Last modified: Feb 18, 2017
Small World Networks - SWN:
Below is a chart showing the number of publications indexed each year at www.pubmed.gov concerning small world networks (SWN).
I will continue to use icons (see below) to explain my theory which in 2010 1) predicted the phenomenon of TAG Sync, 2) provided a new model of
sickness behavior (SBeh), and 3) offered a new theoretical interpretation of electroencephalography (nTIE). My theory applies the constructal law of
physics (CLaw) (Bejan 1997, 2012) to the brain and its environments and suggests that adaptation involves global broad band synchronization (GBBS)
over small world networks (SWN) operating at or near self-organized criticality (SOC). Failure of adaptive (constructal) growth I call “apoptosis of the
self” (cf. sickness behavior) and show that it is detectable in the EEG by a failure of cross-frequency coupling, a reduction in complexity, and intrusion of
sub-vigilant states as described by Ulrich (2013). Much of this work comes from my attempts to develop technology assisted self-regulation (TASR)
such as neurofeedback to function as an adaptogen as in the networks of traditional Asian medical systems (TAMS).
Here are the icons I use to point towards these fundamental concepts, mostly discussed separately elsewhere. Here we discuss small world networks.
CLaw GBBS SWN SOC SBeh nTIE TAMS
A network is a configuration of more or less independent units (called nodes, hubs or modules), plus the communication channels which connect them
(called links, edges, pathways, tracts or wiring). The nodes can be people, devices, molecules, communities, concepts, or discrete regions of the cortex.
In the case of the nodes and hubs of the cortex the pathways (”edges”) include both long and short distance white matter tracts which are subject to
network attack. I will show how neurofeedback can precondition the connectome to be resilient to network attack. I will show how this appears in the
real-time qEEG of the spectral display and envelope’s instrument, etc., as well as in the raw EEG.
Imagine you have 16 nodes and 32 wires to connect them. These nodes could represent discrete cortical hubs and the wires (”edges”) white matter
tracts that connect the hubs. For convenience the nodes are each represented by a black dot, and the dots (nodes) are arranged in a circle. We will
investigate three different wiring strategies which we are called regular, small world, and random.
Neurofeedback strengthens the connectome against network attack.
The small world network of the human connectome is embedded in small world networks of social, cognitive, technological and
environmental interactions. In turn we host small world networks of bones, microbes, genes, proteins and so forth. Global broad
band synchronization over small world networks operating near self-organized criticality is essential for growth and survival.
Failure of this process leads to canonical sickness behavior and “apoptosis of the self”.
Each of the three network types has 16 nodes and 32 “edges” with which to connect the nodes.
Regular network: (also called rigid or lattice network): In our example, every node has 4 edge connections to 4 other nearby nodes. You could call
each node plus its neighbors a cluster “(C)”. Note that in order to get from one green node to the other in this rigid network requires traveling a path
length (”L”) of at least 4 edges (count the shortest path between the green dots.)
Random network: Some nodes may have less or more clustering (”C”) than the rigid/regular network. Note that in order to get from one green node
to the other requires traveling a path length of only 1 edge, not a minimum of 4 as for the rigid regular network. Note that some nodes have fewer
connections (reduced clustering). This reduces their modularity and makes them more prone to dysregulation and network attack.
Small world network: In between the rigid and the random networks is another type of network called the “small world network”. Notice that it took 3
jumps to get from one of the green nodes to the other (not 4 jumps as in the rigid network or 1 jump as in the random network). In the small world
network the nodes are less clustered than in the rigid network but more clustered than in the random network.
The illustration below shows that somewhere along the continuum between rigid and random there is a range (seen in green in the middle) in which
1) the clustering (modularity) is high enough yet 2) the average path length between nodes is small enough.
Illustration adapted from Watts DJ, Strogatz SH (1998) - Collective
dynamics of 'small world' networks. Nature. 1998 Jun 4;
In the region (green) where modularity (clustering) is high enough and average path length is short enough, one finds the emergent small world
characteristics of organisms/organizations that persist and resonate over space and time. It is only within this narrow band that systems
adapt/persist/evolve (APE). As we will see, reductions in clustering (C) and/or increases in path length (L) often lead to sickness behavior. More
importantly, adaptogens (including neurofeedback) function to optimize “C” and “L”.
Single channel neurofeedback can increase the clustering coefficient “C” by synchronizing the cortex under the single exploratory electrode. Dual and
multi channel neurofeedback can reduce average path length “L” by adding extra edges between nodes.
Improvement in small world network efficiency may be the most important factor in relapse (sickness) prevention.
Illustration adapted from Watts DJ, Strogatz SH (1998) - Collective
dynamics of 'small world' networks. Nature. 1998 Jun 4;
Neurofeedback (NFB) strengthens the
connectome against network attack. Single
channel NFB can increase the clustering
coefficient (”C”) of a single node. Dual channel
NFB can add extra shortcuts to reduce
average path length (”L”) and improve small-
world network efficiency.
Small World Networks and Sickness Behavior:
My model of sickness behavior (SBeh - discussed elsewhere) is that it involves maladaptive behavior and
pre-programmed apoptosis of the self resulting from inadequate global broad band synchronization (GBBS)
over small world networks (SWN) operating at or near self-organized criticality (SOC). It is triggered by such
events as prenatal and childhood adversity, trauma, toxins, genetics and familial factors, chronic social
defeat, chronic predator stress, inadequate neuroprotection and neuroplasticity, and so forth. The effects
include the loss of white matter connections (as suggested in the accompanying illustration) and reduction
of small world network efficiency. Neurofeedback functions like an adaptogen to increase processing
efficiency and reduce sickness behavior. Two channel synchrony training adds long distance shortcuts to
Vincent K, et al (2013) - Altered network communication following a neuroprotective drug treatment. PLoS
One. 2013; 8(1):e54478. [Free Full Text]
TAG Sync - a sudden increased synchronization of theta, alpha and gamma EEG - appears to be the EEG signature of insight, the gap/bardo between
two thoughts, and updating of the inner world map. In 2013 Borjigin, et al showed it to be the EEG signature of the near death experience. I discovered
this signature in 2009-2010 and developed a protocol to produce this phenomenon over the DMN/FPN Kernal. I call this the “General Adaptation
Protocol - GAP”.
In 2005 Fair et al described the maturing architecture of the brain’s default network. I have adapted Fair’s Fig 3 to show the difference between the
DMN of a 7-9 year old child and that of an adult. This is a very important point because later studies by Daniels et al showed that many individuals with
overwhelming childhood adversity remain stunted, perhaps for life, with the connectome of a 7-9 year old.
Default Mode Network / Frontal-Parietal Network Kernal - DMN/FPN Kernal
Note the tweezers in the image. This symbolizes the plucking and dissipation of essential connections (”edges”) between nodes. Some 7-9 year olds
never develop the connectome of the adult. As discussed above there are many reasons for developmental failure. Those with a 7-9 year old
connectome, regardless of biological age, are fundamentally missing the connections shown on the right above in “Children vs. Adults”. You may
recognize the DMN/FPN kernal described above. This can be trained by observing TAG sync (cross-frequency coupling) over the DMN/FPN kernal
using 2 exploratory electrodes at a time (2 channel NFB). I call this the general adaptation protocol - GAP.
Let’s take a look in detail at the expected but not always attained development over time of four of the network connections shown above. The charts
below were adapted from Fair et al (2013) and show alterations in the correlation coefficient (r) between two nodes as it changes between ages 7 and
The failure of long distance connections to develop beyond those of a 10 year old (see graphs below) reduces the efficiency of the small world
networks. This may represent a tipping point at which simple adolescent neuroses turn into adult neuropsychiatric conditions such as depression,
anxiety, schizophrenia, epilepsy, dementia, etc. - all of which include canonical sickness behavior. (Servaas et al 2015).
So single channel neurofeedback (NFB) may increase the Clustering Coefficient “C” in the region below the electrode, say F3 in the illustration below.
Two channel neurofeedback, by introducing synchrony between two sites, say F3 and P3 (the left FPN network), can add a long distance shortcut to
the connectome and reduce the average path length “L”. In this way NFB acts as an adaptogen by increasing small world network efficiency
(increased “C” and decreased “L”), and by increasing processing of complexity.
How does neurofeedback add random edges (connections) to increase small world network
“… simultaneous activation of two brain regions communicating through phase synchronization will probably also induce synaptic plasticity between
these regions. This is particularly likely when phase synchronization-mediated communication occurs repeatedly or for an extended
period…Moreover, if synaptic connections between two regions have been strengthened, phase synchronization may be more easily induced, and
the two regions will be more likely to communicate with each other.” Fell et al 2011.
Craniopathy, Small World Networks and Neurofeedback.
“... the human skull is a small world network, with two well delimited connectivity modules: one facial organized around the ethmoid bone, and one
cranial organized around the sphenoid bone.” 
This is a wonderful example of the nested embedding of small world networks. The SWNs of the brain are embedded in the more rigid SWNs of the
cranium, embedded in the SWNs of body, environmental, social, technological and informational SWNs.
It is not surprising that disturbances in the small world networks of the brain’s cranial environment can lead to executive dysfunction .
Neurofeedback may be facilitated by recognizing the role of the craniosacral reciprocal tension network in executive dysfunction as well as
susceptibility to chronic naso-sinus fungal biofilm  and direct brain reactivity .
Network support and neuroplasticity (needed for effective NFB) can be impaired due to common TMJ and bite problems - “occlusal disharmony” [6, 7].
It is interesting to reconsider Janet Travell who on page 112 of Volume 1 of “Myofasical Pain and Dysfunction” cites her experience with orthotics to
correct postural instability due to Morton’s foot (a second metatarsal or toe longer than the first). Within moments of standing on corrective orthotics
some clients could open their jaws 20-30% wider. It is also interesting to know that recently “Morton’s long second toe” has been found to be a genetic
marker for pyridoxal 5’ phosphate single nucleotide polymorphisms which have a great effect of neuroprotection and neuroplasticity, glucose tolerance,
metabolic syndrome, etc. 
 Esteve-Altava B, et al (2013) - Grist for Riedl's mill: a network model perspective on the integration and modularity of the human skull. J
Exp Zool B Mol Dev Evol. 2013 Dec; 320(8):489-500. [Abstract]
 Brook AH, et al (2014) - General and craniofacial development are complex adaptive processes influenced by diversity. Aust Dent J. 2014
Jun; 59 Suppl 1:13-22. [Abstract]
 Beckett JS, et al (2014) - Altered brain connectivity in sagittal craniosynostosis. J Neurosurg Pediatr. 2014 Jun; 13(6):690-8. [Abstract]
 Brewer JH, et al (2014) - Chronic illness associated with mold and mycotoxins - is naso-sinus fungal biofilm the culprit. Toxins 6, 66-80.
[Free Full Text]
 Kare MR, et al (1969) - Direct Pathway to the Brain. Science, Vol. 163, No 3870 (Feb 28, 1969), pp. 952-953. [Abstract]
 Mori D, et al (2013) - Occlusal disharmony leads to learning deficits associated with decreased cellular proliferation in the hippocampal
dentate gyrus of SAMP8 mice. Neuroscience Letters 534 ( 2013) 228-232. [Abstract]
 Kubo KY, et al (2007) - Occlusal disharmony induces spatial memory impairment and hippocampal neuron degeneration via stress in
SAMP8 mice. Neuroscience Letters 414 (2007) 188-191. [Abstract]
Nichols TW, et al (2014) - Morton's foot and pyridoxal 5'-phosphate deficiency: genetically linked traits. Med Hypotheses. 2014 Dec; 83(6):644-