# Part 3: Connecting networks with synapses

## Introduction

In this handout we look at using synapse models to connect neurons. After you have worked through this material, you will know how to:

• set synapse model parameters before creation
• define synapse models with customised parameters
• use synapse models in connection routines
• query the synapse values after connection
• set synapse values during and after connection

More advanced examples can be found at Example Networks, or have a look at at the source directory of your NEST installation in the subdirectory: pynest/examples/.

## Parameterising synapse models

NEST provides a variety of different synapse models. You can see the available models by using the command nest.Models(mtype='synapses'), which picks only the synapse models out of the list of all available models.

Synapse models can be parameterised analogously to neuron models. You can discover the default parameter settings using GetDefaults(model) and set them with SetDefaults(model,params):

nest.SetDefaults("stdp_synapse",{"tau_plus": 15.0})

Any synapse generated from this model will then have all the standard parameters except for the tau_plus, which will have the value given above.

Moreover, we can also create customised variants of synapse models using CopyModel(), exactly as demonstrated for neuron models:

nest.CopyModel("stdp_synapse","layer1_stdp_synapse",{"Wmax": 90.0})

Now layer1_stdp_synapse will appear in the list returned by Models(), and can be used anywhere that a built-in model name can be used.

### STDP synapses

For the majority of synapses, all of their parameters are accessible via GetDefaults() and SetDefaults(). Synapse models implementing spike-timing dependent plasticity are an exception to this, as their dynamics are driven by the post-synaptic spike train as well as the pre-synaptic one. As a consequence, the time constant of the depressing window of STDP is a parameter of the post-synaptic neuron. It can be set as follows:

nest.Create("iaf_psc_alpha", params={"tau_minus": 30.0})

or by using any of the other methods of parameterising neurons demonstrated in the first two parts of this introduction.

## Connecting with synapse models

The synapse model as well as parameters associated with the synapse type can be set in the synapse specification dictionary accepted by the connection routine.

conn_dict = {"rule": "fixed_indegree", "indegree": K}
syn_dict = {"model": "stdp_synapse", "alpha": 1.0}
nest.Connect(epop1, epop2, conn_dict, syn_dict)

If no synapse model is given, connections are made using the model static_synapse.

## Distributing synapse parameters

The synapse parameters are specified in the synapse dictionary which is passed to the Connect-function. If the parameter is set to a scalar all connections will be drawn using the same parameter. Parameters can be randomly distributed by assigning a dictionary to the parameter. The dictionary has to contain the key distribution setting the target distribution of the parameters (for example normal). Optionally, parameters associated with the distribution can be set (for example mu). Here we show an example where the parameters alpha and weight of the stdp synapse are uniformly distributed.

alpha_min = 0.1
alpha_max = 2.
w_min = 0.5
w_max = 5.

syn_dict = {"model": "stdp_synapse",
"alpha": {"distribution": "uniform", "low": alpha_min, "high": alpha_max},
"weight": {"distribution": "uniform", "low": w_min, "high": w_max},
"delay": 1.0}
nest.Connect(epop1, neuron, "all_to_all", syn_dict)

Available distributions and associated parameters are described in Connection Management, the most common ones are:

Distributions Keys
normal mu, sigma
lognormal mu, sigma
uniform low, high
uniform_int low, high
binomial n, p
exponential lambda
gamma order, scale
poisson lambda

## Querying the synapses

The function GetConnections(source=None, target=None, synapse_model=None) returns a list of connection identifiers that match the given specifications. There are no mandatory arguments. If it is called without any arguments, it will return all the connections in the network. If source is specified, as a list of one or more nodes, the function will return all outgoing connections from that population:

nest.GetConnections(epop1)

Similarly, we can find the incoming connections of a particular target population by specifying target as a list of one or more nodes:

nest.GetConnections(target=epop2)

will return all connections beween all neurons in the network and neurons in epop2. Finally, the search can be restricted by specifying a given synapse model:

nest.GetConnections(synapse_model="stdp_synapse")

will return all the connections in the network which are of type stdp_synapse. The last two cases are slower than the first case, as a full search of all connections has to be performed.The arguments source, target and synapse_model can be used individually, as above, or in any conjunction:

nest.GetConnections(epop1, epop2, "stdp_synapse")

will return all the connections that the neurons in epop1 have to neurons in epop2 of type stdp_synapse. Note that all these querying commands will only return the local connections, i.e. those represented on that particular MPI process in a distributed simulation.

Once we have the array of connections, we can extract data from it using GetStatus(). In the simplest case, this returns a list of dictionaries, containing the parameters and variables for each connection found by GetConnections. However, usually we don’t want all the information from a synapse, but some specific part of it. For example, if we want to check we have connected the network as intended, we might want to examine only the parameter target of each connection. We can extract just this information by using the optional keys argument of GetStatus():

conns = nest.GetConnections(epop1, synapse_model="stdp_synapse")
targets = nest.GetStatus(conns, "target")

The variable targets is now list of all the target values of the connections found. If we are interested in more than one parameter, keys can be a list of keys as well:

conns = nest.GetConnections(epop1, synapse_model="stdp_synapse")
conn_vals = nest.GetStatus(conns, ["target","weight"])

The variable conn_vals is now a list of lists, containing the target and weight values for each connection found.

To get used to these methods of querying the synapses, it is recommended to try them out on a small network where all connections are known.

## Coding style

As your simulations become more complex, it is very helpful to develop a clean coding style. This reduces the number of errors in the first place, but also assists you to debug your code and makes it easier for others to understand it (or even yourself after two weeks). Here are some pointers, some of which are common to programming in general and some of which are more NEST specific. Another source of useful advice is PEP-8, which, conveniently, can be automatically checked by many editors and IDEs.

### Numbers and variables

Simulations typically have lots of numbers in them - we use them to set parameters for neuron models, to define the strengths of connections, the length of simulations and so on. Sometimes we want to use the same parameters in different scripts, or calculate some parameters based on the values of other parameters. It is not recommended to hardwire the numbers into your scripts, as this is error-prone: if you later decide to change the value of a given parameter, you have to go through all your code and check that you have changed every instance of it. This is particularly difficult to catch if the value is being used in different contexts, for example to set a weight in one place and to calculate the mean synaptic input in another.

A better approach is to set a variable to your parameter value, and then always use the variable name every time the value is needed. It is also hard to follow the code if the definitions of variables are spread throughout the script. If you have a parameters section in your script, and group the variable names according to function (e.g. neuronal parameters, synaptic parameters, stimulation parameters,...) then it is much easier to find and check them. Similarly, if you need to share parameters between simulation scripts, it is much less error-prone to define all the variable names in a separate parameters file, which the individual scripts can import. Thus a good rule of thumb is that numbers should only be visible in distinct parameter files or parameter sections, otherwise they should be represented by variables.

### Repetitive code, copy-and-paste, functions

Often you need to repeat a section of code with minor modifications. For example, you have two multimeters and you wish to extract the recorded variable from each of them and then calculate its maximum. The temptation is to write the code once, then copy-and-paste it to its new location and make any necessary modifications:

dma = nest.GetStatus(ma, keys="events")[0]
Vma = dma["Vm"]
amax = max(Vma)
dmb = nest.GetStatus(mb, keys="events")[0]
Vmb = dmb["Vm"]
bmax = max(Vmb)
print(amax-bmax)

There are two problems with this. First, it makes the main section of your code longer and harder to follow. Secondly, it is error-prone. A certain percentage of the time you will forget to make all the necessary modifications after the copy-and-paste, and this will introduce errors into your code that are hard to find, not only because they are semantically correct and so don’t cause an obvious error, but also because your eye tends to drift over them:

dma = nest.GetStatus(multimeter1, keys="events")[0]
Vma = dma["Vm"]
amax = max(Vma)
dmb = nest.GetStatus(multimeter2, keys="events")[0]
Vmb = dmb["Vm"]
bmax = max(Vma)
print(amax-bmax)

The best way to avoid this is to define a function:

def getMaxMemPot(Vdevice):
dm = nest.GetStatus(Vdevice, keys="events")[0]
return max(dm["Vm"])

Such helper functions can usefully be stored in their own section, analogous to the parameters section. Now we can write down the functionality in a more concise and less error-prone fashion:

amax = getMaxMemPot(multimeter1)
bmax = getMaxMemPot(multimeter2)
print(amax-bmax)

If you find that this clutters your code, as an alternative you can write a lambda function as an argument for map, and enjoy the feeling of smugness that will pervade the rest of your day. A good policy is that if you find yourself about to copy-and-paste more than one line of code, consider taking the few extra seconds required to define a function. You will easily win this time back by spending less time looking for errors.

### Subsequences and loops

When preparing a simulation or collecting or analysing data, it commonly happens that we need to perform the same operation on each node (or a subset of nodes) in a population. As neurons receive ids at the time of creation, it is possible to use your knowledge of these ids explictly:

Nrec = 50
neuronpop = nest.Create("iaf_psc_alpha", 200)
sd = nest.Create("spike_detector")
nest.Connect(range(1,N_rec+1),sd,"all_to_all")

However, this is not at all recommended!. This is because as you develop your simulation, you may well add additional nodes - this means that your initially correct range boundaries are now incorrect, and this is an error that is hard to catch. To get a subsequence of nodes, use a slice of the relevant population:

nest.Connect(neuronpop[:Nrec],spikedetector,"all_to_all")

An even worse thing is to use knowledge about neuron ids to set up loops:

for n in range(1,len(neuronpop)+1):
nest.SetStatus([n], {"V_m": -67.0})

Not only is this error prone as in the previous example, the majority of PyNEST functions are expecting a list anyway. If you give them a list, you are reducing the complexity of your main script (good) and pushing the loop down to the faster C++ kernel, where it will run more quickly (also good). Therefore, instead you should write:

nest.SetStatus(neuronpop, {"V_m": -67.0})

See Part 2 for more examples on operations on multiple neurons, such as setting the status from a random distribution and connecting populations.

If you really really need to loop over neurons, just loop over the population itself (or a slice of it) rather than introducing ranges:

for n in neuronpop:
my_weird_function(n)

Thus we can conclude: instead of range operations, use slices of and loops over the neuronal population itself. In the case of loops, check first whether you can avoid it entirely by passing the entire population into the function - you usually can.

## Command overview

These are the new functions we introduced for the examples in this handout.

### Querying Synapses

• GetConnections(neuron, synapse_model="None"))

Return an array of connection identifiers.

Parameters:

• source - list of source GIDs
• target - list of target GIDs
• synapse_model - string with the synapse model

If GetConnections is called without parameters, all connections in the network are returned. If a list of source neurons is given, only connections from these pre-synaptic neurons are returned. If a list of target neurons is given, only connections to these post-synaptic neurons are returned. If a synapse model is given, only connections with this synapse type are returned. Any combination of source, target and synapse_model parameters is permitted. Each connection id is a 5-tuple or, if available, a NumPy array with the following five entries: source-gid, target-gid, target-thread, synapse-id, port

Note: Only connections with targets on the MPI process executing the command are returned.