scholarly journals Residual Predictive Information Flow in the Tight Coupling Limit: Analytic Insights from a Minimalistic Model

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1010
Author(s):  
Benjamin Wahl ◽  
Ulrike Feudel ◽  
Jaroslav Hlinka ◽  
Matthias Wächter ◽  
Joachim Peinke ◽  
...  
Keyword(s):  
Information Flow ◽  
Coupling Strength ◽  
Social Groups ◽  
Coupled System ◽  
Model Description ◽  
Causal Connection ◽  
Noise Strength ◽  
Tight Coupling ◽  
Predictive Information ◽  
Analytic Expressions

In a coupled system, predictive information flows from the causing to the caused variable. The amount of transferred predictive information can be quantified through the use of transfer entropy or, for Gaussian variables, equivalently via Granger causality. It is natural to expect and has been repeatedly observed that a tight coupling does not permit to reconstruct a causal connection between causing and caused variables. Here, we show that for a model of interacting social groups, carried from the master equation to the Fokker–Planck level, a residual predictive information flow can remain for a pair of uni-directionally coupled variables even in the limit of infinite coupling strength. We trace this phenomenon back to the question of how the synchronizing force and the noise strength scale with the coupling strength. A simplified model description allows us to derive analytic expressions that fully elucidate the interplay between deterministic and stochastic model parts.

scholarly journals Generation and dynamics of entangled fermion–photon–phonon states in nanocavities

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 491-511 ◽  
Author(s):  
Mikhail Tokman ◽  
Maria Erukhimova ◽  
Yongrui Wang ◽  
Qianfan Chen ◽  
Alexey Belyanin
Keyword(s):  
Emission Spectra ◽  
Coupled System ◽  
Vibrational Modes ◽  
Tripartite Entanglement ◽  
Quantum Emitter ◽  
Parametric Resonances ◽  
Analytic Expressions ◽  
Entangled Quantum States ◽  
Formation And Evolution ◽  
Quantum Optomechanics

AbstractWe develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled simultaneously to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tripartite entanglement are realized near the parametric resonances in a coupled system. The model includes dissipation and decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg–Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

scholarly journals Galvanic Phase Coupling of Superconducting Flux Qubits

2021 ◽  
Vol 11 (23) ◽  
pp. 11309
Author(s):  
Mun Dae Kim
Keyword(s):  
Coupling Strength ◽  
Fault Tolerant ◽  
Coupled System ◽  
Inductive Coupling ◽  
Galvanic Coupling ◽  
Flux Qubits ◽  
Superconducting Flux Qubits ◽  
Qubit Gate ◽  
Central Loop ◽  
Fundamental Boundary

We investigate the galvanic coupling schemes of superconducting flux qubits. From the fundamental boundary conditions, we obtain the effective potential of the coupled system of two or three flux qubits to provide the exact Lagrangian of the system. While usually the two-qubit gate has been investigated approximately, in this study we derive the exact inductive coupling strength between two flux qubits coupled directly and coupled through a connecting central loop. We observe that the inductive coupling strength needs to be included exactly to satisfy the criteria of fault-tolerant quantum computing.

A Novel Dual-Mass Accelerometer Exploiting Mode Localization in Electrostatically Coupled Resonators

2021 ◽  
Author(s):  
Ming Lyu ◽  
Jian Zhao ◽  
Najib Kacem ◽  
Pengbo Liu
Keyword(s):  
Coupling Strength ◽  
Axial Load ◽  
Amplitude Ratio ◽  
Coupled System ◽  
Inertial Forces ◽  
Governing Equations ◽  
Coupled Resonators ◽  
Critical Amplitude ◽  
Mode Localization ◽  
Vibration Magnitude

Abstract A novel dual-mass accelerometer is proposed while exploiting the phenomenon of mode localization in two electrostatically coupled resonators with an adjustable coupling strength. The external inertial forces are transmitted differentially to the resonators in term of axial load change through the two levering mechanisms, breaking the balanced state and resulting in a drastic change in the amplitudes of the two resonators. Based on the Euler Bernoulli theory, the governing equations of the coupled system are derived and numerically solved. The sensitivity in term of relative shift of amplitude ratio can be improved by 4 orders of magnitude compared to frequency shift. Finally, the effect of the quality factor on the sensor dynamics has also been investigated, and the results show that it only affects the vibration magnitude of the resonators while operating below the critical amplitude.

The synchronization of asymmetric-structured electric coupling neuronal system

2018 ◽  
Vol 32 (04) ◽  
pp. 1850040 ◽  
Author(s):  
Guanping Wang ◽  
Wuyin Jin ◽  
Hao Liu ◽  
Wei Sun
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Single Neuron ◽  
Specific Area ◽  
Coupled System ◽  
Neuronal System ◽  
Electric Coupling ◽  
System Synchronization ◽  
Hr Model ◽  
Delay Difference

Based on the Hindmarsh–Rose (HR) model, the synchronization dynamics of asymmetric-structured electric coupling two neuronal system is investigated in this paper. It is discovered that when the time-delay scope and coupling strength for the synchronization are correlated positively under unequal time delay, the time-delay difference does not make a clear distinction between the two individual inter-spike intervals (ISI) bifurcation diagrams of the two coupled neurons. Therefore, the superficial difference of the system synchronization dynamics is not obvious for the unequal time-delay feedback. In the asymmetrical current incentives under asymmetric electric coupled system, the two neurons can only be almost completely synchronized in specific area of the interval which end-pointed with two discharge modes for a single neuron under different stimuli currents before coupling, but the intervention of time-delay feedback, together with the change of the coupling strength, can make the coupled system not only almost completely synchronized within anywhere in the front area, but also outside of it.

scholarly journals Information flow in social groups

2004 ◽  
Vol 337 (1-2) ◽  
pp. 327-335 ◽  
Author(s):  
Fang Wu ◽  
Bernardo A. Huberman ◽  
Lada A. Adamic ◽  
Joshua R. Tyler
Keyword(s):  
Information Flow ◽  
Social Groups

Analytical Study of Dispersion of Stress Waves in a Weakly Coupled Layered System

1995 ◽  
Author(s):  
A. F. Vakakis ◽  
C. Cetinkaya
Keyword(s):  
Practical Importance ◽  
Coupled System ◽  
Stress Waves ◽  
Layered System ◽  
Convolution Integrals ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Analytic Expressions ◽  
Convolution Kernels ◽  
As Stress

Abstract Dispersion of transient stress waves in the first layer of a weakly coupled semi-infinite bi-layered system is carried out. Fourier transform inversions are performed analytically by making use of the fact that the weakly coupled system possesses small propagation zones (PZs) in the frequency domain. Low- and high-frequency asymptotic approximations to the transient waves are computed, taking into account frequency components of the transfer function in the first and second PZs, respectively. The derived analytic expressions are superpositions of non-oscillating terms and convolution integrals with decaying oscillatory kernels. Depending on the frequency and the amplitude of the convolution kernels, the dispersed waves overshoot or undershoot the applied impulsive excitation. This result is of significant practical importance in the design of layered systems as stress attenuators.

scholarly journals Using noise to augment synchronization among oscillators

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaykumar Vaidya ◽  
Mohammad Khairul Bashar ◽  
Nikhil Shukla
Keyword(s):  
White Noise ◽  
Coupling Strength ◽  
Coupled System ◽  
External Noise ◽  
Capacitive Coupling ◽  
Frequency Locking ◽  
Relaxation Oscillators ◽  
Computing Platforms ◽  
Analog Systems ◽  
Computational Properties

AbstractNoise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms.

scholarly journals Can Transfer Entropy Infer Information Flow in Neuronal Circuits for Cognitive Processing?

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 385 ◽  
Author(s):  
Ali Tehrani-Saleh ◽  
Christoph Adami
Keyword(s):  
Cognitive Processing ◽  
Information Flow ◽  
Cognitive Task ◽  
Evolutionary Process ◽  
Logic Gates ◽  
Ground Truth ◽  
Transfer Entropy ◽  
Causal Connection ◽  
Directed Information ◽  
Flow Of Information

How cognitive neural systems process information is largely unknown, in part because of how difficult it is to accurately follow the flow of information from sensors via neurons to actuators. Measuring the flow of information is different from measuring correlations between firing neurons, for which several measures are available, foremost among them the Shannon information, which is an undirected measure. Several information-theoretic notions of “directed information” have been used to successfully detect the flow of information in some systems, in particular in the neuroscience community. However, recent work has shown that directed information measures such as transfer entropy can sometimes inadequately estimate information flow, or even fail to identify manifest directed influences, especially if neurons contribute in a cryptographic manner to influence the effector neuron. Because it is unclear how often such cryptic influences emerge in cognitive systems, the usefulness of transfer entropy measures to reconstruct information flow is unknown. Here, we test how often cryptographic logic emerges in an evolutionary process that generates artificial neural circuits for two fundamental cognitive tasks (motion detection and sound localization). Besides counting the frequency of problematic logic gates, we also test whether transfer entropy applied to an activity time-series recorded from behaving digital brains can infer information flow, compared to a ground-truth model of direct influence constructed from connectivity and circuit logic. Our results suggest that transfer entropy will sometimes fail to infer directed information when it exists, and sometimes suggest a causal connection when there is none. However, the extent of incorrect inference strongly depends on the cognitive task considered. These results emphasize the importance of understanding the fundamental logic processes that contribute to information flow in cognitive processing, and quantifying their relevance in any given nervous system.

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