Network Oscillations Research Articles

Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics

In this paper, we provide theoretical as well as numerical results concerning recurrent oscillations in Cohen-Grossberg neural networks with variable inputs and strengths of connectivity for cells, which are unpredictable or Poisson stable functions. A special case of the compartmental coefficients with periodic and unpredictable ingredients is also carefully researched. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects contributions of the ingredients to final outputs of the neural networks. Sufficient conditions are obtained to guarantee the existence of exponentially stable unpredictable outputs of the models. They are specified for Poisson stability by utilizing the original method of included intervals. Examples with numerical simulations that support the theoretical results are provided.

Experimental demonstration of coupled differential oscillator networks for versatile applications.

Oscillatory neural networks (ONNs) exhibit a high potential for energy-efficient computing. In ONNs, neurons are implemented with oscillators and synapses with resistive and/or capacitive coupling between pairs of oscillators. Computing is carried out on the basis of the rich, complex, non-linear synchronization dynamics of a system of coupled oscillators. The exploited synchronization phenomena in ONNs are an example of fully parallel collective computing. A fast system's convergence to stable states, which correspond to the desired processed information, enables an energy-efficient solution if small area and low-power oscillators are used, specifically when they are built on the basis of the hysteresis exhibited by phase-transition materials such as VO2. In recent years, there have been numerous studies on ONNs using VO2. Most of them report simulation results. Although in some cases experimental results are also shown, they do not implement the design techniques that other works on electrical simulations report that allow to improve the behavior of the ONNs. Experimental validation of these approaches is necessary. Therefore, in this study, we describe an ONN realized in a commercial CMOS technology in which the oscillators are built using a circuit that we have developed to emulate the VO2 device. The purpose is to be able to study in-depth the synchronization dynamics of relaxation oscillators similar to those that can be performed with VO2 devices. The fabricated circuit is very flexible. It allows programming the synapses to implement different ONNs, calibrating the frequency of the oscillators, or controlling their initialization. It uses differential oscillators and resistive synapses, equivalent to the use of memristors. In this article, the designed and fabricated circuits are described in detail, and experimental results are shown. Specifically, its satisfactory operation as an associative memory is demonstrated. The experiments carried out allow us to conclude that the ONN must be operated according to the type of computational task to be solved, and guidelines are extracted in this regard.

Lobe‐specific changes in white matter volume and myelination following 6‐month 40 Hz gamma sensory stimulation in patients on the Alzheimer’s disease spectrum

AbstractBackgroundAlthough morphometric changes in Alzheimer’s Disease (AD) occur both in gray and white matter, gray matter changes had been the primary focus of previous work. Recent studies have highlighted the importance of pathological changes in white matter and myelination in AD patients, including early changes to oligodendrocytes and transcription of myelin protein genes in the white matter prior to symptoms of cognitive decline, even in subjects with AD but without other neurological comorbidities (Ferrer et al., 2020). Since neuronal activities, particularly network oscillations have been shown to promote myelination, the present study examined how 40Hz gamma stimulation affected white matter volume and myelination in different cortical lobes in patients with AD.MethodData were obtained from the Overture trial (NCT03555281) in which treatment participants received daily, at‐home, 40Hz gamma sensory stimulation for six months, while placebo participants received sham stimulation (treatment‐to‐placebo ratio 2:1). Magnetic resonance imaging (MRI) data were collected at 1.5 Tesla at baseline, month 3, and month 6. MRI T1 images and T1w/T2w ratios were used to estimate volume (N = 38) and myelination (N = 36), respectively. Using Bayesian linear mixed effects modeling, we estimated white matter volume and myelination percent changes with respect to baseline. Treatment group results were reported in relation to the placebo group.ResultWith respect to the placebo group: In the left hemisphere, the treatment group exhibited reduced white matter atrophy in the frontal lobe (‐3.27±1.4, p = 0.0225), in the temporal lobe (‐3.9±1.76, p = 0.0306), in the parietal lobe (‐3.32±1.43, p = 0.0236), in the occipital lobe (‐4.1±1.72, p = 0.0195) and reduced demyelination in the frontal lobe (‐5.13±2.12, p = 0.0186), in the temporal lobe (‐5.33±2.42, p = 0.0321), in the parietal lobe (‐5.7±2.07 (p = 0.0079), in the occipital lobe (‐5.65±2.52, p = 0.0296). In the right hemisphere, the treatment group trended towards reduced white matter volume loss and demyelination in all lobes, however, demyelination was significantly reduced in the parietal lobe (‐4.48±2.09, p = 0.037), and in the occipital lobe (‐5.5±2.22, p = 0.0165).ConclusionWhite matter atrophy and demyelination were statistically significantly reduced in all lobes of the left hemisphere and trended towards reduction in the right hemisphere, demonstrating that 40Hz sensory stimulation can reduce the neurodegeneration associated with AD.

A Stochastic Binary Vertex-Triggering Resetting Algorithm for Global Synchronization of Pulse-Coupled Oscillators

In this paper, we propose a novel stochastic binary resetting algorithm for networks of pulse-coupled oscillators (or, simply, agents) to reach global synchronization. The algorithm is simple to state: Every agent in a network oscillates at a common frequency. Upon completing an oscillation, an agent generates a Bernoulli random variable to decide whether it sends pulses to all of its out-neighbours or it stays quiet. Upon receiving a pulse, an agent resets its state by following a binary phase update rule. We show that such an algorithm can guarantee <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global</i> synchronization of the agents almost surely as long as the underlying information flow topology is a rooted directed graph. The proof of the result relies on the use of a stochastic hybrid dynamical system approach. Toward the end of the paper, we present numerical demonstrations for the validity of the result and, also, numerical studies about the units of time needed to reach synchronization for networks with various information flow topologies.

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay.

The analog Hopfield neural network with time delay and random connections has been studied for its similarities in activity to human electroencephalogram and its usefulness in other areas of the applied sciences such as speech recognition, image analysis, and electrocardiogram modeling. Our goal here is to understand the mechanisms that affect the rhythmic activity in the neural network and how the addition of a Gaussian noise contributes to the network behavior. The neural network studied is composed of ten identical neurons. We investigated the excitatory and inhibitory networks with symmetric (square matrix) and asymmetric (triangular matrix) connections. The differential equations that model the network are solved numerically using the stochastic second-order Runge-Kutta method. Without noise, the neural networks with symmetric and asymmetric matrices possessed different synchronization properties: fully connected networks were synchronized both in time and in amplitude, while asymmetric networks were synchronized in time only. Saturation outputs of the excitatory neural networks do not depend on the time delay, whereas saturation oscillation amplitudes of inhibitory networks increase with the time delay until the steady state. The addition of the Gaussian noise is shown to significantly amplify small-amplitude oscillations, dramatically accelerates the rate of amplitude growth to saturation, and changes synchronization properties of the neural network outputs.

Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

This paper studies the problem of locating the sparse set of sources of forcing inputs driving linear systems from noisy measurements when the initial state is unknown. This problem is particularly relevant to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide upper bounds on: (i) the probability that the group LASSO estimator incorrectly identifies the locations and (ii) the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -norm of the estimation error. Our bounds depend on the number of measurements, inputs, and sensors; the sensor noise variance; and the minimum singular value of the observability and impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for the left invertible linear systems with delay. Finally, we validate the performance of the estimator on synthetic models and the IEEE 68-bus, 16-machine power system.

Impact of time varying interaction: Formation and annihilation of extreme events in dynamical systems.

This study investigates the emergence of extreme events in two different coupled systems: the FitzHugh-Nagumo neuron model and the forced Liénard system, both based on time-varying interactions. The time-varying coupling function between the systems determines the duration and frequency of their interaction. Extreme events in the coupled system arise as a result of the influence of time-varying interactions within various parameter regions. We specifically focus on elucidating how the transition point between extreme events and regular events shifts in response to the duration of interaction time between the systems. By selecting the appropriate interaction time, we can effectively mitigate extreme events, which is highly advantageous for controlling undesired fluctuations in engineering applications. Furthermore, we extend our investigation to networks of oscillators, where the interactions among network elements are also time dependent. The proposed approach for coupled systems holds wide applicability to oscillator networks.

High-frequency oscillation network mapping predict prognosis after radiofrequency thermocoagulation for epilepsy

High-frequency oscillation network mapping predict prognosis after radiofrequency thermocoagulation for epilepsy

Helioseismic Investigation of Quasi-biennial Oscillation Source Regions

We studied the temporal evolution of quasi-biennial oscillations (QBOs) using acoustic mode oscillation frequencies from the Global Oscillation Network Group. The data used here span more than 25 yr, covering solar cycles 23 and 24 and the ascending phase of cycle 25. The analysis reveals that QBO-like signals are present in both the cycles, but with different periods. The dominant QBO period in cycle 23 is found to be about 2 yr, while it is about 3 yr in cycle 24. Furthermore, the quasi-biennial oscillatory signals are present only during the ascending and high-activity phases of cycle 23 and quickly weaken around 2005, during the declining phase. In comparison, the QBO signals are present throughout cycle 24, starting from 2009 to 2017. We also explored the depth dependence in QBO signals and obtained a close agreement at all depths, except in the near-surface shear layer. A detailed analysis of the near-surface shear layer suggests that the source region of QBOs is probably within a few thousand kilometers just below the surface.

Learning algorithms for oscillatory neural networks as associative memory for pattern recognition

Alternative paradigms to the von Neumann computing scheme are currently arousing huge interest. Oscillatory neural networks (ONNs) using emerging phase-change materials like VO2 constitute an energy-efficient, massively parallel, brain-inspired, in-memory computing approach. The encoding of information in the phase pattern of frequency-locked, weakly coupled oscillators makes it possible to exploit their rich non-linear dynamics and their synchronization phenomena for computing. A single fully connected ONN layer can implement an auto-associative memory comparable to that of a Hopfield network, hence Hebbian learning rule is the most widely adopted method for configuring ONNs for such applications, despite its well-known limitations. An extensive amount of literature is available about learning in Hopfield networks, with information regarding many different learning algorithms that perform better than the Hebbian rule. However, not all of these algorithms are useful for ONN training due to the constraints imposed by their physical implementation. This paper evaluates different learning methods with respect to their suitability for ONNs. It proposes a new approach, which is compared against previous works. The proposed method has been shown to produce competitive results in terms of pattern recognition accuracy with reduced precision in synaptic weights, and to be suitable for online learning.

Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

We review an approach for reconstructing oscillatory networks’ undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network’s coupling matrix in the first approximation in the coupling strength.

Cluster synchronization control for coupled genetic oscillator networks under denial-of-service attacks: Pinning partial impulsive strategy

This paper focuses on the security cluster synchronization (CS) of coupled genetic oscillator networks (GONs) with parameters mismatch under denial-of-service (DoS) attacks. Firstly, a model of DoS attacks on the control channel of GONs is established. Then, in order to achieve secure CS of GONs under DoS attacks, a pinning partial impulsive control (PPIC) strategy is proposed for the first time. Compared with the existing pinning impulsive control and partial impulsive control, the PPIC control method only controls part of the molecules of part of the genetic oscillators, so it has better performance in saving control cost. Moreover, we design an algorithm to obtain sufficient conditions for secure CS and the DoS attacks duration ratio that the system can tolerate. In addition, when the system is immune to DoS attacks, it can still achieve CS under PPIC. Finally, two numerical examples based on MATLAB software are presented to demonstrate the effectiveness of the results. The secure synchronization region is obtained, and the convergence efficiency of error systems under PPIC and pinning impulsive control is compared in the simulation.

Mobile oscillators network with amplification

In this work, we investigate the dynamics of a multilayer network of mobile agents with amplification where each agent is composed of two parts: internal dynamics defined by a Rössler chaotic oscillator and external dynamics defined by the random motion of this agent in 2D space. Each agent characterized by a communication range named ‘vision range’ which is the greatest distance within which two agents can exchange information and therefore establish a coupling. Thus, two cases were studied: the case where only the external dynamic influences the internal dynamic and the case where there is a mutual influence of the internal dynamic on the external dynamic and vice versa. The study of the effects of these parameters leads the internal dynamics of the network to the synchronization (resp. attenuation) and the spatial motion of the agent to the phase synchronization.

A Peptide-Based Oscillator.

Living organisms are replete with rhythmic and oscillatory behavior at all levels, to the extent that oscillations have been termed as a defining attribute of life. Recent studies of synthetic oscillators that mimic such functions have shown decayed cycles in batch-mode reactions or sustained oscillatory kinetics under flow conditions. Considering the hypothesized functionality of peptides in early chemical evolution and their central role in current bio-nanotechnology, we now reveal a peptide-based oscillator. Oscillatory behavior was achieved by coupling coiled-coil-based replication processes as positive feedback to controlled initiation and inhibition pathways in a continuously stirred tank reactor (CSTR). Our results stress that assembly into the supramolecular structure and specific interactions with the replication substrates are crucial for oscillations. The replication-inhibition processes were first studied in batch mode, which produced a single damped cycle. Thereafter, combined experimental and theoretical characterization of the replication process in a CSTR under different flow and environmental (pH, redox) conditions demonstrated reasonably sustained oscillations. We propose that studies in this direction might pave the way to the design of robust oscillation networks that mimic the autonomous behavior of proteins in cells (e.g., in the cyanobacterial circadian clock) and hence hint at feasible pathways that accelerated the transition from simple peptides to extant enzymes.

Synthetic genetic oscillators demonstrate the functional importance of phenotypic variation in pneumococcal-host interactions

Phenotypic variation is the phenomenon in which clonal cells display different traits even under identical environmental conditions. This plasticity is thought to be important for processes including bacterial virulence, but direct evidence for its relevance is often lacking. For instance, variation in capsule production in the human pathogen Streptococcus pneumoniae has been linked to different clinical outcomes, but the exact relationship between variation and pathogenesis is not well understood due to complex natural regulation. In this study, we use synthetic oscillatory gene regulatory networks (GRNs) based on CRISPR interference (CRISPRi) together with live cell imaging and cell tracking within microfluidics devices to mimic and test the biological function of bacterial phenotypic variation. We provide a universally applicable approach for engineering intricate GRNs using only two components: dCas9 and extended sgRNAs (ext-sgRNAs). Our findings demonstrate that variation in capsule production is beneficial for pneumococcal fitness in traits associated with pathogenesis providing conclusive evidence for this longstanding question.

Correlation Between Cued Fear Memory Retrieval and Oscillatory Network Inhibition in the Amygdala Is Disrupted by Acute REM Sleep Deprivation

The basolateral amygdaloid complex (BLA) is critically involved in emotional behaviors, such as aversive memory formation. In particular, fear memory after cued fear conditioning is strongly associated with the BLA, whereas both the BLA and hippocampus are essential for contextual fear memory formation. In the present study, we examined the effects of acute (3 h) sleep deprivation (SD) on BLA-associated fear memory in juvenile (P24-32) rats and performed in vitro electrophysiology using whole-cell patch clamping from the basolateral nucleus (BA) of the BLA. BA projection neurons exhibit the network oscillation, i.e., spontaneous oscillatory bursts of inhibitory transmission at 0.1–3 Hz, as previously reported. In the present study, SD either before or after fear conditioning (FC) disturbed the acquisition of tone-associated fear memory without significant effects on contextual fear memory. FC reduced the power of the oscillatory activity, but SD did not further reduce the oscillation power. Oscillation power was correlated with tone-associated freezing rate (FR) in SD-free fear-conditioned rats, but this relation was disrupted in SD treated group. Rhythm index (RI), the rhythmicity of the oscillation, quantified by autocorrelation analysis, also correlated with tone-associated FR in the combined data, including FC alone and FC with SD. These results suggest that slow network oscillation in the amygdala contributes to the formation of amygdala-dependent fear memory in relation to sleep.

Combining magnetoencephalography with telemetric streaming of intracranial recordings and deep brain stimulation—A feasibility study

Abstract The combination of subcortical Local Field Potential (LFP) recordings and stimulation with Magnetoencephalography (MEG) in Deep Brain Stimulation (DBS) patients enables the investigation of cortico-subcortical communication patterns and provides insights into DBS mechanisms. Until now, these recordings have been carried out in post-surgical patients with externalised leads. However, a new generation of telemetric stimulators makes it possible to record and stream LFP data in chronically implanted patients. Nevertheless, whether such streaming can be combined with MEG has not been tested. In the present study, we tested the most commonly implanted telemetric stimulator—Medtronic Percept PC with a phantom in three different MEG systems: two cryogenic scanners (CTF and MEGIN) and an experimental Optically Pumped Magnetometry (OPM)-based system. We found that when used in combination with the new SenSight segmented leads, Percept PC telemetric streaming only generates band-limited interference in the MEG at 123 Hz and harmonics. However, the “legacy streaming mode” used with older lead models generates multiple, dense artefact peaks in the physiological range of interest (below 50 Hz). The effect of stimulation on MEG critically depends on whether it is done in bipolar (between two contacts on the lead) or monopolar (between a lead contact and the stimulator case) mode. Monopolar DBS creates severe interference in the MEG as previously reported. However, we found that the OPM system is more resilient to this interference and could provide artefact-free measurements, at least for limited frequency ranges. A resting measurement in the MEGIN system from a Parkinson’s patient implanted with Percept PC and subthalamic SenSight leads revealed artefact patterns consistent with our phantom recordings. Moreover, analysis of LFP-MEG coherence in this patient showed oscillatory coherent networks consistent in their frequency and topography with those described in published group studies done with externalised leads. In conclusion, Percept PC telemetric streaming with SenSight leads is compatible with MEG. Furthermore, OPM sensors could provide additional new opportunities for studying DBS effects.

Time-delay-induced spiral chimeras on a spherical surface of globally coupled oscillators.

We consider globally coupled networks of identical oscillators, located on the surface of a sphere with interaction time delays, and show that the distance-dependent time delays play a key role for the spiral chimeras to occur as a generic state in different systems of coupled oscillators. For the phase oscillator system, we analyze the existence and stability of stationary solutions along the Ott-Antonsen invariant manifold to find the bifurcation structure of the spiral chimera state. We demonstrate via an extensive numerical experiment that the time-delay-induced spiral chimeras are also present for coupled networks of the Stuart-Landau and Van der Pol oscillators in the same parameter regime as that of phase oscillators, with a series of evenly spaced band-type regions. It is found that the spiral chimera state occurs as a consequence of a resonant-type interplay between the intrinsic period of an individual oscillator and the interaction time delay as a topological structure property.

Deep ensemble geophysics-informed neural networks for the prediction of celestial pole offsets

SUMMARY Celestial Pole Offsets (CPO), denoted by dX and dY, describe the differences in the observed position of the pole in the celestial frame with respect to a certain precession-nutation model. Precession and nutation components are part of the transformation matrix between terrestrial and celestial systems. Therefore, various applications in geodetic science such as high-precision spacecraft navigation require information regrading precession and nutation. For this purpose, CPO can be added to the precession-nutation model to precisely describe the motion of the celestial pole. However, as Very Long Baseline Interferometry (VLBI)—currently the only technique providing CPO—requires long data processing times resulting in several weeks of latency, predictions of CPO become necessary. Here we present a new methodology named Deep Ensemble Geophysics-Informed Neural Networks (DEGINNs) to provide accurate CPO predictions. The methodology has three main elements: (1) deep ensemble learning to provide the prediction uncertainty; (2) broad-band Liouville equation as a geophysical constraint connecting the rotational dynamics of CPO to the atmospheric and oceanic Effective Angular Momentum (EAM) functions and (3) coupled oscillatory recurrent neural networks to model the sequential characteristics of CPO time-series, also capable of handling irregularly sampled time-series. To test the methodology, we use the newest version of the final CPO time-series of International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04. We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications. Furthermore, for validation purposes we generate an independent global VLBI solution for CPO since 1984 up to the end of 2022 and analyse the series. We draw the following conclusions. First, the prediction performance of DEGINNs demonstrates up to 25 and 33 percent improvement, respectively, for dX and dY, with respect to the rapid data provided by IERS. Secondly, predictions made with the help of EAM are more accurate compared to those without EAM, thus providing a clue to the role of atmosphere and ocean on the excitation of CPO. Finally, free core nutation period shows temporal variations with a dominant periodicity of around one year, partially excited by EAM.

Oscillatory network markers of subcallosal cingulate deep brain stimulation for depression

Identifying functional biomarkers related to treatment success can aid in expediting therapy optimization, as well as contribute to a better understanding of the neural mechanisms of the treatment-resistant depression (TRD) and subcallosal cingulate deep brain stimulation (SCC-DBS).Magnetoencephalography data were obtained from 16 individuals with SCC-DBS for TRD and 25 healthy subjects. The first objective of the study was to identify region-specific oscillatory modulations that both (i) discriminate individuals with TRD (with SCC-DBS OFF) from healthy controls, and (ii) discriminate TRD treatment responders from non-responders (with SCC-DBS ON). The second objective of this work was to further explore the effects of stimulation intensity and frequency on oscillatory activity in the identified brain regions of interest.Oscillatory power analyses led to the identification of brain regions that differentiated responders from non-responders based on modulations of increased alpha (8–12 Hz) and decreased gamma (32–116 Hz) power within nodes of the default mode, central executive, and somatomotor networks, Broca's area, and lingual gyrus. Within these nodes, it was also found that low stimulation frequency had stronger effects on oscillatory modulation than increased stimulation intensity.The identified functional network biomarkers implicate modulation of TRD-related activity in brain regions involved in emotional control/processing, motor control, and the interaction between speech, vision, and memory, which have all been implicated in depression. These electrophysiological biomarkers have the potential to be used as functional proxies for therapy optimization. Additional stimulation parameter analyses revealed that oscillatory modulations can be strengthened by increasing stimulation intensity or reducing frequency, which may represent potential avenues of direction in non-responders.