhdON1ay4pnsiIzo2w9zAl+dUSiVi9KgdEhHHxfbXgpdu9+fnrKykNP84TrMZxE1UbBSx8bGowlwoK4XSEsg6BCYTHD4InqRtSh1R77Gqk/fvGrrU1FRZv359vZ1v165ddOtWuy5xLbDcImQXVhAXYSXMy9rh5/q5L96Xz+fbjcJ9vVpEMrVPC5qF++8+llJqg4ik+u2A3p1zJjAMqAAKMAogFQF/EZG0+ozlQnS712pD3C5Kco5RcDQHcbsxmUw0i40g3KKoPh9zV3YuXSuOo/oPQ0XF1HlcF2rzdbsciaYFsbziSvJKKimucHJJi0ifrq6ru7xDHJuyihnTpRl9WkXV+DhBZr2IzKq+QSkVgVHOWNMaPKfdTn5aOhXFJQCEhVpoFhmK2YSRsK2hEB4JEVGoMiemQUMCG7CHr8VVHgRmi0hBHcWjafUmITKUskoXSdGhPiXarUeLWbQvn/uHtMMWYsIWYuKXI9o3lmQNgIhsVEp9BDgwKhZmi8hjQJMdbKo1bOJygqMSlInS4jIKDmfhdjkxKUVcZCjhNgsqJAQioiA8CmUNzvnrvl5pt8BYlWsj8C4wXxpL/7rWJBSXO4i0haCUwmRSJCeeu27w+Qjw/e48DhVWsCKtgDFdjOXlG1PCruYnEXkVQCkVH+hgNM1XIm5w2I1k7XTgKq/geF4h5RV2AMJiYmgWbTPWwI6IhlBb0LdlX6d8PaWU+i0wFpgOvKaU+gR4R0QO1EWAwezkEo1aw3DsRAXZRRUkRIbSyocR3SKCW8CkjML5N/VtwcH8coZ3jKu7YIPDJKWUG+PD+d5ABxMsdLsPfuJygr3CSNYYy+kWF5ZwIq8QtwjKZKZZuzZExDe76M8y2K5LazLlSzxztbMBJxAHfKqUWujpPmsSbDYb+fn5xMfH6wbcQESEhmBSCqsP86UrHC6OlzsIUQpTZTE2m432cWFNZRrXrUAf4EalVCcRuTvQAQWabvcNhL0SThQgdjtlJiuF+UW47MbVtS0inPgOyYTYLr6GgIiQn5+PzYt964uv97T/H3A7kAe8DTwqIg6llAnjXleTSdpt2rQhMzMTvSRocHOLnF7RzC3kFisu9lNzi1DmcGN3ugHjKjsxJpL27dpe5JWNg1LKJiJZGOsDfHfG9orARRZYut0HIbfLuLJ2u0EEKivA6cTpclNW6cTpNtqw2WIlIi6WMoTjad5PgLDZbLRp06auoveZr1faCcANIpJRfaOIuJVSV/svrOBnsVjo0KHDxXfUAuaTNYf5wxc7+d99g+jdLtar17hFWJ5WwNc7cyl3KEJMIYy9JJ6xl8RjMTepimYveLrGdwKFQDLQEZgNrAxcWIGl231wEIcdyT6I+/Au2L8bDqXB0aMgbnIKy/hy7WG2HjCmYUa3aM6kP/yWQXdMw2T2bmpnMPM1aYeembCVUi+KyK9FxLcVMzStjm3JKKS4wsniHce8StoH88v4ZEs2hz2Le3RLimBqnxYkRVrrONLgIyL/p5SKA/oCzTDua28LbFRaUydlxUjaFtx7NkP6ATicAZVGey0stbMwvZLlK7fhdrmwhocz9rGHGPPLX2CLbDw1/31N2lcCvz5j24RzbNO0gKg+SOh3N3RnRLdExvZqccHXFFc6+WL7MVYfKgIgLiyEyb2b06dlo5lzXSOeqZ1LAx2H1rRVb9PiduH+4J9QcLzq+ZyQGBbvK2LN4o24HA6UUlx+121c8/sniW3VMlBh1xmvkrZS6j7gfqCjUmprtaeiaMJdZVpw+X7LUT5afZh/3ZWKNcREaIj5ggnb5Ta6wr/ZlUu5w02ISTGmSzPGXZLg02C1xkop9VdOlSreISKVAQ5JayJEBIrycB/ejRzYgemaGZjMZkyRsbibNYeKSg4168TCFbvYPP/bqsTef8r1TPztY7Tu1SPQ30Kd8fZK+wPge+B54DfVtheLyPFzv0TT6k+F3cUfvtjJkcIKvtqYxeSBFx8w9vXOXBbuywege/MIpvRuml3hF7AfGAzMALp5Zo2cTOLrgGU6kWv+JE47cvQgkrUPSgqQHxbB8Xzo0Av6XI6IsK/jUOZ//w67F78OQIjVyuDbb+HKR/8fzbt0DvB3UPe8StoiUoRRd/jmug1H02rGZjXzj9v7syWjkBsHnH+kZ/WuthGd4tieXcI13RPp3bLmZUwbKxF5o/pjpVQHoBfQG2NVv38qpe4TkfmBiE9rPMRegXvXGmTjckhMQtlsYLFBl56wfxcOh4utH85h0d9eJ2PdRgBCIyMZfu+djH74gUbZDX4+3naPrxCRoUqpYoyiUGDUmQBj6nZ0nUSnaRcwb+tRCssc3DS4HQD9k+Pon3zugicOl5ulB46zPbuE/xvW3ihdGGbhydEdApasG1qRDs9CIWnAVwBKqZbAN4BO2prPxO1GmUzIof24V85DVi8ChwMGDkON/xkqqR35LQ+yfHcZq666g+LcPAAiE+K54qH7GPHADCLiGn2Bo7N4e6U91PN/VN2Go2ne2Zl1gvv+vRGLWTGgYzM6JV14dKgILDtYQEG5k13HSunR3Ng/EEmzzO4i94Sd/FIHvdtEEtJAp5KJyFGl1AeBjkNrWKSkEPeBLcj6ZZBzDDIPnnqybSfoOYQdG/ey7M1fs/3b+VUVyVr37smI++5i8G03Yw0PD1D0gedrcZUpwDwRKVZKPQX0B54TkU11Ep2mnUf31tHcNaIDrePC6Hie+uE5xZVE20IIs5ixhpi4uV9LTAq6XSTB1wWHy01+iYPcE3ZKKl1V24+XOkiKDs6FCbwhIi8HOgYt+InbhTsnHdnwA2zfAJmZ4Pa0g4go1MArKLkkhdXzlrFsygPkpxszi0OsVvpPuY7h991NpyGDGlTPVF3xdcrXb0VkjlJqKDAOeAl4Cxjk98g0rRoR4eM1h7m8SwJt441P2U9d1/2c+5Y7XMzbk8fS/ccZ2akZN/RqDlB1dV2fRIR9OWUcL3FU3VcyK4iPspIYZSXKFvzFHk7WYrjYNk07k4jg3rYC+WkhHNgLJcWnnuzcAxkyjh1Zxfz0v0/Y9s1vcDudACR0SGbYPdMZcuetRCUmBCj64ORr0j55iTAReFNEvlRKPePfkDTtbG//kMafvtpF/+RYPvnFEMymsz9xu0X4Kb2Qr3flUlzpQgGVLne93zsus7sIs5hQSqGUwuESBIgJCyEx2kqzCMs54w9iuj6D5rXq7U0phXz9AWQdMp6MjEYNGceR2Pb89OV81l07o+petclspvc1Exh27530GDemUVQvqwu+Ju0spdQ/MRrxi0qpUKBh3pDTGpQpA9swZ81hbh+WfM6Etze3lE+35ZDlqWbWsVkYk3s3r7eFPRxON3kldo6dcFBmd9GzTSRRNqN5JSeEEWJWhDawud8Xqc+wqgbHGw+8CpiBt0XkhTOeHwl8iTHYDeBzEfm975FrgSD2Ctz7NiEr52Madg2mbikAmEZcjXvDSkp7D2f95gOsfvZtDm8+9evUqkc3Lpv+cwZOm0pMi+aBCr/B8DVpTwXGAy+JSKFSqgXwqP/D0po6u9PNFxuymDKwDUopYiOsfP/Y8LMSdm6Jnbnbj7HlqNHtFhcWwvU9m9O/dd1XM3OLUFDqILfYTmGp81T3t0lR6XAT5VkYKCK0wV4x+K0+g1LKDLyO8YE/E1inlPpKRHaesetyEWlS6xg0ZCeLoEjmHiQnHdm6Cfbtxu1wYuqWgr2sjC2Hy1i7cB87fvVWVfd3eFwsA26ZwpDpP6dd/776XrUPatI9bgOmKKWqv3aB/0LSmjoR4c5Za1m5L59Kh4tbhyYDnJawyx0u5u/JZ+mB4zjdgtWsGHtJAqO7NMNaD6OxRYSth4opd7irtsWFG93fcRGW01cWa6BO1mdQSk0HbsBYNCQEPN2evl0FDwT2i8hBz+s/AiZhLEiiNUCug9uQH74EE6g2xrRL+g/BJSHss7Rm3W0z2Tz3GypLSgCj+7vnVWO5bPrP6X3NBCyhDXcAZiD5mrS/xFjxZyOgKyFpdUIpxc1D2nP4eDk92sSc9pxbhFXphXzjuW8NMKhdDNd2TyQ2zFJnMdmdbnKL7TSPDiXEbNyrjgkPQZU7SYy2khBpbcylT7/AKK60gZq3+9bA4WqPMzn3ANbLlFJbgCPAr0Rkx5k7KKVmAjMB2rVrV8NwtJoQETiwE/fy74xCKC4XxMQiQ8ZzOKeCdZ99zfqPPuNEzrGq13QYlMrAaVNJ+dmNRCclBjD6xsHXpN1GRMbXSSRak3Yor4z0vFKGdzUa9cS+LRnTI4lQy+ldywpYc6iI4kpXnd+3drmN7u9jxXaKyoxuvRCTonmMcYXQPiGsUVxRe8Ef7f5cb5Sc8Xgj0F5ESpRSV2F8WOhy1otEZgGzAFJTU888huZnIm4kcz/uH740lsHMzTaeUIrsqJZsPG5h3cS7yd1/ar51UpdODPr5zxhwyxSSOncKUOSNk69Je5VSqpdeok/zpwPHSrj25RWEmBULfj2C5jHGzeCTCTurqILQEBMJEVaUUkzp3ZzcUked3bcuLndyrNhOfokdl6f3WwFxERbCrKc+RDSRhA3+afeZQPWC8G0wrqariMiJal9/p5R6QymVICJ5tTivVkNir8C96UdkxTxjGUyX0bNVQCgbyyNZv3Efh7cuq9o/unkSqTfdyMBpU2mf2l/fp64jvibtocAdSqk0jG4yhVHGtLffI9OajI6JEQzq1IwIW8hZXcxrDhXy/oaj9GoZyT2Djb/57eLCaFeHo8Iz8ssprjD+QEWEmkmKshIfZcHSQCuX+cFQYLpS6iA1b/frgC6e+uVZwE3ALdV38AxszRERUUoNxJiZku+Pb0DznrsgB1kyF9m0ylisAyitcLCp0MSGjBPs37SjqkqZLTqa/jdey4BbpnDJyGGYQ3xNKZqvfH2HJ9RJFFqTIiLMXZ/FyG5JNIs0rp7fnJ5yVlc4QNekCGwWE83CLbhF/Hp163KLUaWs2E77eBuRnilaLWJCibK5SIy2Em5tsCO//anW7V5EnEqpBzHqlJuBd0Vkh1LqXs/zbwGTgfuUUk6gHLhJTmYHrd7I6kXI4q+xO11szyxmXbadndsP4HJ4bhGFhtLr6vEMvGUKPa8ai8VmC3DETYtPSVtEMuoqEK3p+MeC/fxt3l6u6tOS1+/oDxhd4S63sDqjkPVZJ3hwSDvMJkWMzcJz4zoTdo6EXhMiwolyJ7nFdvJLHLg9KSG32F6VtBOirCToKvvVHQKmAR1F5PdKqXZAC8Cnvwci8h3w3Rnb3qr29WvAa7UPV/OWu7wYWf4tlJZgvv5uXE4nu11xrF1zhC27s6goqwBAmUx0u3IUA6dNpe91VxMWE3ORI3sGrblcqGpX3w1tkZxg5GvtccU5Gq+IrK2T6LRG6frU1nzwUwZX9Eiq6mbberSEL3ccI6fEDsDmI8WktDEWj/NXwj5SUEF2USWVzlMXb1E2M4lRVuL1OtoX8gbgBq4Afg8UA58BAwIZlFYzVXOrD+/CvW8LsvB7Dh2vYMPinaz/9KvTRn63H9CfgdOmkvqzG4lp0ZzKw4ep2LQF86WXYG3ZAoCC+QvI/OMLRA0cQPJLLwLgKi5m4yU9MEVEkLJ/V9Xx9k+fQenmzXR8/e9EXz4EgLIdOyndspWIPr0J73Hu0sTaKb52j+vGq/ns4LESFmzL4d7RxijStvHh/PjUKEJDzKQdL2fu9hwO5JcDkBBh4druSfRrXftLXadLUOrU/O4Kh5tKp2ANUSREWkiMshIequ/BeWGQiPRXSm0CEJECpZT+lNPAiMuFe9MyZOMyVMcOFBwrYN2S9az5ZjvZOYXAegASO3dk4C1T6ZrchoiCAlo+MLPqajnzhZc4/vlcOrzyMgk/m+I5MFTs209Y10tPnczsaVdn3N2wHzmCI+cYpmqrdBUuXkLW83+mxQP3ViVtV3ExubM/ImrIYCJ696qT96Oh8vUvlm68mk9KK53c8OoqisocdG0VxchuSQAUljv5audRNh8xKplFWs2M75rAsA5xhNSgLrfd4SQ9K599GcfYfiCbXenHyCsoRbmdOBxOiksrKC6rpKS0grJyOyXlxnTj2KgwYqLCiI0MIyYq3Pjasy0hLopeXVrRp2tbWiQ06SXjHZ6KZgKglErE+PCuNQDisCMbV+BeMpeKA3vZfDCftXku9m0/WNXTFRETTc+B/Rn5h9+RPCAFpRRbBl5O4eHDxE0cT9ilRkKO6NUTR04O5mrd41FDBtNj8XysbVpXbTOF2Ug9knFWV3i3b7/EcSwXS0J81bbwrpcSP3Uykf37V20rWbeBw88+R0RqCt2/nntq+8ZNRPTpjWrCdcl9Tdp+abxe1CCexqnFCEqA+0Rki6/n0QIvIjSE+8d0Yl92CX3bxVJU4eD73XmsTC/ELWAxK67o1IwrL4n3qhu8otLBpl2H2bTrEPsyjnHgcC77D+Vy6OhxXC7f80h+YSn5haUX3a9FQjR9u7alT9c29Lm0Df26taV9q/imcn/u78BcIEkp9UeMAWNPBTYk7UJEBDm0F/cPX+HetpE9ezJYu/cYWw7mYXca7SQkNJTe115F6jXjcTz6GCH795Cc0q/qdzph6o24SsswhZ2aqdHi3hm0uHfGaecKiY4mpPvpH2rP1y5MFguhrVudti127JXEjr3y9GPGNyPhpqlVHxYAHPnH2TVxEta2ben142JMYU1zAJyvSftk421e08brZQ3iNGCE50p+AkYhBb38ZwNQbnfxyry9DL00gWGXGoVSZozsSLnDzaJ9RtlRu0tQwJD2sUzslnDBSmaZOQWs2ZrGmi1prNmaxubdmdg9o1irU0rRPDGWNi3iadc6ga7JSbRvGUNcVBhR4TYiwkOJCg8lMsJGZHgokWGhCEJRcTlFxeUUlpRTVFxG4cnHxeVk5RSydU8mW/dmkp13gnkrdjBvxakCXbFRYVw5pDuTx/Vn7JDu2ELrriJbIInIbKXUBmA0xnSv60Rk10VepgWA2+VE1i1BfvyG3G07WLM7m9W7cygstVft0zzUQs9uXZi4dB7hsbEAHFi9GmurlrgrKzF7uq5b/+qRQHwLAET06U2Hv7102jZHbi6h7dthu6TLaQn7xMpVRA4cgMnSONvfmXwdPV698ULNGu9FaxCLSPUVhFZjFGLQGoBP1x5m1tKDzN+WzaLfjCDEbCxRufpQEfP3GnM++7SM5OruSbSKPrv2cMaRfOat2MGy9ftYszWNrJzC055XSnFphxYM6JVMj04t6dwukZi4GAgNp1WziKo1qr29Ak5sFkViswvfP3e73aRn5bNp92G27M5ky+5MNu8+zLHjxcyZv4E58zcQHWnjmpG9mTw2hdGDu2Lx0+C5QPMMPm0jIruB3YGORzs3d3EhsmgOFSsXs2njflbvzmb/0apaNcR3aM+QO6aRcu0EDl99HeHNEwiLPnV13On1VwMRtk/Cu15Kr1XLcBWd+r7K9+1nz+SbCE1uT68VPzSJbnOvkrZS6nwfuSYopSaIyF99OKe3NYhPugtjpSEtSLncUjXY66bL2rE+rYDbhyWTU2Kntae62dAOsaQXlDOqUzM6NDvV3WZ3OFm16QDzVuxg/oqd7E7LPu3Y0ZE2BvZKpl/3ZC7t1IbWbVsSagulZUwoyYlhVecH6myNapPJRMe2iXRsm8iNVxr33USE9Kx8Pl+0iU/nb2Dz7kxmf7OW2d+spVlMOJOu6MuUcSkMT+2CuQEXZfEUOvkCSAl0LNq5uSorODBzMqs2pbPpQB6Vnu5vS6iV9kro2bUzYzf8hMlk/B4mbNtESFxsACOuOWUynRa7My8f2yVdiExNOS1hO3JzsSQ2zjrnypvaBUqppz1fXooxUvwrz+NrgGUicrfXJ1RqCjDu5GuUUrcCA0XkF+fYdxTGiPWhInJWZaQzFg5IycjQ08jrk8Pl5u2lB/liQxZfPDy0qsRncaWTv/6YQYndybNjO59VoOTIsULmr9jJvJU7WLJ6NyVlp9agiIqwMXpwV8Zc1pUBPTvQLDGO/BInZfZT96vDLCZaxoZW1QAPBvsycvh0/kbmzN/AroOnPngkt47n8RnjuWXiQEJCanYVoJTaICKp/oq1Bud/HfiPiKwLVAznk5qaKuvXrw90GPXK7XLBxh8oadONtR99zopZ/yF7996q5zteNpAhd95Kv+uupuBf7xA7dgyRKf0vcMSGTURwl1dgDjc+xBf/tIY9N02j5S/uD2gXf21cqM17daUtIs96DrQA6C8ixZ7HzwBzfIznojWIPcfuDbwNTDhXwvbEpRcOCCAFfLXpCHuzS1i0PYdr+hsDTCKtZmLDjF+t4+UOwq1msvNOMHfRJj5dsJFVmw6cdpwenVsybmgPxl3encv6dKrqWj5wrIzDx417cWaTIiHKQlKUlYhQ77u/60uX9s15fOYEHp85gR37j/Dp/I18PG89aZl53PPMbP78zgKevGcCU8enNsQr71HAPUqpDKAUXb44IMRhx521l91/fIZlC9ax/cgJXE6j3G5UfDM6VJTSf+QwBn/zedVrIh5/LFDh1hulVFXCBihesxax2yHI/kb4i1dX2lU7K7Ub6CMilZ7HocAWEenqwzFCgL0Y98WzMGoS31J9CT5P0ZYlwG1n3N8+r6b4iTsQck9UEBEaUjW/eXNGATuyizla7ubmfi2qusOLKpxUlJbz9dItfLpgI8s37MPt6ca2hVoYM7gr44b2YOzl3WnbIo6SShe5xXZiwkKqCp0UlzvJKqhosGtUu1xuPv5+PX+c9R0HDxtrXnTt0IIn772KG8b0requvJhAXml77mkP4xzVz4KhQmJTaPfuI+mc2LmB1XO+ZtW3yzmWlVv1XI8JVzJs5nR6XjUWV3Y2oXqpUgBKN2/Bdsklp66+16xFnM6qgi7B7kJt3tek/SQwFWMEuQDXAx+LyPM+BnQV8AqnahD/sXoNYqXU28CNnPpD4bzYH62m0HgD7euNR3jik23cNqw9j07syv68Mr7emcv+/DIABrWN4bqucXyxeDOfLtjIkjV7qqZhWS0hjB3SjRvH9Wfi8F5ERdiodLrJK7aTe8JOucPYLyYshO6tIwP2PdYFp9PF7G/W8qdZ33Po6HEAenZpxVP3TuTaUb0v2msQBN3jG0QkKO9pN+Z2707fy64XnmHJl8vYfay4auxGTFICnU3CZbdPo+cLfwhwlMFPnE62XzGWin376fT2P2k2MfiX0PBb0vYcrD/GJ28w7mdvqmV8ftGYG2+w2JRRwA2vrGJY10QG9GjO7lwjWYeZFS2dxWzbsJOvl2yhrMLo0g4JMXHFwK5MHtefa0b1JjbKmEpSWObgSEElReWnpm5ZzIqESCuJ0Ub3d2Nkdzh578vVvPD2vKpR8f26teXVJ37GgJ7J531dECRtfU+7nrjtdspXLmL1P/7B8h82kV1gtDEF9Bw/mmH3z6THhCsxmUwoL3tqmjp3ZSXZb/yT4998S/fvvsIUGjxjYc7Hr0k7WDW2xhsMDuSUsD7tOD8bbHS5HS6s4D+rD5FdbtxHc5SUYD+UwepV28g4cmrYwdD+nbl54gAmXdGH+NhIY6CInBrdfbSwkvS88qo1qhOjrcSGhzS47u+aqqh08O+5q/jzO/PJyS9m7ce/oWeX1ufdPwiS9k6MQajpBNk97cbS7t2FeaS/+gKL3/2MbVkF2D09VNExUXRrmcjwh39Bp5l3BTjKhk1crqoR5m67nWP/fo+k6bdhsgZfUc9aD0TTmp7c4kquemk5brfQKj6CXfllbDlagtPpJHPPQY7t3s+OnelVZRDbtIjj51cP4tZrB9GxrTHVotLhJvN4BbnFdppFWGifYNxfSoiyoKDJrlFtC7Vw300juOO6y1iyZs8FE3aQCP7+xAbKvmcrG1/8A8vn/cSBo0VV27v07caIXz5M36k3EBKESaUhqj4lLPNPL5Lzz39Rsn49nf/11gVeFXx00taqVF82LzEqlGv6t+JAXhn/3XiUiuJi9m3cwcGteygpNRb3CLWGcO2oPtx+3WBGDrgUs9mEyy0cO1FJbrGDE9W6v0/vCjfRIjb4u6jqWpjNysQRDWIxhNvPs/339RpFI5K/6FsWPvIb1u/JosRutA1baAjd2rRk2EMP0u3+mU2iUEigNJt0DYXzF9Di3pmBDsVnvi7NGYoxQCy5+mtFRDfeBu7HXcd4/uvdvHxLH3q0MRYDeGhcZ+59ayk/LP2RrLTMqn37dWvLHdcNYcr4FOKiT63Wk3OikvTc8qo1qpWCeE/3d0yY/nzYgFUvzm4DrgZ0GdMaSF+3gaV/f4v1H36Ky2XcZmrZohkj7r+LwQ8/jC2ycQ3CDFaR/frSc9mS00qflm7ZSnivnkE/VsDXv6RfAkXABqDyIvtqDcjyPXnsOVrMM1/u4q83XMK/567i33NXkZ1nlAwMs1mYOi6VGVOGktKjPWDUGS+tdFUNHAuzmHHL6WtUh5ibxn3qxkxEXq7+WCn1EqcKLGkXUZmTxcp7ZrJy5RayPO1JmUx0aZXAsNumkfLsbzHrLvB6Vz1hl2zazO5JNxI9cjid35kV1HXMfU3abURkfJ1EotWrzONllFa6uLSlUXf73tEdWbB+L1uWraTru7Or5lRf2qE5MyYP45arBxIXHY7TJeQUVZJbbKe4wkVMeAjdWxlXB1E2M/3aR2FrJHW3tfMKBzoGOohgV5yRxrK//pUf3/uME4UlAIRFRTL03rsYcf/dJCS3D3CE2kmu4mJMEeGEtm0b1AkbfE/aq5RSvURkW51Eo9WL5Xtyufvt9XRqHsl/Z/Tny4WbePOjH9l54CgAIWYT14/tx8wpQxmW0gWAwjIne7NLOV7qqFrX3qTAajZV3QtXSumE3QgppbbhWY4Xo7ZCIvBc4CIKXm63m/Q3/86iV99iW0YuDrsDgITocAZfnsrId94msmWLAEepnSlm+DB6LJyHJSn465X7mrSHAncopdIwuseDZuqH5r2YKCvYK9ixbi/d5n5JaVkFYKwZPWPyMO688XJaJJxaASi7qJK03PKqx9FhISRFWWkWaamzRTq0oHJ1ta+dQI6InL0+ahPmdjrZ8eY/WPzqW+z2fPgF6DliIKN/9TBdJ14VdKV3tdOFtjk1i8NdUUHGb56k5f97EFvHDgGM6my+Jm099aOBcbjcfLL6MN9vPcpjk7oz67vNLFy0jkN70qr2GdgrmftvHsn1Y/qiTCbyih3kFFVWLcgRH2Ehu6jSKH4SZSXUEtwDNTS/+z3wkIgUAiil4pRSL4vInYENK/DKMg/x48x7WLNuK9l5xQCEmBQ92yYx4e9/pv211wc4Qq0mjvz1VfI+nkPZjl10X/BtUH3g8nU97YDXGtZ843ILr87bQ8a+g8z/9BtKjhcCRhf4DWNT+MW0kfTv3o7CMidpeZUUlDoQwBqiSIq2opTCEmKib7voC55Ha9R6n0zYACJSoJTqF8B4Aq5o+xZ+eOI3LP1uFRUu485BbFQYI26axLBnnyWyZcsAR6jVRsuHHqQiLY3Wv3o4qBI21GCetlIqDuiCMfUDABFZ5s+gtJoTERbvOMaQLvEs3XWUv/3vB/as2oK93OgCj4uN5J6pw7h36jBioiM4WljJhvQTOF2nKuPFhBvd35rmYVJKxYlIAYBSqhlNtMZD+n/fYfk/Z7Fm7e6qNpNoszB62iSGvv4GIaG2ixxBawjMERFnFV1x2+1BUT3N13nadwMPYSynuRkYDPwEXOH3yLQa+dUHW/h46U5sxdkc3Z+O222UQ+zUoSWP3TGan41PIdRqjI4sKnOQXWTUCQ+zmkiMMrq/rSG6+1s7zcsYg1A/xRiQNhX4Y2BDqj8iwv7lq/hy6i3szymo2t6zW1tGP/wgl951j9crtmkNU+HiJRx68ndc8sH7Ab/H7eun5YeAAcBqERmllOoKPOv/sDRviQhOt2ACvlu2nQVfzCN/v6cQioJhg7vzxPQx9OzWntxiB2n5drq2NJJ2dFgIreNCaRZhCco1qrXgICLvKaXWY3w4V8ANIrIzwGHVOXtxMZs/+4LFb7xDxrqNgDF0vnfn1lzzz1dpdcXYwAao1QsRIWfWO1RmHCL/87m0/tUjAY3H16RdISIVnuk9oSKyWyl1aZ1Epl3UpowCnvhoM668o2Tt2Vu1ZnOozcp14wbwyM9HEhkdQ16Jg305xuhvpcDpFkJMxhStdvFhFzqFpgHgSdKNPlEDVJwoZNHPb+PH75dT7DSqlkUmxDP0jlsYesNVJFx2eYAj1OqTUorO784i7+M5JE0/X0Xf+uNr0s5USsUCXwALlVIFwBF/B6Vd3OHsAv72zvf8+L2xuDtA+1bx3H/zCCZPGEhOiZtSh5vSE0b3d0SoUaUsIdJCiJ6mpWlnKco8xI9/fokf/zuH0hNG5dbYUAvjX36BIdOnYQ0Pv8gRtMbKHBFB8zvvqHosTiduux1zAH4nfB09fnL+wjNKqaVADDDP71FpZzEGmOXw1co9FKYd4PNFm3F5lu/r0LE1j9w2mulXp2I2m7A73WQUnDDWqPbcp26sa1RrWm0d/nwO3z3yBNsOH8PpqQTYvnsnLh/cj8teew1LmE7W2inO4wUcuO8BTOERdH7nn/Veq9zXgWgKmAZ0FJHfK6XaAX2BtXUQm+ZRaXfyh9krePU/i3GcMAbCmM0mrhvTj6nXXE7r1i0wmxUmzxW0NcREzzaRROr71Jp2Xulff8n8Z//I5g27q8q99Rzch7FPPUbnCRP14DLtnJxFRZRu2YoKsWDPzCS0Xbt6Pb+v3eNvAG6MASm/B4qBzzAGp2l+VOlw8d2mwyxeuY05X63iRKGncIPVwoQrU5l+3TBiY4250y6BMLMJh0uwhhhJOsrWJGfkaEFMKTUeeBVjPNfbIvLCGc8rz/NXAWXAHSKy0Z8xOJ1ONj7yEEs/+Zq0nEIAzCZFj3bNGffUr+h0V8NbqlGrX7YOyXT59ztY27UltHWrej+/r3/ZB4lIf6XUJqgqshD4iWuNzNrdWVz/+McUHM5APMv3xSXE8rNrhzBhRH+iwo25oFZP93dStJUwq+7+1oKXUsoMvA5cCWQC65RSX50xCn0CRg2ILsAg4E3P/7XmKC9n4x9+y4JZH5LlqVwWajEzdMJwxjz/R+K69/THabQmIuqy038txe2ut25yX5O2w9P4BEAplYhx5a3V0vGSShat3cvL7y1h65Z9VdtbJ7fmkdtHM/OaFMwmE5sPFRMZaq5ao1p3f2sNxEBgv4gcBFBKfQRM4vQR6ZOA90REgNVKqVilVEsROXr24bxTdiSLH+69h1XL1pNXVAZAuMXM4D5dGPfef4jp1r3G35CmAeR/Npfsf71D108/wlwP66H7mrT/DswFmiul/ghMAZ7ye1RNSEWlgxuf/YLlyzfiKDGuAExmE737deOWSZczoGs7UjpEE2I2PsX1bRelE7XWELUGDld7nMnZV9Hn2qc14HPSdrvdfPf0H1n0p5eo8AwuS4wNZ/TN13DZn/5MaGycr4fUtLO47XaOvPoPKvbtJ//zL0i67ed1fk5fR4/PVkptAEZ7Nl0rIrv9H1bjJiIcyS3i7TkreOezFeQWGGvtWmw2Ro7sz63XXk6bxBhCQ0wkRp2+tqtO2FoDda5fXKnBPiilZgIzAdqdZxCQyWTiwJr1VLiFRJuFcbdfz+C/v0aIVZcZ1fzHZLXS5d9vc2LlKhJvnVYv5/R19Hgq8CSQ7HntPUop9NKc3vvLnLX87b2lFB3Jqiox2q1za7qn9OSOqwcRFWYlPtJKYrSVaJse/a01GplA22qP23B2jQdv9kFEZgGzAFJTU89K6idd9/wzjLn/Li69+ipCQvTATK1u2Dp1xNapY72dz9ff5NnAo8A29L1sr9kdTj5ftIk3PvyRddvSq7ZfN7ovD04bxZC+HTmUX0G41azXqNYaq3VAF6VUByALuAm45Yx9vgIe9NzvHgQU1eZ+dvuUfpDSpBcj0+qZIy+P9Ecfp+3TT2JLTq6Tc/iatHNF5Ks6iaQRWrLlEI++No/0XfsoKzXKiEZG2Ejudgn33TyKKZd1ICrM+BG0T9DlRLXGS0ScSqkHgfkYU77eFZEdSql7Pc+/BXyHMd1rP8aUr+mBilfTaiLrxZconDcfV1ERXT//pE7O4WvSflop9TawGKg8uVFEPvdrVA2YiPDZjzt55X9L2bhxD8ZAWEhum8QNEy5j7Ig+tEmIJCnKSqRNT9PSmg4R+Q4jMVff9la1rwV4oL7j0jR/afPbJwBo9fBDdXYOX5P2dKArYOFU97gATT5pZ+ae4IFX57N69VZO5BtVy5RStOjQnuuvGsxd4/vQPMZGXITu/tY0TWuMQqKjSf7LCxffsTbn8HH/PiLSq04iaaBWbDvEn99bwg/LtuCwOwAIiwhj/JWpPH77KNolxRFmNes1qjVN05qYoh+XET30cpTZf72qvibt1Uqp7k1hLd0LKSiu4P/eXMTiHzeRfySnantUQjzDhvXnlQfG0DY+IoARapqmaYGU8eTvOPbuf2j77O9oMfNuvx3X16Q9FLhdKZWGcU9bYdyKahJTvtKz8nj705W8M3cVhUXG0n0hVgv9U7tzx3VDuGZwZ5pFWjHpaVqapmlNWsyIYeR99AmmMP8OMvY1aY/369kbgJIKO798awnzl27i2OEjVQPLoprF0Te1J3+aMZo+HZphMevub03TNM0QO/ZKeq9dhSW+mV+P62tFtAy/nj2I7c04xlufrOCjb9dSUOSpWGYxM2VsCndPHsqAXslVpUU1TdM07UzVE7aI+KVYli4TVE3+iTL+3+uLWfLjJgpzjlVtj46LoVufbrz8wFhSOicFMEJN0zStoSlcuIjMP77AJR/+D2vLFrU6lk7awOKNB/nHxyv4YfkWKsuN6echlhDGD+/DHddfxthBXbCE6DnVmqZpmu9yZ39I+Z695LzzLm2feqJWxwpI0lZKjcdY7N4MvC0iL5zxvPI8fxVGZaQ7RGSjP2M4cLSA+1+Zx7q1OygvLKzaHpPQjL4p3Xn5vivp0T7en6fUNE3TmqD2z/+RqMuH0PzOO2p9rHpP2p71uF8HrsRYIGCdUuqrM6aRTQC6eP4NAt7k7GX8fFZpdzDr2028/9Uadmzbh9tl1IexhFoZOqQnD/5sGFcN6lLb02iapmlaFWvLFrSYcZdfjhWIK+2BwH4ROQjgWRxgElA9aU8C3vOUNVytlIpVSrWs6eIBOw8cZdqfvmLfzn24Kiqqtrds35rLBvXk5XuvoEWcnletaZqm1S1XSQkF331PwtQpNXp9IJL2uRa6P/Mq+lz7tAZqlLRvf/zf7N5nrPAXERPFuCv688gtw0jpXLsBAZqmaZrmLXE62TP1FuIn31Dj0eSBSNreLHTvzT4opWYCMwHatWt33hPOnDKMT37YyeWX9eapmwbotXU1TdO0eqdCQuj62SeYwmw1PkYgspc3C917sw8iMguYBZCamnpWUj9pxpRhzJgyrKbxapqmaZpf1CZhAwSiOsg6oItSqoNSygrcBJy5RvdXwG3KMBgoqun9bE3TNE1rLOr9SltEnEqpB4H5GFO+3hWRHUqpez3Pv4Wx5u5VwH6MKV/T6ztOTdM0TQs2Abm5KyLfYSTm6tveqva1AA/Ud1yapmmaFszUyQUwGjqlVC5wodroCUBePYUTzDFAcMShY/A+hvYiklgfwTQ0ut37JBji0DF4F8N523yjSdoXo5RaLyKpTT2GYIlDxxA8MTRmwfD+BkMMwRKHjqH2MehlqjRN0zStgdBJW9M0TdMaiKaUtGcFOgCCIwYIjjh0DIZgiKExC4b3NxhigOCIQ8dgqHEMTeaetqZpmqY1dE3pSlvTNE3TGrRGl7SVUuOVUnuUUvuVUr85x/NKKfV3z/NblVL9AxDDNM+5tyqlViml+tR3DNX2G6CUcimlJgciBqXUSKXUZqXUDqXUj/6OwZs4lFIxSqmvlVJbPHH4tZiPUupdpdQxpdT28zxf57+TjZ1u997FUG0/3e4barsXkUbzD6PC2gGgI2AFtgDdz9jnKuB7jEVJBgNrAhDDECDO8/WEQMRQbb8lGIVuJgfgfYjFWJK1nedxUoB+J54AXvR8nQgcB6x+jGE40B/Yfp7n6/R3srH/0+3e+xiq7afbfQNt943tSrtqrW4RsQMn1+qurmqtbhFZDcQqpVrWZwwiskpECjwPV2MsiOJP3rwPAL8APgOO+fn83sZwC/C5iBwCEJFAxSFAlFJKAZEYjdfprwBEZJnnmOdT17+TjZ1u917G4KHbvaFBtvvGlrTPtw63r/vUdQzV3YXxacufLhqDUqo1cD3wFnXDm/fhEiBOKfWDUmqDUuq2AMXxGtANYyW5bcBDIuKug1jOp65/Jxs73e69jEG3+9M0yHbf2BaW9tta3XUcg7GjUqMwGu9QP57f2xheAX4tIi5Vg4XY/RRDCJACjAbCgJ+UUqtFZG89xzEO2AxcAXQCFiqllovICT/GcSF1/TvZ2Ol2730Mr6Db/UkNst03tqTtt7W66zgGlFK9gbeBCSKS78fzextDKvCRp+EmAFcppZwi8kU9xpAJ5IlIKVCqlFoG9AH82Xi9iWM68IIYN5r2K6XSgK7AWj/GcSF1/TvZ2Ol2730Mut2f0jDbvb8HAATyH8aHkINAB04NPuhxxj4TOf3m/9oAxNAOY9nRIYF6H87Y/z/4f0CKN+9DN2CxZ99wYDvQMwBxvAk84/m6OZAFJPg5jmTOPyClTn8nG/s/3e69j+GM/XW7b4DtvlFdaUsQrNXtZQy/A+KBNzyfeJ3ixwL2XsZQp7yJQUR2KaXmAVsBN/C2iJxzekRdxgE8B/xHKbUNowH9WkT8tgqQUupDYCSQoJTKBJ4GLNXOr9ePrwXd7n2KoU7pdn9KXbV7XRFN0zRN0xqIxjZ6XNM0TdMaLZ20NU3TNK2B0Elb0zRN0xoInbQ1TdM0rYHQSVvTNE3TGgidtDVN0zStgdBJW9M0TdMaiEZVXEWrW0qpHsCrGJWd3geSMFapWRfQwDRNqzO63QcXXVxF84pSygZsBKZglAfcDWwQkRsCGpimaXVGt/vgo6+0NW+NATaJyA4ApZQVeDmwIWmaVsd0uw8y+p625q1+GJ+4UUq1AkpEZGVgQ9I0rY7pdh9kdNLWvFWJsXQcwPMYK+domta46XYfZHTS1rz1ATBcKbUHY5m7n5RSrwQ2JE3T6phu90FGD0TTNE3TtAZCX2lrmqZpWgOhk7amaZqmNRA6aWuapmlaA6GTtqZpmqY1EDppa5qmaVoDoZO2pmmapjUQOmlrmqZpWgOhk7amaZqmNRD/H2wYibvJINk6AAAAAElFTkSuQmCC",
+ "text/plain": [
+ "<Figure size 504x168 with 2 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib as mpl\n",
+ "\n",
+ "# Choose a colormap (you can change it to your preferred one)\n",
+ "color_map_density = mpl.colormaps['Blues']\n",
+ "color_map_current = mpl.colormaps['Reds']\n",
+ "\n",
+ "# Create a new figure and axes for subfigure 1\n",
+ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(7, 7/3))\n",
+ "\n",
+ "# Plot the data\n",
+ "\n",
+ "# Define a list of linestyles\n",
+ "linestyles = ['-', '--', '-.',':']\n",
+ "\n",
+ "#### PLOT DENSITY\n",
+ "for n in range(1,K+1):\n",
+ "\n",
+ " line_color = color_map_density(n/K)\n",
+ " \n",
+ " # Cycle through the linestyles list\n",
+ " line_style = linestyles[n % len(linestyles)]\n",
+ "\n",
+ " ax1.plot(alpha_list, rho_alpha[n], linewidth=2, label='n=' + str(n),color=line_color, linestyle = line_style)\n",
+ " \n",
+ "# Set the x and y axis labels\n",
+ "ax1.set_xlabel(r'$\\alpha$', fontsize=10)\n",
+ "ax1.set_ylabel(r'mean density $\\rho^{(n)}$', fontsize=10)\n",
+ "ax1.text(0.05,0.85,'(a)',fontsize=10,transform=ax1.transAxes)\n",
+ "\n",
+ "# Add a legend\n",
+ "ax1.legend(loc='upper center', fontsize=10,ncol=2)\n",
+ "\n",
+ "#### PLOT CURRENT\n",
+ "for n in range(1,K+1):\n",
+ "\n",
+ " line_color = color_map_current(n/K)\n",
+ " \n",
+ " # Cycle through the linestyles list\n",
+ " line_style = linestyles[n % len(linestyles)]\n",
+ "\n",
+ " #if n != 0:\n",
+ " ax2.plot(alpha_list, J_alpha[n], linewidth=2, label='n=' + str(n),\n",
+ " color=line_color, linestyle=line_style)\n",
+ " \n",
+ "# Set the x and y axis labels\n",
+ "ax2.set_xlabel(r'$\\alpha$', fontsize=10)\n",
+ "ax2.set_ylabel(r'current $J^{(n)}$', fontsize=10)\n",
+ "ax2.text(0.05,0.85,'(b)',fontsize=10,transform=ax2.transAxes)\n",
+ "\n",
+ "# Adjust the plot layout\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Add a legend\n",
+ "ax2.legend(loc='upper center',fontsize=10, ncol=2)\n",
+ "\n",
+ "plt.savefig('figure_tutorial2.pdf', dpi=300)\n",
+ "\n",
+ "# Show the plot\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plotting density and current vs $\\alpha$ is useful for estimating values of $\\alpha$ for which the PSA of given order $K$ is no longer a good approximation. As $\\alpha$ is increased, the last term in the PSA begins to dominate, leading to wrong values of density and current. We know that the bounds are $0\\leq \\rho_i\\leq 1$ for the density, and $0\\leq J\\leq \\alpha$ for the current, so any value outside those bounds indicates that $\\alpha$ is too big. \n",
+ "\n",
+ "We also expect the density and current to be non-decreasing in $\\alpha$. Their values may eventually saturate when the slowest hopping rate becomes rate-limiting, but we do not expect them to deacrease in $\\alpha$. This can be easily checked by computing the first derivative with respect to $\\alpha$. We expect the PSA to fail for $\\alpha$ for which the first derivative of mean density or current becomes negative. \n",
+ "\n",
+ "Below, we find the smallest $\\alpha$ in `alpha_list` for which any of the conditions above is not fulfilled. This value can be taken as an approximate $\\alpha$ at which the PSA at this particular order is no longer realiable. In practice, it is best to consider $\\alpha$ that is much smaller than this value. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def derivative(a, x):\n",
+ " result = 0\n",
+ " n = 0\n",
+ " for an in a:\n",
+ " n += 1\n",
+ " result += an * n * x**(n-1)\n",
+ " return result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Derivative of the particle current is greater than 1 for alpha = 0.75\n",
+ "Derivative of the mean density is less than 0 for alpha = 0.8\n",
+ "Particle current is greater than alpha for alpha = 0.95\n"
+ ]
+ }
+ ],
+ "source": [
+ "alpha_found1 = False\n",
+ "alpha_found2 = False\n",
+ "alpha_found3 = False\n",
+ "alpha_found4 = False\n",
+ "alpha_found5 = False\n",
+ "alpha_found6 = False\n",
+ "alpha_found7 = False\n",
+ "\n",
+ "for alpha in alpha_list:\n",
+ " \n",
+ " # current\n",
+ " J = current(Jcoeff, alpha)[-1]\n",
+ " \n",
+ " # derivative of the current\n",
+ " dJ = derivative(Jcoeff, alpha)\n",
+ " \n",
+ " # mean density\n",
+ " rho = local_density(rhocoeff, alpha)\n",
+ " mean_rho = mean_density(rho)[-1]\n",
+ " \n",
+ " # derivative of the mean density\n",
+ " mean_rhocoeff = []\n",
+ " for order in range(1,K+1):\n",
+ " rhocoeff_sum = 0\n",
+ " for site in range(L):\n",
+ " rhocoeff_sum += rhocoeff[site][order]\n",
+ " mean_rhocoeff.append(rhocoeff_sum/L)\n",
+ " dmean_rho = derivative(mean_rhocoeff, alpha)\n",
+ "\n",
+ " if (mean_rho < 0) and (alpha_found1 == False):\n",
+ " alpha_found1 = True\n",
+ " print('Mean density is less than 0 for alpha =',alpha)\n",
+ " \n",
+ " if (mean_rho > 1) and (alpha_found2 == False):\n",
+ " alpha_found2 = True\n",
+ " print('Mean density is greater than 1 for alpha =',alpha)\n",
+ " \n",
+ " if (dmean_rho < 0) and (alpha_found3 == False):\n",
+ " alpha_found3 = True\n",
+ " print('Derivative of the mean density is less than 0 for alpha =',alpha)\n",
+ " \n",
+ " if (J < 0) and (alpha_found4 == False):\n",
+ " alpha_found4 = True\n",
+ " print('Particle current is less than 0 for alpha =',alpha)\n",
+ " \n",
+ " if (J > alpha) and (alpha_found5 == False):\n",
+ " alpha_found5 = True\n",
+ " print('Particle current is greater than alpha for alpha =',alpha)\n",
+ " \n",
+ " if (dJ < 0) and (alpha_found6 == False):\n",
+ " alpha_found6 = True\n",
+ " print('Derivative of the particle current is less than 0 for alpha =',alpha)\n",
+ " \n",
+ " if (dJ > 1) and (alpha_found7 == False):\n",
+ " alpha_found7 = True\n",
+ " print('Derivative of the particle current is greater than 1 for alpha =',alpha)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--
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