Networked Systems Framework - Revision history

Jrising at 02:04, 11 April 2012

2012-04-11T02:04:45Z

← Older revision		Revision as of 19:04, 10 April 2012
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	The Networked Systems Framework represents a variety of tangentially related work, falling into the ~~following groups~~.		The Networked Systems Framework represents a variety of tangentially related work, falling into various groups.

			Most of this work is now in C++, but that design choice will not a constraint on modelers. One piece of the work ("Toolbox") is a general system for accessing R, Matlab, and other languages, allowing models to be written using them and their libraries to be used.

	==Intelligent Variables==		==Intelligent Variables==

Jrising at 01:29, 22 March 2012

2012-03-22T01:29:56Z

← Older revision		Revision as of 18:29, 21 March 2012
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	* Relationships between the time series take the form of LTI transfer functions, as a "relationship matrix".		* Relationships between the time series take the form of LTI transfer functions, as a "relationship matrix".
	* Depending on the problem, SVD, autoregression eigenvectors, or an simulated annealing approach produce a range for the resulting coefficients based on the null-space of the relationship matrix.		* Depending on the problem, SVD, autoregression eigenvectors, or an simulated annealing approach produce a range for the resulting coefficients based on the null-space of the relationship matrix.

			I also have a library of functions for manipulating functions that consist of piece-wise segments of the form <math>\sum_i P_i(x) e^{c_i x}</math>, where <math>P_i(x)</math> is a polynomial of an arbitrary degree. The parameters are stored efficiently, and the form works well for empirically-derived probability functions.

	''As case studies, I have applied this method to simulated ecosystems, weather stations, and the stock market.''		''As case studies, I have applied this method to simulated ecosystems, weather stations, and the stock market.''

Jrising at 01:22, 22 March 2012

2012-03-22T01:22:03Z

← Older revision		Revision as of 18:22, 21 March 2012
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	To estimate the parameters of endogenous relationships from data, I developed a collection of mathematical called "system regression". System regression takes a collection of time series which all of which may affect the others. The method assumes that the entire underlying dynamics are a result are a result of these interactions, with error in the observations.		To estimate the parameters of endogenous relationships from data, I developed a collection of mathematical called "system regression". System regression takes a collection of time series which all of which may affect the others. The method assumes that the entire underlying dynamics are a result are a result of these interactions, with error in the observations.

	~~\begin{itemize}~~		* Shared frequencies are used as indications of relationships.
	~~\item~~ Shared frequencies are used as indications of relationships.		* Time series are allowed to be sampled at scattered times.
	~~\item~~ Time series are allowed to be sampled at scattered times.		* Frequency-domain representations use scattered frequency components, where an iterative method identifies the frequencies that best explain all the signals.
	~~\item~~ Frequency-domain representations use scattered frequency components, where an iterative method identifies the frequencies that best explain all the signals.		* Relationships between the time series take the form of LTI transfer functions, as a "relationship matrix".
	~~\item~~ Relationships between the time series take the form of LTI transfer functions, as a "relationship matrix".		* Depending on the problem, SVD, autoregression eigenvectors, or an simulated annealing approach produce a range for the resulting coefficients based on the null-space of the relationship matrix.
	~~\item~~ Depending on the problem, SVD, autoregression eigenvectors, or an simulated annealing approach produce a range for the resulting coefficients based on the null-space of the relationship matrix.
	~~\end{itemize}~~

	''As case studies, I have applied this method to simulated ecosystems, weather stations, and the stock market.''		''As case studies, I have applied this method to simulated ecosystems, weather stations, and the stock market.''

Jrising at 18:37, 20 March 2012

2012-03-20T18:37:49Z

← Older revision		Revision as of 11:37, 20 March 2012
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	Intelligent variables also allows models to be applied on a network or map. The differential equations system is wrapped in system dynamical terms (with stocks and flows, delays, and random shocks), which can be modeled in aggregate or separately at interacting nodes. Both stock and variable relationships can be expressed once, with node-specific parameters, and then modeled implicitly.		Intelligent variables also allows models to be applied on a network or map. The differential equations system is wrapped in system dynamical terms (with stocks and flows, delays, and random shocks), which can be modeled in aggregate or separately at interacting nodes. Both stock and variable relationships can be expressed once, with node-specific parameters, and then modeled implicitly.

			''As a case study, I disaggregated the Solow Growth model onto a circle graph of firms.''

			==System Regressions==

			To estimate the parameters of endogenous relationships from data, I developed a collection of mathematical called "system regression". System regression takes a collection of time series which all of which may affect the others. The method assumes that the entire underlying dynamics are a result are a result of these interactions, with error in the observations.

	''As a case ~~study~~, I ~~disaggregated~~ the ~~Solow Growth model onto a circle graph of firms~~.''		\begin{itemize}
			\item Shared frequencies are used as indications of relationships.
			\item Time series are allowed to be sampled at scattered times.
			\item Frequency-domain representations use scattered frequency components, where an iterative method identifies the frequencies that best explain all the signals.
			\item Relationships between the time series take the form of LTI transfer functions, as a "relationship matrix".
			\item Depending on the problem, SVD, autoregression eigenvectors, or an simulated annealing approach produce a range for the resulting coefficients based on the null-space of the relationship matrix.
			\end{itemize}

			''As case studies, I have applied this method to simulated ecosystems, weather stations, and the stock market.''

	==Toolbox: Integrating Analytics==		==Toolbox: Integrating Analytics==

	==~~Case Studies~~==		Toolbox is a framework for combining source code from multiple languages, and allowing variables to pass transparently between them. I have built pieces for shell scripting, Mathematica, Matlab, and R, as well as transparently running the processing for shell programs and Matlab on another computer (over SSH).

			==Software Frameworks==

			I have some software frameworks that might be relevant to this work, but I won't document them yet: Coderack, Plugins, Agents, Clockmaker

Jrising at 15:46, 20 March 2012

2012-03-20T15:46:28Z

← Older revision		Revision as of 08:46, 20 March 2012
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	The framework can read and write delimited files and geotiffs, as well as "delayed" maps, which only read values as they're required.		The framework can read and write delimited files and geotiffs, as well as "delayed" maps, which only read values as they're required.

	I have used this framework to model hydrology on a map, and converting that map to a river network, on a network.		''I have used this framework to model hydrology on a map, and converting that map to a river network, on a network.''

	===Differential Equations Variables===		===Differential Equations Variables===
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	The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.		The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.

	As case studies, I implement the Solow Growth model (using scalar variables) and full suite of Magnetohydrodynamics equations for modeling the sun's corona (in radial 3-space).		''As case studies, I implement the Solow Growth model (using scalar variables) and full suite of Magnetohydrodynamics equations for modeling the sun's corona (in radial 3-space).''

	===Networked System Dynamics===		===Networked System Dynamics===
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	Intelligent variables also allows models to be applied on a network or map. The differential equations system is wrapped in system dynamical terms (with stocks and flows, delays, and random shocks), which can be modeled in aggregate or separately at interacting nodes. Both stock and variable relationships can be expressed once, with node-specific parameters, and then modeled implicitly.		Intelligent variables also allows models to be applied on a network or map. The differential equations system is wrapped in system dynamical terms (with stocks and flows, delays, and random shocks), which can be modeled in aggregate or separately at interacting nodes. Both stock and variable relationships can be expressed once, with node-specific parameters, and then modeled implicitly.

	As a case study, I disaggregated the Solow Growth model onto a circle graph of firms.
			''As a case study, I disaggregated the Solow Growth model onto a circle graph of firms.''

	==Toolbox: Integrating Analytics==		==Toolbox: Integrating Analytics==

	==Case Studies==		==Case Studies==

Jrising at 15:44, 20 March 2012

2012-03-20T15:44:54Z

← Older revision		Revision as of 08:44, 20 March 2012
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	The framework can read and write delimited files and geotiffs, as well as "delayed" maps, which only read values as they're required.		The framework can read and write delimited files and geotiffs, as well as "delayed" maps, which only read values as they're required.

			I have used this framework to model hydrology on a map, and converting that map to a river network, on a network.

	===Differential Equations Variables===		===Differential Equations Variables===
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	The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.		The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.

	===System ~~Dynamical Variables~~===		As case studies, I implement the Solow Growth model (using scalar variables) and full suite of Magnetohydrodynamics equations for modeling the sun's corona (in radial 3-space).

			===Networked System Dynamics===

			Intelligent variables also allows models to be applied on a network or map. The differential equations system is wrapped in system dynamical terms (with stocks and flows, delays, and random shocks), which can be modeled in aggregate or separately at interacting nodes. Both stock and variable relationships can be expressed once, with node-specific parameters, and then modeled implicitly.

			As a case study, I disaggregated the Solow Growth model onto a circle graph of firms.

	==Toolbox: Integrating Analytics==		==Toolbox: Integrating Analytics==

	==Case Studies==		==Case Studies==

Jrising at 15:21, 20 March 2012

2012-03-20T15:21:22Z

← Older revision		Revision as of 08:21, 20 March 2012
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	Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:		Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:

	<syntaxhighlight lang="~~c++~~">		<syntaxhighlight lang="cpp">
	q = -k * Grad(u);		q = -k * Grad(u);
	Diff(u) = (-1 / c_p * rho) * Div(q);		Diff(u) = (-1 / c_p * rho) * Div(q);

Jrising at 15:17, 20 March 2012

2012-03-20T15:17:11Z

← Older revision		Revision as of 08:17, 20 March 2012
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	Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:		Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:

	<~~nowiki~~>		<syntaxhighlight lang="c++">
	q = -k * Grad(u);		q = -k * Grad(u);
	Diff(u) = (-1 / c_p * rho) * Div(q)		Diff(u) = (-1 / c_p * rho) * Div(q);
	</~~nowiki~~>		</syntaxhighlight>

	The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.		The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.

Jrising at 15:15, 20 March 2012

2012-03-20T15:15:29Z

← Older revision		Revision as of 08:15, 20 March 2012
Line 17:		Line 17:
	Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:		Variables can represent relationships between other variables, so that <math>\vec{F} = m \vec{a}</math> describes a persistent relationship that determines the value of <math>\vec{F}</math>, based on the instantaneous value of <math>\vec{a}</math>. I have a framework for this for differential equations in 3-space. So, for example, I can model a heat diffusion system as follows:

	<~~code~~>		<nowiki>
	q = -k * Grad(u)		q = -k * Grad(u);
	Diff(u) = (-1 / c_p * rho) * Div(q)		Diff(u) = (-1 / c_p * rho) * Div(q)
	</~~code~~>		</nowiki>

	The equations themselves are saved within <code>Diff(u)</code>, so that the model can be run through time.		The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so that the model can be run through time.

	===System Dynamical Variables===		===System Dynamical Variables===

Jrising at 15:13, 20 March 2012

2012-03-20T15:13:26Z

← Older revision		Revision as of 08:13, 20 March 2012
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	<code>		<code>
	Diff(u) = (k / c_p * rho) * ~~Grad(Grad~~(u))		q = -k * Grad(u)
			Diff(u) = (-1 / c_p * rho) * Div(q)
	</code>		</code>