Network Oscillations Research Articles

Resonant Solitary States in Complex Networks

Abstract Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators with inertia is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node.
Here, we reveal the mechanism behind this multistability: additional solitary frequencies arise from the coupling between network modes and the solitary oscillator's frequency, leading to significant energy transfer. This can cause the solitary node's frequency to resonate with a Laplacian eigenvalue. We analyze which network structures enable this resonance and explain longstanding numerical observations.
Another solitary state that is known in the literature is characterized by the effective decoupling of the synchronized network and the solitary node at the natural frequency. Our framework unifies the description of solitary states near and far from resonance, allowing to predict the behavior of complex networks from their topology.

Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses

We present numerical results for the effects of influence by high-amplitude periodic pulse series on a network of nonlocally coupled Hindmarsh–Rose neurons with 2D geometry of the topology. We consider the case when the pulse amplitude is larger than the amplitude of oscillations in the autonomous network for a wide range of pulse frequencies. An initial regime in the network is a spiral wave chimera. We show that the effects of external influence strongly depend on a balance between the pulse frequency and frequencies of the spectral peaks of the autonomous network. Except for the destructive role of the pulses, when they lead to loss of stability of the initial regime, we have also revealed a constructive role. We have found for the first time the emergence of a new type of multi-front spiral waves, when the wavefront represents a set of several close fronts, and the wave dynamics are significantly different from common spiral waves: neurons oscillate independently to the wave rotation, the rotation velocity is in many times less than for the common spiral wave, etc. We have also discovered several types of cluster spatiotemporal structures induced by the pulses.

Sensitivity of Global Oscillation Frequencies to Solar Activity on Short Timescales

Sun’s oscillations frequencies vary with the changing magnetic activity and hold a strong positive correlation. While most of the analysis for global modes have been carried out using time series longer than a solar rotation, only a few studies are available showing their variation on shorter timescales. Using Doppler observations from Global Oscillation Network Group during the period 1995–2024, we analyze oscillation frequencies computed on a timescale of nine days and compare them with those obtained from 108 days. We also study their sensitivity in cycles 23 and 24 to the change in solar activity as represented by the 10.7 cm radio flux.

Regulation of Cx36 trafficking through the early secretory pathway by COPII cargo receptors and Grasp55

Gap junctions formed by the major neuronal connexin Cx36 function as electrical synapses in the nervous system and provide unique functions such as synchronizing neuron activities or supporting network oscillations. Although the physiological significance of electrical synapses for neuronal networks is well established, little is known about the pathways that regulate the transport of its main component: Cx36. Here we have used HEK293T cells as an expression system in combination with siRNA and BioID screens to study the transition of Cx36 from the ER to the cis Golgi. Our data indicate that the C-terminal tip of Cx36 is a key factor in this process, mediating binding interactions with two distinct components in the early secretory pathway: the COPII complex and the Golgi stacking protein Grasp55. The C-terminal amino acid valine serves as an ER export signal to recruit COPII cargo receptors Sec24A/B/C at ER exit sites, whereas the PDZ binding motif “SAYV” mediates an interaction with Grasp55. These two interactions have opposing effects in their respective compartments. While Sec24 subunits carry Cx36 out of the ER, Grasp55 stabilizes Cx36 in the Golgi as shown in over expression experiments. These early regulatory steps of Cx36 are expected to be essential for the formation, function, regulation and plasticity of electrical synapses in the developing and mature nervous system.

Alpha coherence is a network signature of cognitive recovery from disorders of consciousness.

Alpha (8-12 Hz) frequency band oscillations are among the most informative features in electroencephalographic (EEG) assessment of patients with disorders of consciousness (DoC). Because interareal alpha synchrony is thought to facilitate long-range communication in healthy brains, coherence measures of resting-state alpha oscillations may provide insights into a patients capacity for higher-order cognition beyond channel-wise estimates of alpha power. In multi-channel EEG, global coherence methods may be used to augment standard spectral analysis methods by both estimating the strength and identifying the structure of coherent oscillatory networks. We performed global coherence analysis in 95 separate clinical EEG recordings (28 healthy controls and 33 patients with acute or chronic DoC, 25 of whom returned for follow-up) collected between two academic medical centers. We found that posterior alpha coherence is associated with recovery of higher-level cognition. We developed a measure of network organization, based on the distance between eigenvectors of the alpha cross-spectral matrix, that detects recovery of posterior alpha networks. In patients who have emerged from a minimally conscious state, we showed that coherence-based alpha networks are reconfigured prior to restoration of alpha power to resemble those seen in healthy controls. This alpha network measure performs well in classifying recovery from DoC (AUC = 0.78) compared to common representations of functional connectivity using the weighted phase lag index (AUC = 0.50 - 0.57). Lastly, we observed that activity within these alpha networks is suppressed during positive responses to task-based EEG command-following paradigms, supporting the potential utility of this biomarker to detect covert cognition. Our findings suggest that restored alpha networks may represent a sensitive early signature of cognitive recovery in patients with DoC. Therefore, network detection methods may augment the utility of EEG assessments for DoC.

7170 Plasticity of the Hypothalamic Tuberoinfundibular Dopaminergic Neuronal Network in Lactating Rats

Abstract Disclosure: P. Papaioannou: None. T. Georgescu: None. D.R. Grattan: None. S. Bunn: None. S. Yip: None. The tuberoinfundibular dopaminergic (TIDA) neurons play a crucial role in regulating prolactin secretion. Their synchronized network activity with slow but highly rhythmic firing pattern is important for dopamine release in rats[1]. While this unique TIDA network activity is vital for prolactin negative feedback in non-lactating conditions, its behaviour during lactation, when prolactin demand is high, remains unknown. Our hypothesis posited that the TIDA neuronal network in lactating rats becomes desynchronized, disrupting the negative feedback loop. To test this, we utilized ex-vivo Ca2+ imaging to simultaneously monitor population-wide TIDA neuron activity in non-lactating (NL; n=13) and lactating (L; n=10) rats injected with a cre-inducible adeno-associated virus (AAV) containing the Ca2+ indicator, GCaMP6s, into their arcuate nucleus. Analysis of neuronal network synchronicity revealed significant desynchronization in the TIDA network during lactation, as indicated by a markedly lower mean correlation coefficient matrix (CM) compared to non-lactating conditions (NL: 0.87±0.02, n= 26 sections vs L: 0.22±0.03, n=29 sections; p<0.001, Student’s t-test). Furthermore, the oscillatory activity patterns of these desynchronized TIDA neurons displayed a significantly lower cell rhythmicity index (RI) in lactating animals compared to non-lactating ones (NL: 0.17±0.01, n=186 cells vs L: 0.70±0.02, n=77 cells; p<0.001, Student’s t-test). Interestingly, within these low rhythmic neurons, some exhibited higher while others showed lower firing frequencies compared to non-lactating TIDA neurons. After 7 days post-weaning (n=4 animals), the TIDA network activity returned to non-lactating behaviour (CM = 0.85 ± 0.04, n=6 sections and RI = 0.17±0.01; n=47 cells). In summary, our findings demonstrate a reversible reconfiguration of the TIDA neuronal networks during lactation, characterized by low rhythmic oscillations and individual unique firing patterns, leading to diminished intercellular synchrony that may impede dopamine release, ultimately facilitating prolactin release to support lactation. Once weaned, the TIDA neuronal network reset to NL state to allow a new reproductive cycle. [1] Lyons, D. J., Horjales-Araujo, E. & Broberger, C. Synchronized network oscillations in rat tuberoinfundibular dopamine neurons: switch to tonic discharge by thyrotropin-releasing hormone. Neuron 65, 217-229, doi:10.1016/j.neuron.2009.12.024 (2010). Presentation: 6/2/2024

On coupled oscillators modeling bio-inspired acoustic sensors: Bifurcation analysis toward tunability enhancement.

Oscillators exhibiting an Andronov-Hopf bifurcation are candidates to mimic the functionality of the cochlea, since the transfer response of these oscillators is compressive and frequency selective. The former implies that small stimuli are amplified and strong stimuli are attenuated, while the latter means that the oscillator only reacts in a (small) frequency band. However, this implies that many oscillators are needed to cover a relevant frequency band. By introducing the notion of tunable characteristic frequencies, i.e., the characteristic frequency can be adjusted by a controllable input, the number of oscillators can be eventually reduced. Subsequently, the tunability enhancement of coupled oscillators is investigated by analyzing the local dynamics of a network of oscillators. For this, necessary conditions for the emergence of Andronov-Hopf bifurcations are determined for networks consisting of two groups, i.e., a group is a network of identical oscillators. By choosing the eigenvalues of the product of the cross-coupling matrix as bifurcation parameters and exploiting the structure of the transfer matrix of this network, the critical points and, thus, the characteristic frequency at this point can be derived. Tunability of the characteristic frequency is then enabled by controlling the asymmetry between the groups of oscillators.

Hidden data recovery using reservoir computing: Adaptive network model and experimental brain signals.

The problem of hidden data recovery is crucial in various scientific and technological fields, particularly in neurophysiology, where experimental data can often be incomplete or corrupted. We investigate the application of reservoir computing (RC) to recover hidden data from both model Kuramoto network system and real neurophysiological signals (EEG). Using an adaptive network of Kuramoto phase oscillators, we generated and analyzed macroscopic signals to understand the efficiency of RC in hidden signal recovery compared to linear regression (LR). Our findings indicate that RC significantly outperforms LR, especially in scenarios with reduced signal information. Furthermore, when applied to real EEG data, RC achieved more accurate signal reconstruction than traditional spline interpolation methods. These results underscore RC's potential for enhancing data recovery in neurophysiological studies, offering a robust solution to improve data integrity and reliability, which is essential for accurate scientific analysis and interpretation.

Spiking activities in small neural networks induced by external forcing.

Neurons in an excitable mode do not show spiking activity and, therefore, do not contribute to information transfer transmission and its processing. However, some external influences, coupling, or time delay can lead to the appearance of oscillations in individual systems or networks. The main goal of this paper is to uncover the connection parameters and parameters of external influences that lead to the arising of spiking behavior in a small network of locally coupled FitzHugh-Nagumo oscillators. In this study, we analyze the dynamics of a small network in the absence and presence of several types of external influences. First, we consider the impact of periodic-pulse exposure generated as a periodic sequence of Gaussian pulses. Second, we show what behavior can be induced by far less regular pulsed influence (Lévy noise) and its special case called white Gaussian noise. For all types of influences, we have identified the appropriate parameters (local coupling strength, intensity, and frequency) that induce spiking activity in the small network.

Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine

Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules. Published by the American Physical Society 2024

A dataset of manually annotated filaments from H-alpha observations.

We present the Manually Annotated GONG Filaments in H-alpha Observations (MAGFiLO v1.0) dataset. This dataset contains 10,244 annotated filaments from 1,593 observations captured by the Global Oscillation Network Group (GONG), spanning the years 2011 through 2022. Each annotation details one filament's segmentation, minimum bounding box, spine, and magnetic field chirality. With a total of over one thousand person-hours of annotation, and a double-blind review process, we ensured high-quality ground-truth data. Our inter-annotator agreement reaches a Kappa score of 0.66. We also verified that the hemispheric preference of filaments as annotated in MAGFiLO aligns with the findings from similar datasets of much smaller sample sizes. MAGFiLO is the first dataset of its size, enabling advanced deep learning models to identify filaments and their features with unprecedented precision. It also provides a testbed for solar physicists interested in large-scale analysis of filaments. In this report, we document the details of the annotation and the post-processing phases that were applied.

Transition among oscillation death, amplitude death, and revival of oscillation in coupled time-delayed systems with diffusivity and common environment

In this paper, we study the transition between different oscillation suppression, revival of oscillation, and oscillatory states in time-delayed chaotic oscillators coupled through simultaneous diffusive and environmental coupling. The present paper, for the first time, reports the occurrence of oscillation death and nontrivial amplitude death states in coupled intrinsic time-delayed systems. Moreover, we explore the revival of the oscillations from these diverse oscillation suppression states. We analyze the stability of the coupled time-delayed system and through extensive numerical investigations, we delineate all the dynamical states in the parameter space. The study is extended to a network of time-delayed oscillators and identical transition scenarios have been obtained. Finally, we support our results in an electronic hardware circuit-based experiment and demonstrate that all the transition scenarios are robust enough in a real world system where the presence of noise, fluctuations, and parameter mismatch are inevitable.

Exploring neural oscillations during speech perception via surrogate gradient spiking neural networks.

Understanding cognitive processes in the brain demands sophisticated models capable of replicating neural dynamics at large scales. We present a physiologically inspired speech recognition architecture, compatible and scalable with deep learning frameworks, and demonstrate that end-to-end gradient descent training leads to the emergence of neural oscillations in the central spiking neural network. Significant cross-frequency couplings, indicative of these oscillations, are measured within and across network layers during speech processing, whereas no such interactions are observed when handling background noise inputs. Furthermore, our findings highlight the crucial inhibitory role of feedback mechanisms, such as spike frequency adaptation and recurrent connections, in regulating and synchronizing neural activity to improve recognition performance. Overall, on top of developing our understanding of synchronization phenomena notably observed in the human auditory pathway, our architecture exhibits dynamic and efficient information processing, with relevance to neuromorphic technology.

Strong coupling yields abrupt synchronization transitions in coupled oscillators

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions—such as synchrony and rotating wave solutions—following perturbation or parameter variation. In the limit of weak coupling, these transitions can be understood in terms of commonly studied phase approximations. As the coupling strength increases, however, predicting the location and criticality of transition, whether continuous or discontinuous, from the phase dynamics may depend on the order of the phase approximation—or a phase description of the network dynamics that neglects amplitudes may become impossible altogether. Here we analyze synchronization transitions and their criticality systematically for varying coupling strength in theory and experiments with coupled electrochemical oscillators. First, we analyze bifurcations analysis of synchrony and splay states in an abstract phase model and discuss conditions under which synchronization transitions with different criticalities are possible. In particular, we show that such conditions can be understood by considering the relative contributions of higher harmonics to the phase dynamics. Second, we illustrate that transitions with different criticality indeed occur in experimental systems. Third, we highlight that the amplitude dynamics observed in the experiments can be captured in a numerical bifurcation analysis of delay-coupled oscillators. Our results showcase that reduced order phase models may miss important features that one would expect in the dynamics of the full system. Published by the American Physical Society 2024

On the influence of input triggering on the dynamics of the Jansen–Rit oscillators network

Our investigation delves into the intricate dynamical properties of a network of coupled neural oscillators, each comprising identical Jansen–Rit masses. The connections between these nodes follow the renowned Watts–Strogatz topology. Every node receives inputs from two primary sources: external and internal inputs derived from its neighboring nodes’ outputs. In this paper, we aim to explore the consequences of changing these two inputs and analyze the results generated. To begin with, we analyzed the model using the mean-field approximation, assuming identical outputs across all nodes due to identical internal and external inputs. Subsequently, we relaxed this assumption, and a more detailed analysis of both states is discussed. As a result of the mean-field approach, we observed that there was no phase transition, despite apparent changes in behavior. However, the relaxation of the mean-field assumption led to the occurrence of the first (discontinuous) and second (continuous) phase transitions. Moreover, our findings indicate that by relaxing the mean-field assumption in our analysis of the single Jansen–Rit neural mass model, theta waves can be generated. Our study provides a comprehensive examination of various observed behaviors by the model, including transitions between synchrony and asynchrony. Additionally, our work highlights the potential contribution of external and internal inputs in studying phase transition and synchronization of neural mass models. Overall, our investigation sheds light on the intricate dynamics of coupled neural oscillators and their sensitivity to varying inputs.

Enhanced network synchronization connectivity following transcranial direct current stimulation (tDCS) in bipolar depression: Effects on EEG oscillations and deep learning-based predictors of clinical remission

AimTo investigate oscillatory networks in bipolar depression, effects of a home-based tDCS treatment protocol, and potential predictors of clinical response. Methods20 participants (14 women) with bipolar disorder, mean age 50.75 ± 10.46 years, in a depressive episode of severe severity (mean Montgomery-Åsberg Rating Scale (MADRS) score 24.60 ± 2.87) received home-based transcranial direct current stimulation (tDCS) treatment for 6 weeks. Clinical remission defined as MADRS score < 10. Resting-state EEG data were acquired at baseline, prior to the start of treatment, and at the end of treatment, using a portable 4-channel EEG device (electrode positions: AF7, AF8, TP9, TP10). EEG band power was extracted for each electrode and phase locking value (PLV) was computed as a functional connectivity measure of phase synchronization. Deep learning was applied to pre-treatment PLV features to examine potential predictors of clinical remission. ResultsFollowing treatment, 11 participants (9 women) attained clinical remission. A significant positive correlation was observed with improvements in depressive symptoms and delta band PLV in frontal and temporoparietal regional channel pairs. An interaction effect in network synchronization was observed in beta band PLV in temporoparietal regions, in which participants who attained clinical remission showed increased synchronization following tDCS treatment, which was decreased in participants who did not achieve clinical remission. Main effects of clinical remission status were observed in several PLV bands: clinical remission following tDCS treatment was associated with increased PLV in frontal and temporal regions and in several frequency bands, including delta, theta, alpha and beta, as compared to participants who did not achieve clinical remission. The highest deep learning prediction accuracy 69.45 % (sensitivity 71.68 %, specificity 66.72 %) was obtained from PLV features combined from theta, beta, and gamma bands. ConclusionstDCS treatment enhances network synchronization, potentially increasing inhibitory control, which underscores improvement in depressive symptoms. Baseline EEG-based measures might aid predicting clinical response.

Activation of D2-like dopamine receptors improves the neuronal network and cognitive function of PPT1KI mice.

Palmitoyl-protein thioesterase 1 (PPT1) is a lysosomal depalmitoylation enzyme that mediates protein posttranslational modifications. Loss-of-function mutation of PPT1 causes a failure of the lysosomal degradation of palmitoylated proteins and results in a congenital disease characterized by progressive neuronal degeneration referred to as infantile neuronal ceroid lipofuscinosis (INCL). A mouse knock-in model of PPT1 (PPT1-KI) was established by introducing the R151X mutation into exon 5 of the PPT1 gene, which exhibited INCL-like pathological lesions. We previously reported that hippocampal γ oscillations were impaired in PPT1 mice. Hippocampal γ oscillations can be enhanced by selective activation of the dopamine D4 receptor (DR4), a dopamine D2-like receptor. In this study, we investigated the changes in DR expression and the effects of dopamine and various DR agonists on neural network activity, cognition and motor function in PPT1KI mice. Cognition and motor defects were evaluated via Y-maze, novel object recognition and rotarod tests. Extracellular field potentials were elicited in hippocampal slices, and neuronal network oscillations in the gamma frequency band (γ oscillations) were induced by perfusion with kainic acid (200 nM). PPT1KI mice displayed progressive impairments in γ oscillations and hippocampus-related memory, as well as abnormal expression profiles of dopamine receptors with preserved expression of DR1 and 3, increased membrane expression of DR4 and decreased DR2 levels. The immunocytochemistry analysis revealed the colocalization of PPT1 with DR4 or DR2 in the soma and large dendrites of both WT and PPT1KI mice. Immunoprecipitation confirmed the interaction between PPT1 and DR4 or DR2. The impaired γ oscillations and cognitive functions were largely restored by the application of exogenous dopamine, the selective DR2 agonist quinpirole or the DR4 agonist A412997. Furthermore, the administration of A412997 (0.5 mg/kg, i.p.) significantly upregulated the activity of CaMKII in the hippocampus of 5-month-old PPT1KI mice. Collectively, these results suggest that the activation of D2-like dopamine receptors improves cognition and network activity in PPT1KI mice and that specific DR subunits may be potential targets for the intervention of neurodegenerative disorders, such as INCL.

Oscillations in an artificial neural network convert competing inputs into a temporal code.

The field of computer vision has long drawn inspiration from neuroscientific studies of the human and non-human primate visual system. The development of convolutional neural networks (CNNs), for example, was informed by the properties of simple and complex cells in early visual cortex. However, the computational relevance of oscillatory dynamics experimentally observed in the visual system are typically not considered in artificial neural networks (ANNs). Computational models of neocortical dynamics, on the other hand, rarely take inspiration from computer vision. Here, we combine methods from computational neuroscience and machine learning to implement multiplexing in a simple ANN using oscillatory dynamics. We first trained the network to classify individually presented letters. Post-training, we added temporal dynamics to the hidden layer, introducing refraction in the hidden units as well as pulsed inhibition mimicking neuronal alpha oscillations. Without these dynamics, the trained network correctly classified individual letters but produced a mixed output when presented with two letters simultaneously, indicating a bottleneck problem. When introducing refraction and oscillatory inhibition, the output nodes corresponding to the two stimuli activate sequentially, ordered along the phase of the inhibitory oscillations. Our model implements the idea that inhibitory oscillations segregate competing inputs in time. The results of our simulations pave the way for applications in deeper network architectures and more complicated machine learning problems.

Aging transitions of multimodal oscillators in multilayer networks

When individual oscillators age and become inactive, the collective dynamics of coupled oscillators is often affected as well. Depending on the fraction of inactive oscillators or cascading failures that percolate from crucial information exchange points, the critical shift toward macroscopic inactivity in coupled oscillator networks is known as the aging transition. Here, we study this phenomenon in two overlayed square lattices that together constitute a multilayer network, whereby one layer is populated with slow Poincaré oscillators and the other with fast Rulkov neurons. Moreover, in this multimodal setup, the excitability of fast oscillators is influenced by the phase of slow oscillators that are gradually inactivated toward the aging transition in the fast layer. Through extensive numerical simulations, we find that the progressive inactivation of oscillators in the slow layer nontrivially affects the collective oscillatory activity and the aging transitions in the fast layer. Most counterintuitively, we show that it is possible for the intensity of oscillatory activity in the fast layer to progressively increase to up to 100%, even when up to 60% of units in the slow oscillatory layer are inactivated. We explain our results with a numerical analysis of collective behavior in individual layers, and we discuss their implications for biological systems. Published by the American Physical Society 2024

Spectral energy transfer on complex networks: a filtering approach

The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier–Stokes equations in which energy “cascades” from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.