remote synchronization: detailed account of a peculiar
TRANSCRIPT
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
What is remote synchronization?
Synchronised
Non-synchronised Non-synchronised
A B C
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Remote synchronization from mismatches
Image credit: cited study, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Remote synchronization as morphogenesis
Image credit: Wikipedia, others
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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?
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Rosazza & Minati, 2011; © Springer Verlag
A simple, reconfigurable non-linear network
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Oscillator equations
Parametric mismatch~0.5% in physical system
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Applications in versatile pattern generation
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Numerical simulations reveal three regimesa:
G6=
0.19
6,
G7=
-1.3
65
Broadband chaos
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Numerical simulations reveal three regimesa:
G6=
0.19
6,
G7=
-1.3
65b:
G6=
0.09
6,
G7=
-1.5
3
Broadband chaos
Quasi-periodicity
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Numerical simulations reveal three regimesa:
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Numerical simulations reveal three regimes
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Numerical simulations reveal three regimes
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Effect of parametric mismatches
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP, others, public domain
Experimental implementation
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Experimental implementation
Top-levelFPAA
architecture
Upon permission and courtesy of Anadigm, Inc.
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Experimental implementation
The Configurable Analog Module (CAM)
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
Upon permission and courtesy of Anadigm, Inc.
L. Minati
Experimental implementation
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
Upon permission and courtesy of Anadigm, Inc.
L. Minati
Experimental implementation
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
Upon permission and courtesy of Anadigm, Inc.
L. Minati
Experimental implementation
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
Upon permission and courtesy of Anadigm, Inc.
L. Minati
Experimental implementation
Continuous-value, discrete-time
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
Upon permission and courtesy of Anadigm, Inc.
L. Minati
Experimental implementation
From: A. Buscarino et al., A Concise Guide to Chaotic Electronic Circuits, 73 , SpringerBriefs in Applied Sciences and Technology
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Experimental implementation
A soft of “Chimera”: an analogplug-in system for digital computer
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP, Wikipedia
Remote sync. close to quasi-periodicity
Correlation dimension (D2)
Remote synchronization (η)
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Experimental data - basicsSpectrogram Phase sync. Amplitude sync.
Reminiscent of adiffraction pattern?
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP, Wikipedia
Non-stationarity
Adjacenttime-windows…
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2015. © AIP
Non-stationarity
…reminiscent of observations in resting-state functional MRI
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
→ fL=fB
From synchronization to causality
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Effect of “lesioning” by noise injection
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Ring size and auxiliary system simulations
Response(ring)
Auxiliary (chain)
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Propagation of external perturbations
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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.
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Simplified chain model
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Demodulation and interference
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Demodulation and interference
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Instancing filters at specific points of chain
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Revised Granger model: baseband + sideband
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Image source: Minati et al., CHAOS 2018. © AIP
Small-world features, nonetheless…
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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!
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Remote synchronization from mismatches
Image credit: cited study, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Non-monotonic effect of the coupling strength
Image credit: Karakaya et al. PRE 2019, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Non-monotonic effect of the coupling strength
Image credit: Karakaya et al. PRE 2019, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Non-monotonic effect of the coupling strength
Image credit: Karakaya et al. PRE 2019, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati
Non-monotonic effect of the coupling strength
Image credit: Karakaya et al. PRE 2019, © APS
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
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
Remote synchronization: detailed account of a peculiar pattern-formation mechanism
L. Minati