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197	197
198	198	Now if we run our simulation again, we can see the effect of this heterogeneity in the neuron population.
199	199
200		-TO BE COMPLETED
	200	+(% class="box successmessage" %)
	201	+(((
	202	+**Slide** showing addition of second population, and of connections between them
	203	+)))
201	201
202		-(% class="wikigeneratedid" id="HSummary28Inthistutorial2CyouhavelearnedtodoX202629" %)
203		-(% class="small" %)**Summary (In this tutorial, you have learned to do X…)**
	205	+(% class="wikigeneratedid" %)
	206	+So far we have a population of neurons, but there are no connections between them, we don't have a network. Let's add a second population of the same size as the first, but we'll set the offset current to zero, so they don't fire action potentials spontaneously.
204	204
205		-.
	208	+(% class="box infomessage" %)
	209	+(((
	210	+**Screencast** - current state of editor
	211	+\\(% style="color:#000000" %)"""Simple network model using PyNN"""
	212	+\\import pyNN.nest as sim(%%)
	213	+(% style="color:#000000" %)from pyNN.utility.plotting import Figure, Panel(%%)
	214	+(% style="color:#000000" %)from pyNN.random import RandomDistribution(%%)
	215	+(% style="color:#000000" %)sim.setup(timestep=0.1)(%%)
	216	+(% style="color:#000000" %)cell_type  = sim.IF_curr_exp(
	217	+ (% style="color:#e74c3c" %) (% style="color:#000000" %)v_rest=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}),
	218	+ v_thresh=RandomDistribution('normal', {'mu': -55.0, 'sigma': 1.0}),
	219	+ v_reset=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}), (%%)
	220	+(% style="color:#000000" %) t_refrac=1, tau_m=10, cm=1, i_offset=0.1)(%%)
	221	+(% style="color:#000000" %)population1 = sim.Population(100, cell_type, label="Population 1")(%%)
	222	+(% style="color:#e74c3c" %)population2 = sim.Population(100, cell_type, label="Population 2")
	223	+population2.set(i_offset=0)(%%)
	224	+(% style="color:#000000" %)population1.record("v")(%%)
	225	+(% style="color:#e74c3c" %)population2.record("v")(%%)
	226	+(% style="color:#000000" %)sim.run(100.0)(%%)
	227	+(% style="color:#000000" %)data_v = population1.get_data().segments[0].filter(name='v')[0]
	228	+Figure(
	229	+ Panel(
	230	+ data_v[:, 0:5],
	231	+ xticks=True, xlabel="Time (ms)",
	232	+ yticks=True, ylabel="Membrane potential (mV)"
	233	+ ),
	234	+ title="Response of first five neurons with heterogeneous parameters",
	235	+ annotations="Simulated with NEST"
	236	+).show()
	237	+)))
206	206
207		-(% class="wikigeneratedid" id="HAcknowledgementsifappropriate" %)
208		-(% class="small" %)**Acknowledgements if appropriate**
	239	+Now we want to create synaptic connections between the neurons in Population 1 and those in Population 2. There are lots of different ways these could be connected.
209	209
210		-.
	241	+(% class="box successmessage" %)
	242	+(((
	243	+**Slide** showing all-to-all connections
	244	+)))
211	211
212		-(% class="wikigeneratedid" id="HReferencestowebsites28Formoreinformation2Cvisitusat202629" %)
213		-(% class="small" %)**References to websites (For more information, visit us at…)**
	246	+We could connect all neurons in Population 1 to all those in Population 2.
214	214
215		-.
	248	+(% class="box successmessage" %)
	249	+(((
	250	+**Slide** showing random connections
	251	+)))
216	216
217		-(% class="wikigeneratedid" id="HContactinformation28Forquestions2Ccontactusat202629" %)
218		-(% class="small" %)**Contact information (For questions, contact us at…)**
	253	+We could connect the populations randomly, in several different ways.
219	219
220		-.
	255	+(% class="box successmessage" %)
	256	+(((
	257	+**Slide** showing distance-dependent connections
	258	+)))
	259	+
	260	+(% class="wikigeneratedid" %)
	261	+We could connect the populations randomly, but with a probability of connection that depends on the distance between the neurons.
	262	+
	263	+(% class="box successmessage" %)
	264	+(((
	265	+**Slide** showing explicit lists of connections
	266	+)))
	267	+
	268	+(% class="wikigeneratedid" %)
	269	+Or we could connect the neurons in a very specific manner, based on an explicit list of connections.
	270	+
	271	+(% class="wikigeneratedid" %)
	272	+Just as PyNN provides a variety of neuron models, so it comes with a range of connection algorithms built in. You can also add your own connection methods.
	273	+
	274	+(% class="box successmessage" %)
	275	+(((
	276	+**Slide** showing addition of second population, and of connections between them, labelled as a Projection.
	277	+)))
	278	+
	279	+(% class="wikigeneratedid" %)
	280	+In PyNN, we call a group of connections between two populations a _Projection_. To create a Projection, we need to specify the presynaptic population, the postsynaptic population, the connection algorithm, and the synapse model. Here we're using the simplest synapse model available in PyNN, for which the synaptic weight is constant over time, there is no plasticity.
	281	+
	282	+(% class="box infomessage" %)
	283	+(((
	284	+**Screencast** - current state of editor
	285	+\\(% style="color:#000000" %)"""Simple network model using PyNN"""
	286	+\\import pyNN.nest as sim(%%)
	287	+(% style="color:#000000" %)from pyNN.utility.plotting import Figure, Panel(%%)
	288	+(% style="color:#000000" %)from pyNN.random import RandomDistribution(%%)
	289	+(% style="color:#000000" %)sim.setup(timestep=0.1)(%%)
	290	+(% style="color:#000000" %)cell_type  = sim.IF_curr_exp(
	291	+ (% style="color:#e74c3c" %) (% style="color:#000000" %)v_rest=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}),
	292	+ v_thresh=RandomDistribution('normal', {'mu': -55.0, 'sigma': 1.0}),
	293	+ v_reset=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}), (%%)
	294	+(% style="color:#000000" %) t_refrac=1, tau_m=10, cm=1, i_offset=0.1)(%%)
	295	+(% style="color:#000000" %)population1 = sim.Population(100, cell_type, label="Population 1")(%%)
	296	+(% style="color:#000000" %)population2 = sim.Population(100, cell_type, label="Population 2")
	297	+population2.set(i_offset=0)
	298	+population1.record("v")
	299	+population2.record("v")(%%)
	300	+(% style="color:#e74c3c" %)connection_algorithm = sim.FixedProbabilityConnector(p=0.5)
	301	+synapse_type = sim.StaticSynapse(weight=0.5, delay=0.5)
	302	+connections = sim.Projection(population1, population2, connection_algorithm, synapse_type)(%%)
	303	+(% style="color:#000000" %)sim.run(100.0)(%%)
	304	+(% style="color:#000000" %)data_v = population1.get_data().segments[0].filter(name='v')[0]
	305	+Figure(
	306	+ Panel(
	307	+ data_v[:, 0:5],
	308	+ xticks=True, xlabel="Time (ms)",
	309	+ yticks=True, ylabel="Membrane potential (mV)"
	310	+ ),
	311	+ title="Response of first five neurons with heterogeneous parameters",
	312	+ annotations="Simulated with NEST"
	313	+).show()
	314	+)))
	315	+
	316	+(% class="wikigeneratedid" %)
	317	+Finally, let's update our figure, by adding a second panel to show the responses of Population 2.
	318	+
	319	+(% class="box infomessage" %)
	320	+(((
	321	+**Screencast** - current state of editor
	322	+\\(% style="color:#000000" %)"""Simple network model using PyNN"""
	323	+\\import pyNN.nest as sim(%%)
	324	+(% style="color:#000000" %)from pyNN.utility.plotting import Figure, Panel(%%)
	325	+(% style="color:#000000" %)from pyNN.random import RandomDistribution(%%)
	326	+(% style="color:#000000" %)sim.setup(timestep=0.1)(%%)
	327	+(% style="color:#000000" %)cell_type  = sim.IF_curr_exp(
	328	+ (% style="color:#e74c3c" %) (% style="color:#000000" %)v_rest=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}),
	329	+ v_thresh=RandomDistribution('normal', {'mu': -55.0, 'sigma': 1.0}),
	330	+ v_reset=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}), (%%)
	331	+(% style="color:#000000" %) t_refrac=1, tau_m=10, cm=1, i_offset=0.1)(%%)
	332	+(% style="color:#000000" %)population1 = sim.Population(100, cell_type, label="Population 1")(%%)
	333	+(% style="color:#000000" %)population2 = sim.Population(100, cell_type, label="Population 2")
	334	+population2.set(i_offset=0)
	335	+population1.record("v")
	336	+population2.record("v")(%%)
	337	+(% style="color:#000000" %)connection_algorithm = sim.FixedProbabilityConnector(p=0.5)
	338	+synapse_type = sim.StaticSynapse(weight=0.5, delay=0.5)
	339	+connections = sim.Projection(population1, population2, connection_algorithm, synapse_type)(%%)
	340	+(% style="color:#000000" %)sim.run(100.0)(%%)
	341	+(% style="color:#e74c3c" %)data1_v(% style="color:#000000" %) = population1.get_data().segments[0].filter(name='v')[0](%%)
	342	+(% style="color:#e74c3c" %)data2_v = population2.get_data().segments[0].filter(name='v')[0](%%)
	343	+(% style="color:#000000" %)Figure(
	344	+ Panel(
	345	+ (% style="color:#e74c3c" %)data1_v(% style="color:#000000" %)[:, 0:5],
	346	+ xticks=True, (% style="color:#e74c3c" %)--xlabel="Time (ms)",--(%%)
	347	+(% style="color:#000000" %) yticks=True, ylabel="Membrane potential (mV)"
	348	+ ),
	349	+ (% style="color:#e74c3c" %)Panel(
	350	+ data2_v[:, 0:5],
	351	+ xticks=True, xlabel="Time (ms)",
	352	+ yticks=True"
	353	+ ),(%%)
	354	+(% style="color:#000000" %) title="Response of (% style="color:#e74c3c" %)simple network(% style="color:#000000" %)",
	355	+ annotations="Simulated with NEST"
	356	+).show()
	357	+
	358	+**Run script in terminal, show figure**
	359	+)))
	360	+
	361	+(% class="wikigeneratedid" %)
	362	+and there we have it, our simple neuronal network of integrate-and-fire neurons, written in PyNN, simulated with NEST. If you prefer to use the NEURON simulator, PyNN makes this very simple, we import the PyNN-for-NEURON module instead.
	363	+
	364	+(% class="box infomessage" %)
	365	+(((
	366	+**Screencast** - current state of editor
	367	+\\(% style="color:#000000" %)"""Simple network model using PyNN"""
	368	+\\import pyNN.(% style="color:#e74c3c" %)neuron(% style="color:#000000" %) as sim(%%)
	369	+(% style="color:#000000" %)from pyNN.utility.plotting import Figure, Panel(%%)
	370	+(% style="color:#000000" %)from pyNN.random import RandomDistribution(%%)
	371	+(% style="color:#000000" %)sim.setup(timestep=0.1)(%%)
	372	+(% style="color:#000000" %)cell_type  = sim.IF_curr_exp(
	373	+ (% style="color:#e74c3c" %) (% style="color:#000000" %)v_rest=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}),
	374	+ v_thresh=RandomDistribution('normal', {'mu': -55.0, 'sigma': 1.0}),
	375	+ v_reset=RandomDistribution('normal', {'mu': -65.0, 'sigma': 1.0}), (%%)
	376	+(% style="color:#000000" %) t_refrac=1, tau_m=10, cm=1, i_offset=0.1)(%%)
	377	+(% style="color:#000000" %)population1 = sim.Population(100, cell_type, label="Population 1")(%%)
	378	+(% style="color:#000000" %)population2 = sim.Population(100, cell_type, label="Population 2")
	379	+population2.set(i_offset=0)
	380	+population1.record("v")
	381	+population2.record("v")(%%)
	382	+(% style="color:#000000" %)connection_algorithm = sim.FixedProbabilityConnector(p=0.5)
	383	+synapse_type = sim.StaticSynapse(weight=0.5, delay=0.5)
	384	+connections = sim.Projection(population1, population2, connection_algorithm, synapse_type)(%%)
	385	+(% style="color:#000000" %)sim.run(100.0)(%%)
	386	+(% style="color:#000000" %)data1_v = population1.get_data().segments[0].filter(name='v')[0]
	387	+data2_v = population2.get_data().segments[0].filter(name='v')[0]
	388	+Figure(
	389	+ Panel(
	390	+ data1_v[:, 0:5],
	391	+ xticks=True,
	392	+ yticks=True, ylabel="Membrane potential (mV)"
	393	+ ),
	394	+ Panel(
	395	+ data2_v[:, 0:5],
	396	+ xticks=True, xlabel="Time (ms)",
	397	+ yticks=True"
	398	+ ),(%%)
	399	+(% style="color:#000000" %) title="Response of simple network",
	400	+ annotations="Simulated with (% style="color:#e74c3c" %)NEURON(% style="color:#000000" %)"
	401	+).show()
	402	+
	403	+**Run script in terminal, show figure**
	404	+)))
	405	+
	406	+(% class="wikigeneratedid" %)
	407	+As you would hope, NEST and NEURON give essentially identical results.
	408	+
	409	+(% class="box successmessage" %)
	410	+(((
	411	+**Slide** recap of learning objectives
	412	+)))
	413	+
	414	+That is the end of this tutorial, in which I've demonstrated how to build a simple network using PyNN, and to simulate it using two different simulators, NEST and NEURON.
	415	+
	416	+Of course, PyNN allows you to create much more complex networks than this, with more realistic neuron models, synaptic plasticity, spatial structure, and so on. You can also use other simulators, such as Brian or SpiNNaker, and you can run simulations in parallel on clusters or supercomputers.
	417	+
	418	+We will be releasing a series of tutorials, throughout the rest of 2021 and 2022, to introduce these more advanced features of PyNN, so keep an eye on the EBRAINS website.
	419	+
	420	+(% class="box successmessage" %)
	421	+(((
	422	+**Slide** acknowledgements, contact information
	423	+)))
	424	+
	425	+(% class="wikigeneratedid" %)
	426	+PyNN has been developed by many different people, with financial support from several different organisations. I'd like to mention in particular the CNRS and the European Commission, through the FACETS, BrainScaleS and Human Brain Project grants.
	427	+
	428	+(% class="wikigeneratedid" %)
	429	+For more information visit neuralensemble.org/PyNN. If you have questions you can contact us through the PyNN Github project, the NeuralEnsemble forum, EBRAINS support, or the EBRAINS Community.