In this article, we propose a deep structure decomposition of turbulent flows, on multiple scales. We have derived a computational method based on an analogy to the physical computation of signal distortion. Dynamical cascade diagrams are computed from a partition function. Data clusters are arranged by binding synergies of quadrupoles, computed in an atomic structure. This quantum field decomposition of turbulent flows derives a modeling approach to data mining analysis tools. In this article we propose in contribution to space weather forecasting:

  1. The analysis of possible cyclic patterns in total electron distributions in the ionosphere.

  2. Prediction and monitoring of turbulent flows utilizing a quantum computing method.

  3. Progressive, finer structure communication, enhanced visualization, reconstruction, and storage of the quantum information carriers.

  4. Spatio-temporal, 3D rendering of disturbances in a turbulent flow from stereoscopic images.

Quantum turbulence

In the theory of stochastic resonances, we have derived a Green function that optimizes filtering criteria, in scale-spaces3-5. At a given scale, the filter bandwidth is derived from the generalized uncertainty relation.

The quantum fields encode transition symmetries of synergistically coupled clusters of information in Lagrangian dynamics. The scale-space waves propagate information by applying the principle of least action. The essential part of implementing the least action while conforming with the conservation of the information transfer is the scale-space tunneling, introduced in our work6. In a bipartite data distribution, the information is exchanged synergistically, resonating up- and down-scale waves in dynamical equilibrium. A quadrupole information carrier encodes the binding synergies encapsulated within an atomic structure.

This genotype basis for generating information in space-time suggests the emergence of multiple fields, not limited to conventionally four. The equations describing the coupling of gravity, electromagnetic, strong, and weak fields in multiple scales have been shown, however, to give only partial answers in the 4-dimensional space-time.

Quantum information carriers

The information is transformed by two operators, rotor and divergence, acting on the scale-space wave, and propagated across the scales. The multiscale decomposition of a partition function binds data in the minimal circular paths of the information flow. A quadrupole information carrier encodes the binding structure of a circular data pattern.

Two-dimensional, up and down scale-space waves are brought into a stochastic resonance dynamically, at the scale dimension, β. At the stochastic resonances, multidimensional information is expanded along the 5-dimensional manifolds. In a hierarchy of scale-spaces, the waves resonance couples information synergistically, satisfying the mass conservation principle. The information transfer by the scale-space wave information propagation is preserved via quantum tunneling.

The scale-space approach makes the hierarchy of bipartite segments suitable for progressive signal transmission and reconstruction in finer details. It enables optimal trade-off usage of available transmission bandwidth and computing power. Storage and retrieval of information with this approach make data available for enhanced visualization along the computed coordinate frames, in a hierarchy of scale-spaces.

Data clusters arranged by binding synergies of quadrupoles, in an atomic structure, derive a modeling approach to a data mining analysis tool. High dimensional data sets are arranged in topological maps at multiple scales of decomposition.

Proof of the concept

This approach has been applied in multidimensional data mining and knowledge discovery. The scale invariances have been assessed for various data sets. We have analyzed a high-dimensional set of proteins4. An approach to attention, memory, and behavioral data-driven study has been proposed11. We have described a hierarchical scale quantization algorithm for multispectral still images9 and motion information10. A stochastic interpretation of the 5d stereograms along the scale dimension has been described7. A recurrent scheme of adaptive filtering has been studied in visual textures segmentation8.

  1. Enhanced visualization by color code stretching, in multiple of scales: color enhancement of highly correlated images has been a useful method in visualizing spatial features in remote sensing1. We propose here its application along the computed principal components of quadrupole information carriers. The color code visually enhances information presented with quadrupoles by equalizing its singular values.

  2. Spatio-temporal, 3D rendering from stereoscopic images: in this research, we propose a joint spatio-temporal, resonance matching, for a robust 3D visualization of disturbances in a turbulent flow. Conservation of the information transfer across the scales makes it suitable for localization and monitoring of the propagation of disturbances in a turbulent flow.

  3. Temporal analysis of the prediction model: scaling multidimensional information with stochastic resonances gives in theory an answer to the emergence of periodic tables of the atomic elements. In this article, we propose the analysis of the prediction model in conjunction with the structure decomposition arranged in the atomic structures. This makes data available for research analysis of possible cyclic patterns in the total electron distributions in the ionosphere. Such an analysis would bring, in our view, an additional useful factor to monitor in space weather forecasting.

Concluding remarks

The multi-scale modeling approach to the prediction and monitoring of turbulent flow has been proposed. The quantum fields adaptive signal processing optimizes a bipartite segmentation of data streams, in a hierarchy of scale. This decomposition method arranges data in an atomic structure suitable for research analysis of possible cyclic patterns in the total electron distributions in the ionosphere. Topological maps of data in the hierarchy of binary images make them suitable to progressively transfer finer details in a communication stream, and enhanced visualization, reconstruction, and storage of data.


1 Gillespie, A.R. et al.: Color enhancement of highly correlated images. I. Decorrelation and HSI contrast stretches. Remote Sensing of Environment Volume 20, Issue 3, December 1986, Pages 209-235.
2 Jovovic, M., Quantum fields adaptive signal processing and communication in multiple of scales, 2022.
3 Jovovic, M., Stochastic Resonance Synergetics – Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015.
4 Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
5 Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003.
6 Jovovic, M., Hierarchical scale quantization and coding of motion information in image sequences, Informacione Tehnologije VI, Zabljak, 2002.
7 Jovovic, M., A Markov random fields model for describing unhomogeneous textures: generalized random stereograms. IEEE Workshop Proceedings on Visualization and Machine Vision, and IEEE Workshop Proceedings on Biomedical Image Analysis, Seattle, 1994.
8 Jovovic, M., Texture Discrimination by Adaptive Filtering, 17th. European Conference on Visual Perception, Eindhoven, 1994.
9 Jovovic, M., Space-Color Quantization of Multispectral Images in Hierarchy of Scales, Int. Conf. on Image Processing, Thessaloniki, pp. 914-917, 2001.
10 Jovovic, M., Image segmentation for feature selection from motion and photometric information by clustering, SPIE Symposium on Visual Information Processing V, Orlando, 1996.
11 Jovovic, M., “Attention, Memories and Behavioral Data-driven Study”, Advances in Neurology and Neuroscience, 2019.