From 0f18392c1440e43a6cc9fbea784ed8a38bb96b2e Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 12 Oct 2024 21:37:46 +0000 Subject: [PATCH] build based on 37a12b2 --- dev/.documenter-siteinfo.json | 2 +- dev/api/index.html | 40 ++++++++++++------------ dev/assets/Manifest.toml | 4 +-- dev/getting_started/index.html | 2 +- dev/index.html | 2 +- dev/release_notes/index.html | 2 +- dev/tutorials/basal_ganglia/index.html | 2 +- dev/tutorials/neural_assembly/index.html | 2 +- dev/tutorials/parkinsons/index.html | 2 +- dev/tutorials/ping_network/index.html | 2 +- dev/tutorials/resting_state/index.html | 2 +- dev/tutorials/spectralDCM/index.html | 2 +- 12 files changed, 32 insertions(+), 32 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 2542ea0..e915961 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-12T21:33:19","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-12T21:37:36","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html index 35b38f2..ba79fd1 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,5 +1,5 @@ -API · Neuroblox
GitHub

API Documentation

Neuroblox.BalloonModel — Type

Arguments:

  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • lnκ: logarithmic prefactor to signal decay H[1], set to 0 for standard parameter value.
  • lnτ: logarithmic prefactor to transit time H[3], set to 0 for standard parameter value.
  • lnϵ: logarithm of ratio of intra- to extra-vascular signal

NB: the prefix ln of the variables u, ν, q as well as the parameters κ, τ denotes their transformation into logarithmic space to enforce their positivity. This transformation is considered in the derivates of the model equations below.

Citations:

  1. Stephan K E, Weiskopf N, Drysdale P M, Robinson P A, and Friston K J. Comparing Hemodynamic Models with DCM. NeuroImage 38, no. 3 (2007): 387–401. doi: 10.1016/j.neuroimage.2007.07.040
  2. Hofmann D, Chesebro A G, Rackauckas C, Mujica-Parodi L R, Friston K J, Edelman A, and Strey H H. Leveraging Julia's Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed, 2023. doi: 10.1101/2023.10.27.564407
source
Neuroblox.Generic2dOscillator — Type
Generic2dOscillator(name, namespace, ...)
+API · Neuroblox
GitHub
API Documentation
Neuroblox.BalloonModel — Type
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • lnκ: logarithmic prefactor to signal decay H[1], set to 0 for standard parameter value.
  • lnτ: logarithmic prefactor to transit time H[3], set to 0 for standard parameter value.
  • lnϵ: logarithm of ratio of intra- to extra-vascular signal
NB: the prefix ln of the variables u, ν, q as well as the parameters κ, τ denotes their transformation into logarithmic space to enforce their positivity. This transformation is considered in the derivates of the model equations below. 
Citations:
  1. Stephan K E, Weiskopf N, Drysdale P M, Robinson P A, and Friston K J. Comparing Hemodynamic Models with DCM. NeuroImage 38, no. 3 (2007): 387–401. doi: 10.1016/j.neuroimage.2007.07.040
  2. Hofmann D, Chesebro A G, Rackauckas C, Mujica-Parodi L R, Friston K J, Edelman A, and Strey H H. Leveraging Julia's Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed, 2023. doi: 10.1101/2023.10.27.564407
source
Neuroblox.Generic2dOscillator — Type
Generic2dOscillator(name, namespace, ...)
 
 The Generic2dOscillator model is a generic dynamic system with two state
 variables. The dynamic equations of this model are composed of two ordinary
@@ -16,15 +16,15 @@
         \dot{V} &= d \, \tau (-f V^3 + e V^2 + g V + \alpha W + \gamma I) \\
         \dot{W} &= \dfrac{d}{	au}\,\,(c V^2 + b V - \beta W + a)
         \end{align}
-```
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.
Citations: FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal 1: 445, 1961.
Nagumo et.al, An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of the IRE 50: 2061, 1962.
Stefanescu, R., Jirsa, V.K. Reduced representations of heterogeneous mixed neural networks with synaptic coupling. Physical Review E, 83, 2011.
Jirsa VK, Stefanescu R.  Neural population modes capture biologically realistic large-scale network dynamics. Bulletin of Mathematical Biology, 2010.
Stefanescu, R., Jirsa, V.K. A low dimensional description of globally coupled heterogeneous neural networks of excitatory and inhibitory neurons. PLoS Computational Biology, 4(11), 2008).
source
Neuroblox.HarmonicOscillator — Type
HarmonicOscillator(name, namespace, ω, ζ, k, h)
+```
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.
Citations: FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal 1: 445, 1961.
Nagumo et.al, An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of the IRE 50: 2061, 1962.
Stefanescu, R., Jirsa, V.K. Reduced representations of heterogeneous mixed neural networks with synaptic coupling. Physical Review E, 83, 2011.
Jirsa VK, Stefanescu R.  Neural population modes capture biologically realistic large-scale network dynamics. Bulletin of Mathematical Biology, 2010.
Stefanescu, R., Jirsa, V.K. A low dimensional description of globally coupled heterogeneous neural networks of excitatory and inhibitory neurons. PLoS Computational Biology, 4(11), 2008).
source
Neuroblox.HarmonicOscillator — Type
HarmonicOscillator(name, namespace, ω, ζ, k, h)
 
 Create a harmonic oscillator blox with the specified parameters.
 The formal definition of this blox is:
\[\frac{dx}{dt} = y-(2*\omega*\zeta*x)+ k*(2/\pi)*(atan((\sum{jcn})/h)
-\frac{dy}{dt} = -(\omega^2)*x\]
where ``jcn`` is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • ω: Base frequency. Note the default value is scaled to give oscillations in milliseconds to match other blocks.
  • ζ: Damping ratio.
  • k: Gain.
  • h: Threshold.
source
Neuroblox.JansenRit — Type
JansenRit(name, namespace, τ, H, λ, r, cortical, delayed)
+\frac{dy}{dt} = -(\omega^2)*x\]
where ``jcn`` is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • ω: Base frequency. Note the default value is scaled to give oscillations in milliseconds to match other blocks.
  • ζ: Damping ratio.
  • k: Gain.
  • h: Threshold.
source
Neuroblox.JansenRit — Type
JansenRit(name, namespace, τ, H, λ, r, cortical, delayed)
 
 Create a Jansen Rit blox as described in Liu et al.
 The formal definition of this blox is:
\[\frac{dx}{dt} = y-\frac{2}{\tau}x
-\frac{dy}{dt} = -\frac{x}{\tau^2} + \frac{H}{\tau} [\frac{2\lambda}{1+\text{exp}(-r*\sum{jcn})} - \lambda]\]
where $jcn$ is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • τ: Time constant. This is changed from the original source as the time constant was in seconds, while all our blocks are in milliseconds.
  • H: See equation for use.
  • λ: See equation for use.
  • r: See equation for use.
  • cortical: Boolean to determine whether to use cortical or subcortical parameters. Specifying any of the parameters above will override this.
  • delayed: Boolean to indicate whether states are delayed
Citations:
  1. Liu C, Zhou C, Wang J, Fietkiewicz C, Loparo KA. The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations. Neural Netw. 2020 Mar;123:381-392. doi: 10.1016/j.neunet.2019.12.021.
source
Neuroblox.KuramotoOscillator — Type
KuramotoOscillator(name, namespace, ...)
+\frac{dy}{dt} = -\frac{x}{\tau^2} + \frac{H}{\tau} [\frac{2\lambda}{1+\text{exp}(-r*\sum{jcn})} - \lambda]\]
where $jcn$ is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • τ: Time constant. This is changed from the original source as the time constant was in seconds, while all our blocks are in milliseconds.
  • H: See equation for use.
  • λ: See equation for use.
  • r: See equation for use.
  • cortical: Boolean to determine whether to use cortical or subcortical parameters. Specifying any of the parameters above will override this.
  • delayed: Boolean to indicate whether states are delayed
Citations:
  1. Liu C, Zhou C, Wang J, Fietkiewicz C, Loparo KA. The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations. Neural Netw. 2020 Mar;123:381-392. doi: 10.1016/j.neunet.2019.12.021.
source
Neuroblox.KuramotoOscillator — Type
KuramotoOscillator(name, namespace, ...)
 
 Simple implementation of the Kuramoto oscillator as described in the original paper [1].
 Useful for general models of synchronization and oscillatory behavior.
@@ -46,15 +46,15 @@
         \end{equation}
 ```
 
-where $W_i$ is a Wiener process and $\zeta_i$ is the noise strength.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.                   Default parameter values are taken from [2].
Citations:
  1. Kuramoto, Y. (1975). Self-entrainment of a population of coupled non-linear oscillators.  In: Araki, H. (eds) International Symposium on Mathematical Problems in Theoretical Physics.  Lecture Notes in Physics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013365
  2. Sermon JJ, Wiest C, Tan H, Denison T, Duchet B. Evoked resonant neural activity long-term  dynamics can be reproduced by a computational model with vesicle depletion. Neurobiol Dis.  2024 Jun 14;199:106565. doi: 10.1016/j.nbd.2024.106565. Epub ahead of print. PMID: 38880431.
source
Neuroblox.LarterBreakspear — Type
LarterBreakspear(name, namespace, ...)
+where $W_i$ is a Wiener process and $\zeta_i$ is the noise strength.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.                   Default parameter values are taken from [2].
Citations:
  1. Kuramoto, Y. (1975). Self-entrainment of a population of coupled non-linear oscillators.  In: Araki, H. (eds) International Symposium on Mathematical Problems in Theoretical Physics.  Lecture Notes in Physics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013365
  2. Sermon JJ, Wiest C, Tan H, Denison T, Duchet B. Evoked resonant neural activity long-term  dynamics can be reproduced by a computational model with vesicle depletion. Neurobiol Dis.  2024 Jun 14;199:106565. doi: 10.1016/j.nbd.2024.106565. Epub ahead of print. PMID: 38880431.
source
Neuroblox.LarterBreakspear — Type
LarterBreakspear(name, namespace, ...)
 
 Create a Larter Breakspear blox described in Endo et al. For a full list of the parameters used see the reference.
-If you need to modify the parameters, see Chesebro et al. and van Nieuwenhuizen et al. for physiological ranges.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.
Citations:
  1. Endo H, Hiroe N, Yamashita O. Evaluation of Resting Spatio-Temporal Dynamics of a Neural Mass Model Using Resting fMRI Connectivity and EEG Microstates. Front Comput Neurosci. 2020 Jan 17;13:91. doi: 10.3389/fncom.2019.00091.
  2. Chesebro AG, Mujica-Parodi LR, Weistuch C. Ion gradient-driven bifurcations of a multi-scale neuronal model. Chaos Solitons Fractals. 2023 Feb;167:113120. doi: 10.1016/j.chaos.2023.113120. 
  3. van Nieuwenhuizen, H, Chesebro, AG, Polis, C, Clarke, K, Strey, HH, Weistuch, C, Mujica-Parodi, LR. Ketosis regulates K+ ion channels, strengthening brain-wide signaling disrupted by age. Preprint. bioRxiv 2023.05.10.540257; doi: https://doi.org/10.1101/2023.05.10.540257. 
source
Neuroblox.OUBlox — Type
Ornstein-Uhlenbeck process Blox
variables:     x(t):  value     jcn:   input  parameters:     τ:      relaxation time 	μ:      average value 	σ:      random noise (variance of OU process is τ*σ^2/2) returns:     an ODE System (but with brownian parameters)
source
Neuroblox.WilsonCowan — Type
WilsonCowan(name, namespace, τ_E, τ_I, a_E, a_I, c_EE, c_IE, c_EI, c_II, θ_E, θ_I, η)
+If you need to modify the parameters, see Chesebro et al. and van Nieuwenhuizen et al. for physiological ranges.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Other parameters: See reference for full list. Note that parameters are scaled so that units of time are in milliseconds.
Citations:
  1. Endo H, Hiroe N, Yamashita O. Evaluation of Resting Spatio-Temporal Dynamics of a Neural Mass Model Using Resting fMRI Connectivity and EEG Microstates. Front Comput Neurosci. 2020 Jan 17;13:91. doi: 10.3389/fncom.2019.00091.
  2. Chesebro AG, Mujica-Parodi LR, Weistuch C. Ion gradient-driven bifurcations of a multi-scale neuronal model. Chaos Solitons Fractals. 2023 Feb;167:113120. doi: 10.1016/j.chaos.2023.113120. 
  3. van Nieuwenhuizen, H, Chesebro, AG, Polis, C, Clarke, K, Strey, HH, Weistuch, C, Mujica-Parodi, LR. Ketosis regulates K+ ion channels, strengthening brain-wide signaling disrupted by age. Preprint. bioRxiv 2023.05.10.540257; doi: https://doi.org/10.1101/2023.05.10.540257. 
source
Neuroblox.OUBlox — Type
Ornstein-Uhlenbeck process Blox
variables:     x(t):  value     jcn:   input  parameters:     τ:      relaxation time 	μ:      average value 	σ:      random noise (variance of OU process is τ*σ^2/2) returns:     an ODE System (but with brownian parameters)
source
Neuroblox.WilsonCowan — Type
WilsonCowan(name, namespace, τ_E, τ_I, a_E, a_I, c_EE, c_IE, c_EI, c_II, θ_E, θ_I, η)
 
 Create a standard Wilson Cowan blox.
 The formal definition of this blox is:
\[\frac{dE}{dt} = \frac{-E}{\tau_E} + \frac{1}{1 + \text{exp}(-a_E*(c_{EE}*E - c_{IE}*I - \theta_E + \eta*(\sum{jcn}))}
-\frac{dI}{dt} = \frac{-I}{\tau_I} + \frac{1}{1 + exp(-a_I*(c_{EI}*E - c_{II}*I - \theta_I)}\]
where $jcn$ is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Others: See equation for use.
source
Neuroblox.WinnerTakeAllBlox — Type
WinnerTakeAllBlox
Creates a winner-take-all local circuit found in neocortex, typically 5 pyramidal (excitatory) neurons send synapses to a single interneuron (inhibitory) and receive feedback inhibition from that interneuron.
source
LinearAlgebra.eigen — Method
function LinearAlgebra.eigen(M::Matrix{Dual{T, P, np}}) where {T, P, np}
+\frac{dI}{dt} = \frac{-I}{\tau_I} + \frac{1}{1 + exp(-a_I*(c_{EI}*E - c_{II}*I - \theta_I)}\]
where $jcn$ is any input to the blox.
Arguments:
  • name: Name given to ODESystem object within the blox.
  • namespace: Additional namespace above name if needed for inheritance.
  • Others: See equation for use.
source
Neuroblox.WinnerTakeAllBlox — Type
WinnerTakeAllBlox
Creates a winner-take-all local circuit found in neocortex, typically 5 pyramidal (excitatory) neurons send synapses to a single interneuron (inhibitory) and receive feedback inhibition from that interneuron.
source
LinearAlgebra.eigen — Method
function LinearAlgebra.eigen(M::Matrix{Dual{T, P, np}}) where {T, P, np}
 
 Dispatch of LinearAlgebra.eigen for dual matrices with complex numbers. Make the eigenvalue decomposition 
 amenable to automatic differentiation. To do so compute the analytical derivative of eigenvalues
@@ -64,7 +64,7 @@
 - `M`: matrix of type Dual of which to compute the eigenvalue decomposition. 
 
 Returns:
-- `Eigen(evals, evecs)`: eigenvalue decomposition returned as type LinearAlgebra.Eigen
source
Neuroblox.ARVTarget — Method
ARVTarget Time series data is bandpass filtered and then the power spectrum is computed for a given time interval (control bin), returned as the average value of the power spectral density within a certain frequency band ([lb, ub]).
source
Neuroblox.CDVTarget — Method
CDVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians. Circular difference is quantified as the angle of circular_location.
source
Neuroblox.PDVTarget — Method
PDVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians. Phase deviation is quantified as the angle difference between a given set of signals.
source
Neuroblox.PLVTarget — Method
PLVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians.
source
Neuroblox.addnontunableparams — Method
function addnontunableparams(param, model)
+- `Eigen(evals, evecs)`: eigenvalue decomposition returned as type LinearAlgebra.Eigen
source
Neuroblox.ARVTarget — Method
ARVTarget Time series data is bandpass filtered and then the power spectrum is computed for a given time interval (control bin), returned as the average value of the power spectral density within a certain frequency band ([lb, ub]).
source
Neuroblox.CDVTarget — Method
CDVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians. Circular difference is quantified as the angle of circular_location.
source
Neuroblox.PDVTarget — Method
PDVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians. Phase deviation is quantified as the angle difference between a given set of signals.
source
Neuroblox.PLVTarget — Method
PLVTarget Time series data is bandpass filtered and hilbert-transformed. Phase angle is computed in radians.
source
Neuroblox.addnontunableparams — Method
function addnontunableparams(param, model)
 
 Function adds parameters of a model that were not marked as tunable to a list of tunable parameters
 and respects the MTK ordering of parameters.
@@ -74,12 +74,12 @@
 - `sys`: MTK system
 
 Returns:
-- `completeparamlist`: complete parameter list of a system, including those that were not tagged as tunable
source
Neuroblox.bandpassfilter — Method
bandpassfilter takes in time series data and bandpass filters it. It has the following inputs:     data: time series data     lb: minimum cut-off frequency     ub: maximum cut-off frequency     fs: sampling frequency     order: filter order
source
Neuroblox.boldsignal — Method
Arguments:
  • name: Name given to ODESystem object within the blox.
  • lnϵ  : logarithm of ratio of intra- to extra-vascular signal
NB: the prefix ln of the variables ν, q as well as the parameters ϵ denotes their transformation into logarithmic space to enforce their positivity.
Citations:
  1. Stephan K E, Weiskopf N, Drysdale P M, Robinson P A, and Friston K J. Comparing Hemodynamic Models with DCM. NeuroImage 38, no. 3 (2007): 387–401. doi: 10.1016/j.neuroimage.2007.07.040
  2. Hofmann D, Chesebro A G, Rackauckas C, Mujica-Parodi L R, Friston K J, Edelman A, and Strey H H. Leveraging Julia's Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed, 2023. doi: 10.1101/2023.10.27.564407
source
Neuroblox.complexwavelet — Function
complexwavelet creates a complex morlet wavelet by windowing a complex sine wave with a Gaussian taper.  The morlet wavelet is a special case of a bandpass filter in which the frequency response is Gaussian-shaped. Convolution with a complex wavelet is equivalent to performing a Hilbert transform of a bandpass filtered signal.
It has the following inputs:     data: time series data      dt  : data sampling rate      lb  : lower bound wavelet frequency (in Hz)     ub  : upper bound wavelet frequency (in Hz)     a   : amplitude of the Gaussian taper, default is 1     n   : number of wavelet cycles of the Gaussian taper, defines the trade-off between temporal precision and frequency precision           larger n gives better frequency precision at the cost of temporal precision           default is 6 Hz     m   : x-axis offset, default is 0     num_wavelets : number of wavelets to create, default is 5
And outputs:     complex_wavelet : a family of complex morlet wavelets
source
Neuroblox.csd2mar — Method
This function converts a cross-spectral density (CSD) into a multivariate auto-regression (MAR) model. It first transforms the CSD into its cross-correlation function (Wiener-Kinchine theorem) and then computes the MAR model coefficients. csd       : cross-spectral density matrix of size MxN; M: number of samples, N: number of cross-spectral dimensions (number of variables squared) w         : frequencies dt        : time step size p         : number of time steps of auto-regressive model
This function returns coeff     : array of length p of coefficient matrices of size sqrt(N)xsqrt(N) noise_cov : noise covariance matrix
source
Neuroblox.csd_approx — Method
This function implements equation 2 of the spectral DCM paper, Friston et al. 2014 "A DCM for resting state fMRI".
+- `completeparamlist`: complete parameter list of a system, including those that were not tagged as tunable
source
Neuroblox.bandpassfilter — Method
bandpassfilter takes in time series data and bandpass filters it. It has the following inputs:     data: time series data     lb: minimum cut-off frequency     ub: maximum cut-off frequency     fs: sampling frequency     order: filter order
source
Neuroblox.boldsignal — Method
Arguments:
  • name: Name given to ODESystem object within the blox.
  • lnϵ  : logarithm of ratio of intra- to extra-vascular signal
NB: the prefix ln of the variables ν, q as well as the parameters ϵ denotes their transformation into logarithmic space to enforce their positivity.
Citations:
  1. Stephan K E, Weiskopf N, Drysdale P M, Robinson P A, and Friston K J. Comparing Hemodynamic Models with DCM. NeuroImage 38, no. 3 (2007): 387–401. doi: 10.1016/j.neuroimage.2007.07.040
  2. Hofmann D, Chesebro A G, Rackauckas C, Mujica-Parodi L R, Friston K J, Edelman A, and Strey H H. Leveraging Julia's Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed, 2023. doi: 10.1101/2023.10.27.564407
source
Neuroblox.complexwavelet — Function
complexwavelet creates a complex morlet wavelet by windowing a complex sine wave with a Gaussian taper.  The morlet wavelet is a special case of a bandpass filter in which the frequency response is Gaussian-shaped. Convolution with a complex wavelet is equivalent to performing a Hilbert transform of a bandpass filtered signal.
It has the following inputs:     data: time series data      dt  : data sampling rate      lb  : lower bound wavelet frequency (in Hz)     ub  : upper bound wavelet frequency (in Hz)     a   : amplitude of the Gaussian taper, default is 1     n   : number of wavelet cycles of the Gaussian taper, defines the trade-off between temporal precision and frequency precision           larger n gives better frequency precision at the cost of temporal precision           default is 6 Hz     m   : x-axis offset, default is 0     num_wavelets : number of wavelets to create, default is 5
And outputs:     complex_wavelet : a family of complex morlet wavelets
source
Neuroblox.csd2mar — Method
This function converts a cross-spectral density (CSD) into a multivariate auto-regression (MAR) model. It first transforms the CSD into its cross-correlation function (Wiener-Kinchine theorem) and then computes the MAR model coefficients. csd       : cross-spectral density matrix of size MxN; M: number of samples, N: number of cross-spectral dimensions (number of variables squared) w         : frequencies dt        : time step size p         : number of time steps of auto-regressive model
This function returns coeff     : array of length p of coefficient matrices of size sqrt(N)xsqrt(N) noise_cov : noise covariance matrix
source
Neuroblox.csd_approx — Method
This function implements equation 2 of the spectral DCM paper, Friston et al. 2014 "A DCM for resting state fMRI".
 Note that nomenclature is taken from SPM12 code and it does not seem to coincide with the spectral DCM paper's nomenclature. 
 For instance, Gu should represent the spectral component due to external input according to the paper. However, in the code this represents
 the hidden state fluctuations (which are called Gν in the paper).
 Gn in the code corresponds to Ge in the paper, i.e. the observation noise. In the code global and local components are defined, no such distinction
-is discussed in the paper. In fact the parameter γ, corresponding to local component is not present in the paper.
source
Neuroblox.get_dynamic_states — Method
function get_dynamic_states(sys)
+is discussed in the paper. In fact the parameter γ, corresponding to local component is not present in the paper.
source
Neuroblox.get_dynamic_states — Method
function get_dynamic_states(sys)
 
 Function extracts states from the system that are dynamic variables, 
 get also indices of external inputs (u(t)) and measurements (like bold(t))
@@ -88,7 +88,7 @@
 
 Returns:
 - `sts`: states/unknowns of the system that are neither external inputs nor measurements, i.e. these are the dynamic states
-- `idx`: indices of these states
source
Neuroblox.get_input_equations — Method
Returns the equations for all input variables of a system, 
 assuming they have a form like : `sys.input_variable ~ ...`
 so only the input appears on the LHS.
 
@@ -98,20 +98,20 @@
 
 If blox isa AbstractComponent, it is assumed that it contains a `connector` field,
 which holds a `BloxConnector` object with all relevant connections 
-from lower levels and this level.
source
Neuroblox.idft — Method
Plain implementation of idft because AD dispatch versions for ifft don't work still!
source
Neuroblox.idft — Method
Plain implementation of idft because AD dispatch versions for ifft don't work still!
source
Neuroblox.inner_namespaceof — Method
Returns the complete namespace EXCLUDING the outermost (highest) level.
 This is useful for manually preparing equations (e.g. connections, see BloxConnector),
-that will later be composed and will automatically get the outermost namespace.
source
Neuroblox.learningrate — Method
This function computes learning rate. It has the following inputs:     outcomes: vector of 1's and 0's for behavioral outcomes     windows: number of windows to split the outcome data into And the following outputs:     rate: the learning rate across each window
source
Neuroblox.mar2csd — Method
This function converts multivariate auto-regression (MAR) model parameters to a cross-spectral density (CSD). A     : coefficients of MAR model, array of length p, each element contains the regression coefficients for that particular time-lag. Σ     : noise covariance matrix of MAR p     : number of time lags freqs : frequencies at which to evaluate the CSD sf    : sampling frequency
This function returns: csd   : cross-spectral density matrix of size MxN; M: number of samples, N: number of cross-spectral dimensions (number of variables squared)
source
Neuroblox.mar_ml — Method
Maximum likelihood estimator of a multivariate, or vector auto-regressive model.     y : MxN Data matrix where M is number of samples and N is number of dimensions     p : time lag parameter, also called order of MAR model     return values     mar["A"] : model parameters is a NxNxP tensor, i.e. one NxN parameter matrix for each time bin k ∈ {1,...,p}     mar["Σ"] : noise covariance matrix
source
Neuroblox.matlab_norm — Method
function matlab_norm(A, p)
+that will later be composed and will automatically get the outermost namespace.
source
Neuroblox.learningrate — Method
This function computes learning rate. It has the following inputs:     outcomes: vector of 1's and 0's for behavioral outcomes     windows: number of windows to split the outcome data into And the following outputs:     rate: the learning rate across each window
source
Neuroblox.mar2csd — Method
This function converts multivariate auto-regression (MAR) model parameters to a cross-spectral density (CSD). A     : coefficients of MAR model, array of length p, each element contains the regression coefficients for that particular time-lag. Σ     : noise covariance matrix of MAR p     : number of time lags freqs : frequencies at which to evaluate the CSD sf    : sampling frequency
This function returns: csd   : cross-spectral density matrix of size MxN; M: number of samples, N: number of cross-spectral dimensions (number of variables squared)
source
Neuroblox.mar_ml — Method
Maximum likelihood estimator of a multivariate, or vector auto-regressive model.     y : MxN Data matrix where M is number of samples and N is number of dimensions     p : time lag parameter, also called order of MAR model     return values     mar["A"] : model parameters is a NxNxP tensor, i.e. one NxN parameter matrix for each time bin k ∈ {1,...,p}     mar["Σ"] : noise covariance matrix
source
Neuroblox.matlab_norm — Method
function matlab_norm(A, p)
 
 Simple helper function to implement the norm of a matrix that is equivalent to the one given in MATLAB for order=1, 2, Inf. 
 This is needed for the reproduction of the exact same results of SPM12.
 
 Arguments:
 - `A`: matrix
-- `p`: order of norm
source
Neuroblox.paramscoping — Method
function paramscoping(;kwargs...)
 
 Scope arguments that are already a symbolic model parameter thereby keep the correct namespace 
 and make those that are not yet symbolic a symbol.
-Keyword arguments are used, because parameter definition require names, not just values.
source
Neuroblox.phase_cos_blox — Method
phasecosblox is creating a cos with angular frequency ω and variable phase phaseinter has the following parameters:     ω: angular frequency     t: time     phaseinter: a function that returns phase as a function of time and returns:     the resulting value
Usage:     phaseint = phaseinter(0:0.1:50,phasedata)     phaseout(t) = phasecosblox(0.1,t,phaseint)     which is now a function of time and can be used in an input blox     you can also use the dot operator to calculate time-series     signal = phaseout.(collect(0:0.01:50))
source
Neuroblox.phase_inter — Method
phaseinter is creating a function that interpolates the phase data for any time given phaseinter has the following parameters:     phaserange:  a range, e.g. 0:0.1:50 which should reflect the time points of the data     phasedata: phase at equidistant time points and returns:     an function that returns an interpolated phase for t in range
source
Neuroblox.phase_sin_blox — Method
phasesinblox is creating a sin with angular frequency ω and variable phase phaseinter has the following parameters:     ω: angular frequency     t: time     phaseinter: a function that returns phase as a function of time and returns:     the resulting value
Usage:     phaseint = phaseinter(0:0.1:50,phasedata)     phaseout(t) = phasesinblox(0.1,t,phaseint)     which is now a function of time and can be used in an input blox     you can also use the dot operator to calculate time-series     signal = phaseout.(collect(0:0.01:50))
source
Neuroblox.random_initials — Method
random_initials creates a vector of random initial conditions for an ODESystem that is composed of a list of blox.  The function finds the initial conditions in the blox and then sets a random value in between range tuple given for that state.
It has the following inputs:     odesys: ODESystem     blox  : list of blox
And outputs:     u0 : Float64 vector of initial conditions
source
Neuroblox.setup_sDCM — Method
function setup_sDCM(data, stateevolutionmodel, initcond, csdsetup, priors, hyperpriors, indices)
+Keyword arguments are used, because parameter definition require names, not just values.
source
Neuroblox.phase_cos_blox — Method
phasecosblox is creating a cos with angular frequency ω and variable phase phaseinter has the following parameters:     ω: angular frequency     t: time     phaseinter: a function that returns phase as a function of time and returns:     the resulting value
Usage:     phaseint = phaseinter(0:0.1:50,phasedata)     phaseout(t) = phasecosblox(0.1,t,phaseint)     which is now a function of time and can be used in an input blox     you can also use the dot operator to calculate time-series     signal = phaseout.(collect(0:0.01:50))
source
Neuroblox.phase_inter — Method
phaseinter is creating a function that interpolates the phase data for any time given phaseinter has the following parameters:     phaserange:  a range, e.g. 0:0.1:50 which should reflect the time points of the data     phasedata: phase at equidistant time points and returns:     an function that returns an interpolated phase for t in range
source
Neuroblox.phase_sin_blox — Method
phasesinblox is creating a sin with angular frequency ω and variable phase phaseinter has the following parameters:     ω: angular frequency     t: time     phaseinter: a function that returns phase as a function of time and returns:     the resulting value
Usage:     phaseint = phaseinter(0:0.1:50,phasedata)     phaseout(t) = phasesinblox(0.1,t,phaseint)     which is now a function of time and can be used in an input blox     you can also use the dot operator to calculate time-series     signal = phaseout.(collect(0:0.01:50))
source
Neuroblox.random_initials — Method
random_initials creates a vector of random initial conditions for an ODESystem that is composed of a list of blox.  The function finds the initial conditions in the blox and then sets a random value in between range tuple given for that state.
It has the following inputs:     odesys: ODESystem     blox  : list of blox
And outputs:     u0 : Float64 vector of initial conditions
source
Neuroblox.setup_sDCM — Method
function setup_sDCM(data, stateevolutionmodel, initcond, csdsetup, priors, hyperpriors, indices)
 
 Interface function to performs variational inference to fit model parameters to empirical cross spectral density.
 The current implementation provides a Variational Laplace fit (see function above `variationalbayes`).
@@ -131,15 +131,15 @@
 - `hyperpriors` : dataframe of parameters with the following columns:
 -- `Πλ_pr`      : prior precision matrix for λ hyperparameter(s)
 -- `μλ_pr`      : prior mean(s) for λ hyperparameter(s)
-- `indices`  : indices to separate model parameters from other parameters. Needed for the computation of AD gradient.
source
Neuroblox.spm_logdet — Method
function spm_logdet(M)
+- `indices`  : indices to separate model parameters from other parameters. Needed for the computation of AD gradient.
source
Neuroblox.spm_logdet — Method
function spm_logdet(M)
 
 SPM12 style implementation of the logarithm of the determinant of a matrix.
 
 Arguments:
-- `M`: matrix
source
Neuroblox.system_from_graph — Function
system_from_graph(g::MetaDiGraph, p=Num[]; name, simplify=true, graphdynamics=false, kwargs...)
Take in a MetaDiGraph g describing a network of neural structures (and optionally a vector of extra parameters p) and construct a System which can be used to construct various Problem types (i.e. ODEProblem) for use with DifferentialEquations.jl solvers.
If simplify is set to true (the default), then the resulting system will have structural_simplify called on it with any remaining keyword arguments forwared to structural_simplify. That is,
@named sys = system_from_graph(g; kwarg1=x, kwarg2=y)
is equivalent to
@named sys = system_from_graph(g; simplify=false)
-sys = structural_simplify(sys; kwarg1=x, kwarg2=y)
See the docstring for structural_simplify for information on which options it supports.
If graphdynamics=true (defaults to false), the output will be a GraphSystem from GraphDynamics.jl, and the kwargs will be sent to the GraphDynamics constructor instead of using ModelingToolkit.jl. The GraphDynamics.jl backend is typically significantly faster for large neural systems than the default backend, but is experimental and does not yet support all Neuroblox.jl features. 
source
Neuroblox.system_from_graph — Function
system_from_graph(g::MetaDiGraph, p=Num[]; name, simplify=true, graphdynamics=false, kwargs...)
Take in a MetaDiGraph g describing a network of neural structures (and optionally a vector of extra parameters p) and construct a System which can be used to construct various Problem types (i.e. ODEProblem) for use with DifferentialEquations.jl solvers.
If simplify is set to true (the default), then the resulting system will have structural_simplify called on it with any remaining keyword arguments forwared to structural_simplify. That is,
@named sys = system_from_graph(g; kwarg1=x, kwarg2=y)
is equivalent to
@named sys = system_from_graph(g; simplify=false)
+sys = structural_simplify(sys; kwarg1=x, kwarg2=y)
See the docstring for structural_simplify for information on which options it supports.
If graphdynamics=true (defaults to false), the output will be a GraphSystem from GraphDynamics.jl, and the kwargs will be sent to the GraphDynamics constructor instead of using ModelingToolkit.jl. The GraphDynamics.jl backend is typically significantly faster for large neural systems than the default backend, but is experimental and does not yet support all Neuroblox.jl features. 
source
Neuroblox.vecparam — Method
vecparam(param::OrderedDict)
 
 Function to flatten an ordered dictionary of model parameters and return a simple list of parameter values.
 
 Arguments:
-- `param`: dictionary of model parameters (may contain numbers and lists of numbers)
source

+- `param`: dictionary of model parameters (may contain numbers and lists of numbers)
source
diff --git a/dev/assets/Manifest.toml b/dev/assets/Manifest.toml index 94c551b..3a67237 100644 --- a/dev/assets/Manifest.toml +++ b/dev/assets/Manifest.toml @@ -1559,9 +1559,9 @@ version = "1.11.0" [[deps.ModelingToolkit]] deps = ["AbstractTrees", "ArrayInterface", "BlockArrays", "Combinatorics", "Compat", "ConstructionBase", "DataStructures", "DiffEqBase", "DiffEqCallbacks", "DiffEqNoiseProcess", "DiffRules", "Distributed", "Distributions", "DocStringExtensions", "DomainSets", "DynamicQuantities", "ExprTools", "Expronicon", "FindFirstFunctions", "ForwardDiff", "FunctionWrappers", "FunctionWrappersWrappers", "Graphs", "InteractiveUtils", "JuliaFormatter", "JumpProcesses", "Latexify", "Libdl", "LinearAlgebra", "MLStyle", "NaNMath", "NonlinearSolve", "OffsetArrays", "OrderedCollections", "PrecompileTools", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "SciMLStructures", "Serialization", "Setfield", "SimpleNonlinearSolve", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "SymbolicUtils", "Symbolics", "URIs", "UnPack", "Unitful"] -git-tree-sha1 = "6bd76441412fece207dd24dfa016d0d6e89cb8c1" +git-tree-sha1 = "72281d6f80d09d46d49e9ae292b2376de1c29ce8" uuid = "961ee093-0014-501f-94e3-6117800e7a78" -version = "9.45.0" +version = "9.46.0" [deps.ModelingToolkit.extensions] MTKBifurcationKitExt = "BifurcationKit" diff --git a/dev/getting_started/index.html b/dev/getting_started/index.html index 2d52914..2e45211 100644 --- a/dev/getting_started/index.html +++ b/dev/getting_started/index.html @@ -78,4 +78,4 @@ lines!(ax, sol.t, E1, label = "E") lines!(ax, sol.t, I1, label = "I") Legend(fig[1,2], ax) -figExample block output

[1] Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical journal, 12(1), 1-24.

[2] Destexhe, A., & Sejnowski, T. J. (2009). The Wilson–Cowan model, 36 years later. Biological cybernetics, 101(1), 1-2.

This page was generated using Literate.jl.

+figExample block output

[1] Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical journal, 12(1), 1-24.

[2] Destexhe, A., & Sejnowski, T. J. (2009). The Wilson–Cowan model, 36 years later. Biological cybernetics, 101(1), 1-2.

This page was generated using Literate.jl.

diff --git a/dev/index.html b/dev/index.html index c73ed52..bc9a682 100644 --- a/dev/index.html +++ b/dev/index.html @@ -4,4 +4,4 @@ using PkgAuthentication PkgAuthentication.install("juliahub.com") Pkg.Registry.add() -Pkg.add("Neuroblox")

Licensing

Neuroblox is free for non-commerical and academic use. For full details of the license, please see the Neuroblox EULA. For commercial use, get in contact with sales@neuroblox.org.

+Pkg.add("Neuroblox")

Licensing

Neuroblox is free for non-commerical and academic use. For full details of the license, please see the Neuroblox EULA. For commercial use, get in contact with sales@neuroblox.org.

diff --git a/dev/release_notes/index.html b/dev/release_notes/index.html index d2513d2..c467dc6 100644 --- a/dev/release_notes/index.html +++ b/dev/release_notes/index.html @@ -1,2 +1,2 @@ -Release Notes · Neuroblox
GitHub
+Release Notes · Neuroblox
GitHub
diff --git a/dev/tutorials/basal_ganglia/index.html b/dev/tutorials/basal_ganglia/index.html index 9a9113f..26b5db1 100644 --- a/dev/tutorials/basal_ganglia/index.html +++ b/dev/tutorials/basal_ganglia/index.html @@ -213,4 +213,4 @@ gamma_label_position = (60, 2), title = "STN (PD)") -figExample block output

We see the emergence of strong beta oscillations in the Parkinsonian condition compared to the baseline condition for all neural populations. This aligns with the findings of Adam et al. and reflects the pathological synchrony observed in Parkinson's disease.

References

Adam, Elie M., et al. "Deep brain stimulation in the subthalamic nucleus for Parkinson's disease can restore dynamics of striatal networks." Proceedings of the National Academy of Sciences 119.19 (2022): e2120808119.

This page was generated using Literate.jl.

+figExample block output

We see the emergence of strong beta oscillations in the Parkinsonian condition compared to the baseline condition for all neural populations. This aligns with the findings of Adam et al. and reflects the pathological synchrony observed in Parkinson's disease.

References

Adam, Elie M., et al. "Deep brain stimulation in the subthalamic nucleus for Parkinson's disease can restore dynamics of striatal networks." Proceedings of the National Academy of Sciences 119.19 (2022): e2120808119.

This page was generated using Literate.jl.

diff --git a/dev/tutorials/neural_assembly/index.html b/dev/tutorials/neural_assembly/index.html index d10e207..a778e53 100644 --- a/dev/tutorials/neural_assembly/index.html +++ b/dev/tutorials/neural_assembly/index.html @@ -183,4 +183,4 @@ fig = Figure(); ax = Axis(fig[1,1]; xlabel = "time (ms)", ylabel = "Voltage (mv)") lines!(ax, sol.t, mnv) -fig ## to display the figureExample block output

and finally the AC powerspectrum

powerspectrumplot(AC,sol)
Example block output

Sugestion : Try changing the image samples and notice the change in the spatial firing patterns in VAC and AC neurons. One can make multiple cortical blocks simillar to AC and connect them in various connection topologies. All of them can directly or indirectly get input from VAC.

This page was generated using Literate.jl.

+fig ## to display the figureExample block output

and finally the AC powerspectrum

powerspectrumplot(AC,sol)
Example block output

Sugestion : Try changing the image samples and notice the change in the spatial firing patterns in VAC and AC neurons. One can make multiple cortical blocks simillar to AC and connect them in various connection topologies. All of them can directly or indirectly get input from VAC.

This page was generated using Literate.jl.

diff --git a/dev/tutorials/parkinsons/index.html b/dev/tutorials/parkinsons/index.html index e7a73f3..c21322d 100644 --- a/dev/tutorials/parkinsons/index.html +++ b/dev/tutorials/parkinsons/index.html @@ -108,4 +108,4 @@ [143.60674274098432, 8.117509909895832, -13.184645285375899, -11.992280007404794, -19.162378618894284, 3.0607632418163657, 0.1, 0.2, -112.0, -16.0, 0.4, 0.4, 0.9999999999999999, 0.19999999999999998, 659.773119179332, 1.054791635893819] [144.37829154534262, 7.827497471199225, -13.189804282236642, -11.99489891885093, -12.367623657501781, 4.218241303604233, 0.1, 0.2, -112.0, -16.0, 0.4, 0.4, 0.9999999999999999, 0.19999999999999998, 660.1679327670073, 1.054776643253788] [144.82912539272962, 7.537103836151018, -13.19319994530957, -11.996607873608935, -5.786786325488266, 5.308834687904132, 0.1, 0.2, -112.0, -16.0, 0.4, 0.4, 0.9999999999999999, 0.19999999999999998, 660.5623367039717, 1.054761551961573] - [144.9746128202959, 7.2465246567592, -13.195480028260556, -11.997752273630809, 0.559054744746166, 6.334773028196878, 0.1, 0.2, -112.0, -16.0, 0.4, 0.4, 0.9999999999999999, 0.19999999999999998, 660.9563313011192, 1.0547463621195476]

[1] Liu, C., Zhou, C., Wang, J., Fietkiewicz, C., & Loparo, K. A. (2020). The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations. Neural Networks, 123, 381-392.

This page was generated using Literate.jl.

+ [144.9746128202959, 7.2465246567592, -13.195480028260556, -11.997752273630809, 0.559054744746166, 6.334773028196878, 0.1, 0.2, -112.0, -16.0, 0.4, 0.4, 0.9999999999999999, 0.19999999999999998, 660.9563313011192, 1.0547463621195476]

[1] Liu, C., Zhou, C., Wang, J., Fietkiewicz, C., & Loparo, K. A. (2020). The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations. Neural Networks, 123, 381-392.

This page was generated using Literate.jl.

diff --git a/dev/tutorials/ping_network/index.html b/dev/tutorials/ping_network/index.html index 0aa726f..705bfc2 100644 --- a/dev/tutorials/ping_network/index.html +++ b/dev/tutorials/ping_network/index.html @@ -46,4 +46,4 @@ sol = solve(prob, Tsit5(), saveat=0.1); ## Solve the problem and save at 0.1ms resolution.

Plotting the results

Now that we have a whole simulation, let's plot the results and see how they line up with the original figures. We're looking to reproduce the dynamics shown in Figure 1 of Börgers et al. [1]. To create raster plots in Neuroblox for the excitatory and inhibitory populations, it is as simple as:

fig = Figure()
 rasterplot(fig[1,1], exci, sol; threshold=20.0, title="Excitatory Neurons")
 rasterplot(fig[2,1], inhib, sol; threshold=20.0, title="Inhibitory Neurons")
-fig
Example block output

The upper panel should show the dynamics in Figure 1.C, with a clear population of excitatory neurons firing together from the external driving current, and the other excitatory neurons exhibiting more stochastic bursts. The lower panel should show the dynamics in Figure 1.A, with the inhibitory neurons firing in a more synchronous manner than the excitatory neurons.

Conclusion

And there you have it! A complete PING demonstration that reproduces the dynamics of a published paper in a matter of 30 seconds, give or take. Have fun making your own!

References

  1. Börgers C, Epstein S, Kopell NJ. Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model. Proc Natl Acad Sci U S A. 2008 Nov 18;105(46):18023-8. DOI: 10.1073/pnas.0809511105.
  2. Traub, RD, Miles, R. Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge, UK, 1991.
  3. Wang, X-J, Buzsáki, G. Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci., 16:6402–6413, 1996.

This page was generated using Literate.jl.

+figExample block output

The upper panel should show the dynamics in Figure 1.C, with a clear population of excitatory neurons firing together from the external driving current, and the other excitatory neurons exhibiting more stochastic bursts. The lower panel should show the dynamics in Figure 1.A, with the inhibitory neurons firing in a more synchronous manner than the excitatory neurons.

Conclusion

And there you have it! A complete PING demonstration that reproduces the dynamics of a published paper in a matter of 30 seconds, give or take. Have fun making your own!

References

  1. Börgers C, Epstein S, Kopell NJ. Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model. Proc Natl Acad Sci U S A. 2008 Nov 18;105(46):18023-8. DOI: 10.1073/pnas.0809511105.
  2. Traub, RD, Miles, R. Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge, UK, 1991.
  3. Wang, X-J, Buzsáki, G. Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci., 16:6402–6413, 1996.

This page was generated using Literate.jl.

diff --git a/dev/tutorials/resting_state/index.html b/dev/tutorials/resting_state/index.html index db7f5fe..691c952 100644 --- a/dev/tutorials/resting_state/index.html +++ b/dev/tutorials/resting_state/index.html @@ -72,4 +72,4 @@ end end -heatmap(log10.(p) .* (p .< 0.05))Example block output

Fig.: log10(p value) displaying statistally significant correlation between time series

heatmap(wm)
Example block output

Fig.: Connection Adjacency Matrix that was used to connect the neural mass models

Notice how the correlation heatmap qualitatively matches the sparsity structure that we printed above with wm_sparse.

This page was generated using Literate.jl.

+heatmap(log10.(p) .* (p .< 0.05))Example block output

Fig.: log10(p value) displaying statistally significant correlation between time series

heatmap(wm)
Example block output

Fig.: Connection Adjacency Matrix that was used to connect the neural mass models

Notice how the correlation heatmap qualitatively matches the sparsity structure that we printed above with wm_sparse.

This page was generated using Literate.jl.

diff --git a/dev/tutorials/spectralDCM/index.html b/dev/tutorials/spectralDCM/index.html index 6f53750..73174af 100644 --- a/dev/tutorials/spectralDCM/index.html +++ b/dev/tutorials/spectralDCM/index.html @@ -191,4 +191,4 @@ iteration: 26 - F:441.60046163460436 - dF predicted:0.014909851262424247 iteration: 27 - F:441.6125182427677 - dF predicted:0.023692652609255654 iteration: 28 - F:441.633311380813 - dF predicted:0.038242149593463746 -convergence

Plot Results

Plot the free energy evolution over optimization iterations:

freeenergy(state)
Example block output

Plot the estimated posterior of the effective connectivity and compare that to the true parameter values. Bar hight are the posterior mean and error bars are the standard deviation of the posterior.

ecbarplot(state, setup, A_true)
Example block output

References

[1] Novelli, Leonardo, Karl Friston, and Adeel Razi. “Spectral Dynamic Causal Modeling: A Didactic Introduction and Its Relationship with Functional Connectivity.” Network Neuroscience 8, no. 1 (April 1, 2024): 178–202.
[2] Hofmann, David, Anthony G. Chesebro, Chris Rackauckas, Lilianne R. Mujica-Parodi, Karl J. Friston, Alan Edelman, and Helmut H. Strey. “Leveraging Julia’s Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed.” bioRxiv: The Preprint Server for Biology, 2023.

This page was generated using Literate.jl.

+convergence

Plot Results

Plot the free energy evolution over optimization iterations:

freeenergy(state)
Example block output

Plot the estimated posterior of the effective connectivity and compare that to the true parameter values. Bar hight are the posterior mean and error bars are the standard deviation of the posterior.

ecbarplot(state, setup, A_true)
Example block output

References

[1] Novelli, Leonardo, Karl Friston, and Adeel Razi. “Spectral Dynamic Causal Modeling: A Didactic Introduction and Its Relationship with Functional Connectivity.” Network Neuroscience 8, no. 1 (April 1, 2024): 178–202.
[2] Hofmann, David, Anthony G. Chesebro, Chris Rackauckas, Lilianne R. Mujica-Parodi, Karl J. Friston, Alan Edelman, and Helmut H. Strey. “Leveraging Julia’s Automated Differentiation and Symbolic Computation to Increase Spectral DCM Flexibility and Speed.” bioRxiv: The Preprint Server for Biology, 2023.

This page was generated using Literate.jl.