transientDynamics

Class NetworkLeakyIntegratorWithIntrinsicPlasticityODE

java.lang.Object

transientDynamics.NetworkLeakyIntegratorWithIntrinsicPlasticityODE

All Implemented Interfaces:

org.apache.commons.math3.ode.FirstOrderDifferentialEquations

public class NetworkLeakyIntegratorWithIntrinsicPlasticityODE
extends java.lang.Object
implements org.apache.commons.math3.ode.FirstOrderDifferentialEquations

This class implements the ODE of a network of leaky integrators with intrinsic plasticity. It is used in the class TransientDynamicsOfLeakyIntegratorsWithIntrinsicPlasticity.

Since:

2012

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	NetworkLeakyIntegratorWithIntrinsicPlasticityODE.Properties Properties of each neuron: membrane potential, gain, threshold.

Constructor Summary

Constructors

Constructor and Description
NetworkLeakyIntegratorWithIntrinsicPlasticityODE(double[] gamma, double[][] w, double[] epsilon_a, double[] epsilon_b, double[] lambda_1, double[] lambda_2) Creates a new leaky integrator network according to the specified parameters.

Method Summary

Methods

Modifier and Type	Method and Description
void	computeDerivatives(double time, double[] state, double[] stateDot) Calculates the first derivatives of the ODE.
static double	firingRate(int neuron, double[] state) Calculates the firing rate of the given neuron in the given state.
static double	g(double x, double a, double b) Transfer function $g(x, a, b) = \frac{1}{1 + e^{-a(x-b)}}$.
int	getDimension() Returns the dimension of the ODE.
static double	getValue(int neuron, double[] state, NetworkLeakyIntegratorWithIntrinsicPlasticityODE.Properties property) Get the value of a property of a neuron in the given state.
static double	gInverse(double y, double a, double b) Inverse transfer function $g^{-1}(y,a,b) = -\frac{1}{a} \log \left( \frac{y_{\mathrm{max}}-y_{\mathrm{min}}}{y-y_{\mathrm{min}}} - 1 \right) + b$.
static void	setValue(int neuron, double[] state, NetworkLeakyIntegratorWithIntrinsicPlasticityODE.Properties property, double value) Set the value of a property of a neuron to the given state.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NetworkLeakyIntegratorWithIntrinsicPlasticityODE

public NetworkLeakyIntegratorWithIntrinsicPlasticityODE(double[] gamma,
                                                double[][] w,
                                                double[] epsilon_a,
                                                double[] epsilon_b,
                                                double[] lambda_1,
                                                double[] lambda_2)

Creates a new leaky integrator network according to the specified parameters.

Parameters:

gamma - leaks $\Gamma$

w - weighted adjacency matrix $w$

epsilon_a - transfer function gain learning rates $\epsilon_a$

epsilon_b - transfer function threshold learning rates $\epsilon_b$

lambda_1 - target firing rate distribution parameter 1 $\lambda_1$

lambda_2 - target firing rate distribution parameter 2 $\lambda_2$

Method Detail

getDimension

public int getDimension()

Returns the dimension of the ODE.

Specified by:

getDimension in interface org.apache.commons.math3.ode.FirstOrderDifferentialEquations

Returns:

3 * networkSize

computeDerivatives

public void computeDerivatives(double time,
                      double[] state,
                      double[] stateDot)

Calculates the first derivatives of the ODE.

Specified by:

computeDerivatives in interface org.apache.commons.math3.ode.FirstOrderDifferentialEquations

Parameters:

time - time $t$

state - vector $(x_1(t), a_1(t), b_1(t), x_2(t), a_2(t), b_2(t), \dots, x_n(t), a_n(t), b_n(t))$

stateDot - vector $(\dot x_1(t), \dot a_1(t), \dot b_1(t), \dots)$

getValue

public static double getValue(int neuron,
              double[] state,
              NetworkLeakyIntegratorWithIntrinsicPlasticityODE.Properties property)

Get the value of a property of a neuron in the given state.

Parameters:

neuron - index of the neuron in the network

state - overall network state

property - property to get (firing rate, gain, threshold)

Returns:

value

setValue

public static void setValue(int neuron,
            double[] state,
            NetworkLeakyIntegratorWithIntrinsicPlasticityODE.Properties property,
            double value)

Set the value of a property of a neuron to the given state. The corresponding field in the given state will be changed according to the property type and the neuron index.

Parameters:

neuron - index of the neuron in the network

state - overall network state to change

property - property to set (firing rate, gain, threshold)

value - value to set

firingRate

public static double firingRate(int neuron,
                double[] state)

Calculates the firing rate of the given neuron in the given state.

Parameters:

neuron - index of neuron

state - the whole network state as used in computeDerivatives including membrane potentials, gains and thresholds

Returns:

firing rate $y = g(x,a,b)$

g

public static double g(double x,
       double a,
       double b)

Transfer function $g(x, a, b) = \frac{1}{1 + e^{-a(x-b)}}$.

Parameters:

x - membrane potential $x$

a - transfer function gain $a$

b - transfer function threshold $b$

Returns:

firing rate $y = g(x, a, b)$

gInverse

public static double gInverse(double y,
              double a,
              double b)

Inverse transfer function $g^{-1}(y,a,b) = -\frac{1}{a} \log \left( \frac{y_{\mathrm{max}}-y_{\mathrm{min}}}{y-y_{\mathrm{min}}} - 1 \right) + b$.

Parameters:

y - firing rate $y$

a - transfer function gain $a$

b - transfer function threshold $b$

Returns:

firing rate $y = g(x, a, b)$