diff --git a/README.md b/README.md
index 07161e20b445488b240bbd9fa5bfe0dddb7cf149..705b6d5739513867e10ed99fa6b95fa1e0c10069 100644
--- a/README.md
+++ b/README.md
@@ -26,11 +26,11 @@ reproduce the results of all three papers.
The entire framework is summarized in the figure below:
-In principle, we strictly separate the structure of the network
-(defined by population sizes, synapse numbers/indegrees etc.) from its dynamics
-(neuron model, neuron parameters, strength of external
-input, etc.). The complete set of default parameters for all components
-of the framework is defined in `default_params.py`.
+We separate the structure of the network (defined by population sizes,
+synapse numbers/indegrees etc.) from its dynamics (neuron model,
+neuron parameters, strength of external input, etc.). The complete set
+of default parameters for all components of the framework is defined
+in `default_params.py`.
--------------------------------------------------------------------------------
@@ -127,8 +127,8 @@ The multi-area model can be run in different modes.
1. Full model
- Simulating the entire networks with all 32 areas and the connections between
- them is the default mode configure in `default_params.py`.
+ Simulating the entire networks with all 32 areas with default
+ connectivity as defined in `default_params.py`.
2. Down-scaled model
@@ -154,13 +154,18 @@ The multi-area model can be run in different modes.
4. Cortico-cortical connections replaced
- In addition, it is possible to replace the cortico-cortical connections between simulated
- areas with the options `het_poisson_stat` or `current_nonstat`.
+ In addition, it is possible to replace the cortico-cortical
+ connections between simulated areas with the options
+ `het_poisson_stat` or `current_nonstat`. This mode can be used with
+ the full network of 32 areas or for a subset of them (therefore
+ combining this mode with the previous mode 'Subset of the
+ network').
## Testsuite
-The `tests/` folder holds a testsuite that tests different aspects of network model initalization and meanfield calculations.
-It can be conveniently run by executing `pytest` in the `tests/` folder:
+The `tests/` folder holds a testsuite that tests different aspects of
+network model initalization and mean-field calculations. It can be
+conveniently run by executing `pytest` in the `tests/` folder:
cd tests/
pytest
@@ -189,8 +194,11 @@ The SLN fit in `multiarea_model/data_multiarea/VisualCortex_Data.py` and `figure
## Contributors
-All authors of the publications [1-3] made contributions to the scientific content.
-The code base was written by Maximilian Schmidt, Jannis Schuecker, and Sacha van Albada. Testing and review was supported by Alexander van Meegen.
+All authors of the publications [1-3] made contributions to the
+scientific content. The code base was written by Maximilian Schmidt,
+Jannis Schuecker, and Sacha van Albada with small contributions from
+Moritz Helias. Testing and review was supported by Alexander van
+Meegen.
## Citation
diff --git a/multiarea_model/data_multiarea/raw_data/BinzeggerData.csv b/multiarea_model/data_multiarea/raw_data/BinzeggerData.csv
index 73d65c610b74b9a03805a55c595d760460e77f73..9373c0d24c9902db66a69e1155e758c9f6128a0d 100644
--- a/multiarea_model/data_multiarea/raw_data/BinzeggerData.csv
+++ b/multiarea_model/data_multiarea/raw_data/BinzeggerData.csv
@@ -1,4 +1,4 @@
-# Taken from Binzegger, T., Douglas, R. J., & Martin, K. a C. (2004). A quantitative map of the circuit of cat primary visual cortex. The Journal of Neuroscience : The Official Journal of the Society for Neuroscience, 24(39), 8441–53. https://doi.org/10.1523/JNEUROSCI.1400-04.2004
+# Taken from Binzegger, T., Douglas, R. J., & Martin, K. a C. (2004). A quantitative map of the circuit of cat primary visual cortex. The Journal of Neuroscience : The Official Journal of the Society for Neuroscience, 24(39), 8441–53. https://doi.org/10.1523/JNEUROSCI.1400-04.2004. The full table of data is also available in Izhikevich, E. M., & Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Sciences of the United States of America, 105(9), 3593–8. https://doi.org/10.1073/pnas.0712231105.
percent of cells (respect to total area) number of synapses per neuron nb1 p2/3 b2/3 nb2/3 ss4(L4) ss4(L2/3) p4 b4 nb4 p5(L2/3) p5(L5/6) b5 nb5 p6(L4) p6(L5/6) b6 nb6 corticocortical TCs TCn TIs TIn TRN
nb1 1.5 8890 10.1 6.3 0.6 1.1 0 0 0.1 0 0 0.1 0 0 0 0 0 0 0 77.6 0 4.1
diff --git a/multiarea_model/data_multiarea/raw_data/Euclidean_Distances.csv b/multiarea_model/data_multiarea/raw_data/Euclidean_Distances.csv
index ea01607ab8fff3d374112e7baf05266735f139b8..4ca2add1eb9eee4efddb1610e47092c738857fa7 100644
--- a/multiarea_model/data_multiarea/raw_data/Euclidean_Distances.csv
+++ b/multiarea_model/data_multiarea/raw_data/Euclidean_Distances.csv
@@ -1,4 +1,4 @@
-#Taken from Cocomac database (www.cocomac.org), the center of the areas is computed (Details to be clarified) and the distance between two areas is taken to be the euclidian distance between the center points
+# Taken from CoCoMac database (www.cocomac.org), the distance between two areas is taken to be the Euclidian distance between the center points
V1 V2 V3 VP V3A V4 VOT V4t MT FST PITd PITv CITd CITv AITd AITv STPp STPa TF TH MSTd MSTl PO PIP LIP VIP MIP MDP DP 7a FEF 46
V1 0 7.669 10.407 14.918 9.502 20.718 20.303 15.964 17.943 26.424 22.552 25.953 29.645 32.295 35.085 34.961 35.125 34.287 20.186 15.843 13.643 19.724 9.591 4.85 18.223 14.97 12.83 18.891 16.286 21.617 49.116 53.474
diff --git a/multiarea_model/data_multiarea/raw_data/Intrinsic_FLN_Data.csv b/multiarea_model/data_multiarea/raw_data/Intrinsic_FLN_Data.csv
index 4c5839bdffe4a733122eeb46edeba389c468b384..ab1086d43df2b17c97edd3bd1f05ec1b8e60c397 100644
--- a/multiarea_model/data_multiarea/raw_data/Intrinsic_FLN_Data.csv
+++ b/multiarea_model/data_multiarea/raw_data/Intrinsic_FLN_Data.csv
@@ -1,4 +1,4 @@
-# Data from supplement of Markov et al. (2011) "Weight Consistency Specifies Regularities of Macaque Cortical Networks"
+# Data from supplement of Markov et al. (2011) "Weight Consistency Specifies Regularities of Macaque Cortical Networks" Cereb Cortex. 21(6):1254-72. doi: 10.1093/cercor/bhq201.
V1 0.85 0.05
V2 0.75 0.05
diff --git a/multiarea_model/data_multiarea/raw_data/Laminar_Thickness_cat.csv b/multiarea_model/data_multiarea/raw_data/Laminar_Thickness_cat.csv
index 1d3ba5487f09d630d83d20ee65cbc924a555eec6..b20e9f387e64a5898be18bef52a73c4056ac2232 100644
--- a/multiarea_model/data_multiarea/raw_data/Laminar_Thickness_cat.csv
+++ b/multiarea_model/data_multiarea/raw_data/Laminar_Thickness_cat.csv
@@ -1,4 +1,4 @@
-# Thickness of Laminae and errors taken from Table 1 of Beaulieu, C., & Colonnier, M. (1983). The number of neurons in the different laminae of the binocular and monocular regions of area 17 in the cat. Journal of Comparative Neurology, 344. Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/cne.902170308/abstract for cat area 17, layer names are taken from the table
+# Thickness of laminae and errors taken from Table 1 of Beaulieu, C., & Colonnier, M. (1983). The number of neurons in the different laminae of the binocular and monocular regions of area 17 in the cat. Journal of Comparative Neurology, 344. Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/cne.902170308/abstract for cat area 17, layer names are taken from the table
1 0.166 0.010
2 0.128 0.026
diff --git a/multiarea_model/data_multiarea/raw_data/SchemeTranslation.csv b/multiarea_model/data_multiarea/raw_data/SchemeTranslation.csv
index 5912697e14d3d49f6a925e9cda20a07c4379e8dc..3ef71b0dfe897cd464cd5fa44ec9914556ee1756 100644
--- a/multiarea_model/data_multiarea/raw_data/SchemeTranslation.csv
+++ b/multiarea_model/data_multiarea/raw_data/SchemeTranslation.csv
@@ -1,6 +1,6 @@
-# This translation is compiled by collecting information from Markov et al. (2011), Hilgetag et al. (2015), and David van Essen (2002) ""Organization of Visual Areas in Macaque and Human Cerebral Cortex"
+# This translation is compiled by collecting information from Markov et al. (2011), Hilgetag et al. (2015), and David Van Essen (2002) "Organization of Visual Areas in Macaque and Human Cerebral Cortex"
-Area Barbas Area Fellmann/van Essen [2]
+Area Barbas Area Fellemann/Van Essen
TEO PITd
TEO PITv
TEO VOT
diff --git a/multiarea_model/data_multiarea/raw_data/Thom_Distances.csv b/multiarea_model/data_multiarea/raw_data/Thom_Distances.csv
index 2613f8b51a6f1ccd046da4b3dcea1f4f27fc7a18..9595495c421a4d57772e2807226b62ce910e8d51 100644
--- a/multiarea_model/data_multiarea/raw_data/Thom_Distances.csv
+++ b/multiarea_model/data_multiarea/raw_data/Thom_Distances.csv
@@ -1,4 +1,4 @@
-#Taken from Cocomac database (www.cocomac.org), the center of the areas is computed (Details to be clarified) and the distance between two areas is taken to be the distance between the center points, which is computed via a sophisticated method of Thom Oostendorp
+#Taken from CoCoMac database (www.cocomac.org), the distance between two areas is taken to be the distance between the center points, which is computed via a sophisticated method of Thom Oostendorp
V1 V2 V3 VP V3A V4 VOT V4t MT FST PITd PITv CITd CITv AITd AITv STPp STPa TF TH MSTd MSTl PO PIP LIP VIP MIP MDP DP 7a FEF 46
V1 0 18.71 10.685 19.494 9.639 21.216 22.492 16.695 18.994 26.502 23.301 26.687 30.883 34.236 37.03 37.114 36.349 34.388 23.492 20.946 13.495 19.112 8.973 4.904 19.298 15.454 13.004 18.594 17.428 23.416 49.578 52.619
diff --git a/multiarea_model/data_multiarea/raw_data/cortical_surface.csv b/multiarea_model/data_multiarea/raw_data/cortical_surface.csv
index c3571b7de7f8fcf290d86ab86b8e50b7af6e4ffa..37bbde6cacea4a2b2082fa390af2c476013911ba 100644
--- a/multiarea_model/data_multiarea/raw_data/cortical_surface.csv
+++ b/multiarea_model/data_multiarea/raw_data/cortical_surface.csv
@@ -1,4 +1,4 @@
-# Computed with Caret software, Details to be clarified, unit is mm2
+# Computed with Caret software, unit is mm2
7a 157.342
DP 113.834
diff --git a/multiarea_model/data_multiarea/raw_data/hierarchy_Markov.csv b/multiarea_model/data_multiarea/raw_data/hierarchy_Markov.csv
index 087e739bffbf55288e2146c125968c415549f960..c0b9d188b25372b16fc6398e5751c6289b3cad85 100644
--- a/multiarea_model/data_multiarea/raw_data/hierarchy_Markov.csv
+++ b/multiarea_model/data_multiarea/raw_data/hierarchy_Markov.csv
@@ -1,4 +1,4 @@
-Taken from Markov et al. (2014) "Anatomy of Hierarchy: Feedforward and Feedback Pathways in Macaque Visual Cortex"
+Taken from Markov et al. (2014) "Anatomy of Hierarchy: Feedforward and Feedback Pathways in Macaque Visual Cortex", Journal of Comparative Neurology, 522(1), 225-259.
V1,0.,1.
V2,0.2831,2.
diff --git a/multiarea_model/data_multiarea/raw_data/hierarchy_Reid.csv b/multiarea_model/data_multiarea/raw_data/hierarchy_Reid.csv
index 4b9d33ae5ff0da18803bd1f09952aa2733b5c5e2..872803d7747bf0ec12bdc9eecf287243f2a75c25 100644
--- a/multiarea_model/data_multiarea/raw_data/hierarchy_Reid.csv
+++ b/multiarea_model/data_multiarea/raw_data/hierarchy_Reid.csv
@@ -1,4 +1,4 @@
-Taken from Reid et al. (2009) "Optimization of cortical hierarchies with continuous scales and ranges", Fig 4.
+Taken from Fig. 4 of Reid et al. (2009) "Optimization of cortical hierarchies with continuous scales and ranges", Neuroimage, 47(2), 611-617.
7a 0.6622
PITv 0.6048
diff --git a/multiarea_model/default_params.py b/multiarea_model/default_params.py
index 6d18b3dde74d439c9826b0ff2b1e9f6618e6c34a..15dbba6707ed60c612b65957666d5cf25fbf616d 100644
--- a/multiarea_model/default_params.py
+++ b/multiarea_model/default_params.py
@@ -36,7 +36,7 @@ av_indegree_OKusky = raw_data['av_indegree_OKusky']
Simulation parameters
"""
sim_params = {
- # master seed for random
+ # master seed for random number generators
'master_seed': 0,
# simulation step (in ms)
'dt': 0.1,
@@ -62,7 +62,7 @@ network_params = {
'N_scaling': 1.,
# Scaling of indegrees
'K_scaling': 1.,
- # Full_scale rates for scaling synaptic weights
+ # Full-scale rates for scaling synaptic weights
'fullscale_rates': None
}
@@ -120,8 +120,7 @@ connection_params = {
# Whether to apply the stabilization method of
# Schuecker, Schmidt et al. (2017). Default is False.
# Options are True to perform the stabilization or
- # a numpy.ndarray specifying the stabilized matrix or
- # a tuple of strings where the first component specifies a binary
+ # a string that specifies the name of a binary
# numpy file containing the connectivity matrix
'K_stable': False,
@@ -132,7 +131,7 @@ connection_params = {
# the cortico-cortical input is loaded from `replace_cc_input_source`.
'replace_cc': False,
- # Whether to replace non-simulated areas by poisson sources
+ # Whether to replace non-simulated areas by Poisson sources
# with the same global rate rate_ext ('hom_poisson_stat') or
# by specific rates ('het_poisson_stat')
# or by time-varying specific current ('het_current_nonstat')
@@ -164,7 +163,7 @@ connection_params = {
# constant --> conserve syn. volume density
'rho_syn': 'constant',
- # Increase the external poisson indegree onto 5E and 6E
+ # Increase the external Poisson indegree onto 5E and 6E
'fac_nu_ext_5E': 1.,
'fac_nu_ext_6E': 1.,
# to increase the ext. input to 23E and 5E in area TH
@@ -222,7 +221,7 @@ input_params = {
# synapse type for Poisson input
'syn_type_ext': 'static_synapse_hpc',
- # Rate of the Poissonian spike generator (in Hz).
+ # Rate of the Poissonian spike generator (in spikes/s).
'rate_ext': 10.,
# Whether to switch on time-dependent DC input
diff --git a/multiarea_model/multiarea_model.py b/multiarea_model/multiarea_model.py
index 54cd8da453a9b05327aece2208ef54f4f1a4eb1a..fb7c0a162b3031cbb174f5f9692e82ba16090a56 100644
--- a/multiarea_model/multiarea_model.py
+++ b/multiarea_model/multiarea_model.py
@@ -3,7 +3,7 @@ multiarea_model
==============
Network class to instantiate and administer instances of the
-multi-area model of macaque visual cortex by Schmidt el. (2018).
+multi-area model of macaque visual cortex by Schmidt et al. (2018).
Classes
-------
@@ -90,7 +90,7 @@ class MultiAreaModel:
self.custom_params = network_spec
p_ = 'multiarea_model/data_multiarea/custom_data_files'
# Draw random integer label for data script to avoid clashes with
- # parallely created class instances
+ # parallelly created class instances
rand_data_label = np.random.randint(10000)
print("RAND_DATA_LABEL", rand_data_label)
tmp_parameter_fn = os.path.join(base_path,
@@ -238,14 +238,14 @@ class MultiAreaModel:
This function:
- adjusts the synaptic weights such that the population-averaged
- stationary spike rates approximately match the given `fullscale_rates`.
+ stationary spike rates approximately match the given `full-scale_rates`.
- scales the population sizes with `N_scaling` and indegrees with `K_scaling`.
- scales the synapse numbers with `N_scaling`*`K_scaling`.
"""
# population sizes
self.N_vec *= self.params['N_scaling']
- # Scale the synaptic weights before the indegrees to use fullscale indegrees
+ # Scale the synaptic weights before the indegrees to use full-scale indegrees
self.adj_W_to_K()
# Then scale the indegrees and synapse numbers
self.K_matrix *= self.params['K_scaling']
diff --git a/multiarea_model/theory_helpers.py b/multiarea_model/theory_helpers.py
index af2b4b60ae5b310d92d28b87586756beb51a172c..b01de239b62c29bbf2f7e35dd09072832cfde752 100644
--- a/multiarea_model/theory_helpers.py
+++ b/multiarea_model/theory_helpers.py
@@ -4,7 +4,7 @@ theory_helpers
Helper function for the theory class.
Evaluates the Siegert formula and its
-derivations.
+derivatives.
Functions
@@ -15,6 +15,7 @@ Authors
--------
Maximilian Schmidt
Jannis Schuecker
+Moritz Helias
"""
@@ -29,7 +30,7 @@ def nu0_fb(tau_m, tau_s, tau_r, V_th, V_r, mu, sigma):
"""
Compute the stationary firing rate of a neuron with synaptic
filter of time constant tau_s driven by Gaussian white noise, from
- Fourcoud & Brunel 2002. #
+ Fourcaud & Brunel 2002. #
Parameters
----------
diff --git a/run_example.py b/run_example.py
index 40251bf2e45cac06ac20dd1b0d4019116a968897..8945b41318bfc141cdf5eca49d64cc94280130d5 100644
--- a/run_example.py
+++ b/run_example.py
@@ -16,8 +16,7 @@ Full model. Needs to be simulated with sufficient
resources, for instance on a compute cluster.
"""
d = {}
-conn_params = {'replace_non_simulated_areas': 'het_poisson_stat',
- 'g': -11.,
+conn_params = {'g': -11.,
'K_stable': 'K_stable.npy',
'fac_nu_ext_TH': 1.2,
'fac_nu_ext_5E': 1.125,
@@ -32,7 +31,7 @@ network_params = {'N_scaling': 1.,
'neuron_params': neuron_params}
sim_params = {'t_sim': 2000.,
- 'num_processes': 360,
+ 'num_processes': 720,
'num_rec_processes': 1,
'local_num_threads': 1,
'input_params': input_params,
@@ -51,7 +50,7 @@ start_job(M.simulation.label, submit_cmd, jobscript_template)
"""
Down-scaled model.
Neurons and indegrees are both scaled down to 10 %.
-Can be usually simulated on a local machine.
+Can usually be simulated on a local machine.
Warning: This will not yield reasonable dynamical results from the
network and is only meant to demonstrate the simulation workflow.
diff --git a/tests/test_network_scaling.py b/tests/test_network_scaling.py
index ecb1a52bbdc0a2c317b4221fff8e815a17de8ea8..7bca72175264f45e2e70e0f6973559bcd51c72de 100644
--- a/tests/test_network_scaling.py
+++ b/tests/test_network_scaling.py
@@ -4,58 +4,58 @@ import numpy as np
import json
-def test_network_scaling():
- """
- Test the downscaling option of the network.
-
- - Test whether indegrees and neuron number are correctly scaled down.
- - Test whether the resulting mean and variance of the input currents
- as well as the resulting rates are identical, based on mean-field theory.
- """
-
- network_params = {}
- M0 = MultiAreaModel(network_params, theory=True)
- K0 = M0.K_matrix
- W0 = M0.W_matrix
- N0 = M0.N_vec
- syn0 = M0.syn_matrix
- p, r0 = M0.theory.integrate_siegert()
-
- d = vector_to_dict(r0[:, -1],
- M0.area_list,
- M0.structure)
-
- with open('mf_rates.json', 'w') as f:
- json.dump(d, f)
-
- network_params = {'N_scaling': .1,
- 'K_scaling': .1,
- 'fullscale_rates': 'mf_rates.json'}
- theory_params = {'initial_rates': r0[:, -1]}
- M = MultiAreaModel(network_params, theory=True, theory_spec=theory_params)
-
- K = M.K_matrix
- W = M.W_matrix
- N = M.N_vec
- syn = M.syn_matrix
- p, r = M.theory.integrate_siegert()
-
- assert(np.allclose(K, network_params['K_scaling'] * K0))
- assert(np.allclose(N, network_params['N_scaling'] * N0))
- assert(np.allclose(syn, network_params['K_scaling'] * network_params['N_scaling'] * syn0))
- assert(np.allclose(W, W0 / np.sqrt(network_params['K_scaling'])))
-
- r0_extend = np.append(r0[:, -1], M0.params['input_params']['rate_ext'])
- tau_m = M.params['neuron_params']['single_neuron_dict']['tau_m']
- C_m = M.params['neuron_params']['single_neuron_dict']['C_m']
-
- mu0 = (1e-3 * tau_m * np.dot(M0.K_matrix * M0.J_matrix, r0_extend)
- + tau_m / C_m * M0.add_DC_drive)
- mu = 1e-3 * tau_m * np.dot(M.K_matrix * M.J_matrix, r0_extend) + tau_m / C_m * M.add_DC_drive
-
- sigma0 = np.sqrt(1e-3 * tau_m * np.dot(M0.K_matrix * M0.J_matrix**2, r0_extend))
- sigma = np.sqrt(1e-3 * tau_m * np.dot(M.K_matrix * M.J_matrix**2, r0_extend))
-
- assert(np.allclose(mu, mu0))
- assert(np.allclose(sigma, sigma0))
- assert(np.allclose(r[:, -1], r0[:, -1]))
+#def test_network_scaling():
+"""
+Test the downscaling option of the network.
+
+- Test whether indegrees and neuron number are correctly scaled down.
+- Test whether the resulting mean and variance of the input currents
+ as well as the resulting rates are identical, based on mean-field theory.
+"""
+
+network_params = {}
+M0 = MultiAreaModel(network_params, theory=True)
+K0 = M0.K_matrix
+W0 = M0.W_matrix
+N0 = M0.N_vec
+syn0 = M0.syn_matrix
+p, r0 = M0.theory.integrate_siegert()
+
+d = vector_to_dict(r0[:, -1],
+ M0.area_list,
+ M0.structure)
+
+with open('mf_rates.json', 'w') as f:
+ json.dump(d, f)
+
+network_params = {'N_scaling': .1,
+ 'K_scaling': .1,
+ 'fullscale_rates': 'mf_rates.json'}
+theory_params = {'initial_rates': r0[:, -1]}
+M = MultiAreaModel(network_params, theory=True, theory_spec=theory_params)
+
+K = M.K_matrix
+W = M.W_matrix
+N = M.N_vec
+syn = M.syn_matrix
+p, r = M.theory.integrate_siegert()
+
+assert(np.allclose(K, network_params['K_scaling'] * K0))
+assert(np.allclose(N, network_params['N_scaling'] * N0))
+assert(np.allclose(syn, network_params['K_scaling'] * network_params['N_scaling'] * syn0))
+assert(np.allclose(W, W0 / np.sqrt(network_params['K_scaling'])))
+
+r0_extend = np.append(r0[:, -1], M0.params['input_params']['rate_ext'])
+tau_m = M.params['neuron_params']['single_neuron_dict']['tau_m']
+C_m = M.params['neuron_params']['single_neuron_dict']['C_m']
+
+mu0 = (1e-3 * tau_m * np.dot(M0.K_matrix * M0.J_matrix, r0_extend)
+ + tau_m / C_m * M0.add_DC_drive)
+mu = 1e-3 * tau_m * np.dot(M.K_matrix * M.J_matrix, r0_extend) + tau_m / C_m * M.add_DC_drive
+
+sigma0 = np.sqrt(1e-3 * tau_m * np.dot(M0.K_matrix * M0.J_matrix**2, r0_extend))
+sigma = np.sqrt(1e-3 * tau_m * np.dot(M.K_matrix * M.J_matrix**2, r0_extend))
+
+assert(np.allclose(mu, mu0))
+assert(np.allclose(sigma, sigma0))
+assert(np.allclose(r[:, -1], r0[:, -1]))