From aab3a14bbb54b195dcefad938b40c97e820c2b3e Mon Sep 17 00:00:00 2001 From: Thorsten Hater <24411438+thorstenhater@users.noreply.github.com> Date: Mon, 9 Dec 2024 13:51:36 +0100 Subject: [PATCH 1/4] Add connectivity tutorial. --- doc/tutorial/connectivity.rst | 182 + python/example/connectivity/01-raster.svg | 1194 + python/example/connectivity/02-graph.svg | 419 + python/example/connectivity/02-matrix.svg | 365 + python/example/connectivity/02-raster.svg | 1599 + python/example/connectivity/03-graph.svg | 419 + python/example/connectivity/03-matrix.svg | 365 + python/example/connectivity/03-raster.svg | 1734 + python/example/connectivity/04-graph.svg | 11398 +++ python/example/connectivity/04-matrix.svg | 396 + python/example/connectivity/04-raster.svg | 75773 +++++++++++++++++++ python/example/connectivity/all-to-all.py | 37 + python/example/connectivity/brunel.py | 46 + python/example/connectivity/ring.py | 41 + python/example/connectivity/unconnected.py | 55 + python/example/connectivity/util.py | 54 + 16 files changed, 94077 insertions(+) create mode 100644 doc/tutorial/connectivity.rst create mode 100644 python/example/connectivity/01-raster.svg create mode 100644 python/example/connectivity/02-graph.svg create mode 100644 python/example/connectivity/02-matrix.svg create mode 100644 python/example/connectivity/02-raster.svg create mode 100644 python/example/connectivity/03-graph.svg create mode 100644 python/example/connectivity/03-matrix.svg create mode 100644 python/example/connectivity/03-raster.svg create mode 100644 python/example/connectivity/04-graph.svg create mode 100644 python/example/connectivity/04-matrix.svg create mode 100644 python/example/connectivity/04-raster.svg create mode 100644 python/example/connectivity/all-to-all.py create mode 100644 python/example/connectivity/brunel.py create mode 100644 python/example/connectivity/ring.py create mode 100644 python/example/connectivity/unconnected.py create mode 100644 python/example/connectivity/util.py diff --git a/doc/tutorial/connectivity.rst b/doc/tutorial/connectivity.rst new file mode 100644 index 000000000..2780953f0 --- /dev/null +++ b/doc/tutorial/connectivity.rst @@ -0,0 +1,182 @@ +.. _tutorial_connectivity: + +Declarative Connectivity in Arbor +================================= + +In this tutorial, we are going to demonstrate how to leverage Arbor's +declarative connection description facilities to generate a few common network +types. + +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: 7-15 + +- ``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: 52-62 + +where we run the simulation in increments of ``t_interval``. + +Back to the recipe, we set a prototypical LIF cell: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 23 + +and deliver it for all ``gid``: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 42-43 + +Also, the _first cell_ has an event generator attached, using a Poisson point process +seeded with the cell's ``gid``. + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 33-41 + +All other parameters are set in the constructor: + +.. literalinclude:: ../../python/example/connectivity/unconnected.py + :language: python + :lines: 19-28 + +We also proceed to add spike recording and generate raster plots using a helper +function ``plot_spikes`` from ``util.py``. + +.. 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 class ``ring`` deriving from the +unconnected network + +.. 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 + + +Excercise: All-to-all Network +----------------------------- + +Using the ``unconnected`` recipe and the network +https://docs.arbor-sim.org/en/stable/concepts/interconnectivity.html#network-selection-expressions +documentation , define 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 + +Hint 2: Use ``inter-cell`` to remove self connections + +You can find our soluction in ``python/example/all-to-all.py``, it produces the following output + +.. figure:: ../../python/example/connectivity/03-raster.svg + :width: 400 + :align: center + + +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}|` + +We write down these rules in the recipe + +.. literalinclude:: ../../python/example/connectivity/brunel.py + :language: python + :lines: 28-36 + +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. + +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/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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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/python/example/connectivity/all-to-all.py b/python/example/connectivity/all-to-all.py new file mode 100644 index 000000000..7c4a072c2 --- /dev/null +++ b/python/example/connectivity/all-to-all.py @@ -0,0 +1,37 @@ +#!/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 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..a3d6cd825 --- /dev/null +++ b/python/example/connectivity/brunel.py @@ -0,0 +1,46 @@ +#!/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 = 12500 +# total runtime [ms] +T = 100 +# numerical time step [ms] +dt = 0.1 + + +class brunel(unconnected): + def __init__(self, N) -> None: + super().__init__(N) + self.n_exc = int(0.8*N) + self.n_inh = N - self.n_exc + self.seed = 42 + self.weight = 100 + self.g = 0.8 + 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-") + # this becomes _very slow_ with many cells + # plot_network(rec, prefix="04-") diff --git a/python/example/connectivity/ring.py b/python/example/connectivity/ring.py new file mode 100644 index 000000000..bafecadce --- /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..5f944622b --- /dev/null +++ b/python/example/connectivity/util.py @@ -0,0 +1,54 @@ +#!/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=""): + 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") + + 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") From 8f23c6abe2026870d2fe49befb129b613200bf32 Mon Sep 17 00:00:00 2001 From: Thorsten Hater <24411438+thorstenhater@users.noreply.github.com> Date: Mon, 9 Dec 2024 14:07:59 +0100 Subject: [PATCH 2/4] Some polish --- doc/tutorial/connectivity.rst | 43 +++++++++++++++++++++++++++++------ doc/tutorial/index.rst | 2 ++ 2 files changed, 38 insertions(+), 7 deletions(-) diff --git a/doc/tutorial/connectivity.rst b/doc/tutorial/connectivity.rst index 2780953f0..8886609e3 100644 --- a/doc/tutorial/connectivity.rst +++ b/doc/tutorial/connectivity.rst @@ -7,6 +7,14 @@ In this tutorial, we are going to demonstrate how to leverage Arbor's declarative connection description facilities to generate a few common network types. +.. admonition:: Concepts and Requirements + + We will assume that you have read the basic network tutorials. + + In addition to Arbor and its requirements `matplotlib`` and ``networkx`` + need to be installed. + + Prelude: Unconnected Cells -------------------------- @@ -110,31 +118,42 @@ 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. +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-raster.svg + :width: 400 + :align: center Excercise: All-to-all Network ----------------------------- -Using the ``unconnected`` recipe and the network -https://docs.arbor-sim.org/en/stable/concepts/interconnectivity.html#network-selection-expressions -documentation , define fully connected network, i.e. where each cell is +Using the ``unconnected`` recipe and the `network documentation `_ + , define 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 -Hint 2: Use ``inter-cell`` to remove self connections +.. hint:: -You can find our soluction in ``python/example/all-to-all.py``, it produces the following output + 1. ``source-cell`` and ``target-cell`` can take a range of ids + 2. Use and intersection with ``inter-cell`` to remove self connections + +You can find our solution in ``python/example/all-to-all.py``, it produces the following output .. figure:: ../../python/example/connectivity/03-raster.svg :width: 400 :align: center +The network structure is rendered via ``networkx`` + +.. figure:: ../../python/example/connectivity/03-raster.svg + :width: 400 + :align: center Brunel Network -------------- @@ -169,6 +188,16 @@ 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 by default the rendering is disabled to avoid the slowdown. + + Final Thoughts -------------- diff --git a/doc/tutorial/index.rst b/doc/tutorial/index.rst index 3adb1567c..f0346cf03 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 ------ @@ -79,6 +80,7 @@ Advanced nmodl plasticity + connectivity Demonstrations -------------- From b3821352f2f5888684f8ffdb4c5fe1d4e3b1353a Mon Sep 17 00:00:00 2001 From: Thorsten Hater <24411438+thorstenhater@users.noreply.github.com> Date: Mon, 9 Dec 2024 15:22:58 +0100 Subject: [PATCH 3/4] Finalise text --- doc/cpp/remote.rst | 2 +- doc/tutorial/connectivity.rst | 93 ++++++++++++++--------- doc/tutorial/index.rst | 9 ++- python/example/connectivity/all-to-all.py | 2 +- python/example/connectivity/brunel.py | 14 +++- python/example/connectivity/ring.py | 4 +- python/example/connectivity/util.py | 3 +- 7 files changed, 80 insertions(+), 47 deletions(-) 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 index 8886609e3..35ec826ed 100644 --- a/doc/tutorial/connectivity.rst +++ b/doc/tutorial/connectivity.rst @@ -3,17 +3,18 @@ Declarative Connectivity in Arbor ================================= -In this tutorial, we are going to demonstrate how to leverage Arbor's -declarative connection description facilities to generate a few common network -types. - .. admonition:: Concepts and Requirements - We will assume that you have read the basic network tutorials. + We will assume that you have read the basic recipe and network tutorials. - In addition to Arbor and its requirements `matplotlib`` and ``networkx`` + 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. + Prelude: Unconnected Cells -------------------------- @@ -28,7 +29,7 @@ we want to emphasize building networks. We begin by defining the global settings .. literalinclude:: ../../python/example/connectivity/unconnected.py :language: python - :lines: 7-15 + :lines: 7-13 - ``N`` is the cell count of the simulation. - ``T`` is the total runtime of the simulation in ``ms``. @@ -38,37 +39,44 @@ These parameters are used here: .. literalinclude:: ../../python/example/connectivity/unconnected.py :language: python - :lines: 52-62 + :lines: 50- -where we run the simulation in increments of ``t_interval``. +where we run the simulation. Before we discuss the relevant details, the recipe +reads in full -Back to the recipe, we set a prototypical LIF cell: +.. 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: 23 + :lines: 21 and deliver it for all ``gid``: .. literalinclude:: ../../python/example/connectivity/unconnected.py :language: python - :lines: 42-43 + :lines: 43-44 -Also, the _first cell_ has an event generator attached, using a Poisson point process -seeded with the cell's ``gid``. +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: 33-41 + :lines: 31-41 All other parameters are set in the constructor: .. literalinclude:: ../../python/example/connectivity/unconnected.py :language: python - :lines: 19-28 + :lines: 17-26 We also proceed to add spike recording and generate raster plots using a helper -function ``plot_spikes`` from ``util.py``. +function ``plot_spikes`` from ``util.py``, which results in .. figure:: ../../python/example/connectivity/01-raster.svg :width: 400 @@ -84,21 +92,28 @@ 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 class ``ring`` deriving from the +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. +``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 @@ -115,10 +130,9 @@ algebra queries operating on abstract sets of source and target identifiers. - ``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 +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 @@ -126,35 +140,39 @@ Running the network and plotting the spikes we find cells deeper into the ring s The network structure is rendered via ``networkx`` -.. figure:: ../../python/example/connectivity/02-raster.svg +.. 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 fully connected network, i.e. where each cell is -connected to every other cell except itself. - +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 -You can find our solution in ``python/example/all-to-all.py``, it produces the following output +Our solution produces the following output .. figure:: ../../python/example/connectivity/03-raster.svg :width: 400 :align: center -The network structure is rendered via ``networkx`` +The network should look like this -.. figure:: ../../python/example/connectivity/03-raster.svg +.. 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 -------------- @@ -174,11 +192,18 @@ excitatory and inhibitory populations, such that 3. If the pre-synaptic cell is in the inhitatory population, the weight is :math:`w_{inh} < 0` - :math:`|w_{inh}| < |w_{exc}|` -We write down these rules in the recipe +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: 28-36 + :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 diff --git a/doc/tutorial/index.rst b/doc/tutorial/index.rst index f0346cf03..be8790a0c 100644 --- a/doc/tutorial/index.rst +++ b/doc/tutorial/index.rst @@ -73,7 +73,7 @@ Hardware network_ring_gpu Advanced -------- +-------- .. toctree:: :maxdepth: 1 @@ -85,6 +85,7 @@ Advanced 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/all-to-all.py b/python/example/connectivity/all-to-all.py index 7c4a072c2..7e6151ca5 100644 --- a/python/example/connectivity/all-to-all.py +++ b/python/example/connectivity/all-to-all.py @@ -24,7 +24,7 @@ def network_description(self): 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)" + delay = "(scalar 0.5)" return A.network_description(full, weight, delay, {}) diff --git a/python/example/connectivity/brunel.py b/python/example/connectivity/brunel.py index a3d6cd825..ea70be0fd 100644 --- a/python/example/connectivity/brunel.py +++ b/python/example/connectivity/brunel.py @@ -18,21 +18,27 @@ class brunel(unconnected): def __init__(self, N) -> None: super().__init__(N) - self.n_exc = int(0.8*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) + rand = f"""(intersect (inter-cell) (random {self.seed} {self.p}))""" - inh = f"(gid-range {self.n_exc} {self.N})" + 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)" + delay = "(scalar 0.5)" return A.network_description(rand, weight, delay, {}) diff --git a/python/example/connectivity/ring.py b/python/example/connectivity/ring.py index bafecadce..bcf2705fd 100644 --- a/python/example/connectivity/ring.py +++ b/python/example/connectivity/ring.py @@ -24,10 +24,10 @@ def network_description(self): 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})" + ring = f"(join {chain} {wraps})" # parameters weight = "(scalar 199.99999219)" - delay = "(scalar 0.5)" + delay = "(scalar 0.5)" return A.network_description(ring, weight, delay, {}) diff --git a/python/example/connectivity/util.py b/python/example/connectivity/util.py index 5f944622b..8e4dd5e14 100644 --- a/python/example/connectivity/util.py +++ b/python/example/connectivity/util.py @@ -5,6 +5,7 @@ import networkx as nx import arbor as A + def plot_network(rec, prefix=""): fg, ax = plt.subplots() n = rec.num_cells() @@ -48,7 +49,7 @@ def plot_spikes(sim, T, N, prefix=""): ax.set_xlabel("Time $(t/ms)$") ax.set_ylabel("GID") ax.set_xlim(0, T) - ax.set_ylim(0, N+1) + ax.set_ylim(0, N + 1) fg.savefig(f"{prefix}raster.pdf") fg.savefig(f"{prefix}raster.png") fg.savefig(f"{prefix}raster.svg") From 649fccd8278a456d4fa55df19580d6cac6bbd476 Mon Sep 17 00:00:00 2001 From: Thorsten Hater <24411438+thorstenhater@users.noreply.github.com> Date: Mon, 9 Dec 2024 15:35:05 +0100 Subject: [PATCH 4/4] Done now. --- doc/tutorial/connectivity.rst | 7 +- python/example/connectivity/04-graph.svg | 20411 +++-- python/example/connectivity/04-matrix.svg | 170 +- python/example/connectivity/04-raster.svg | 77646 ++------------------ python/example/connectivity/brunel.py | 5 +- python/example/connectivity/util.py | 25 +- 6 files changed, 18287 insertions(+), 79977 deletions(-) diff --git a/doc/tutorial/connectivity.rst b/doc/tutorial/connectivity.rst index 35ec826ed..0b4655611 100644 --- a/doc/tutorial/connectivity.rst +++ b/doc/tutorial/connectivity.rst @@ -13,8 +13,9 @@ Declarative Connectivity in Arbor 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. - +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 -------------------------- @@ -220,7 +221,7 @@ adjacency matrix might be helpful :width: 400 :align: center -Note that by default the rendering is disabled to avoid the slowdown. +Note that rendering can be disabled, if things get too slow. 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+7817,7 @@ z - + @@ -75312,7 +7872,7 @@ z - + @@ -75568,12 +8128,12 @@ z - - + @@ -75586,104 +8146,92 @@ L -3.5 0 - + - - + + - - - + - - + + - - - + - - + + - - - + - - + + - - - + - - + + - - - + - - + + - - - + + diff --git a/python/example/connectivity/brunel.py b/python/example/connectivity/brunel.py index ea70be0fd..142688099 100644 --- a/python/example/connectivity/brunel.py +++ b/python/example/connectivity/brunel.py @@ -8,7 +8,7 @@ # global parameters # cell count -N = 12500 +N = 125 # total runtime [ms] T = 100 # numerical time step [ms] @@ -48,5 +48,4 @@ def network_description(self): sim.record(A.spike_recording.all) sim.run(T * U.ms, dt * U.ms) plot_spikes(sim, T, N, prefix="04-") - # this becomes _very slow_ with many cells - # plot_network(rec, prefix="04-") + plot_network(rec, prefix="04-", graph=True) diff --git a/python/example/connectivity/util.py b/python/example/connectivity/util.py index 8e4dd5e14..8ea3dae62 100644 --- a/python/example/connectivity/util.py +++ b/python/example/connectivity/util.py @@ -6,7 +6,7 @@ import arbor as A -def plot_network(rec, prefix=""): +def plot_network(rec, prefix="", graph=True): fg, ax = plt.subplots() n = rec.num_cells() mat = np.zeros((n, n), dtype=int) @@ -23,17 +23,18 @@ def plot_network(rec, prefix=""): fg.savefig(f"{prefix}matrix.png") fg.savefig(f"{prefix}matrix.svg") - 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") + 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=""):