We have studied evolution dynamics of stochastic resonance synergies along various dimensions and scales. The evolving network dynamics is described by scale-space wave information propagation, via coordinate transformations and the scale-space tunnelling. Multidimensional information is expressed in a cascade of binding information quanta dynamically, in 5D.

The emergence of an equivocal interpretation of time and space in the evolving network dynamics derives from the quantum information scaling properties. Scaling multidimensional information with stochastic resonances gives in theory an answer, also, to the emergency of periodic tables in the structure decomposition of atomic elements. This makes data available for monitoring, communication and control.

In this article we reflect on patterns of memory formations, inheritance and limits in the information transfer.

Entanglement and "non-local realism"

Understanding quantum information exchange without local hidden variables, brings us closer to a way of developing quantum computing systems. This year's Nobel prize physicists showed a violation of John Bell's inequality, experimentally. "Non-local realism" has been used as a simple phrase in describing particle entanglement in the quantum systems involved.

In addition to spatial, time translational symmetry has been observed in nature and studied in technological approaches to quantum computing. Naturally evolving periodic crystals appear more resilient to noise. Controlling temporal coherence of time crystals makes them suitable for quantum memories.

We foresee a vibrational dynamics approach to controllable quantum networks. The scale-space wave information propagation along with the path integral formulation, as described in our work, are a convenient model formation for quantum computing and programming, in our view.

Riemann hypothesis and the fine structure constant

Asymptotic 3-partite data bindings, 3-6-9 signatures in Riemann's hypothesis proof induction6, make a mathematical bridge to the quantum field theory. The partition function is singular in scale at both ends of conjoined spaces, at the infinitely large and at the smallest.

The polynomial decomposition of partition function, at the smallest scale, limits the asymptotic freedom of information exchange that binds data clusters together. This asymptotic coupling of data translates to the fine structure constant, in the particle physics interpretation5.

Multi-dimensional data scaling – dynamical cascade approach

The integral property of the scale-space decomposition is derived by dividing the partition function in a hierarchical network of coupled oscillators. Topological maps of the partition function decompositions have been shown in our work1-5. Dynamical cascades of the evolving patterns of quadrupole transformations have been studied. Holographic coding of the genotype quantum information carriers has been proposed.

Does Gregor Mendel's inheritance framework apply to particle physics?

Data analysis of various degrees of entanglement, along different dimensions and scales have been described in our work. Circular patterns, encoding information in the internal states of an atomic structure have been studied. Spin-charge inheritance and the emergent chirality of the quantum properties distribution have been shown in scale-space.

Concluding remarks

In this article, we have reflected on dynamical evolution of synergistic correlations in quantum states. We have extended consideration of bipartite correlations to quadrupoles of information carriers. We have reflected on data couplings in memories and inheritance of quantum properties, in scale-space. The limiting case of data couplings -- the asymptotic freedom of motion has been discussed.

In our view, this approach shows a new way of looking at quantum information decomposition in physics and neuroscience7.

References

1 Jovovic, M., Image segmentation for feature selection from motion and photometric information by clustering, SPIE Symposium on Visual Information Processing V, Orlando, 1996.
2 Jovovic, M., Space-Color Quantization of Multispectral Images in Hierarchy of Scales, Int. Conf. on Image Processing, Thessaloniki, Greece, pp. 914-917, 2001.
3 Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003.
4 Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
5 Jovovic, M., Stochastic Resonance Synergetics – Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015.
6 Jovovic, M., Why does a universe begin? -- Reflecting on infinity in triplets, Meer Magazine, May 5, 2021.
7 Jovovic, M., Multidimensional Information Scaling: Manifestation of the Mind-Body Connection, EC Neurology 13.11: 26-28, 2021.