A temporal sequence synergies, analysis and coding
-- Preliminary report --
Milan Jovovic, 31th August 2011
Abstract: Computation of renormalized synergies is proposed in signal analysis and coding. It quantizes
information in a compact code to be used efficiently in storage, transmission, and in data encryption.
We propose it within a quantum information theory that lays down a new perspective to networked
systems dynamics and computation.
Introduction: A multi-scale method of polynomial complexity has been derived for robust data analysis,
coding and control [1]. This computational method captures a physical model for the generation of the
underlying data. Despite its non-linear and dynamical nature, it aims for the simplest explanation,
coding and control.
In particular, we are interested in its application to the networked systems dynamics and computation.
A computable set of spatio-temporal events, organized in graph structure, is proposed as a coding
scheme. The coupling parameter β quantify the synergy exchange, while traversing the graph. We
therefore denote this methodology as a scale-space computing.
Method: Renormalization technique, based on our scale-space approach is used here in computation of
temporal sequence synergies, from the brain wave recordings. Mathematical foundations are written in
[1]. Computation is carried out by the scale-space wave information propagation. At the point of a ‘wave
collapse’, Δβ+ = Δβ- = 0, a quantum of information is split in two. On the other hand, the critical point of
dynamical stability, Δβ+ = Δβ- ≠ 0, defines the condition of ‘wave resonance’, and quantizing the
information within a ‘nucleon’. Conditions of static stability are defined by the positive definitiveness of
the free energy for the quanta of information, and the synergy coupling within -1 ≤ β ≤ +1.
Results: A temporal sequence of a brain wave recording is shown decomposed into one and two
‘nucleons’ of information in Figures 1. and 2., respectively. Two scale-space waves resonate information
within a ‘nucleon’. Their positive/negative envelopes are depicted in the color graphs, where green/red
belongs to one, and yellow/blue to another wave. In Figure 1., the ‘nucleon’ resonates information with
a coupling parameter β within the static stability range, -1 < β < +1. Two ‘nucleons’ in Figure 2. are
brought to resonance at the static stability limit point, β=1. The first ‘nucleon’ in Figure 2.(a) is heavier in
terms of a number of data points then the second, shown in Figure 2.(b).
Discussion: In temporal sequences decomposition, renormalized synergies are coupled by the means of
scale-space wave information propagation that exchange energies along the voltage levels and temporal
dimensions. The heavier quanta of information cluster the higher voltage peaks. This can be observed by
the “green” clusters, which are the heaviest in all of the graphs. Also in Figure 2., the heavier ‘nucleon’,
in (a), clusters the higher voltage peaks then that in (b). This means that the short term events,
associated here with the higher voltage peaks in signal, will dominantly cluster in the heavier quanta of
information. At the point of the limiting static stability, β=1, the lightest quanta (yellow in Figure 2.)
cluster unipolar voltage values, negative in the ‘nucleon’ (a), and positive in (b).
We propose, accordingly, this method as a database and a search engine tool, facilitating efficient
analysis, storage, and transmission by its structure decomposition.
References: 1. http://grids.ucs.indiana.edu/ptliupages/publications/Milan_report.pdf
Figure 1: A single ‘nucleon’ decomposition, at -1 < β < +1.
(a)
(b)
Figure 2: Two ‘nucleons’ decomposition at the limit of the static stability, β=1.
