Remote synchronization: detailed account of a peculiar

Ludovico Minati

Remote synchronization: detailed account of a peculiar pattern-formation mechanism

Tokyo Institute of Technology, Tokyo, JapanInstitute of Nuclear Physics - Polish Academy of Sciences (IFJ-PAN), Kraków, Poland

University of Trento, Trento, Italy

Context

A “rewarding” experiment about relationship(s) between structural connectivity and synchronization in an electronic network

Image credit: O. Sporns, SPM Course


L. Minati

What is remote synchronization?

Synchronised

Non-synchronised Non-synchronised

A B C


L. Minati

Remote synchronization from mismatches

Image credit: cited study, © APS


L. Minati

Remote synchronization as morphogenesis

Image credit: Wikipedia, others


L. Minati

Remote synchronization in brain networks?

Sensory-motor network: directly wired Default-mode network: emergent

No direct anatomical link to posterior areas.Remotely synchronized?


L. Minati

Image source: Rosazza & Minati, 2011; © Springer Verlag

A simple, reconfigurable non-linear network


L. Minati

Oscillator equations

Parametric mismatch~0.5% in physical system


L. Minati

Applications in versatile pattern generation


L. Minati

Image source: Minati et al., IEEE Access 2018. © IEEE

Phase vs. amplitude synchronization

Phase coherence

Instantaneous amplitude (envelope)

Maximum cross-correlation or mutual information


L. Minati

Numerical simulations reveal three regimesa:

G6=

0.19

6,

G7=

-1.3

65

Broadband chaos


L. Minati

Image source: Minati et al., CHAOS 2015. © AIP


G6=

0.19

6,

G7=

-1.3

65b:

G6=

0.09

6,

G7=

-1.5

3

Broadband chaos

Quasi-periodicity


L. Minati



G6=

0.19

6,

G7=

-1.3

65b:

G6=

0.09

6,

G7=

-1.5

3c:

G6=

0.18

8,

G7=

-1.1

4

Broadband chaos

Quasi-periodicity

Narrowbandchaos


L. Minati


Numerical simulations reveal three regimes


L. Minati


Numerical simulations reveal three regimes


L. Minati


Effect of parametric mismatches


L. Minati

Image source: Minati et al., CHAOS 2015. © AIP, others, public domain

Experimental implementation


L. Minati



Top-levelFPAA

architecture

Upon permission and courtesy of Anadigm, Inc.


L. Minati


The Configurable Analog Module (CAM)



L. Minati




L. Minati




L. Minati




L. Minati


Continuous-value, discrete-time



L. Minati


From: A. Buscarino et al., A Concise Guide to Chaotic Electronic Circuits, 73 , SpringerBriefs in Applied Sciences and Technology


L. Minati


A soft of “Chimera”: an analogplug-in system for digital computer


L. Minati

Image source: Minati et al., CHAOS 2015. © AIP, Wikipedia

Remote sync. close to quasi-periodicity

Correlation dimension (D2)

Remote synchronization (η)


L. Minati


Experimental data - basicsSpectrogram Phase sync. Amplitude sync.

Reminiscent of adiffraction pattern?


L. Minati

Image source: Minati et al., CHAOS 2018. © AIP, Wikipedia

Non-stationarity

Adjacenttime-windows…


L. Minati


Non-stationarity

…reminiscent of observations in resting-state functional MRI


L. Minati

Source: Tagliazucchi et al., Front. Hum. Neurosci 2012

Experimental data – focus on spectrumfC, Carrier

fH, Higher sideband

fL, Lower sideband

Two concomitant spectral relations:

1) fB = fH - fC = fC - fL

2) fH = fL + fC

Reminiscent of classic AM modulation!

fB, Baseband

Lower sideband and baseband overlap!Image credit: Wikipedia


L. Minati

→ fL=fB

From synchronization to causality


L. Minati

Y y1

…

• Regression of the present of the target on its own past:

y2

yM

• Regression of the present of the target on its past and the past of the source:

][ 2,|| njjjj e=

][ 2,|| njijjij e=],|[ ,,,,,|

−−−= ninjnjnjnjij yyyye

]|[ ,,,,|−−= njnjnjnjj yyye

n-1, n-2, … n

targetyj

yi

Yk

source

},{\},...,1{ jiMk =

othersources

−niy ,

jij

jjjiT

|

|ln

2

1

=→

jij

jjjiF

|

|ln

=→

Granger causality (GC) Transfer Entropy (TE)

Gaussian

[J.F. Geweke, J. AM. Stat. Assoc. 77, 1982] [L. Barnett et al., Phys. Rev. Lett. 103, 2009]

Courtesy: Luca Faes

Mutual information and causality

Mutual info.

Grangerwith quadratic+

cross-terms

LinearGranger

TransferEntropy


L. Minati


Effect of “lesioning” by noise injection


L. Minati


Ring size and auxiliary system simulations

Response(ring)

Auxiliary (chain)


L. Minati


Propagation of external perturbations


L. Minati

Image source: Minati et al., CHAOS 2018. © AIP, ANT Neuro

Simplified chain model

1) An open network is considered in the form of a chain.2) Two dynamical equations are removed.3) Γ(x,y) is removed for all voltages except v3. 4) The parameters are set identically across all nodes.


L. Minati

Simplified chain model


L. Minati


Demodulation and interference


L. Minati


Demodulation and interference


L. Minati


Instancing filters at specific points of chain


L. Minati


Revised Granger model: baseband + sideband


L. Minati


Small-world features, nonetheless…


L. Minati

Small-world features, nonetheless…

Source: Bullmore & Sporns, 2012; Nat Rev Neurosci, © 2012 Macmillan Publishers Limited

Small-worldness in the brain (and not only) is an efficient trade-off!


L. Minati

Conclusions

1) A complex mechanism of pattern generation was demonstrated.

2) Is this just “apparent” remoteness?Central importance of measure choice…

3) To what systems may such mechanism apply?Broadband vs. narrowband chaos, spectral relationships


L. Minati

Remote synchronization from mismatches

Image credit: cited study, © APS


L. Minati

Non-monotonic effect of the coupling strength

Image credit: Karakaya et al. PRE 2019, © APS


L. Minati




L. Minati




L. Minati




L. Minati

Thank you for your attention

References:1. Minati L. Remote synchronization of amplitudes across an experimental ring of non-

linear oscillators. CHAOS. 2015 Dec; 25(12):123107.2. Minati L, Faes L, Frasca M, Oświȩcimka P, Drożdż S. Apparent remote

synchronization of amplitudes: a demodulation and interference effect. CHAOS. 2018 Jun; 28, 063124.

3. Minati L, Across Neurons and Silicon: Some Experiments Regarding the Pervasiveness of Nonlinear Phenomena. Acta Phys Pol B 2018; 49:2029.

4. Karakaya B, Minati L, Gambuzza LV, Frasca M. Fading of remote synchronization in tree networks of Stuart-Landau oscillators. Phys Rev E. 2019; 99:052301.

[email protected] [email protected] [email protected] http://www.lminati.it


L. Minati

Documents

Remote synchronization: detailed account of a peculiar