PROCEEDINGS ARTICLE | June 24, 2014

Proc. SPIE. 9118, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XII

KEYWORDS: Electrodes, Ions, Diffusion, Head, Electroencephalography, Feedback loops, Neuroimaging, Thermodynamics, Correlation function, Brain

Since the Brain Order Disorder (BOD) group reported on a high density Electroencephalogram (EEG) to capture
the neuronal information using EEG to wirelessly interface with a Smartphone [1,2], a larger BOD group has been
assembled, including the Obama BRAIN program, CUA Brain Computer Interface Lab and the UCSD Swartz
Computational Neuroscience Center. We can implement the pair-electrodes correlation functions in order to operate
in a real time daily environment, which is of the computation complexity of O(N<sup>3</sup>) for N=10<sup>2~3</sup> known as functional
f-EEG. The daily monitoring requires two areas of focus. Area #(1) to quantify the neuronal information flow under
arbitrary daily stimuli-response sources. Approach to #1: (i) We have asserted that the sources contained in the EEG
signals may be discovered by an unsupervised learning neural network called blind sources separation (BSS) of
independent entropy components, based on the irreversible Boltzmann cellular thermodynamics(ΔS < 0), where the
entropy is a degree of uniformity. What is the entropy? Loosely speaking, sand on the beach is more uniform at a higher
entropy value than the rocks composing a mountain – the internal binding energy tells the paleontologists the existence of
information. To a politician, landside voting results has only the winning information but more entropy, while a non-uniform
voting distribution record has more information. For the human’s effortless brain at constant temperature, we can solve the
minimum of Helmholtz free energy (H = E − TS) by computing BSS, and then their pairwise-entropy source correlation
function. (i) Although the entropy itself is not the information per se, but the concurrence of the entropy sources is the
information flow as a functional-EEG, sketched in this 2<sup>nd</sup> BOD report. Area #(2) applying EEG bio-feedback will
improve collective decision making (TBD). Approach to #2: We introduce a novel performance quality metrics, in terms
of the throughput rate of faster (Δt) & more accurate (ΔA) decision making, which applies to individual, as well as team
brain dynamics. Following Nobel Laureate Daniel Kahnmen’s novel “Thinking fast and slow”, through the brainwave
biofeedback we can first identify an individual’s “anchored cognitive bias sources”. This is done in order to remove the
biases by means of individually tailored pre-processing. Then the training effectiveness can be maximized by the collective
product Δt * ΔA. For Area #1, we compute a spatiotemporally windowed EEG in vitro average using adaptive time-window
sampling. The sampling rate depends on the type of neuronal responses, which is what we seek. The averaged traditional
EEG measurements and are further improved by BSS decomposition into finer stimulus-response source mixing matrix [A]
having finer & faster spatial grids with rapid temporal updates. Then, the functional EEG is the second order co-variance
matrix defined as the electrode-pair fluctuation correlation function C(s~, s~’) of independent thermodynamic source
components. (1) We define a 1-D Space filling curve as a spiral curve without origin. This pattern is historically known
as the Peano-Hilbert arc length a. By taking the most significant bits of the Cartesian product a≡ O(x * y * z), it
represents the arc length in the numerical size with values that map the 3-D neighborhood proximity into a 1-D neighborhood
arc length representation. (2) 1-D Fourier coefficients spectrum have no spurious high frequency contents, which typically
arise in lexicographical (zig-zag scanning) discontinuity [Hsu & Szu, “Peano-Hilbert curve,” SPIE 2014]. A simple Fourier
spectrum histogram fits nicely with the Compressive Sensing CRDT Mathematics. (3) Stationary power spectral density is
a reasonable approximation of EEG responses in striate layers in resonance feedback loops capable of producing a 100, 000
neuronal collective Impulse Response Function (IRF). The striate brain layer architecture represents an ensemble <IRF<
e.g. at V1-V4 of Brodmann areas 17-19 of the Cortex, i.e. stationary Wiener-Kintchine-Einstein Theorem. Goal#1:
functional-EEG: After taking the 1-D space-filling curve, we compute the ensemble averaged 1-D Power Spectral Density
(PSD) and then make use of the inverse FFT to generate f-EEG. (ii) Goal#2 individual wellness baseline (IWB): We need
novel change detection, so we derive the ubiquitous fat-tail distributions for healthy brains PSD in outdoor environments
(Signal=310°C; Noise=27°C: SNR=310/300; 300°K=(1/40)eV). The departure from IWB might imply stress, fever, a sports
injury, an unexpected fall, or numerous midnight excursions which may signal an onset of dementia in Home Alone Senior
(HAS), discovered by telemedicine care-giver networks. Aging global villagers need mental healthcare devices that are
affordable, harmless, administrable (AHA) and user-friendly, situated in a clothing article such as a baseball hat and able
to interface with pervasive Smartphones in daily environment.