Inheritance diagram for WienerCpp:

Public Member Functions
	WienerCpp (class Time *time, double w, double n, double lambda, double n_rc, double lambda_rc)
	Constructor. More...

virtual string	getParameter (const string &p) const
	Get parameter. More...

virtual void	setParameter (const string &p, const string &d)
	Set parameter. More...

virtual void	init ()
	Initialise time-dependent values.

Public Member Functions inherited from Wiener
virtual void	prepareNextState ()
	Calculate next value (preparing next step). More...

Public Member Functions inherited from RandN
	RandN ()
	Construct.

	~RandN ()
	Destruct.

double	dRandN ()
	Retrieve random variable. More...

double	dRandE ()
	Retrieve random variable. More...

Public Member Functions inherited from StochasticVariable
	StochasticVariable (class Time *time, const string &name="", const string &type="Stochastic Variable")
	Create.

double	operator() ()
	Returns the value at the current time step. More...

double	d ()
	Returns the increment at the current time step. More...

Public Member Functions inherited from StochasticProcess
	StochasticProcess (class Time *time, const string &name="", const string &type="Stochastic")
	Create.

virtual	~StochasticProcess ()
	Destroy.

virtual void	proceedToNextState ()
	Proceed one time step. More...

bool	isNextStatePrepared ()
	Whether.

virtual double	getIncrement ()
	Returns the increment. More...

virtual double	getCurrentValue ()
	Returns the value of the process. More...

virtual double	getNextValue ()
	Returns the next value of the process. More...

virtual void	setNextValue (double d)
	Set the next value of the process. More...

virtual void	setCurrentValue (double d)
	Set the current value of the process. More...

void	setDescription (string s)
	Set stochastic description.

string	getDescription ()
	Get the name. More...

Public Member Functions inherited from Parametric
string	getType () const
	Type of object.

string	getName () const
	Name of object.

void	setName (const string &name)
	Name of object.

string	getConfiguration () const
	Returns the configuration of the object. More...

string	getAllParameters () const
	String with all parameter settings.

void	addParameter (const string &name)
	Add a parameter. More...

void	rmParameter (const string &name)
	Remove a parameter. More...

Public Member Functions inherited from TimeDependent
	TimeDependent (class Time *time)
	Construct. More...

virtual class Time *	getTime () const
	Return pointer to the time object.

Public Member Functions inherited from Physical
	Physical ()
	Construct.

	Physical (const Physical &)
	Copy.

	Physical (string name)
	Construct.

	Physical (string name, string unitPrefix, string unitSymbol)
	Construct.

	Physical (string name, Unit unit)
	Construct.

virtual string	getPhysicalDescription ()
	Returns the physical description. More...

virtual string	getUnitName ()
	Returns the unit name.

virtual string	getUnitSymbol ()
	Returns the unit name.

virtual void	setPhysicalDescription (string name)
	Set the name. Same as setDescription(). More...

virtual void	setUnit (Unit u)
	Set the unit.

virtual void	setUnitPrefix (int n)
	Set unit prefix. More...

virtual Unit	getUnit () const
	Retrieve the unit.

Additional Inherited Members
Protected Member Functions inherited from Parametric
	Parametric (const string &name, const string &type)
	Create object of type and name.

virtual	~Parametric ()
	Destroy object.

Protected Attributes inherited from StochasticProcess
double	stochCurrentValue
	the current value

double	stochNextValue
	the next value (direct future)

bool	stochNextStateIsPrepared
	whether prepareNextState() was successful

string	stochDescription
	the name of the quantity

Detailed Description

Condensed Poisson Process.

Lets assume a set of Poisson process $s^i_t, i=1..n$ , where $t$ denotes time, and $i$ is the index of the process. Each process is multiplied by a weight $w_i$ , $s^i_t$ takes values of $0$ or $1$ (where $1$ indicates an event), and events occur with a rate of $\lambda_i$ . We are interested in the sum

$s_t = \sum_i w_i s^i_t.$

Let's assume that in this collection of events coincident events happen. Coincidences are events which occur at the same time at various processes. If these events are viewed as a separate process $s^c_i$ with a weight $w_c$ and a rate $\lambda_c$ , all processes stay independent. The impact of the coincidence events depends on the sum of the weights of the processes taking part. We shall call the sum of the weights of the processes which take part the Coincidence Weight. The coincidences occur with a specific rate which we will call Coincidence Rate $\lambda_c$ .

Since the events which form the coincidence event are taken out of the process $s_i$ where the happened, the rate of these single processes is expected to decrease, according to the coincidence weight and the coincidence rate: $\lambda_i$ will become $\lambda_i - \frac{w_c\lambda_c}{\sum_iw_i}$ . Thus the sum of events $s_t$ , as well as its mean $\mbox{E}{s_t}$ will not be affected by the correlations:

$s_t = \sum_{i}w_is^i_t + w_cs^c_t.$

$\mbox{E}{s_t} = \sum_i w_i\left(\lambda_i - \frac{w_c\lambda_c}{\sum_iw_i}\right) + w_c\lambda_c$

$= \sum_i w_i\lambda_i$

The variance of this process $s_t$ will be:

$\mbox{Var}\{s_t\} = \sum_i w_i^2\left(\lambda_i - \frac{w_c\lambda_c}{\sum_iw_i}\right) + w_c^2\lambda_c.$

These parameters will be used to construct a white-noise (Wiener) process, which feeds the neuron: Let's assume the neuron is connected to many synapses which each have small weights. Lets substitute the correlation weight $w_c$ - since all weights are the same - by the amount $n_c$ of synapses taking part in a coincident pulse times their weight. We will call this amount the Coincidence Width.

Since the coincidence rate $\lambda_c$ will not be higher than the overall rate $\lambda$ , and the coincidence width $ n_c $ will not be higher than the overall number of synapses, it makes sense to use a relative coincidence width which ranges from $ 0 $ to $ 1 $

$n_{rc} = \frac{n_c}{n},$

and a relative coincidence rate which ranges from $0$ to $1$

$\lambda_{rc} = \frac{\lambda_c}{\lambda}$

This amounts to the following expressions for mean and variance of the white-noise process:

$\mu := nw\lambda$

$\sigma^2 := nw^2\lambda\left(1 - n_{rc} \lambda_{rc} + nn_{rc}^2\lambda_{rc} \right)$

The condensed poisson process implements such a white-noise process.

Constructor & Destructor Documentation

WienerCpp::WienerCpp	(	class Time *	time,
		double	w,
		double	n,
		double	lambda,
		double	n_rc,
		double	lambda_rc
	)

Constructor.

Parameters

time	Time object
w	single weight
n	number of processes in the sum of processes
lambda	rate of a single process
n_rc	relative coincidence width
lambda_rc	relative coincidence height

Member Function Documentation

virtual string WienerCpp::getParameter ( const string & name ) const

virtual

Get parameter.

In a derived class, override this to handle every parameter you implement. If a parameter is described using multiple strings separated by space, this indicates a parameter of a parameter.

Reimplemented from Wiener.

virtual void WienerCpp::setParameter	(	const string &	name,
		const string &	value
	)

virtual

Set parameter.

Sets the value of a parameter using strings. If a parameter is described using multiple strings separated by space, this indicates a parameter of a parameter (not implemented yet).

Reimplemented from Wiener.

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation