Research Statement

Milan Jovovic has worked on informatics of complex systems for about 30 years, from different fields of study and perspective. He has acquired a broad theoretical knowledge in the fields, applying mathematical modeling.

He has written a stochastic resonance synergetics theory in scaling multidimensional information for the analysis and study of complex systems. A multidimensional scaling property of the atomic structure has been derived. It makes a bridge to the mathematical foundation of the quantum field theory.

This quantum information theory applies a scale-space tunnelling and the wave information propagation. The coupled information propagation is described by the wave motion through the scale-space.  

At the Safarik University, they have used a behavioral dimensionality paradigm, along with intensity and distance of an auditory signal processing. By this paradigm, they have shown the intensity-independent auditory distance feature detectors, along with the tonotopic map of the auditory cortex, as a result of the information flow propagation. 

At the Indiana University, they have explored covariant differentiability in approaching the scale-space computing, knowledge diagrams and numerical schemes of high- dimensional data sets. An implementation of the statistical maps is analyzed in their report. They have also worked on the multi-core processors research and parallel algorithms. The emphasis was on applications in chemo/bioinformatics and data mining. 

On his postdoc stage at the INRIA, they have worked on a harmonic signal decomposition of the IR satellite images. A turbulent flow was studied and a rain process is shown corresponding to the propagation of perturbation caused by the fusion of convective clouds. 

For his doctoral thesis at the University of Belgrade, they  have worked on learning and control of limb movements as a sequence of synergistic joint motions. The equilibrium points hypothesis has been extended with the quantum information carriers in attention, memory, and behavioral data study. 

He had started working in computational neuroscience and physics as a graduate student at Caltech. His common line of research describes complex systems dynamics based on a coupled wave information propagation in the scale-space, showing a new way of looking at things in neuroscience and physics.

In addition to theoretical work in mathematical physics, his current research interests include neural data science and quantum computing. 

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Quantum Fields Decomposition of Turbulent Flows: Prediction, Monitoring and Communication in Space Weather Forecasting

Quantum Fields Decomposition

In this article we propose a deep structure decomposition of turbulent flows, in 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 fields decomposition of turbulent flows derives a modeling approach to data mining analysis tools. In this article we propose it 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.  


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Quantum fields adaptive signal processing and communication in multiple of scales

In this article we discuss some of the current trends in quantum microscopy. The new imagining technologies on a cell and molecular levels resolution have become promising tools in the analysis and study of biological processes.

Handling a large volume of the microscopy data requires, in our opinion, a multi-scale approach to adaptive signal filtering, communication, and storage. We discuss here, subsequently, some technical aspects of applying the quantum fields adaptive signal processing. 

Quantum fluorescence microscopy

Two-photon absorption effect was initially theorised by Maria Goeppert-Mayer, which later has been applied in quantum microscopy. It has opened a window to imagining, analysis and study of biological processes with a significant increase in data resolution. Quantum fluorescence microscopy makes it possible to acquire figure-background contents in different signal frequencies at a cell and molecular resolution levels, utilising a noninvasive optical biopsy.

Quantum fields adaptive signal filtering in multiple of scales

In the theory of stochastic resonance synergistics, we have derived a Green function that optimises filtering criteria, in scale-spaces [1-3]. At a given scale, the filter bandwidth is derived from the generalised uncertainty relation. 

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 resonate waves couple information synergistically, satisfying the mass conservation principle. The information transfer is preserved by the scale-space wave information propagation and tunnelling. 

A stochastic interpretation of stereograms along a scale dimension has been described, in [4]. A pair of textured images with two distinct regions of textural elements distribution are fused in a stochastic equilibrium. These 5d stereograms have been shown for different levels of figure-background spatial frequencies and textural elements differences. A recurrent scheme of adaptive filtering has been studied in visual textures segmentation, in [5]. 

A holographic representation of quantum fields information carriers, in 3 dimensional space, suggests the emergence of multiple fields, not limited to conventionally four. The equations describing coupling of gravity, electromagnetic, strong and weak fields in multiple of scales have been shown, however, to give only partial answers in the 4 dimensional space-time. 

Progressive transmission, reconstruction and storage of hierarchically segmented data streams

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

We have described a hierarchical scale quantization algorithm for multispectral still images, in [6], and motion information, in [7],  

The Milky Way Fermi’s bubbles

Concluding remarks:

In this article we have reflected on a genotype basis for generating information in space-time. Current trends in quantum microscopy that utilise the two-photon absorption effect significantly increases data resolution and opens a window to imagining, analysis and study of biological processes on a cell and molecular resolution levels.

We have discussed some technical aspects in handling a large volume of data by quantum fields adaptive signal processing and communication. A multi-scale approach to communication streaming, reconstruction, enhanced visualisation, and storage of hierarchically segmented data streams have been proposed. 


[1], Jovovic, M., Stochastic Resonance Synergetics – Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015. 

[2] Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007. 

[3] Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003. 

[4] 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.

[5] Jovovic, M., Texture Discrimination by Adaptive Filtering, 17th. European Conference on Visual Perception, Eindhoven, 1994. 

[6] Jovovic, M., Space-Color Quantization of Multispectral Images in Hierarchy of Scales, Int. Conf. on Image Processing, Thessaloniki, pp. 914-917, 2001.

[7] Jovovic, M., Image segmentation for feature selection from motion and photometric information by clustering, SPIE Symposium on Visual Information Processing V, Orlando, 1996.  

[8] Jovovic, M., Contributing articles, Meer Magazine, 2020-2022.

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Quantum computing a relational database: What is into that circle?

A set theoretical approach to organise data, based on predicate logic, has been proposed by Ted Codd at IBM. The relational model was derived, followed by normalisation procedures. Discovering complex relationships among data by means of database technology helped growth in businesses, spanning from the largest to the smallest. 

In this article we reflect on a scale-space approach in modelling data suitable for quantum computing and analysis. Topological maps of coupled data sets have been applied in various disciplines, mathematically described by the quantum information theory of stochastic resonance synergies, [1]. This scale-space approach organises data in an atomic structure of binding synergies.


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A scale-space description of a quadrupole universe

In this article, we reflect on dynamical evolution of bipartite correlations in quantum states. An especially strong correlation between particles can result in a single unified quantum state, as initially theorised by Einstein, Rosen, and Podolsky. In this unified state, the measurement of one strongly correlated particle has a direct effect on the other, regardless of the distance between them.

A synergistic mechanism of quantum tunnelling that preserves the information exchange in scale-space has been derived in our work, [2]. We have analysed the evolution dynamics of stochastic resonance synergies for different parameters entanglement, along various dimensions and scales, [1-8]. In our description, a wormhole binds two distinct clusters of quantum particles with various degrees of entanglement. 

A quadrupole

“One quadrupole universe” — in rephrasing John Wheeler. Dynamical cascades map multidimensional information in multiple scales. 


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Stochastic Resonance Synergistics — Highlights

A quadrupole:


Scale-space wave information propagation:

Path integral:

Uncertainty relation:

Fields equation:


5d stereograms:


Brain-wave synergies:

3-6-9 signatures in the #Riemann hypothesis proof induction

Stochastic Resonances


Work in progress:

Illuminating relationship between electron — photon couplings and the #FineStructureConstant

Limits in the asymptotic freedom of motion


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On the limits of deterministic description of motion — the uncertainty relation

In this article, we reflect on a classical physics problem in describing the system of 3-body motion of celestial objects, originally considered by Newton. At the other end of the scale, in quantum mechanics, the measurement problem was originally addressed by Heisenberg with the introduction of uncertainty relation. 

The stochastic resonance synergetics addresses both of these issues in a mathematical description that generalizes the uncertainty relation within the quantum field theory. The mathematical formulation describes the connection between the largest and the smallest structures in a coupled network. In our view, it shows an unifying perspective of looking at motion in the hierarchy of scales and coordinate frames, mathematically described in 5-dimensional scale-space. 

Generalized uncertainty relation in scale-space


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On the elements of the prime numbers distribution — a scale-space approach to connectomes

Coupled oscillator

Learn how to see. Realize that everything connects to everything else.” — Leonardo da Vinci

This universal thought of a brilliant polymath has set the observational point of the curious minds since the Renaissance. Educating people to question what they have learned on a path to progress. 

In this article, synchronicity, a connecting principle introduced by Carl Jung is presented. A popular book, “One Two Three… Infinity” by George Gamow discusses the sciences of mathematics and physics. In our work, an integral property of the scale-space decomposition of a partition function is described.

“No matter how thin you slice it, there will always be two sides.” — Baruch Spinoza


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An approach to quantum biology — Setting the numbers in motion

On reversibility of the second law of thermodynamics

Dynamical cascades, in a multi-scale decomposition, have been described in our study. It has been applied in different networked systems, in physics and neuroscience. We describe the genotype decomposition of multidimensional information within an atomic structure. The path integral of information propagation has been derived, making it suitable for quantum computing. 

In this article, we reflect on a computation methodology and data analysis of the epigenetic mechanisms in gene packaging and expression. We propose a data analysis assistance tool in medical applications from the perspective of quantum biology. 


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Mind-Body Connection

Holographic representation

Data analysis in two behavioral experiments have been derived within the theoretical framework of stochastic resonance synergies. One, that involves outside auditory stimulation of the brain [6], and the other, in the coordination of skilled movements that involves the brain-body connections [2], only. 

Functional neuro-cortical mappings have been evaluated at the scale-space frequencies of coupled data clusters. Topology of dynamical cascades of binding synergies have been analyzed. 

In this article we reflect on the multidimensional information scaling property in binding data clusters. In particular, on the mind-body connection. 

“Man fears time, time fears the pyramids” — Old proverb



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Multidimensional Information Flow

Scale-space tunnelling

“No man ever steps in the same river twice. For it’s not the same river and he’s not the same man.” — Heraclitus

Research and study of a large variety of networked complex systems increasingly relies on quantum computing. From quantum physics and biology to cosmology. Quantum information theories and quantum tunnelling play a central role in the quantum computing technologies. 

Stochastic resonance synergetics theory, as described in our reports, is an approach to the networked systems dynamics and computation. We have proposed it with  methodologies for data analysis in computational physics, neuroimaging, attention, memory, and behavioural data-driven studies. 


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