# PySpike¶

PySpike is a Python library for the numerical analysis of spike train similarity. Its core functionality is the implementation of the ISI-distance 1 and SPIKE-distance 2, SPIKE-Synchronization 3, as well as their adaptive generalizations 4. It provides functions to compute multivariate profiles, distance matrices, as well as averaging and general spike train processing. All computation intensive parts are implemented in C via cython to reach a competitive performance (factor 100-200 over plain Python).

PySpike provides the same fundamental functionality as the SPIKY framework for Matlab, which additionally contains spike-train generators, more spike train distance measures and many visualization routines.

All source codes are available on Github and are published under the BSD_License.

## Citing PySpike¶

- If you use PySpike in your research, please cite our SoftwareX publication on PySpike:
Mario Mulansky, Thomas Kreuz,

*PySpike - A Python library for analyzing spike train synchrony*, Software X 5, 183 (2016) [pdf]

Additionally, depending on the used methods: ISI-distance [1], SPIKE-distance [2], SPIKE-Synchronization [3], or their adaptive generalizations [4], please cite one or more of the following publications:

- 1
Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A,

*Measuring spike train synchrony.*J Neurosci Methods 165, 151 (2007) [pdf]- 2
Kreuz T, Chicharro D, Houghton C, Andrzejak RG, Mormann F,

*Monitoring spike train synchrony.*J Neurophysiol 109, 1457 (2013) [pdf]- 3
Kreuz T, Mulansky M and Bozanic N,

*SPIKY: A graphical user interface for monitoring spike train synchrony*, J Neurophysiol 113, 3432 (2015) [pdf]- 4
Satuvuori E, Mulansky M, Bozanic N, Malvestio I, Zeldenrust F, Lenk K, and Kreuz T,

*Measures of spike train synchrony for data with multiple time-scales*, J Neurosci Methods 287, 25 (2017) [pdf]

## Important Changelog¶

With version 0.8.0, Adaptive and Rate Independent algorithms are supported.

With version 0.7.0, support for Python 2 was dropped, PySpike now officially supports Python 3.7, 3.8, 3.9, 3.10.

With version 0.6.0, the spike directionality and spike train order function have been added.

With version 0.5.0, the interfaces have been unified and the specific functions for multivariate computations have become deprecated.

With version 0.2.0, the `SpikeTrain`

class has been introduced to represent spike trains.
This is a breaking change in the function interfaces.
Hence, programs written for older versions of PySpike (0.1.x) will not run with newer versions.

## Requirements and Installation¶

PySpike is available at Python Package Index and this is the easiest way to obtain the PySpike package. If you have pip installed, just run

```
sudo pip install pyspike
```

to install pyspike. PySpike requires numpy as minimal requirement, as well as a C compiler to generate the binaries.

### Install from Github sources¶

You can also obtain the latest PySpike developer version from the github repository. For that, make sure you have the following Python libraries installed:

numpy

cython

matplotlib (for the examples)

pytest (for running the tests)

scipy (also for the tests)

In particular, make sure that cython is configured properly and able to locate a C compiler, otherwise PySpike will use the much slower Python implementations.

To install PySpike, simply download the source, e.g. from Github, and run the `setup.py`

script:

```
git clone https://github.com/mariomulansky/PySpike.git
cd PySpike
python setup.py build_ext --inplace
```

Then you can run the tests using the pytest test framework:

```
pytest
```

Finally, you should make PySpike’s installation folder known to Python to be able to import pyspike in your own projects.
Therefore, add your `/path/to/PySpike`

to the `$PYTHONPATH`

environment variable.

## Examples¶

The following code loads some exemplary spike trains, computes the dissimilarity profile of the ISI-distance of the first two `SpikeTrain`

objects, and plots it with matplotlib:

```
import matplotlib.pyplot as plt
import pyspike as spk
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
isi_profile = spk.isi_profile(spike_trains[0], spike_trains[1])
x, y = isi_profile.get_plottable_data()
plt.plot(x, y, '--k')
print("ISI distance: %.8f" % isi_profile.avrg())
plt.show()
```

The following example computes the multivariate ISI-, SPIKE- and SPIKE-Sync-profile for a list of spike trains loaded from a text file:

```
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
avrg_isi_profile = spk.isi_profile(spike_trains)
avrg_spike_profile = spk.spike_profile(spike_trains)
avrg_spike_sync_profile = spk.spike_sync_profile(spike_trains)
```

More examples with detailed descriptions can be found in the tutorial section.

*The work on PySpike was supported by the European Comission through the Marie
Curie Initial Training Network* Neural Engineering Transformative Technologies
(NETT) *under the project number 289146.*

**Python/C Programming:**Mario Mulansky

Edmund J Butler

**Scientific Methods:**Thomas Kreuz

Daniel Chicharro

Conor Houghton

Nebojsa Bozanic

Mario Mulansky

# Tutorial¶

## Spike trains¶

In PySpike, spike trains are represented by `SpikeTrain`

objects.
A `SpikeTrain`

object consists of the spike times given as numpy arrays as well as the edges of the spike train as `[t_start, t_end]`

.
The following code creates such a spike train with some arbitrary spike times:

```
import numpy as np
from pyspike import SpikeTrain
spike_train = SpikeTrain(np.array([0.1, 0.3, 0.45, 0.6, 0.9], [0.0, 1.0]))
```

### Loading from text files¶

Typically, spike train data is loaded into PySpike from data files.
The most straight-forward data files are text files where each line represents one spike train given as an sequence of spike times.
An exemplary file with several spike trains is PySpike_testdata.txt.
To quickly obtain spike trains from such files, PySpike provides the function `load_spike_trains_from_txt()`

.

```
import numpy as np
import pyspike as spk
spike_trains = spk.load_spike_trains_from_txt("SPIKY_testdata.txt",
edges=(0, 4000))
```

This function expects the name of the data file as first parameter.
Furthermore, the time interval of the spike train measurement (edges of the spike trains) should be provided as a pair of start- and end-time values.
Furthermore, the spike trains are sorted via `np.sort`

(disable this feature by providing `is_sorted=True`

as a parameter to the load function).
As result, `load_spike_trains_from_txt()`

returns a *list of arrays* containing the spike trains in the text file.

**Important note:**

Spike trains are expected to be *sorted*!
For performance reasons, the PySpike distance functions do not check if the spike trains provided are indeed sorted.
Make sure that all your spike trains are sorted, which is ensured if you use the `load_spike_trains_from_txt()`

function with the parameter is_sorted=False (default).
If in doubt, use `SpikeTrain.sort()`

to ensure a correctly sorted spike train.

Alternatively the function `reconcile_spike_trains()`

applies three fixes to a list of SpikeTrain objects. It sorts
the times, it removes all but one of any duplicated time, and it ensures all t_start and t_end values are compatible

```
from pyspike.spikes import reconcile_spike_trains
spike_trains = reconcile_spike_trains(spike_trains)
```

If you need to copy a spike train, use the `SpikeTrain.copy()`

method.
Simple assignment t2 = t1 does not create a copy of the spike train data, but a reference as numpy.array is used for storing the data.

## PySpike algorithms¶

PySpike supports four basic algorithms for comparing spike trains and their adaptive generalizations

The basic algorithms are:

ISI-distance (Inter Spike Intervals)

SPIKE-distance

Rate-Independent SPIKE-distance (RI-SPIKE)

SPIKE sychronization

plus

(5-8) Adaptive generalizations of 1-4 based on the MRTS (Minimum Relevant Time Scale) parameter

Algorithms 3 and 5-8 are new in version 0.8.0.

### ISI-distance¶

The following code loads some exemplary spike trains, computes the dissimilarity profile of the ISI-distance of the first two `SpikeTrain`

s, and plots it with matplotlib:

```
import matplotlib.pyplot as plt
import pyspike as spk
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
isi_profile = spk.isi_profile(spike_trains[0], spike_trains[1])
x, y = isi_profile.get_plottable_data()
plt.plot(x, y, '--k')
print("ISI distance: %.8f" % isi_profile.avrg())
plt.show()
```

The ISI-profile is a piece-wise constant function, and hence the function `isi_profile()`

returns an instance of the `PieceWiseConstFunc`

class.
As shown above, this class allows you to obtain arrays that can be used to plot the function with `plt.plt`

, but also to compute the time average, which amounts to the final scalar ISI-distance.
By default, the time average is computed for the whole `PieceWiseConstFunc`

function.
However, it is also possible to obtain the average of a specific interval by providing a pair of floats defining the start and end of the interval.
For the above example, the following code computes the ISI-distances obtained from averaging the ISI-profile over four different intervals:

```
isi1 = isi_profile.avrg(interval=(0, 1000))
isi2 = isi_profile.avrg(interval=(1000, 2000))
isi3 = isi_profile.avrg(interval=[(0, 1000), (2000, 3000)])
isi4 = isi_profile.avrg(interval=[(1000, 2000), (3000, 4000)])
```

Note, how also multiple intervals can be supplied by giving a list of tuples.

If you are only interested in the scalar ISI-distance and not the profile, you can simply use:

```
isi_dist = spk.isi_distance(spike_trains[0], spike_trains[1], interval=(0, 1000))
```

where `interval`

is optional, as above, and if omitted the ISI-distance is computed for the complete spike train.

### SPIKE-distance¶

To compute for the spike distance profile you use the function `spike_profile()`

instead of `isi_profile`

above.
But the general approach is very similar:

```
import matplotlib.pyplot as plt
import pyspike as spk
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
spike_profile = spk.spike_profile(spike_trains[0], spike_trains[1])
x, y = spike_profile.get_plottable_data()
plt.plot(x, y, '--k')
print("SPIKE distance: %.8f" % spike_profile.avrg())
plt.show()
```

This short example computes and plots the SPIKE-profile of the first two spike trains in the file `PySpike_testdata.txt`

.

In contrast to the ISI-profile, a SPIKE-profile is a piece-wise *linear* function and is therefore represented by a `PieceWiseLinFunc`

object.
Just like the `PieceWiseConstFunc`

for the ISI-profile, the `PieceWiseLinFunc`

provides a `PieceWiseLinFunc.get_plottable_data()`

member function that returns arrays that can be used directly to plot the function.
Furthermore, the `PieceWiseLinFunc.avrg()`

member function returns the average of the profile defined as the overall SPIKE distance.
As above, you can provide an interval as a pair of floats as well as a sequence of such pairs to `avrg`

to specify the averaging interval if required.

Again, you can use:

```
spike_dist = spk.spike_distance(spike_trains[0], spike_trains[1], interval=ival)
```

to compute the SPIKE distance directly, if you are not interested in the profile at all.
The parameter `interval`

is optional and if neglected the whole time interval is used.

### Rate-Independent SPIKE-distance¶

This variant of the SPIKE-distance disregards any differences in base rates and focuses purely on spike timing. It can be calculated by setting the optional parameter “RI=True”:

```
ri_spike_dist = spk.spike_distance(spike_trains[0], spike_trains[1], RI=True)
```

### SPIKE synchronization¶

**Important note:**

SPIKE-Synchronization measures

similarity. That means, a value of zero indicates absence of synchrony, while a value of one denotes the presence of synchrony. This is exactly opposite to the other two measures: ISI- and SPIKE-distance.

SPIKE synchronization is another approach to measure spike synchrony.
In contrast to the SPIKE- and ISI-distance, it measures similarity instead of dissimilarity, i.e. higher values represent larger synchrony.
Another difference is that the SPIKE synchronization profile is only defined exactly at the spike times, not for the whole interval of the spike trains.
Therefore, it is represented by a `DiscreteFunction`

.

To compute for the spike synchronization profile, PySpike provides the function `spike_sync_profile()`

.
The general handling of the profile, however, is similar to the other profiles above:

```
import matplotlib.pyplot as plt
import pyspike as spk
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
spike_profile = spk.spike_sync_profile(spike_trains[0], spike_trains[1])
x, y = spike_profile.get_plottable_data()
```

For the direct computation of the overall spike synchronization value within some interval, the `spike_sync()`

function can be used:

```
spike_sync = spk.spike_sync(spike_trains[0], spike_trains[1], interval=ival)
```

### Adaptive generalizations¶

The adaptive generalizations for all four of these basic measures can be calculated by setting the optional parameter “MRTS=<value>” (MRTS - Minimum Relevant Time Scale). If <value> is greater than zero the respective basic algorithm is modified to reduce emphasis on smaller spike time differences. If MRTS is set to ‘auto’, the threshold is automatically extracted from the data.

Here are a few example lines:

```
a_isi_dist = spk.isi_distance(spike_trains, MRTS=10)
a_spike_profile = spk.spike_profile(spike_trains, MRTS=20)
a_ri_spike_matrix = spk.spike_distance_matrix(spike_trains[0], spike_trains[1], RI=True, MRTS=50)
a_spike_sync_auto = spk.spike_sync(spike_trains[0], spike_trains[1], MRTS='auto')
```

## Computing multivariate profiles and distances¶

To compute the multivariate ISI-profile, SPIKE-profile or SPIKE-Synchronization profile for a set of spike trains, simply provide a list of spike trains to the profile or distance functions. The following example computes the multivariate ISI-, SPIKE- and SPIKE-Sync-profile for a list of spike trains:

```
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt",
edges=(0, 4000))
avrg_isi_profile = spk.isi_profile(spike_trains)
avrg_spike_profile = spk.spike_profile(spike_trains)
avrg_spike_sync_profile = spk.spike_sync_profile(spike_trains)
```

All functions also take an optional parameter `indices`

, a list of indices that allows to define the spike trains that should be used for the multivariate profile.
As before, if you are only interested in the distance values, and not in the profile, you can call the functions: `isi_distance()`

, `spike_distance()`

and `spike_sync()`

with a list of spike trains.
They return the scalar overall multivariate ISI-, SPIKE-distance or the SPIKE-Synchronization value.

The following code is equivalent to the bivariate example above, computing the ISI-Distance between the first two spike trains in the given interval using the `indices`

parameter:

```
isi_dist = spk.isi_distance(spike_trains, indices=[0, 1], interval=(0, 1000))
```

As you can see, the distance functions also accept an `interval`

parameter that can be used to specify the begin and end of the averaging interval as a pair of floats, if neglected the complete interval is used.

**Note:**

Instead of providing lists of spike trains to the profile or distance functions, you can also call those functions with many spike trains as (unnamed) parameters, e.g.:

# st1, st2, st3, st4 are spike trains spike_prof = spk.spike_profile(st1, st2, st3, st4)

Another option to characterize large sets of spike trains are distance matrices.
Each entry in the distance matrix represents a bivariate distance (similarity for SPIKE-Synchronization) of two spike trains.
The distance matrix is symmetric and has zero values (ones) at the diagonal and is computed with the functions `isi_distance_matrix()`

, `spike_distance_matrix()`

and `spike_sync_matrix()`

.
The following example computes and plots the ISI- and SPIKE-distance matrix as well as the SPIKE-Synchronization-matrix, with different intervals.

```
spike_trains = spk.load_spike_trains_from_txt("PySpike_testdata.txt", 4000)
plt.figure()
isi_distance = spk.isi_distance_matrix(spike_trains)
plt.imshow(isi_distance, interpolation='none')
plt.title("ISI-distance")
plt.figure()
spike_distance = spk.spike_distance_matrix(spike_trains, interval=(0,1000))
plt.imshow(spike_distance, interpolation='none')
plt.title("SPIKE-distance")
plt.figure()
spike_sync = spk.spike_sync_matrix(spike_trains, interval=(2000,4000))
plt.imshow(spike_sync, interpolation='none')
plt.title("SPIKE-Sync")
plt.show()
```

## Quantifying Leaders and Followers: Spike Train Order¶

PySpike provides functionality to quantify how much a set of spike trains resembles a synfire pattern (ie perfect leader-follower pattern). For details on the algorithms please see our article in NJP.

The following example computes the Spike Order profile and Synfire Indicator of two Poissonian spike trains.

```
import numpy as np
from matplotlib import pyplot as plt
import pyspike as spk
st1 = spk.generate_poisson_spikes(1.0, [0, 20])
st2 = spk.generate_poisson_spikes(1.0, [0, 20])
d = spk.spike_directionality(st1, st2)
print "Spike Directionality of two Poissonian spike trains:", d
E = spk.spike_train_order_profile(st1, st2)
plt.figure()
x, y = E.get_plottable_data()
plt.plot(x, y, '-ob')
plt.ylim(-1.1, 1.1)
plt.xlabel("t")
plt.ylabel("E")
plt.title("Spike Train Order Profile")
plt.show()
```

Additionally, PySpike can also compute the optimal ordering of the spike trains, ie the ordering that most resembles a synfire pattern. The following example computes the optimal order of a set of 20 Poissonian spike trains:

```
M = 20
spike_trains = [spk.generate_poisson_spikes(1.0, [0, 100]) for m in xrange(M)]
F_init = spk.spike_train_order(spike_trains)
print "Initial Synfire Indicator for 20 Poissonian spike trains:", F_init
D_init = spk.spike_directionality_matrix(spike_trains)
phi, _ = spk.optimal_spike_train_sorting(spike_trains)
F_opt = spk.spike_train_order(spike_trains, indices=phi)
print "Synfire Indicator of optimized spike train sorting:", F_opt
D_opt = spk.permutate_matrix(D_init, phi)
plt.figure()
plt.imshow(D_init)
plt.title("Initial Directionality Matrix")
plt.figure()
plt.imshow(D_opt)
plt.title("Optimized Directionality Matrix")
plt.show()
```