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%matplotlib inline


    

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import pylab
SHOW_FIGURES = False

if not SHOW_FIGURES:
    pylab_show = pylab.show

    def nop(s=None):
        pass

    pylab.show = nop
else:
    pylab.ion()

# ! Introduction
# !=============
# ! This tutorial gives a brief introduction to the ConnPlotter
# ! toolbox.  It is by no means complete.

# ! Load pynest
import nest

# ! Load NEST Topoplogy module (NEST 2.2)
import nest.topology as topo

# ! Make sure we start with a clean slate, even if we re-run the script
# ! in the same Python session.
nest.ResetKernel()

# ! Import math, we need Pi
import math

# ! Configurable Parameters
# ! =======================
# !
# ! Here we define those parameters that we take to be
# ! configurable. The choice of configurable parameters is obviously
# ! arbitrary, and in practice one would have far more configurable
# ! parameters. We restrict ourselves to:
# !
# ! - Network size in neurons ``N``, each layer is ``N x N``.
# ! - Network size in subtended visual angle ``visSize``, in degree.
# ! - Temporal frequency of drifting grating input ``f_dg``, in Hz.
# ! - Spatial wavelength and direction of drifting grating input,
# !   ``lambda_dg`` and ``phi_dg``, in degree/radian.
# ! - Background firing rate of retinal nodes and modulation amplitude,
# !   ``retDC`` and ``retAC``, in Hz.
# ! - Simulation duration ``simtime``; actual simulation is split into
# !   intervals of ``sim_interval`` length, so that the network state
# !   can be visualized in those intervals. Times are in ms.
Params = {'N': 40,
          'visSize': 8.0,
          'f_dg': 2.0,
          'lambda_dg': 2.0,
          'phi_dg': 0.0,
          'retDC': 30.0,
          'retAC': 30.0,
          'simtime': 100.0,
          'sim_interval': 5.0
          }

# ! Neuron Models
# ! =============
# !
# ! We declare models in two steps:
# !
# ! 1. We define a dictionary specifying the NEST neuron model to use
# !    as well as the parameters for that model.
# ! #. We create three copies of this dictionary with parameters
# !    adjusted to the three model variants specified in Table~2 of
# !    Hill & Tononi (2005) (cortical excitatory, cortical inhibitory,
# !    thalamic)
# !
# ! In addition, we declare the models for the stimulation and
# ! recording devices.
# !
# ! The general neuron model
# ! ------------------------
# !
# ! We use the ``iaf_cond_alpha`` neuron, which is an
# ! integrate-and-fire neuron with two conductance-based synapses which
# ! have alpha-function time course.  Any input with positive weights
# ! will automatically directed to the synapse labeled ``_ex``, any
# ! with negative weights to the synapes labeled ``_in``.  We define
# ! **all** parameters explicitly here, so that no information is
# ! hidden in the model definition in NEST. ``V_m`` is the membrane
# ! potential to which the model neurons will be initialized.
# ! The model equations and parameters for the Hill-Tononi neuron model
# ! are given on pp. 1677f and Tables 2 and 3 in that paper. Note some
# ! peculiarities and adjustments:
# !
# ! - Hill & Tononi specify their model in terms of the membrane time
# !   constant, while the ``iaf_cond_alpha`` model is based on the
# !   membrane capcitance. Interestingly, conducantces are unitless in
# !   the H&T model. We thus can use the time constant directly as
# !   membrane capacitance.
# ! - The model includes sodium and potassium leak conductances. We
# !   combine these into a single one as follows:
# $   \begin{equation}-g_{NaL}(V-E_{Na}) - g_{KL}(V-E_K)
# $      = -(g_{NaL}+g_{KL})
# $        \left(V-\frac{g_{NaL}E_{NaL}+g_{KL}E_K}{g_{NaL}g_{KL}}\right)
# $   \end{equation}
# ! - We write the resulting expressions for g_L and E_L explicitly
# !   below, to avoid errors in copying from our pocket calculator.
# ! - The paper gives a range of 1.0-1.85 for g_{KL}, we choose 1.5
# !   here.
# ! - The Hill-Tononi model has no explicit reset or refractory
# !   time. We arbitrarily set V_reset and t_ref.
# ! - The paper uses double exponential time courses for the synaptic
# !   conductances, with separate time constants for the rising and
# !   fallings flanks. Alpha functions have only a single time
# !   constant: we use twice the rising time constant given by Hill and
# !   Tononi.
# ! - In the general model below, we use the values for the cortical
# !   excitatory cells as defaults. Values will then be adapted below.
# !
nest.CopyModel('iaf_cond_alpha', 'NeuronModel',
               params={'C_m': 16.0,
                       'E_L': (0.2 * 30.0 + 1.5 * -90.0) / (0.2 + 1.5),
                       'g_L': 0.2 + 1.5,
                       'E_ex': 0.0,
                       'E_in': -70.0,
                       'V_reset': -60.0,
                       'V_th': -51.0,
                       't_ref': 2.0,
                       'tau_syn_ex': 1.0,
                       'tau_syn_in': 2.0,
                       'I_e': 0.0,
                       'V_m': -70.0})

# ! Adaptation of models for different populations
# ! ----------------------------------------------

# ! We must copy the `NeuronModel` dictionary explicitly, otherwise
# ! Python would just create a reference.

# ! Cortical excitatory cells
# ! .........................
# ! Parameters are the same as above, so we need not adapt anything
nest.CopyModel('NeuronModel', 'CtxExNeuron')

# ! Cortical inhibitory cells
# ! .........................
nest.CopyModel('NeuronModel', 'CtxInNeuron',
               params={'C_m': 8.0,
                       'V_th': -53.0,
                       't_ref': 1.0})

# ! Thalamic cells
# ! ..............
nest.CopyModel('NeuronModel', 'ThalamicNeuron',
               params={'C_m': 8.0,
                       'V_th': -53.0,
                       't_ref': 1.0,
                       'E_in': -80.0})


# ! Input generating nodes
# ! ----------------------

# ! Input is generated by sinusoidally modulate Poisson generators,
# ! organized in a square layer of retina nodes. These nodes require a
# ! slightly more complicated initialization than all other elements of
# ! the network:
# !
# ! - Average firing rate ``rate``, firing rate modulation depth ``amplitude``,
# !   and temporal modulation frequency ``frequency`` are the same for all
# !   retinal nodes and are set directly below.
# ! - The temporal phase ``phase`` of each node depends on its position in
# !   the grating and can only be assigned after the retinal layer has
# !   been created. We therefore specify a function for initalizing the
# !   ``phase``. This function will be called for each node.
def phaseInit(pos, lam, alpha):
    '''Initializer function for phase of drifting grating nodes.

       pos  : position (x,y) of node, in degree
       lam  : wavelength of grating, in degree
       alpha: angle of grating in radian, zero is horizontal

       Returns number to be used as phase of sinusoidal Poisson generator.
    '''
    return 360.0 / lam * (math.cos(alpha) * pos[0] + math.sin(alpha) * pos[1])


nest.CopyModel('sinusoidal_poisson_generator', 'RetinaNode',
               params={'amplitude': Params['retAC'],
                       'rate': Params['retDC'],
                       'frequency': Params['f_dg'],
                       'phase': 0.0,
                       'individual_spike_trains': False})

# ! Recording nodes
# ! ---------------

# ! We use the new ``multimeter`` device for recording from the model
# ! neurons. At present, ``iaf_cond_alpha`` is one of few models
# ! supporting ``multimeter`` recording.  Support for more models will
# ! be added soon; until then, you need to use ``voltmeter`` to record
# ! from other models.
# !
# ! We configure multimeter to record membrane potential to membrane
# ! potential at certain intervals to memory only. We record the GID of
# ! the recorded neurons, but not the time.
nest.CopyModel('multimeter', 'RecordingNode',
               params={'interval': Params['sim_interval'],
                       'record_from': ['V_m'],
                       'record_to': ['memory'],
                       'withgid': True,
                       'withtime': False})

# ! Populations
# ! ===========

# ! We now create the neuron populations in the model, again in the
# ! form of Python dictionaries. We define them in order from eye via
# ! thalamus to cortex.
# !
# ! We first define a dictionary defining common properties for all
# ! populations
layerProps = {'rows': Params['N'],
              'columns': Params['N'],
              'extent': [Params['visSize'], Params['visSize']],
              'edge_wrap': True}
# ! This dictionary does not yet specify the elements to put into the
# ! layer, since they will differ from layer to layer. We will add them
# ! below by updating the ``'elements'`` dictionary entry for each
# ! population.

# ! Retina
# ! ------
layerProps.update({'elements': 'RetinaNode'})
retina = topo.CreateLayer(layerProps)

# retina_leaves is a work-around until NEST 3.0 is released
retina_leaves = nest.GetLeaves(retina)[0]

# ! Now set phases of retinal oscillators; we use a list comprehension instead
# ! of a loop.
[nest.SetStatus([n], {"phase": phaseInit(topo.GetPosition([n])[0],
                                         Params["lambda_dg"],
                                         Params["phi_dg"])})
 for n in retina_leaves]

# ! Thalamus
# ! --------

# ! We first introduce specific neuron models for the thalamic relay
# ! cells and interneurons. These have identical properties, but by
# ! treating them as different models, we can address them specifically
# ! when building connections.
# !
# ! We use a list comprehension to do the model copies.
[nest.CopyModel('ThalamicNeuron', SpecificModel) for SpecificModel in
 ('TpRelay', 'TpInter')]

# ! Now we can create the layer, with one relay cell and one
# ! interneuron per location:
layerProps.update({'elements': ['TpRelay', 'TpInter']})
Tp = topo.CreateLayer(layerProps)

# ! Reticular nucleus
# ! -----------------
# ! We follow the same approach as above, even though we have only a
# ! single neuron in each location.
[nest.CopyModel('ThalamicNeuron', SpecificModel) for SpecificModel in
 ('RpNeuron',)]
layerProps.update({'elements': 'RpNeuron'})
Rp = topo.CreateLayer(layerProps)

# ! Primary visual cortex
# ! ---------------------

# ! We follow again the same approach. We differentiate neuron types
# ! between layers and between pyramidal cells and interneurons. At
# ! each location, there are two pyramidal cells and one interneuron in
# ! each of layers 2-3, 4, and 5-6. Finally, we need to differentiate
# ! between vertically and horizontally tuned populations. When creating
# ! the populations, we create the vertically and the horizontally
# ! tuned populations as separate populations.

# ! We use list comprehesions to create all neuron types:
[nest.CopyModel('CtxExNeuron', layer + 'pyr')
 for layer in ('L23', 'L4', 'L56')]
[nest.CopyModel('CtxInNeuron', layer + 'in')
 for layer in ('L23', 'L4', 'L56')]

# ! Now we can create the populations, suffixes h and v indicate tuning
layerProps.update({'elements': ['L23pyr', 2, 'L23in', 1,
                                'L4pyr', 2, 'L4in', 1,
                                'L56pyr', 2, 'L56in', 1]})
Vp_h = topo.CreateLayer(layerProps)
Vp_v = topo.CreateLayer(layerProps)

# ! Collect all populations
# ! -----------------------

# ! For reference purposes, e.g., printing, we collect all populations
# ! in a tuple:
populations = (retina, Tp, Rp, Vp_h, Vp_v)

# ! Inspection
# ! ----------

# ! We can now look at the network using `PrintNetwork`:
nest.PrintNetwork()

# ! We can also try to plot a single layer in a network. For
# ! simplicity, we use Rp, which has only a single neuron per position.
topo.PlotLayer(Rp)
pylab.title('Layer Rp')
pylab.show()

# ! Synapse models
# ! ==============

# ! Actual synapse dynamics, e.g., properties such as the synaptic time
# ! course, time constants, reversal potentials, are properties of
# ! neuron models in NEST and we set them in section `Neuron models`_
# ! above. When we refer to *synapse models* in NEST, we actually mean
# ! connectors which store information about connection weights and
# ! delays, as well as port numbers at the target neuron (``rport``)
# ! and implement synaptic plasticity. The latter two aspects are not
# ! relevant here.
# !
# ! We just use NEST's ``static_synapse`` connector but copy it to
# ! synapse models ``AMPA`` and ``GABA_A`` for the sake of
# ! explicitness. Weights and delays are set as needed in section
# ! `Connections`_ below, as they are different from projection to
# ! projection. De facto, the sign of the synaptic weight decides
# ! whether input via a connection is handle by the ``_ex`` or the
# ! ``_in`` synapse.
nest.CopyModel('static_synapse', 'AMPA')
nest.CopyModel('static_synapse', 'GABA_A')

# ! Connections
# ! ====================

# ! Building connections is the most complex part of network
# ! construction. Connections are specified in Table 1 in the
# ! Hill-Tononi paper. As pointed out above, we only consider AMPA and
# ! GABA_A synapses here.  Adding other synapses is tedious work, but
# ! should pose no new principal challenges. We also use a uniform in
# ! stead of a Gaussian distribution for the weights.
# !
# ! The model has two identical primary visual cortex populations,
# ! ``Vp_v`` and ``Vp_h``, tuned to vertical and horizonal gratings,
# ! respectively. The *only* difference in the connection patterns
# ! between the two populations is the thalamocortical input to layers
# ! L4 and L5-6 is from a population of 8x2 and 2x8 grid locations,
# ! respectively. Furthermore, inhibitory connection in cortex go to
# ! the opposing orientation population as to the own.
# !
# ! To save us a lot of code doubling, we thus defined properties
# ! dictionaries for all connections first and then use this to connect
# ! both populations. We follow the subdivision of connections as in
# ! the Hill & Tononi paper.
# !
# ! **Note:** Hill & Tononi state that their model spans 8 degrees of
# ! visual angle and stimuli are specified according to this. On the
# ! other hand, all connection patterns are defined in terms of cell
# ! grid positions. Since the NEST Topology Module defines connection
# ! patterns in terms of the extent given in degrees, we need to apply
# ! the following scaling factor to all lengths in connections:
dpc = Params['visSize'] / (Params['N'] - 1)

# ! We will collect all same-orientation cortico-cortical connections in
ccConnections = []
# ! the cross-orientation cortico-cortical connections in
ccxConnections = []
# ! and all cortico-thalamic connections in
ctConnections = []

# ! Horizontal intralaminar
# ! -----------------------
# ! *Note:* "Horizontal" means "within the same cortical layer" in this
# ! case.
# !
# ! We first define a dictionary with the (most) common properties for
# ! horizontal intralaminar connection. We then create copies in which
# ! we adapt those values that need adapting, and
horIntraBase = {"connection_type": "divergent",
                "synapse_model": "AMPA",
                "mask": {"circular": {"radius": 12.0 * dpc}},
                "kernel": {"gaussian": {"p_center": 0.05, "sigma": 7.5 * dpc}},
                "weights": 1.0,
                "delays": {"uniform": {"min": 1.75, "max": 2.25}}}

# ! We use a loop to do the for for us. The loop runs over a list of
# ! dictionaries with all values that need updating
for conn in [{"sources": {"model": "L23pyr"}, "targets": {"model": "L23pyr"}},
             {"sources": {"model": "L23pyr"}, "targets": {"model": "L23in"}},
             {"sources": {"model": "L4pyr"}, "targets": {"model": "L4pyr"},
              "mask": {"circular": {"radius": 7.0 * dpc}}},
             {"sources": {"model": "L4pyr"}, "targets": {"model": "L4in"},
              "mask": {"circular": {"radius": 7.0 * dpc}}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L56pyr"}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L56in"}}]:
    ndict = horIntraBase.copy()
    ndict.update(conn)
    ccConnections.append(ndict)

# ! Vertical intralaminar
# ! -----------------------
# ! *Note:* "Vertical" means "between cortical layers" in this
# ! case.
# !
# ! We proceed as above.
verIntraBase = {"connection_type": "divergent",
                "synapse_model": "AMPA",
                "mask": {"circular": {"radius": 2.0 * dpc}},
                "kernel": {"gaussian": {"p_center": 1.0, "sigma": 7.5 * dpc}},
                "weights": 2.0,
                "delays": {"uniform": {"min": 1.75, "max": 2.25}}}

for conn in [{"sources": {"model": "L23pyr"}, "targets": {"model": "L56pyr"},
              "weights": 1.0},
             {"sources": {"model": "L23pyr"}, "targets": {"model": "L23in"},
              "weights": 1.0},
             {"sources": {"model": "L4pyr"}, "targets": {"model": "L23pyr"}},
             {"sources": {"model": "L4pyr"}, "targets": {"model": "L23in"}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L23pyr"}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L23in"}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L4pyr"}},
             {"sources": {"model": "L56pyr"}, "targets": {"model": "L4in"}}]:
    ndict = verIntraBase.copy()
    ndict.update(conn)
    ccConnections.append(ndict)

# ! Intracortical inhibitory
# ! ------------------------
# !
# ! We proceed as above, with the following difference: each connection
# ! is added to the same-orientation and the cross-orientation list of
# ! connections.
# !
# ! **Note:** Weights increased from -1.0 to -2.0, to make up for missing GabaB
# !
# ! Note that we have to specify the **weight with negative sign** to make
# ! the connections inhibitory.
intraInhBase = {"connection_type": "divergent",
                "synapse_model": "GABA_A",
                "mask": {"circular": {"radius": 7.0 * dpc}},
                "kernel": {"gaussian": {"p_center": 0.25, "sigma": 7.5 * dpc}},
                "weights": -2.0,
                "delays": {"uniform": {"min": 1.75, "max": 2.25}}}

# ! We use a loop to do the for for us. The loop runs over a list of
# ! dictionaries with all values that need updating
for conn in [{"sources": {"model": "L23in"}, "targets": {"model": "L23pyr"}},
             {"sources": {"model": "L23in"}, "targets": {"model": "L23in"}},
             {"sources": {"model": "L4in"}, "targets": {"model": "L4pyr"}},
             {"sources": {"model": "L4in"}, "targets": {"model": "L4in"}},
             {"sources": {"model": "L56in"}, "targets": {"model": "L56pyr"}},
             {"sources": {"model": "L56in"}, "targets": {"model": "L56in"}}]:
    ndict = intraInhBase.copy()
    ndict.update(conn)
    ccConnections.append(ndict)
    ccxConnections.append(ndict)

# ! Corticothalamic
# ! ---------------
corThalBase = {"connection_type": "divergent",
               "synapse_model": "AMPA",
               "mask": {"circular": {"radius": 5.0 * dpc}},
               "kernel": {"gaussian": {"p_center": 0.5, "sigma": 7.5 * dpc}},
               "weights": 1.0,
               "delays": {"uniform": {"min": 7.5, "max": 8.5}}}

# ! We use a loop to do the for for us. The loop runs over a list of
# ! dictionaries with all values that need updating
for conn in [{"sources": {"model": "L56pyr"},
              "targets": {"model": "TpRelay"}},
             {"sources": {"model": "L56pyr"},
              "targets": {"model": "TpInter"}}]:
    ndict = intraInhBase.copy()
    ndict.update(conn)
    ctConnections.append(ndict)

# ! Corticoreticular
# ! ----------------

# ! In this case, there is only a single connection, so we write the
# ! dictionary itself; it is very similar to the corThalBase, and to
# ! show that, we copy first, then update. We need no ``targets`` entry,
# ! since Rp has only one neuron per location.
corRet = corThalBase.copy()
corRet.update({"sources": {"model": "L56pyr"}, "weights": 2.5})

# ! Build all connections beginning in cortex
# ! -----------------------------------------

# ! Cortico-cortical, same orientation
print("Connecting: cortico-cortical, same orientation")
[topo.ConnectLayers(Vp_h, Vp_h, conn) for conn in ccConnections]
[topo.ConnectLayers(Vp_v, Vp_v, conn) for conn in ccConnections]

# ! Cortico-cortical, cross-orientation
print("Connecting: cortico-cortical, other orientation")
[topo.ConnectLayers(Vp_h, Vp_v, conn) for conn in ccxConnections]
[topo.ConnectLayers(Vp_v, Vp_h, conn) for conn in ccxConnections]

# ! Cortico-thalamic connections
print("Connecting: cortico-thalamic")
[topo.ConnectLayers(Vp_h, Tp, conn) for conn in ctConnections]
[topo.ConnectLayers(Vp_v, Tp, conn) for conn in ctConnections]
topo.ConnectLayers(Vp_h, Rp, corRet)
topo.ConnectLayers(Vp_v, Rp, corRet)

# ! Thalamo-cortical connections
# ! ----------------------------

# ! **Note:** According to the text on p. 1674, bottom right, of
# ! the Hill & Tononi paper, thalamocortical connections are
# ! created by selecting from the thalamic population for each
# ! L4 pyramidal cell, ie, are *convergent* connections.
# !
# ! We first handle the rectangular thalamocortical connections.
thalCorRect = {"connection_type": "convergent",
               "sources": {"model": "TpRelay"},
               "synapse_model": "AMPA",
               "weights": 5.0,
               "delays": {"uniform": {"min": 2.75, "max": 3.25}}}

print("Connecting: thalamo-cortical")

# ! Horizontally tuned
thalCorRect.update(
    {"mask": {"rectangular": {"lower_left": [-4.0 * dpc, -1.0 * dpc],
                              "upper_right": [4.0 * dpc, 1.0 * dpc]}}})
for conn in [{"targets": {"model": "L4pyr"}, "kernel": 0.5},
             {"targets": {"model": "L56pyr"}, "kernel": 0.3}]:
    thalCorRect.update(conn)
    topo.ConnectLayers(Tp, Vp_h, thalCorRect)

# ! Vertically tuned
thalCorRect.update(
    {"mask": {"rectangular": {"lower_left": [-1.0 * dpc, -4.0 * dpc],
                              "upper_right": [1.0 * dpc, 4.0 * dpc]}}})
for conn in [{"targets": {"model": "L4pyr"}, "kernel": 0.5},
             {"targets": {"model": "L56pyr"}, "kernel": 0.3}]:
    thalCorRect.update(conn)
    topo.ConnectLayers(Tp, Vp_v, thalCorRect)

# ! Diffuse connections
thalCorDiff = {"connection_type": "convergent",
               "sources": {"model": "TpRelay"},
               "synapse_model": "AMPA",
               "weights": 5.0,
               "mask": {"circular": {"radius": 5.0 * dpc}},
               "kernel": {"gaussian": {"p_center": 0.1, "sigma": 7.5 * dpc}},
               "delays": {"uniform": {"min": 2.75, "max": 3.25}}}

for conn in [{"targets": {"model": "L4pyr"}},
             {"targets": {"model": "L56pyr"}}]:
    thalCorDiff.update(conn)
    topo.ConnectLayers(Tp, Vp_h, thalCorDiff)
    topo.ConnectLayers(Tp, Vp_v, thalCorDiff)

# ! Thalamic connections
# ! --------------------

# ! Connections inside thalamus, including Rp
# !
# ! *Note:* In Hill & Tononi, the inhibition between Rp cells is mediated by
# ! GABA_B receptors. We use GABA_A receptors here to provide some
# ! self-dampening of Rp.
# !
# ! **Note:** The following code had a serious bug in v. 0.1: During the first
# ! iteration of the loop, "synapse_model" and "weights" were set to "AMPA" and
# !  "0.1", respectively and remained unchanged, so that all connections were
# ! created as excitatory connections, even though they should have been
# ! inhibitory. We now specify synapse_model and weight explicitly for each
# ! connection to avoid this.

thalBase = {"connection_type": "divergent",
            "delays": {"uniform": {"min": 1.75, "max": 2.25}}}

print("Connecting: intra-thalamic")

for src, tgt, conn in [(Tp, Rp, {"sources": {"model": "TpRelay"},
                                 "synapse_model": "AMPA",
                                 "mask": {"circular": {"radius": 2.0 * dpc}},
                                 "kernel": {"gaussian": {"p_center": 1.0,
                                                         "sigma": 7.5 * dpc}},
                                 "weights": 2.0}),
                       (Tp, Tp, {"sources": {"model": "TpInter"},
                                 "targets": {"model": "TpRelay"},
                                 "synapse_model": "GABA_A",
                                 "weights": -1.0,
                                 "mask": {"circular": {"radius": 2.0 * dpc}},
                                 "kernel": {"gaussian":
                                            {"p_center": 0.25,
                                             "sigma": 7.5 * dpc}}}),
                       (Tp, Tp, {"sources": {"model": "TpInter"},
                                 "targets": {"model": "TpInter"},
                                 "synapse_model": "GABA_A",
                                 "weights": -1.0,
                                 "mask": {"circular": {"radius": 2.0 * dpc}},
                                 "kernel": {"gaussian":
                                            {"p_center": 0.25,
                                             "sigma": 7.5 * dpc}}}),
                       (Rp, Tp, {"targets": {"model": "TpRelay"},
                                 "synapse_model": "GABA_A",
                                 "weights": -1.0,
                                 "mask": {"circular": {"radius": 12.0 * dpc}},
                                 "kernel": {"gaussian":
                                            {"p_center": 0.15,
                                             "sigma": 7.5 * dpc}}}),
                       (Rp, Tp, {"targets": {"model": "TpInter"},
                                 "synapse_model": "GABA_A",
                                 "weights": -1.0,
                                 "mask": {"circular": {"radius": 12.0 * dpc}},
                                 "kernel": {"gaussian":
                                            {"p_center": 0.15,
                                             "sigma": 7.5 * dpc}}}),
                       (Rp, Rp, {"targets": {"model": "RpNeuron"},
                                 "synapse_model": "GABA_A",
                                 "weights": -1.0,
                                 "mask": {"circular": {"radius": 12.0 * dpc}},
                                 "kernel": {"gaussian":
                                            {"p_center": 0.5,
                                             "sigma": 7.5 * dpc}}})]:
    thalBase.update(conn)
    topo.ConnectLayers(src, tgt, thalBase)

# ! Thalamic input
# ! --------------

# ! Input to the thalamus from the retina.
# !
# ! **Note:** Hill & Tononi specify a delay of 0 ms for this connection.
# ! We use 1 ms here.
retThal = {"connection_type": "divergent",
           "synapse_model": "AMPA",
           "mask": {"circular": {"radius": 1.0 * dpc}},
           "kernel": {"gaussian": {"p_center": 0.75, "sigma": 2.5 * dpc}},
           "weights": 10.0,
           "delays": 1.0}

print("Connecting: retino-thalamic")

for conn in [{"targets": {"model": "TpRelay"}},
             {"targets": {"model": "TpInter"}}]:
    retThal.update(conn)
    topo.ConnectLayers(retina, Tp, retThal)

# ! Checks on connections
# ! ---------------------

# ! As a very simple check on the connections created, we inspect
# ! the connections from the central node of various layers.

# ! Connections from Retina to TpRelay
topo.PlotTargets(topo.FindCenterElement(retina), Tp, 'TpRelay', 'AMPA')
pylab.title('Connections Retina -> TpRelay')
pylab.show()

# ! Connections from TpRelay to L4pyr in Vp (horizontally tuned)
topo.PlotTargets(topo.FindCenterElement(Tp), Vp_h, 'L4pyr', 'AMPA')
pylab.title('Connections TpRelay -> Vp(h) L4pyr')
pylab.show()

# ! Connections from TpRelay to L4pyr in Vp (vertically tuned)
topo.PlotTargets(topo.FindCenterElement(Tp), Vp_v, 'L4pyr', 'AMPA')
pylab.title('Connections TpRelay -> Vp(v) L4pyr')
pylab.show()

# ! Recording devices
# ! =================

# ! This recording device setup is a bit makeshift. For each population
# ! we want to record from, we create one ``multimeter``, then select
# ! all nodes of the right model from the target population and
# ! connect. ``loc`` is the subplot location for the layer.
print("Connecting: Recording devices")
recorders = {}
for name, loc, population, model in [('TpRelay', 1, Tp, 'TpRelay'),
                                     ('Rp', 2, Rp, 'RpNeuron'),
                                     ('Vp_v L4pyr', 3, Vp_v, 'L4pyr'),
                                     ('Vp_h L4pyr', 4, Vp_h, 'L4pyr')]:
    recorders[name] = (nest.Create('RecordingNode'), loc)
    # population_leaves is a work-around until NEST 3.0 is released
    population_leaves = nest.GetLeaves(population)[0]
    tgts = [nd for nd in population_leaves
            if nest.GetStatus([nd], 'model')[0] == model]
    nest.Connect(recorders[name][0], tgts)  # one recorder to all targets

# ! Example simulation
# ! ====================

# ! This simulation is set up to create a step-wise visualization of
# ! the membrane potential. To do so, we simulate ``sim_interval``
# ! milliseconds at a time, then read out data from the multimeters,
# ! clear data from the multimeters and plot the data as pseudocolor
# ! plots.

# ! show time during simulation
nest.SetStatus([0], {'print_time': True})

# ! lower and upper limits for color scale, for each of the four
# ! populations recorded.
vmn = [-80, -80, -80, -80]
vmx = [-50, -50, -50, -50]

nest.Simulate(Params['sim_interval'])

# ! loop over simulation intervals
for t in pylab.arange(Params['sim_interval'], Params['simtime'],
                      Params['sim_interval']):

    # do the simulation
    nest.Simulate(Params['sim_interval'])

    # clear figure and choose colormap
    pylab.clf()
    pylab.jet()

    # now plot data from each recorder in turn, assume four recorders
    for name, r in recorders.items():
        rec = r[0]
        sp = r[1]
        pylab.subplot(2, 2, sp)
        d = nest.GetStatus(rec)[0]['events']['V_m']

        if len(d) != Params['N'] ** 2:
            # cortical layer with two neurons in each location, take average
            d = 0.5 * (d[::2] + d[1::2])

        # clear data from multimeter
        nest.SetStatus(rec, {'n_events': 0})
        pylab.imshow(pylab.reshape(d, (Params['N'], Params['N'])),
                     aspect='equal', interpolation='nearest',
                     extent=(0, Params['N'] + 1, 0, Params['N'] + 1),
                     vmin=vmn[sp - 1], vmax=vmx[sp - 1])
        pylab.colorbar()
        pylab.title(name + ', t = %6.1f ms' % nest.GetKernelStatus()['time'])

    pylab.draw()  # force drawing inside loop
    pylab.show()  # required by ``pyreport``

# ! just for some information at the end
print(nest.GetKernelStatus())