Back
 JQIS  Vol.5 No.2 , June 2015
Stochastic Resonance Synergetics—Quantum Information Theory for Multidimensional Scaling
Abstract: A quantum information theory is derived for multidimensional signals scaling. Dynamical data modeling methodology is described for decomposing a signal in a coupled structure of binding synergies, in scale-space. Mass conservation principle, along with a generalized uncertainty relation, and the scale-space wave propagation lead to a polynomial decomposition of information. Statistical map of data, through dynamical cascades, gives an effective way of coding and assessing its control structure. Using a multi-scale approach, the scale-space wave information propagation is utilized in computing stochastic resonance synergies (SRS), and a data ensemble is conceptualized within an atomic structure. In this paper, we show the analysis of multidimensional data scatter, exhibiting a point scaling property. We discuss applications in image processing, as well as, in neuroimaging. Functional neuro-cortical mapping by multidimensional scaling is explained for two behaviorally correlated auditory experiments, whose BOLD signals are recorded by fMRI. The point scaling property of the information flow between the signals recorded in those two experiments is analyzed in conjunction with the cortical feature detector findings and the auditory tonotopic map. The brain wave nucleons from an EEG scan, along with a distance measure of synchronicity of the brain wave patterns, are also explained.
Cite this paper: Jovovic, M. (2015) Stochastic Resonance Synergetics—Quantum Information Theory for Multidimensional Scaling. Journal of Quantum Information Science, 5, 47-57. doi: 10.4236/jqis.2015.52007.
References

[1]   Cox, T.F. and Cox, M.A.A. (2001) Multidimensional Scaling. Chapman and Hall, London.

[2]   Schwartz, E.L., Shaw, A. and Wolfson, E. (1989) A Numerical Solution to the Generalized Mapmaker’s Problem. IEEE PAMI, 11, 1005-1008.
http://dx.doi.org/10.1109/34.35506

[3]   Cerny, V. (1993) Quantum Computers and Intractable (NP-Complete) Computing Problems. Physical Review A, 48, 116-119.
http://dx.doi.org/10.1103/PhysRevA.48.116

[4]   Cerny, V. (1985) Thermodynamical Approach to the Travelling Salesman Problem: An Efficient Simulation Algorithm. Journal of Optimization problems and Applications, 45, 41-51.
http://dx.doi.org/10.1007/BF00940812

[5]   Jayens, E.T. (1989) Information Theory and Statistical Mechanics. In: Rosenkrantz, R.D., Ed., Papers on Probability, Statistics and Statistical Physics, Springer, Netherlands.

[6]   Bernstain, N. (1967) The Coordination and Regulation of Movement. Pergamon, London.

[7]   Haken, H. (2004) Synergetics. Introduction and Advanced Topics. Springer, Berlin.

[8]   Jovovic, M., Jonic, S. and Popovic, D. (1999) Automatic Synthesis of Synergies for Control of Reaching—Hierarchical Clustering. Medical Engineering Physics, 21/5, 325-337.
http://dx.doi.org/10.1016/s1350-4533(99)00058-2

[9]   Zhang, W-R. and Peace, K.E. (2014) Causality Is Logically Definable—Toward an Equilibrium-Based Computing Paradigm of Quantum Agents and Quantum Intelligence. Journal of Quantum Information Science, 4, 227-268.
http://dx.doi.org/10.4236/jqis.2014.44021

[10]   Rose, K., Gurewitz, E. and Fox, G.C. (1990) A Deterministic Annealing Approach to Clustering. Pattern Recognition Letters, 11, 589-594.
http://dx.doi.org/10.1016/0167-8655(90)90010-Y

[11]   Horn, B.K.P. and Schunk, B.G. (1981) Determining Optical Flow. Artificial Intelligence, 17, 185-203.
http://dx.doi.org/10.1016/0004-3702(81)90024-2

[12]   Delorme, A., Makeig, S., Fabre-Thorpe, M. and Sejnowski, T. (2002) From Single-Trial EEG to Brain Area Dynamics. Neurocomputing, 44-46, 1057-1064.
http://dx.doi.org/10.1016/S0925-2312(02)00415-0

[13]   Kopco, N., Huang, S., Bellieveau, J.W., Raij, T., Tengshe, C. and Ahveninen, J. (2012) Neuronal Representations of Distance in Human Auditory Cortex. Proceedings of the National Academy of Sciences of USA, 109, 11019-11024.
http://dx.doi.org/10.1073/pnas.1119496109

[14]   Zatorre, R.J., Bouffard, M., Ahad, P. and Belin, P. (2002) Where Is “where” in the Human Auditory Cortex? Nature Neuroscience, 5, 905-909.

[15]   Mc Eliece, R.J. (1982) The Theory of Information and Coding. Addison-Wesley Publ. Co., Mass.

[16]   Wiggins, S. (1990) Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-4757-4067-7

[17]   Jovovic, M. and Fox, G.C. (2007) Multi-Dimensional Data Scaling—Dynamical Cascade Approach. Technical Report, Indiana University.
http://grids.ucs.indiana.edu/ptliupages/publications/Milan_report.pdf

 
 
Top