Interested in various methods of visual representation of mutual dynamics the investigated variables. In particular, methods of analysis and graphical representation of such dynamics.
Thank you dear Abedallah. Interesting and useful links.
Dear @Vyacheslav, The following article discusses the issue of the dynamics of two inhibitory neural units; I think it contains valuable knowledge about displaying the mutual dynamics of the test parameters
http://faculty.washington.edu/etsb/pubs/stochastic_dynamics.pdf
@Vyacheslav Lyashenko, quite interesting and scientific question. As far as I know, this area is still being actively researched as visual representation has entered into a new area. I have gone through paper referred by Dr. Abedallah. It seems quite useful so I also recommend that, please.
Vyacheslav, the answer depends upon what you mean "mutual dynamics".
If you have an autonomous object that is characterized by two parameters then you could draw a "phase-space plot" coupled with a vector-field plot of phase velocities.
Here is an example: http://commons.wikimedia.org/wiki/File:Van_der_Pol_phase_space.png
Each point of the plot is a possible state of the system and a vector coming out of this point shows in which direction and with which "phase speed" the system would move from the state.
But if your object is not autonomous you could just plot all its known (directed) trajectories in the phase space and this will still look distantly similar to the vector field.
Thanks for the answer Konstantin. I'm interested in the mapping model mutual dynamics of two or more variables, each of which has its own temporal trajectory. The phase portrait for this does not quite fit. The simplest case of this dynamic mapping - scatter chart to compare pairs of values.
If each variable is one-dimentional and you have a time-series for each of them then a 2D phase portrait with vectors connecting consecutive 2D point will do the job. And it is what I meant in the second part of my first answer. Effectively, it is a interconnected scatterplot that enables one to get an idea of the trend in parameters' evolution.
Thanks Konstantin. Can I illustrative example of such a construction. Do these goals for the software is freely available. Can I enable links where this is viewed.
You need a statistical significant scatterplot previous design in Methods and a graphic interconnection in the Results step of your paper. Have you an hypothesis clearly exposed in your project?
Vyacheslav, I am not sure if there is any specialized software to produce plots of precisely this kind. But it is easy to build them by a custom script in any graphics-capable script language (for scientific use the most common are R and Matlab, although it is not so hard to do this even in plain C, Pascal, Basic and almost any other language).
If you still need an example, I can create one in some time.
Thanks for the clarifying Regina. I'm interested in graphic imaging techniques such dependence.
Unless you have some ideas of what you described as "mutual dynamics", it sounds like a data-mining exercise to me. Just search for data mining software and you can see a few interesting freeware. For general purpose free statistical software, you can take a look of PSPP, which claimed to be a free replacement for the proprietary program SPSS at: http://www.gnu.org/software/pspp.
Dear Hon-Kwong Lui. Thanks for the reply and link.
I will specify the issue. I'm interested in nonstandard (new) approaches.
have you tried phaser?
I've used it in order to model system ecology models with 2 differential equation system
One way to display the mutual dynamics of two or more test perimeters is to use a cospectral bipartite graph, hyper graph, substrate graph or a simple bipartite graph. For examples of cospectral graphs, see Fig. 2.12 , p. 27, in
S.P. Osborne, Cospectral bipartitite graphs for the normalized Laplacian, Ph.D. thesis, Iowa state University, 2013:
https://orion.math.iastate.edu/lhogben/osborne_thesis.pdf
For examples of hyper graph, substrate graph or a simple bipartite graph, see the attached image.
Another way to visualise the mutual dynamics is to construct a vertical (timescale) spiral graph, and compare the highs and lows. This is essentially the approach in Fig. 8, p. 46, in
P. Svaragich, Principia of Polyzodiacal Astrology, Ph.D. thesis, 1996:
http://www.valentino-salvato.com/Astrology/pdf/Principia_of_Polyzodiacal_Astrology_Thesis.pdf
Thank you dear James. Your answers, as always, informative and meaningful.
here is the web-site of the software
http://www.phaser.com/
once you registered, you've got a 30 day free-trial period!
hope this is useful
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