From 1b268ecffcc9fe7dcc1b89071ca50e3158f73704 Mon Sep 17 00:00:00 2001
From: boeschf <48126478+boeschf@users.noreply.github.com>
Date: Tue, 15 Nov 2022 14:43:27 +0100
Subject: [PATCH] SDE examples (#2030)
Addresses #1987
* reproducibility test for random number generator
* C++ example demonstrating Ornstein-Uhlenbeck process
* Python example featuring stochastic mechanism
* stochastic mechanism catalogue
The Python example is contributed by Jannik Luboeinski's (@jlubo): https://github.com/jlubo/arbor_ou_lif_example
and adapted to fit into Arbor.
---
arbor/include/arbor/mechcat.hpp | 1 +
doc/concepts/mechanisms.rst | 52 +
example/CMakeLists.txt | 1 +
example/ornstein_uhlenbeck/CMakeLists.txt | 23 +
.../ornstein_uhlenbeck/ornstein_uhlenbeck.mod | 38 +
example/ornstein_uhlenbeck/ou.cpp | 181 +
example/ornstein_uhlenbeck/readme.md | 7 +
mechanisms/CMakeLists.txt | 6 +
mechanisms/stochastic/ou_input.mod | 86 +
python/example/ou_lif/Readme.md | 37 +
python/example/ou_lif/lif.mod | 72 +
python/example/ou_lif/ou_lif.py | 342 +
python/example/ou_lif/traces.svg | 22364 ++++++++++++++++
python/mechanism.cpp | 1 +
scripts/run_cpp_examples.sh | 2 +-
test/unit/CMakeLists.txt | 5 +-
test/unit/test_rand.cpp | 54 +
test/unit/test_sde.cpp | 10 +-
18 files changed, 23276 insertions(+), 6 deletions(-)
create mode 100644 example/ornstein_uhlenbeck/CMakeLists.txt
create mode 100644 example/ornstein_uhlenbeck/ornstein_uhlenbeck.mod
create mode 100644 example/ornstein_uhlenbeck/ou.cpp
create mode 100644 example/ornstein_uhlenbeck/readme.md
create mode 100644 mechanisms/stochastic/ou_input.mod
create mode 100644 python/example/ou_lif/Readme.md
create mode 100644 python/example/ou_lif/lif.mod
create mode 100644 python/example/ou_lif/ou_lif.py
create mode 100644 python/example/ou_lif/traces.svg
create mode 100644 test/unit/test_rand.cpp
diff --git a/arbor/include/arbor/mechcat.hpp b/arbor/include/arbor/mechcat.hpp
index bfe5113a..45b30f83 100644
--- a/arbor/include/arbor/mechcat.hpp
+++ b/arbor/include/arbor/mechcat.hpp
@@ -112,6 +112,7 @@ private:
ARB_ARBOR_API const mechanism_catalogue& global_default_catalogue();
ARB_ARBOR_API const mechanism_catalogue& global_allen_catalogue();
ARB_ARBOR_API const mechanism_catalogue& global_bbp_catalogue();
+ARB_ARBOR_API const mechanism_catalogue& global_stochastic_catalogue();
// Load catalogue from disk.
ARB_ARBOR_API const mechanism_catalogue load_catalogue(const std::string&);
diff --git a/doc/concepts/mechanisms.rst b/doc/concepts/mechanisms.rst
index 42518b71..02d05ab4 100644
--- a/doc/concepts/mechanisms.rst
+++ b/doc/concepts/mechanisms.rst
@@ -77,6 +77,14 @@ Two catalogues are provided that collect mechanisms associated with specific pro
* ``bbp_catalogue`` For models published by the Blue Brain Project (BBP).
* ``allen_catalogue`` For models published on the Allen Brain Atlas Database.
+A fourth catalogue ``stochastic_catalogue`` provides mechanisms expressed as stochastic differential
+equations:
+
+* *ou_input* Synapse mechanism that can stochastically account for a population of *ou_input*
+ synapses. The mechanism is similar to *expsyn_curr* but with the exponential decay being subject
+ to noise due to a Ornstein-Uhlenbeck process.
+
+
.. _mechanisms_dynamic:
Adding Catalogues to Arbor
@@ -316,6 +324,50 @@ Euler-Maruyama method.
For specifics about the notation to define stochastic processes, please
consult the :ref:`Arbor-specific NMODL extension <format-sde>`.
+.. note::
+
+ While the units of :math:`\textbf{f}(t, \textbf{X}(t))` represent the deterministic rate of
+ change (per millisecond),
+
+ .. math::
+
+ \left[\textbf{f}(t, \textbf{X}(t))\right] = \frac{\left[\textbf{X}(t)\right]}{ms},
+
+ the stochastic terms scale with :math:`t^{-1/2}`,
+
+ .. math::
+
+ \left[\textbf{l}_i(t, \textbf{X}(t))\right] = \frac{\left[\textbf{X}(t)\right]}{\sqrt{ms}}.
+
+
+**Example:** The popular Ornstein-Uhlenbeck process is described by a scalar linear mean-reverting SDE
+and can be written as
+
+.. math::
+
+ X^\prime = -\frac{1}{\tau} (X - \mu) + \sqrt{\frac{2}{Ï„}} \sigma W,
+
+with white noise :math:`W`, and constant model parameters :math:`\tau`, :math:`\mu` and
+:math:`\sigma`. The relaxation time :math:`\tau` determines how fast the process reverts back to its
+mean value :math:`\mu`, and :math:`\sigma` controls the volatility (:math:`\mu` and :math:`\sigma`
+have the same units as :math:`X`). The expected value and variance can be computed analytically and
+yield
+
+.. math::
+
+ \begin{align*}
+ E[X] &= \mu - \left( \mu - X_0\right) e^{-t/\tau}, \\
+ Var[X] &= \sigma^2 \left( 1 - e^{-2 t/\tau} \right),
+ \end{align*}
+
+which in the limit :math:`t \rightarrow \infty` converge to
+
+.. math::
+
+ \begin{align*}
+ E[X] &= \mu, \\
+ Var[X] &= \sigma^2.
+ \end{align*}
API
---
diff --git a/example/CMakeLists.txt b/example/CMakeLists.txt
index f1393268..b341b257 100644
--- a/example/CMakeLists.txt
+++ b/example/CMakeLists.txt
@@ -14,3 +14,4 @@ add_subdirectory(probe-demo)
add_subdirectory(plasticity)
add_subdirectory(lfp)
add_subdirectory(diffusion)
+add_subdirectory(ornstein_uhlenbeck)
diff --git a/example/ornstein_uhlenbeck/CMakeLists.txt b/example/ornstein_uhlenbeck/CMakeLists.txt
new file mode 100644
index 00000000..aa4d7ef9
--- /dev/null
+++ b/example/ornstein_uhlenbeck/CMakeLists.txt
@@ -0,0 +1,23 @@
+make_catalogue_standalone(
+ NAME ou
+ SOURCES "${CMAKE_CURRENT_SOURCE_DIR}"
+ MOD ornstein_uhlenbeck
+ CXX
+ CXX_FLAGS_TARGET ${ARB_CXX_FLAGS_TARGET_FULL}
+ VERBOSE ON)
+
+add_executable(ou EXCLUDE_FROM_ALL ou.cpp)
+add_dependencies(ou ou-catalogue)
+target_compile_options(ou PRIVATE ${ARB_CXX_FLAGS_TARGET_FULL})
+target_include_directories(ou PRIVATE "${CMAKE_CURRENT_BINARY_DIR}/generated/ou")
+
+target_link_libraries(ou PRIVATE arbor arborio ou-catalogue)
+if (ARB_USE_BUNDLED_FMT)
+ target_include_directories(ou PRIVATE "${CMAKE_CURRENT_SOURCE_DIR}/../../ext/fmt/include")
+ target_compile_definitions(ou PRIVATE FMT_HEADER_ONLY)
+else()
+ find_package(fmt REQUIRED)
+ target_link_libraries(ou PRIVATE fmt::fmt-header-only)
+endif()
+
+add_dependencies(examples ou)
diff --git a/example/ornstein_uhlenbeck/ornstein_uhlenbeck.mod b/example/ornstein_uhlenbeck/ornstein_uhlenbeck.mod
new file mode 100644
index 00000000..60f9e3ad
--- /dev/null
+++ b/example/ornstein_uhlenbeck/ornstein_uhlenbeck.mod
@@ -0,0 +1,38 @@
+: Ornstein-Uhlenbeck: linear mean reverting process
+: =================================================
+: dS(t) = kappa [mu - S(t)] dt + sigma dW(t)
+: E[S(t)] = mu - (mu-S_0)*e^(-kappa t)
+: Var[S(t)] = sigma^2/(2 kappa) [1 - e^(-2 kappa t)]
+: in the limit:
+: lim t->∞ E[S(t)] = mu
+: lim t->∞ Var[S(t)] = sigma^2/(2 kappa)
+
+NEURON {
+ SUFFIX ornstein_uhlenbeck
+ GLOBAL kappa, mu, sigma
+}
+
+PARAMETER {
+ kappa = 0.1
+ mu = 1
+ sigma = 0.1
+}
+
+STATE {
+ S
+}
+
+INITIAL {
+ S=2
+}
+
+BREAKPOINT {
+ SOLVE state METHOD stochastic
+}
+
+WHITE_NOISE { W }
+
+DERIVATIVE state {
+ S' = kappa*(mu - S) + sigma*W
+}
+
diff --git a/example/ornstein_uhlenbeck/ou.cpp b/example/ornstein_uhlenbeck/ou.cpp
new file mode 100644
index 00000000..ad8f9c47
--- /dev/null
+++ b/example/ornstein_uhlenbeck/ou.cpp
@@ -0,0 +1,181 @@
+#include <fmt/format.h>
+
+#include <arborio/label_parse.hpp>
+
+#include <arbor/assert.hpp>
+#include <arbor/recipe.hpp>
+#include <arbor/cable_cell_param.hpp>
+#include <arbor/cable_cell.hpp>
+#include <arbor/simulation.hpp>
+
+// forward declaration
+arb::mechanism_catalogue build_catalogue();
+
+// a single-cell recipe with probes
+class recipe: public arb::recipe {
+public:
+ recipe(unsigned ncvs) {
+ using namespace arb;
+ using namespace arborio::literals;
+
+ // build catalogue with stochastic mechanism
+ cell_gprop_.catalogue = global_default_catalogue();
+ cell_gprop_.catalogue.import(build_catalogue(), "");
+ cell_gprop_.default_parameters = neuron_parameter_defaults;
+
+ // paint the process on the whole cell
+ decor dec;
+ double const cv_size = 1.0;
+ dec.set_default(cv_policy_max_extent(cv_size));
+ dec.paint("(all)"_reg , density("hh"));
+ dec.paint("(all)"_reg , density("ornstein_uhlenbeck"));
+
+ // single-cell tree with ncvs control volumes
+ segment_tree tree;
+ tree.append(mnpos, {0, 0, 0.0, 4.0}, {0, 0, ncvs*cv_size, 4.0}, 1);
+ cell_ = cable_cell(morphology(tree), dec);
+ }
+
+ arb::cell_size_type num_cells() const override { return 1; }
+
+ arb::util::unique_any get_cell_description(arb::cell_gid_type) const override { return cell_; }
+
+ arb::cell_kind get_cell_kind(arb::cell_gid_type) const override { return arb::cell_kind::cable; }
+
+ std::vector<arb::probe_info> get_probes(arb::cell_gid_type) const override { return probes_; }
+
+ std::any get_global_properties(arb::cell_kind) const override { return cell_gprop_; }
+
+ void add_probe(arb::probe_tag tag, std::any address) { probes_.emplace_back(std::move(address), tag); }
+
+protected:
+ std::vector<arb::probe_info> probes_;
+ arb::cable_cell_global_properties cell_gprop_;
+ arb::cable_cell cell_;
+};
+
+// sampler for vector probes
+struct sampler {
+ sampler(std::vector<arb_value_type>& data, std::size_t n_cvs, std::size_t n_steps):
+ n_cvs_{n_cvs} , n_steps_{n_steps}, data_{data} {
+ data_.resize(n_cvs*n_steps);
+ }
+
+ void operator()(arb::probe_metadata pm, std::size_t n, const arb::sample_record* samples) {
+ const auto* m = arb::util::any_cast<const arb::mcable_list*>(pm.meta);
+ arb_assert(n_cvs_ == m->size());
+ arb_assert(n_steps_ == n);
+
+ for (std::size_t i=0; i<n; ++i) {
+ const auto* data = arb::util::any_cast<const arb::cable_sample_range*>(samples[i].data);
+ auto [lo, hi] = *data;
+ arb_assert(static_cast<std::size_t>(hi-lo) == n_cvs_);
+ for (std::size_t j=0; j<n_cvs_; ++j) {
+ data_[i*n_cvs_ + j] = lo[j];
+ }
+ }
+ }
+
+ std::size_t n_cvs_;
+ std::size_t n_steps_;
+ std::vector<arb_value_type>& data_;
+};
+
+// compute mean and variance online
+// uses Welford-Knuth algorithm for the variance
+struct accumulator {
+ std::size_t n_ = 0;
+ double mean_ = 0;
+ double var_ = 0;
+
+ accumulator& operator()(double sample) {
+ double const delta = sample - mean_;
+ mean_ += delta / (++n_);
+ var_ += delta * (sample - mean_);
+ return *this;
+ }
+
+ std::size_t n() const noexcept { return n_; }
+ double mean() const noexcept { return mean_; }
+ double variance() const noexcept { return n_ > 1 ? var_/(n_-1) : 0; }
+};
+
+int main(int argc, char** argv) {
+
+ unsigned ncvs = 5000; // number of control volumes
+ double const dt = 1.0/1024; // time step
+ unsigned nsteps = 500; // number of time steps
+
+ // create recipe and add probes
+ recipe rec(ncvs);
+ rec.add_probe(1, arb::cable_probe_density_state_cell{"ornstein_uhlenbeck", "S"});
+
+ // make context and simulation objects
+ auto context = arb::make_context({1, -1});
+ arb::simulation sim = arb::simulation::create(rec)
+ .set_context(context)
+ .set_seed(137);
+
+ // setup sampler and add it to the simulation with regular schedule
+ std::vector<arb_value_type> data;
+ sampler s{data, ncvs, nsteps};
+ auto all_probes = [](arb::cell_member_type) { return true; };
+ sim.add_sampler(all_probes, arb::regular_schedule(dt), s, arb::sampling_policy::lax);
+
+ // run the simulation
+ sim.run(nsteps*dt, dt);
+
+ // evaluate the mean for each time step across the ensembe of realizations
+ // (each control volume is a independent realization of the Ornstein-Uhlenbeck process)
+ std::vector<accumulator> acc(nsteps);
+ for (std::size_t t=0; t<nsteps; ++t) {
+ for (std::size_t i=0; i<ncvs; ++i) {
+ acc[t](s.data_[t*ncvs+ i]);
+ }
+ }
+
+ // analytical solutions
+ auto expected = [](double t) -> std::pair<double,double> {
+ const double mu = 1.0;
+ const double S_0 = 2.0;
+ const double kappa = 0.1;
+ const double sigma = 0.1;
+ return {
+ mu - (mu-S_0)*std::exp(-kappa*t),
+ (sigma*sigma/(2*kappa))*(1.0 - std::exp(-2*kappa*t))
+ };
+ };
+
+ // print mean and expectation
+ for (std::size_t t=0; t<nsteps; t+=10) {
+ fmt::print("time = {:.5f}: mean = {:.5f} expected = {:.5f}\n",
+ dt*t, acc[t].mean(), expected(dt*t).first);
+ }
+ return 0;
+}
+
+// load mechanisms from library and add to new catalogue
+// =====================================================
+
+extern "C" {
+const void* get_catalogue(int*);
+}
+
+arb::mechanism_catalogue build_catalogue() {
+ arb::mechanism_catalogue cat;
+ int n=0;
+ const void* ptr = get_catalogue(&n);
+ const auto* mechs = reinterpret_cast<const arb_mechanism*>(ptr);
+ for (int i=0; i<n; ++i) {
+ const auto& mech = mechs[i];
+ auto ty = mech.type();
+ auto nm = ty.name;
+ auto ig = mech.i_gpu();
+ auto ic = mech.i_cpu();
+ arb_assert(ic || ig);
+ cat.add(nm, ty);
+ if (ic) cat.register_implementation(nm, std::make_unique<arb::mechanism>(ty, *ic));
+ if (ig) cat.register_implementation(nm, std::make_unique<arb::mechanism>(ty, *ig));
+ }
+ return cat;
+}
diff --git a/example/ornstein_uhlenbeck/readme.md b/example/ornstein_uhlenbeck/readme.md
new file mode 100644
index 00000000..a9206687
--- /dev/null
+++ b/example/ornstein_uhlenbeck/readme.md
@@ -0,0 +1,7 @@
+## Miniapp for demonstrating stochastic processes
+
+The simulation consists of a single cell with a stochastic process (Ornstein-Uhlenbeck) painted on
+its control volumes. The stochastic process is described by a linear mean-reverting stochastic
+differential equation which is specified in the accompanying NMODL file. All processes start from
+the same initial condition and are averaged over the control volumes at each time step to generate an
+ensemble statistic. These results are then compared to the analytical solution.
diff --git a/mechanisms/CMakeLists.txt b/mechanisms/CMakeLists.txt
index 9f1c14f5..56c0e208 100644
--- a/mechanisms/CMakeLists.txt
+++ b/mechanisms/CMakeLists.txt
@@ -21,6 +21,12 @@ make_catalogue(
VERBOSE ${ARB_CAT_VERBOSE}
ADD_DEPS ON)
+make_catalogue(
+ NAME stochastic
+ MOD ou_input
+ VERBOSE ${ARB_CAT_VERBOSE}
+ ADD_DEPS ON)
+
# This re-exports
set(arbor-builtin-mechanisms ${arbor-builtin-mechanisms} PARENT_SCOPE)
diff --git a/mechanisms/stochastic/ou_input.mod b/mechanisms/stochastic/ou_input.mod
new file mode 100644
index 00000000..2c63d75a
--- /dev/null
+++ b/mechanisms/stochastic/ou_input.mod
@@ -0,0 +1,86 @@
+: Input current modeled by an Ornstein-Uhlenbeck process
+: Sets non-specific current given mean, volatility and relaxation time
+:
+: Adapted from Jannik Luboeinski's example here: https://github.com/jlubo/arbor_ou_lif_example
+:
+: I_ou input current (nA)
+: μ input current mean (nA)
+: σ input current volatility (nA)
+: Ï„ relaxation time (ms)
+:
+: dI_ou/dt = -(1/τ) * (I_ou - μ) + √(2/τ) * σ * W
+:
+: statistic properties:
+: E[I_ou] = μ - (μ - I_ou_0) * e^(-t/τ)
+: Var[I_ou] = σ^2 * (1 - e^(-2 * t/τ))
+:
+: in the limit t->∞:
+: E[I_ou] = μ
+: Var[I_ou] = σ^2
+
+NEURON {
+ POINT_PROCESS ou_input
+ RANGE mu, sigma, tau
+ NONSPECIFIC_CURRENT I
+}
+
+UNITS {
+ (ms) = (milliseconds)
+ (nA) = (nanoampere)
+}
+
+PARAMETER {
+ mu = 1 (nA) : mean of the stochastic process
+ sigma = 1 (nA) : volatility of the stochastic process
+ tau = 1 (ms) : relaxation time
+}
+
+STATE {
+ I_ou (nA) : instantaneous state
+ active : indicates if the process is currently enabled
+}
+
+ASSIGNED {
+ alpha
+ beta
+}
+
+WHITE_NOISE {
+ W
+}
+
+INITIAL {
+ I_ou = 0
+ active = -1
+ alpha = 1.0/tau
+ beta = sigma * (2.0/tau)^0.5
+}
+
+BREAKPOINT {
+ SOLVE state METHOD stochastic
+ I = -I_ou
+}
+
+DERIVATIVE state {
+ I_ou' = heaviside(active) * (alpha * (mu - I_ou) + beta * W)
+}
+
+NET_RECEIVE(weight) {
+ if (weight >= 0) { : indicates that stimulation begins
+ I_ou = mu : initialize the process at the mean value
+ active = 1
+ }
+ else { : indicates that stimulation ends
+ I_ou = 0 : switch off the process
+ active = -1
+ }
+}
+
+FUNCTION heaviside(x) {
+ if (x >= 0) {
+ heaviside = 1
+ }
+ else {
+ heaviside = 0
+ }
+}
diff --git a/python/example/ou_lif/Readme.md b/python/example/ou_lif/Readme.md
new file mode 100644
index 00000000..dedc039c
--- /dev/null
+++ b/python/example/ou_lif/Readme.md
@@ -0,0 +1,37 @@
+# Ornstein-Uhlenbeck input to LIF neuron
+
+This example is taken from [Jannik Luboeinski's repo](https://github.com/jlubo/arbor_ou_lif_example)
+and adapted for inclusion into Arbor.
+
+The simulation consists of a single compartment cable cell with simple leaky integrate-and-fire (LIF)
+dynamics with Ornstein-Uhlenbeck (OU) input current. The OU input current can approximate the
+synaptic input from a population of neurons. This is mathematically based on the diffusion
+approximation, which analytically describes the input current that arises from presynaptic Poisson
+spiking if the spiking activity is sufficiently high and the evoked postsynaptic potentials are
+sufficiently small compared to the threshold potential [1,2]. Moreover, the exponentially decaying
+autocorrelation function of the OU process resembles that of currents evoked by the spiking activity
+of many neocortical neurons [3].
+
+Here, we use the Ornstein-Uhlenbeck process in the following form, `dI/dt = -(1/τ) * (I - μ) +
+√(2/τ) * σ * W`. Assuming homogeneous Poisson spiking at frequency *f* for a putative population of
+*N* neurons, the mean current is `μ = N * f * w_out`, and the volatility (standard
+deviation) is `σ = √(10^3*N*f/(2*τ))*w_out` where *f* is the firing rate in Hertz, *w_out* is the
+synaptic weight in nC, and *Ï„* is the synaptic time constant in ms (cf. [4, 5]).
+
+
+
+## References:
+
+[1] Ricciardi, LM. 1977. _Diffusion Processes and Related Topics in Biology_.
+Springer, Berlin, Germany.
+
+[2] Moreno-Bote, R; Parga, N. 2010. Response of integrate-and-fire neurons to noisy inputs filtered
+by synapses with arbitrary timescales: Firing rate and correlations. _Neural Comput._ 22.
+
+[3] Destexhe, A; Rudolph, M; Paré, D. 2003. The high-conductance state of neocortical neurons in
+vivo. _Nat. Rev. Neurosci._ 4.
+
+[4] Dayan, P; Abbott, LF. 2001. _Theoretical Neuroscience_. MIT Press, Cambridge/MA, USA.
+
+[5] Luboeinski, J; Tetzlaff, C. 2021. Memory consolidation and improvement by synaptic tagging and
+capture in recurrent neural networks. _Commun. Biol._ 275.
diff --git a/python/example/ou_lif/lif.mod b/python/example/ou_lif/lif.mod
new file mode 100644
index 00000000..9271d6dc
--- /dev/null
+++ b/python/example/ou_lif/lif.mod
@@ -0,0 +1,72 @@
+: Leaky-integrate and fire neuron
+
+: If the threshold potential is crossed, the membrane resistance is set to a very low value
+: to pull the membrane potential towards the reset potential for the duration of the refractory period.
+: After that, the membrane resistance is set to the comparably higher leak resistance again.
+: The threshold potential of Arbor's threshold detector should match the threshold potential here.
+
+: authors: Sebastian Schmitt, Jannik Luboeinski
+: based on https://github.com/tetzlab/FIPPA/blob/main/STDP/mechanisms/lif.mod
+
+NEURON {
+ SUFFIX lif
+ NONSPECIFIC_CURRENT i
+ RANGE R_reset, R_leak, V_reset, V_rev, V_th, I_0, i_factor, t_ref
+}
+
+UNITS {
+ (ms) = (milliseconds)
+ (mV) = (millivolt)
+ (MOhm) = (megaohm)
+}
+
+STATE {
+ refractory_counter
+}
+
+INITIAL {
+ refractory_counter = t_ref + 1 : start not refractory
+
+ v = V_rev : membrane potential
+}
+
+PARAMETER {
+ R_leak = 10 (MOhm) : membrane resistance during leakage (standard case)
+ R_reset = 1e-10 (MOhm) : membrane resistance during refractory period (very small to yield fast reset)
+ I_0 = 0 : constant input current (in nA)
+ i_factor = 1 : conversion factor from nA to mA/cm^2; for point neurons
+
+ V_reset = -70 (mV) : reset potential
+ V_rev = -65 (mV) : reversal potential
+ V_th = -55 (mV) : threshold potential to be crossed for spiking
+ t_ref = 2 (ms) : refractory period
+}
+
+BREAKPOINT {
+ SOLVE state METHOD cnexp
+
+ LOCAL R_mem
+ LOCAL E
+
+ : threshold crossed -> start refractory counter
+ if (v > V_th) {
+ refractory_counter = 0
+ }
+
+ : choose between leak and reset potential
+ if (refractory_counter <= t_ref) { : in refractory period - strong drive of v towards V_reset
+ R_mem = R_reset
+ E = V_reset
+ } else { : outside refractory period
+ R_mem = R_leak
+ E = V_rev
+ }
+
+ i = (((v - E) / R_mem) - I_0) * i_factor : current density in units of mA/cm^2
+}
+
+DERIVATIVE state {
+ if (refractory_counter <= t_ref) {
+ refractory_counter' = 1
+ }
+}
diff --git a/python/example/ou_lif/ou_lif.py b/python/example/ou_lif/ou_lif.py
new file mode 100644
index 00000000..c308ec18
--- /dev/null
+++ b/python/example/ou_lif/ou_lif.py
@@ -0,0 +1,342 @@
+#!/bin/python3
+
+# adapted from Jannik Luboeinski's example here: https://github.com/jlubo/arbor_ou_lif_example
+
+import random
+import subprocess
+import arbor as arb
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def make_catalogue():
+ # build a new catalogue
+ out = subprocess.getoutput("arbor-build-catalogue ou_lif . --cpu True")
+ print(out)
+ # load the new catalogue and extend it with builtin stochastic catalogue
+ cat = arb.load_catalogue("./ou_lif-catalogue.so")
+ cat.extend(arb.stochastic_catalogue(), "")
+ return cat
+
+
+def make_cell():
+
+ # cell morphology
+ # ===============
+
+ tree = arb.segment_tree()
+ radius = 1e-10 # radius of cylinder (in µm)
+ height = 2 * radius # height of cylinder (in µm)
+ tree.append(
+ arb.mnpos,
+ arb.mpoint(-height / 2, 0, 0, radius),
+ arb.mpoint(height / 2, 0, 0, radius),
+ tag=1,
+ )
+ labels = arb.label_dict({"center": "(location 0 0.5)"})
+
+ # LIF density mechanism
+ # =====================
+
+ # surface area of the cylinder in m^2 (excluding the circle-shaped ends, since Arbor does
+ # not consider current flux there)
+ area_m2 = 2 * np.pi * (radius * 1e-6) * (height * 1e-6)
+ area_cm2 = area_m2 * 1e4
+ # conversion factor from nA to mA/cm^2; for point neurons
+ i_factor = (1e-9 / 1e-3) / area_cm2
+ # neuronal capacitance in F
+ C_mem = 1e-9
+ # specific capacitance in F/m^2, computed from absolute capacitance of point neuron
+ c_mem = C_mem / area_m2
+ # reversal potential in mV
+ V_rev = -65.0
+ # spiking threshold in mV
+ V_th = -55.0
+ # initial synaptic weight in nC
+ h_0 = 4.20075
+ # leak resistance in MOhm
+ R_leak = 10.0
+ # membrane time constant in ms
+ tau_mem = 2.0
+
+ lif = arb.mechanism("lif")
+ lif.set("R_leak", R_leak)
+ lif.set("R_reset", 1e-10)
+ # set to initial value to zero (background input is applied via stochastic ou_bg_mech)
+ lif.set("I_0", 0)
+ lif.set("i_factor", i_factor)
+ lif.set("V_rev", V_rev)
+ lif.set("V_reset", -70.0)
+ lif.set("V_th", V_th)
+ # refractory time in ms
+ lif.set("t_ref", tau_mem)
+
+ # stochastic background input current (point mechanism)
+ # =====================================================
+
+ # synaptic time constant in ms
+ tau_syn = 5.0
+ # mean in nA
+ mu_bg = 0.15
+ # volatility in nA
+ sigma_bg = 0.5
+ # instantiate mechanism
+ ou_bg = arb.mechanism("ou_input")
+ ou_bg.set("mu", mu_bg)
+ ou_bg.set("sigma", sigma_bg)
+ ou_bg.set("tau", tau_syn)
+
+ # stochastic stimulus input current (point mechanism)
+ # ===================================================
+
+ # number of neurons in the putative population
+ N = 25
+ # firing rate of the putative neurons in Hz
+ f = 100
+ # synaptic weight in nC
+ w_out = h_0 / R_leak
+ # mean in nA
+ mu_stim = N * f * w_out
+ # volatility in nA
+ sigma_stim = np.sqrt((1000.0 * N * f) / (2 * tau_syn)) * w_out
+ # instantiate mechanism
+ ou_stim = arb.mechanism("ou_input")
+ ou_stim.set("mu", mu_stim)
+ ou_stim.set("sigma", sigma_stim)
+ ou_stim.set("tau", tau_syn)
+
+ # paint and place mechanisms
+ # ==========================
+
+ decor = arb.decor()
+ decor.set_property(Vm=V_rev, cm=c_mem)
+ decor.paint("(all)", arb.density(lif))
+ decor.place('"center"', arb.synapse(ou_stim), "ou_stim")
+ decor.place('"center"', arb.synapse(ou_bg), "ou_bg")
+ decor.place('"center"', arb.threshold_detector(V_th), "spike_detector")
+
+ return arb.cable_cell(tree, decor, labels)
+
+
+class ou_recipe(arb.recipe):
+ def __init__(self, cell, cat):
+ arb.recipe.__init__(self)
+
+ # simulation runtime parameters in ms
+ self.runtime = 20000
+ self.dt = 0.2
+
+ # initialize catalogue and cell properties
+ self.the_props = arb.neuron_cable_properties()
+ self.the_props.catalogue = cat
+ self.the_cell = cell
+
+ # protocol for stimulation
+ # "time_start": starting time, "scheme": protocol type
+ self.bg_prot = {"time_start": 0, "scheme": "FULL", "label": "ou_bg"}
+ self.stim1_prot = {"time_start": 10000, "scheme": "TRIPLET", "label": "ou_stim"}
+ self.stim2_prot = {
+ "time_start": 15000,
+ "scheme": "ONEPULSE",
+ "label": "ou_stim",
+ }
+
+ def cell_kind(self, gid):
+ return arb.cell_kind.cable
+
+ def cell_description(self, gid):
+ return self.the_cell
+
+ def global_properties(self, kind):
+ return self.the_props
+
+ def num_cells(self):
+ return 1
+
+ def probes(self, gid):
+ # probe membrane potential, total current, and external input currents
+ return [
+ arb.cable_probe_membrane_voltage('"center"'),
+ arb.cable_probe_total_ion_current_cell(),
+ arb.cable_probe_point_state_cell("ou_input", "I_ou"),
+ ]
+
+ def event_generators(self, gid):
+ gens = []
+ # OU stimulus input #1
+ gens.extend(self.get_generators(self.stim1_prot))
+ # OU stimulus input #2
+ gens.extend(self.get_generators(self.stim2_prot))
+ # OU background input
+ gens.extend(self.get_generators(self.bg_prot))
+ return gens
+
+ # Returns arb.event_generator instances that describe the specifics of a given
+ # input/stimulation protocol for a mechanism implementing an Ornstein-Uhlenbeck process.
+ # Here, if the value of the 'weight' parameter is 1, stimulation is switched on,
+ # whereas if it is -1, stimulation is switched off.
+ def get_generators(self, protocol):
+
+ prot_name = protocol["scheme"] # name of the protocol (defining its structure)
+ start_time = protocol["time_start"] # time at which the stimulus starts in s
+ label = protocol["label"] # target synapse (mechanism label)
+
+ if prot_name == "ONEPULSE":
+ # create regular schedules to implement a stimulation pulse that lasts for 0.1 s
+ stim_on = arb.event_generator(
+ label,
+ 1,
+ arb.regular_schedule(start_time, self.dt, start_time + self.dt),
+ )
+ stim_off = arb.event_generator(
+ label,
+ -1,
+ arb.regular_schedule(
+ start_time + 100, self.dt, start_time + 100 + self.dt
+ ),
+ )
+ return [stim_on, stim_off]
+
+ elif prot_name == "TRIPLET":
+ # create regular schedules to implement pulses that last for 0.1 s each
+ stim1_on = arb.event_generator(
+ label,
+ 1,
+ arb.regular_schedule(start_time, self.dt, start_time + self.dt),
+ )
+ stim1_off = arb.event_generator(
+ label,
+ -1,
+ arb.regular_schedule(
+ start_time + 100, self.dt, start_time + 100 + self.dt
+ ),
+ )
+ stim2_on = arb.event_generator(
+ label,
+ 1,
+ arb.regular_schedule(
+ start_time + 500, self.dt, start_time + 500 + self.dt
+ ),
+ )
+ stim2_off = arb.event_generator(
+ label,
+ -1,
+ arb.regular_schedule(
+ start_time + 600, self.dt, start_time + 600 + self.dt
+ ),
+ )
+ stim3_on = arb.event_generator(
+ label,
+ 1,
+ arb.regular_schedule(
+ start_time + 1000, self.dt, start_time + 1000 + self.dt
+ ),
+ )
+ stim3_off = arb.event_generator(
+ label,
+ -1,
+ arb.regular_schedule(
+ start_time + 1100, self.dt, start_time + 1100 + self.dt
+ ),
+ )
+ return [stim1_on, stim1_off, stim2_on, stim2_off, stim3_on, stim3_off]
+
+ elif prot_name == "FULL":
+ # create a regular schedule that lasts for the full runtime
+ stim_on = arb.event_generator(
+ label,
+ 1,
+ arb.regular_schedule(start_time, self.dt, start_time + self.dt),
+ )
+ return [stim_on]
+
+ else:
+ return []
+
+
+if __name__ == "__main__":
+
+ # set up and run simulation
+ # =========================
+
+ # create recipe
+ cell = make_cell()
+ cat = make_catalogue()
+ recipe = ou_recipe(cell, cat)
+
+ # get random seed
+ random_seed = random.getrandbits(64)
+ print("random_seed = " + str(random_seed))
+
+ # select one thread and no GPU
+ alloc = arb.proc_allocation(threads=1, gpu_id=None)
+ context = arb.context(alloc, mpi=None)
+ domains = arb.partition_load_balance(recipe, context)
+
+ # create simulation
+ sim = arb.simulation(recipe, context, domains, seed=random_seed)
+
+ # create schedule for recording
+ reg_sched = arb.regular_schedule(0, recipe.dt, recipe.runtime)
+
+ # set handles to probe membrane potential and currents
+ gid = 0
+ handle_mem = sim.sample((gid, 0), reg_sched) # membrane potential
+ handle_tot_curr = sim.sample((gid, 1), reg_sched) # total current
+ handle_curr = sim.sample((gid, 2), reg_sched) # input current
+
+ sim.record(arb.spike_recording.all)
+ sim.run(tfinal=recipe.runtime, dt=recipe.dt)
+
+ # get traces and spikes from simulator
+ # ====================================
+
+ # there is only one location (single control volume)
+ loc = 0
+ data_mem, data_curr = [], []
+
+ data, _ = sim.samples(handle_mem)[loc]
+ times = data[:, 0]
+
+ # read out neuron data
+ data_mem.append(data[:, 1])
+
+ # get total membrane current
+ data_tot_curr, _ = sim.samples(handle_tot_curr)[loc]
+ data_curr.append(np.negative(data_tot_curr[:, 1]))
+
+ # get Ornstein-Uhlenbeck currents
+ data_input_curr, _ = sim.samples(handle_curr)[loc]
+ data_curr.append(data_input_curr[:, 1])
+ data_curr.append(data_input_curr[:, 2])
+
+ # get spikes
+ spike_times = sim.spikes()["time"]
+
+ # assemble, store, and plot data
+ # ==============================
+
+ data_header = "Time, V, I_stim, I_bg"
+ data_stacked = np.column_stack(
+ [times, np.transpose(data_mem), np.transpose(data_curr)]
+ )
+
+ np.savetxt("traces.txt", data_stacked, fmt="%.4f", header=data_header)
+ np.savetxt("spikes.txt", spike_times, fmt="%.4f")
+
+ fig, axes = plt.subplots(nrows=4, ncols=1, sharex=False, figsize=(10, 10))
+ axes[0].set_title("random_seed = " + str(random_seed))
+ axes[0].plot(data_stacked[:, 0], data_stacked[:, 1], label="V", color="C3")
+ axes[0].plot(
+ spike_times, -55 * np.ones(len(spike_times)), ".", color="blue", markersize=1
+ )
+ axes[1].plot(data_stacked[:, 0], data_stacked[:, 2], label="I_tot", color="C1")
+ axes[2].plot(data_stacked[:, 0], data_stacked[:, 3], label="I_stim", color="C2")
+ axes[3].plot(data_stacked[:, 0], data_stacked[:, 4], label="I_bg", color="C0")
+ axes[3].set_xlabel("Time (ms)")
+ axes[0].set_ylabel("V (mV)")
+ axes[1].set_ylabel("I_tot (nA)")
+ axes[2].set_ylabel("I_stim (nA)")
+ axes[3].set_ylabel("I_bg (nA)")
+ fig.tight_layout()
+ fig.savefig("traces.svg", bbox_inches="tight")
diff --git a/python/example/ou_lif/traces.svg b/python/example/ou_lif/traces.svg
new file mode 100644
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diff --git a/python/mechanism.cpp b/python/mechanism.cpp
index a5ee801f..471d2416 100644
--- a/python/mechanism.cpp
+++ b/python/mechanism.cpp
@@ -200,6 +200,7 @@ void register_mechanisms(pybind11::module& m) {
m.def("default_catalogue", [](){return arb::global_default_catalogue();});
m.def("allen_catalogue", [](){return arb::global_allen_catalogue();});
m.def("bbp_catalogue", [](){return arb::global_bbp_catalogue();});
+ m.def("stochastic_catalogue", [](){return arb::global_stochastic_catalogue();});
m.def("load_catalogue", [](pybind11::object fn) { return arb::load_catalogue(util::to_string(fn)); });
// arb::mechanism_desc
diff --git a/scripts/run_cpp_examples.sh b/scripts/run_cpp_examples.sh
index efbcf815..5af6591c 100755
--- a/scripts/run_cpp_examples.sh
+++ b/scripts/run_cpp_examples.sh
@@ -26,7 +26,7 @@ check () {
fi
}
-for ex in bench brunel gap_junctions generators lfp ring single-cell "probe-demo v" plasticity
+for ex in bench brunel gap_junctions generators lfp ring single-cell "probe-demo v" plasticity ou
do
echo " - $ex"
dir=`echo $ex | tr ' ' '_'`
diff --git a/test/unit/CMakeLists.txt b/test/unit/CMakeLists.txt
index 2a634d44..36892930 100644
--- a/test/unit/CMakeLists.txt
+++ b/test/unit/CMakeLists.txt
@@ -117,11 +117,13 @@ set(unit_sources
test_piecewise.cpp
test_pp_util.cpp
test_probe.cpp
+ test_rand.cpp
test_range.cpp
test_recipe.cpp
test_ratelem.cpp
test_schedule.cpp
test_scope_exit.cpp
+ test_sde.cpp
test_segment_tree.cpp
test_simd.cpp
test_simulation.cpp
@@ -143,7 +145,6 @@ set(unit_sources
test_unique_any.cpp
test_vector.cpp
test_version.cpp
- test_sde.cpp
# unit test driver
test.cpp
@@ -229,4 +230,4 @@ target_compile_definitions(unit PRIVATE "-DDATADIR=\"${CMAKE_CURRENT_SOURCE_DIR}
target_compile_definitions(unit PRIVATE "-DLIBDIR=\"${PROJECT_BINARY_DIR}/lib\"")
target_include_directories(unit PRIVATE "${CMAKE_CURRENT_BINARY_DIR}")
target_include_directories(unit PRIVATE "${CMAKE_CURRENT_BINARY_DIR}/generated/testing")
-target_link_libraries(unit PRIVATE ext-gtest arbor arborenv arborio arborio-private-headers arbor-private-headers arbor-sup)
+target_link_libraries(unit PRIVATE ext-gtest ext-random123 arbor arborenv arborio arborio-private-headers arbor-private-headers arbor-sup)
diff --git a/test/unit/test_rand.cpp b/test/unit/test_rand.cpp
new file mode 100644
index 00000000..8cee82b9
--- /dev/null
+++ b/test/unit/test_rand.cpp
@@ -0,0 +1,54 @@
+#include <array>
+#include <gtest/gtest.h>
+#include "backends/rand_impl.hpp"
+
+bool verify_uniform(arb::cbprng::array_type counter, arb::cbprng::array_type key,
+ std::array<arb::cbprng::value_type, 4> expected) {
+ const auto r = arb::cbprng::generator{}(counter,key);
+ return
+ (r[0] == expected[0]) &&
+ (r[1] == expected[1]) &&
+ (r[2] == expected[2]) &&
+ (r[3] == expected[3]);
+}
+
+bool verify_normal(std::array<arb::cbprng::value_type, 4> uniform, std::array<long long, 4> expected) {
+ const auto [a0, a1] = r123::boxmuller(uniform[0], uniform[1]);
+ const auto [a2, a3] = r123::boxmuller(uniform[2], uniform[3]);
+ return
+ ((long long)(a0*1000000) == expected[0]) &&
+ ((long long)(a1*1000000) == expected[1]) &&
+ ((long long)(a2*1000000) == expected[2]) &&
+ ((long long)(a3*1000000) == expected[3]);
+}
+
+TEST(cbprng, uniform) {
+ EXPECT_TRUE(verify_uniform(
+ {0ull, 0ull, 0ull, 0ull},
+ {0ull, 0ull, 0ull, 0ull},
+ {29492327419918145ull, 4614276061115832004ull, 16925429801461668750ull, 5660986226915721659ull}));
+
+ EXPECT_TRUE(verify_uniform(
+ {1ull, 2ull, 3ull, 4ull},
+ {5ull, 6ull, 7ull, 8ull},
+ {1161205111990270403ull, 7490910075796229492ull, 3916163298891572586ull, 624723054006169054ull}));
+
+ EXPECT_TRUE(verify_uniform(
+ {6666ull, 77ull, 500ull, 8363839ull},
+ {999ull, 137ull, 0xdeadf00dull, 0xdeadbeefull},
+ {3717439728375325370ull, 14259638735392226729ull, 6108569366204981687ull, 8675995625794245694ull}));
+}
+
+TEST(cbprng, normal) {
+ EXPECT_TRUE(verify_normal(
+ {29492327419918145ull, 4614276061115832004ull, 16925429801461668750ull, 5660986226915721659ull},
+ {16723ll, 1664687ll, -761307ll, 1335286ll}));
+
+ EXPECT_TRUE(verify_normal(
+ {1161205111990270403ull, 7490910075796229492ull, 3916163298891572586ull, 624723054006169054ull},
+ {517262ll, 1238884ll, 2529374ll, 610685ll}));
+
+ EXPECT_TRUE(verify_normal(
+ {3717439728375325370ull, 14259638735392226729ull, 6108569366204981687ull, 8675995625794245694ull},
+ {684541ll, 215202ll, 1072054ll, -599461ll}));
+}
diff --git a/test/unit/test_sde.cpp b/test/unit/test_sde.cpp
index da527499..6de99c39 100644
--- a/test/unit/test_sde.cpp
+++ b/test/unit/test_sde.cpp
@@ -205,9 +205,9 @@ void test_statistics(const std::vector<T>& ordered_samples, double mu, double si
EXPECT_TRUE(chi_2_test_variance(sigma*sigma, acc.mean(), acc.variance(), acc.n()));
}
-// ===========================
-// Recipe and global variables
-// ===========================
+// =================================
+// Declarations and global variables
+// =================================
using namespace arb;
using namespace arborio::literals;
@@ -225,6 +225,10 @@ void advance_mean_reverting_stochastic_density_process2(arb_mechanism_ppack* pp)
void advance_mean_reverting_stochastic_process(arb_mechanism_ppack* pp);
void advance_mean_reverting_stochastic_process2(arb_mechanism_ppack* pp);
+// ===========================================
+// Recipe with multiple mechanism replacements
+// ===========================================
+
// helper macro for replacing a mechanism's advance method
#define REPLACE_IMPLEMENTATION(MECH) \
{ \
--
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