diff --git a/doc/cpp/remote.rst b/doc/cpp/remote.rst index df2691285..8e1485c6f 100644 --- a/doc/cpp/remote.rst +++ b/doc/cpp/remote.rst @@ -24,7 +24,7 @@ Control Messages Request termination, giving the reason as a message. - .. cpp:member:: char[512] reason + .. cpp:member:: char reason[512] .. cpp:class:: msg_epoch diff --git a/doc/tutorial/connectivity.rst b/doc/tutorial/connectivity.rst new file mode 100644 index 000000000..0b4655611 --- /dev/null +++ b/doc/tutorial/connectivity.rst @@ -0,0 +1,237 @@ +.. _tutorial_connectivity: + +Declarative Connectivity in Arbor +================================= + +.. admonition:: Concepts and Requirements + + We will assume that you have read the basic recipe and network tutorials. + + In addition to Arbor and its requirements ``matplotlib`` and ``networkx`` + need to be installed. + +In this tutorial, we are going to demonstrate how to leverage Arbor's +declarative connection description facilities to generate a few common network +types. We will gradually build up complexity and generally show the full recipe +first before discussing some of the relevant parts. High-level connectivity +descriptions can be more intuitive for some types of networks as well as more +performant in Python simulations, as the construction is handled entirely in C++. + +Prelude: Unconnected Cells +-------------------------- + +Before we start building actual networks, we will set up the trivial network, +which has no connections at all. This will be written as a recipe class, as +discussed in other tutorials, and later examples will derive from this class to +build upon. If you want, you can skip this part and come back as needed. + +Our cells comprise a simple leaky integrate and fire model, not a cable cell, as +we want to emphasize building networks. We begin by defining the global settings: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 7-13 + +- ``N`` is the cell count of the simulation. +- ``T`` is the total runtime of the simulation in ``ms``. +- ``dt`` is the numerical timestep on which cells evolve. + +These parameters are used here: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 50- + +where we run the simulation. Before we discuss the relevant details, the recipe +reads in full + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 16-47 + +In the recipe, we set a prototypical LIF cell: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 21 + +and deliver it for all ``gid``: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 43-44 + +With large and complicated cells this can sometimes help with performance, here, +it's just a convenient way to structure our recipe. Also, the *first cell* has +an event generator attached, a Poisson point process seeded with the +cell's ``gid``. + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 31-41 + +All other parameters are set in the constructor: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 17-26 + +We also proceed to add spike recording and generate raster plots using a helper +function ``plot_spikes`` from ``util.py``, which results in + +.. figure:: ../../python/example/connectivity/01-raster.svg + :width: 400 + :align: center + +As only the first cell receives spiking inputs, only it will show up on the plot. + +Ring Network +------------ + +Starting from an unconnected set of cells, we can now start building a simple +network. A ring structure is defined by connecting each cell to its predecessor, +i.e. the cell with ``gid = i`` is connected to the cell with ``gid = i - 1`` and +the cell ``gid = 0`` is connected to the last cell ``gid = N - 1``. + +We construct such a network by defining a new recpi ``ring`` deriving from the +unconnected network + +.. literalinclude:: ../../python/example/connectivity/ring.py + :language: python + +The idiomatic way of extending classes with new functionality is to use +inheritance. Importantly, the burden of initializing the base class falls on the +derived class: + +.. literalinclude:: ../../python/example/connectivity/ring.py + :language: python + :lines: 18-20 + +Next, we add a new method that is responsible for the network. Note that this +--- in contrast to most other methods on recipe --- does not have an argument of +``gid``, since it is definining the *global* network. + +.. literalinclude:: ../../python/example/connectivity/ring.py + :language: python + :lines: 22-31 + +Similar to the construction of a ``decor`` or ``cv_policy``, a light-weight +language inspired by LISP or Scheme is used here. For this tutorial, we use +Python format strings to compose expressions. Networks comprise a structure and +parameters --- ``weight`` and ``delay``, which can be scalars as shown, or more +elaborate expressions, such a drawing from a random distribution. + +The structure is defined in terms of combinators reminiscent of relational +algebra queries operating on abstract sets of source and target identifiers. + +- ``source-cell`` and ``target-cell`` construct a set of eligble sources and targets from a single ``gid``. +- ``gid-range`` defines a contiguous range of gids ``[start, end)`` +- ``intersect`` constructs the connections between the ``source`` and ``target`` arguments. +- ``chain`` constructs the set of connections between adjacent neighbours. +- ``join`` takes two sub-structures ``A`` and ``B`` and returns their union. + +Upon close inspection, these combinators directly spell out the prose +description of the ring network given above: Connect adjacent cells and close +the ring by connecting the beginning and end! Running the network and plotting +the spikes we find cells deeper into the ring spiking now + +.. figure:: ../../python/example/connectivity/02-raster.svg + :width: 400 + :align: center + +The network structure is rendered via ``networkx`` + +.. figure:: ../../python/example/connectivity/02-graph.svg + :width: 400 + :align: center + +Excercise: All-to-all Network +----------------------------- + +Using the ``unconnected`` recipe and the +`network documentation `_ +define a fully connected network, i.e. where each cell is connected to every other cell except itself. + +.. hint:: + + 1. ``source-cell`` and ``target-cell`` can take a range of ids + 2. Use and intersection with ``inter-cell`` to remove self connections + +Our solution produces the following output + +.. figure:: ../../python/example/connectivity/03-raster.svg + :width: 400 + :align: center + +The network should look like this + +.. figure:: ../../python/example/connectivity/03-graph.svg + :width: 400 + :align: center + +For reference, we reproduce it here: + +.. literalinclude:: ../../python/example/connectivity/all-to-all.py + :language: python + +Brunel Network +-------------- + +The Brunel network, or in other words, a inhibition-dominated randomly connected +recurrent network, is a common network structure used in computational +neuroscience proposed by Nicolas Brunel in 2000. It contains sparsely connected +inhibitory and excitatory neurons where a critical balance between inhibition +and excitation inputs to each neuron is maintained to ensure a brain-realistic +network-wide dynamics. It entails a few typical dynamics of cortical circuits. + +Practically, we can describe this network by two populations, called the +excitatory and inhibitory populations, such that + +1. Each cell is connected to each other with some probablity :math:`0 < p < 1` + - There no self-connections +2. If the pre-synaptic cell is in the excitatory population, the weight is :math:`w_{exc} > 0` +3. If the pre-synaptic cell is in the inhitatory population, the weight is :math:`w_{inh} < 0` + - :math:`|w_{inh}| < |w_{exc}|` + +The Brunel network simulation can be implemented like this + +.. literalinclude:: ../../python/example/connectivity/brunel.py + :language: python + :lines: 18-32 + +again using the base class ``unconnected`` to define everything except the +network. We implement these by writing down the rules above in the recipe + +.. literalinclude:: ../../python/example/connectivity/brunel.py + :language: python + :lines: 34-42 + +The ``rand`` structure encodes the random connectivity and removes any potential +self-connections by ``intersect`` with ``inter-cell``, as before. Next, we +define the weight according the population of the pre-synaptic neuron. The +population is defined by the ``gid`` of the neuron; the first 80% of cells is +considered excitatory and the remainder inhibitory. The predicate ``inh`` +reifies this description. The weight function ``weight`` then dispatches to one +of two values based on the predicate. + +Rendering the structure becomes slow and frankly unusable, but showing the +adjacency matrix might be helpful + +.. figure:: ../../python/example/connectivity/04-matrix.svg + :width: 400 + :align: center + +Note that rendering can be disabled, if things get too slow. + + +Final Thoughts +-------------- + +Using a few examples we have shown how Arbor's high-level network description +method can be leveraged to generate common structures. The key insight is to +build complex layouts from atomic blocks by using set operators like ``join``, +``difference``, and ``intersect``. There are more to explore in the +documentation, be especially aware of stochastic distributions. We have also +seen how to produce weights and by extension delays using the same, declarative +approach. This functionality is quite young and if any useful additions come to +mind, do not hesitate to request or implement them! diff --git a/doc/tutorial/index.rst b/doc/tutorial/index.rst index 3adb1567c..be8790a0c 100644 --- a/doc/tutorial/index.rst +++ b/doc/tutorial/index.rst @@ -45,6 +45,7 @@ Networks network_ring network_two_cells_gap_junctions brunel + Probes ------ @@ -72,17 +73,19 @@ Hardware network_ring_gpu Advanced -------- +-------- .. toctree:: :maxdepth: 1 nmodl plasticity + connectivity Demonstrations -------------- -We try to collect models scientists have built in our `contributor space `_. -In addition to the tutorials, browsing these models should give you a good idea of what's possible with Arbor -and find get in contact with other Arbor users. +We try to collect models scientists have built in our `contributor space +`_. In addition to the tutorials, browsing +these models should give you a good idea of what's possible with Arbor and find +get in contact with other Arbor users. diff --git a/python/example/connectivity/01-raster.svg b/python/example/connectivity/01-raster.svg new file mode 100644 index 000000000..649012389 --- /dev/null +++ b/python/example/connectivity/01-raster.svg @@ -0,0 +1,1194 @@ + + + + + + + + 2024-12-09T11:18:37.854022 + image/svg+xml + + + Matplotlib v3.9.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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units as U +from util import plot_spikes, plot_network +from unconnected import unconnected + + +# global parameters +# cell count +N = 5 +# total runtime [ms] +T = 1000 +# numerical time step [ms] +dt = 0.1 + + +class all2all(unconnected): + def __init__(self, N) -> None: + super().__init__(N) + + def network_description(self): + # network structure + full = f"(intersect (inter-cell) (source-cell (gid-range 0 {self.N})) (target-cell (gid-range 0 {self.N})))" + # parameters + weight = "(scalar 125)" + delay = "(scalar 0.5)" + return A.network_description(full, weight, delay, {}) + + +if __name__ == "__main__": + rec = all2all(N) + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + sim.run(T * U.ms, dt * U.ms) + plot_spikes(sim, T, N, prefix="03-") + plot_network(rec, prefix="03-") diff --git a/python/example/connectivity/brunel.py b/python/example/connectivity/brunel.py new file mode 100644 index 000000000..142688099 --- /dev/null +++ b/python/example/connectivity/brunel.py @@ -0,0 +1,51 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +from util import plot_spikes, plot_network +from unconnected import unconnected + + +# global parameters +# cell count +N = 125 +# total runtime [ms] +T = 100 +# numerical time step [ms] +dt = 0.1 + + +class brunel(unconnected): + def __init__(self, N) -> None: + super().__init__(N) + # excitatory population: first 80% of the gids + self.n_exc = int(0.8 * N) + # inhibitory population: the remainder + self.n_inh = N - self.n_exc + # seed for random number generation + self.seed = 42 + # excitatory weight + self.weight = 100 + # relative weight of inhibitory connections + self.g = 0.8 + # probability of connecting any two neurons + self.p = 0.1 + + def network_description(self): + rand = f"""(intersect (inter-cell) + (random {self.seed} {self.p}))""" + inh = f"(gid-range {self.n_exc} {self.N})" + weight = f"""(if-else (source-cell {inh}) + (scalar {self.g*self.weight}) + (scalar {self.weight}))""" + delay = "(scalar 0.5)" + return A.network_description(rand, weight, delay, {}) + + +if __name__ == "__main__": + rec = brunel(N) + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + sim.run(T * U.ms, dt * U.ms) + plot_spikes(sim, T, N, prefix="04-") + plot_network(rec, prefix="04-", graph=True) diff --git a/python/example/connectivity/ring.py b/python/example/connectivity/ring.py new file mode 100644 index 000000000..bcf2705fd --- /dev/null +++ b/python/example/connectivity/ring.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +from util import plot_spikes, plot_network +from unconnected import unconnected + + +# global parameters +# cell count +N = 5 +# total runtime [ms] +T = 1000 +# numerical time step [ms] +dt = 0.1 + + +class ring(unconnected): + def __init__(self, N) -> None: + super().__init__(N) + + def network_description(self): + # network structure + wraps = f"(intersect (source-cell {self.N - 1}) (target-cell 0))" + cells = f"(gid-range 0 {self.N})" + chain = f"(chain {cells})" + ring = f"(join {chain} {wraps})" + # parameters + weight = "(scalar 199.99999219)" + delay = "(scalar 0.5)" + return A.network_description(ring, weight, delay, {}) + + +if __name__ == "__main__": + ctx = A.context() + rec = ring(N) + sim = A.simulation(rec, ctx) + sim.record(A.spike_recording.all) + sim.run(T * U.ms, dt * U.ms) + plot_spikes(sim, T, N, prefix="02-") + plot_network(rec, prefix="02-") diff --git a/python/example/connectivity/unconnected.py b/python/example/connectivity/unconnected.py new file mode 100644 index 000000000..16acc9449 --- /dev/null +++ b/python/example/connectivity/unconnected.py @@ -0,0 +1,55 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +from util import plot_spikes + +# global parameters +# cell count +N = 5 +# total runtime [ms] +T = 1000 +# numerical time step [ms] +dt = 0.1 + + +class unconnected(A.recipe): + def __init__(self, N) -> None: + super().__init__() + self.N = N + # Cell prototype + self.cell = A.lif_cell("src", "tgt") + # random seed [0, 100] + self.seed = 42 + # event generator parameters + self.gen_weight = 20 + self.gen_freq = 2.5 * U.kHz + + def num_cells(self) -> int: + return self.N + + def event_generators(self, gid: int): + if gid >= 1: + return [] + seed = self.seed + gid * 100 + return [ + A.event_generator( + "tgt", + self.gen_weight, + A.poisson_schedule(freq=self.gen_freq, seed=seed), + ) + ] + + def cell_description(self, gid: int): + return self.cell + + def cell_kind(self, gid: int) -> A.cell_kind: + return A.cell_kind.lif + + +if __name__ == "__main__": + rec = unconnected(N) + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + sim.run(T * U.ms, dt * U.ms) + plot_spikes(sim, T, N, prefix="01-") diff --git a/python/example/connectivity/util.py b/python/example/connectivity/util.py new file mode 100644 index 000000000..8ea3dae62 --- /dev/null +++ b/python/example/connectivity/util.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python3 + +import matplotlib.pyplot as plt +import numpy as np +import networkx as nx +import arbor as A + + +def plot_network(rec, prefix="", graph=True): + fg, ax = plt.subplots() + n = rec.num_cells() + mat = np.zeros((n, n), dtype=int) + + ctx = A.context() + net = A.generate_network_connections(rec, ctx) + + for conn in net: + i = conn.source.gid + j = conn.target.gid + mat[i, j] += 1 + ax.matshow(mat) + fg.savefig(f"{prefix}matrix.pdf") + fg.savefig(f"{prefix}matrix.png") + fg.savefig(f"{prefix}matrix.svg") + + if graph: + fg, ax = plt.subplots() + g = nx.MultiDiGraph() + g.add_nodes_from(np.arange(n)) + for i in range(n): + for j in range(n): + for _ in range(mat[i, j]): + g.add_edge(i, j) + nx.draw(g, with_labels=True, font_weight="bold") + fg.savefig(f"{prefix}graph.pdf") + fg.savefig(f"{prefix}graph.png") + fg.savefig(f"{prefix}graph.svg") + + +def plot_spikes(sim, T, N, prefix=""): + # Extract spikes + times = [] + gids = [] + for (gid, _), time in sim.spikes(): + times.append(time) + gids.append(gid + 1) + + fg, ax = plt.subplots() + ax.scatter(times, gids, c=gids) + ax.set_xlabel("Time $(t/ms)$") + ax.set_ylabel("GID") + ax.set_xlim(0, T) + ax.set_ylim(0, N + 1) + fg.savefig(f"{prefix}raster.pdf") + fg.savefig(f"{prefix}raster.png") + fg.savefig(f"{prefix}raster.svg")