Computational model of electrically coupled, intrinsically distinct pacemaker neurons.

PubMed

Soto-Treviño, Cristina; Rabbah, Pascale; Marder, Eve; Nadim, Farzan

2005-07-01

Electrical coupling between neurons with similar properties is often studied. Nonetheless, the role of electrical coupling between neurons with widely different intrinsic properties also occurs, but is less well understood. Inspired by the pacemaker group of the crustacean pyloric network, we developed a multicompartment, conductance-based model of a small network of intrinsically distinct, electrically coupled neurons. In the pyloric network, a small intrinsically bursting neuron, through gap junctions, drives 2 larger, tonically spiking neurons to reliably burst in-phase with it. Each model neuron has 2 compartments, one responsible for spike generation and the other for producing a slow, large-amplitude oscillation. We illustrate how these compartments interact and determine the dynamics of the model neurons. Our model captures the dynamic oscillation range measured from the isolated and coupled biological neurons. At the network level, we explore the range of coupling strengths for which synchronous bursting oscillations are possible. The spatial segregation of ionic currents significantly enhances the ability of the 2 neurons to burst synchronously, and the oscillation range of the model pacemaker network depends not only on the strength of the electrical synapse but also on the identity of the neuron receiving inputs. We also compare the activity of the electrically coupled, distinct neurons with that of a network of coupled identical bursting neurons. For small to moderate coupling strengths, the network of identical elements, when receiving asymmetrical inputs, can have a smaller dynamic range of oscillation than that of its constituent neurons in isolation.

Recovery of slow-5 oscillations in a longitudinal study of ischemic stroke patients.

PubMed

La, C; Nair, V A; Mossahebi, P; Stamm, J; Birn, R; Meyerand, M E; Prabhakaran, V

2016-01-01

Functional networks in resting-state fMRI are identified by characteristics of their intrinsic low-frequency oscillations, more specifically in terms of their synchronicity. With advanced aging and in clinical populations, this synchronicity among functionally linked regions is known to decrease and become disrupted, which may be associated with observed cognitive and behavioral changes. Previous work from our group has revealed that oscillations within the slow-5 frequency range (0.01-0.027 Hz) are particularly susceptible to disruptions in aging and following a stroke. In this study, we characterized longitudinally the changes in the slow-5 oscillations in stroke patients across two different time-points. We followed a group of ischemic stroke patients (n = 20) and another group of healthy older adults (n = 14) over two visits separated by a minimum of three months (average of 9 months). For the stroke patients, one visit occurred in their subacute window (10 days to 6 months after stroke onset), the other took place in their chronic window (> 6 months after stroke). Using a mid-order group ICA method on 10-minutes eyes-closed resting-state fMRI data, we assessed the frequency distributions of a component's representative time-courses for differences in regards to slow-5 spectral power. First, our stroke patients, in their subacute stage, exhibited lower amplitude slow-5 oscillations in comparison to their healthy counterparts. Second, over time in their chronic stage, those same patients showed a recovery of those oscillations, reaching near equivalence to the healthy older adult group. Our results indicate the possibility of an eventual recovery of those initially disrupted network oscillations to a near-normal level, providing potentially a biomarker for stroke recovery of the cortical system. This finding opens new avenues in infra-slow oscillation research and could serve as a useful biomarker in future treatments aimed at recovery.

Frequency specific brain networks in Parkinson's disease and comorbid depression.

PubMed

Qian, Long; Zhang, Yi; Zheng, Li; Fu, Xuemei; Liu, Weiguo; Shang, Yuqing; Zhang, Yaoyu; Xu, Yuanyuan; Liu, Yijun; Zhu, Huaiqiu; Gao, Jia-Hong

2017-02-01

The topological organization underlying the human brain was extensively investigated using resting-state functional magnetic resonance imaging, focusing on a low frequency of signal oscillation from 0.01 to 0.1 Hz. However, the frequency specificities with regard to the topological properties of the brain networks have not been fully revealed. In this study, a novel complementary ensemble empirical mode decomposition (CEEMD) method was used to separate the fMRI time series into five characteristic oscillations with distinct frequencies. Then, the small world properties of brain networks were analyzed for each of these five oscillations in patients (n = 67) with depressed Parkinson's disease (DPD, n = 20) , non-depressed Parkinson's disease (NDPD, n = 47) and healthy controls (HC, n = 46). Compared with HC, the results showed decreased network efficiency in characteristic oscillations from 0.05 to 0.12 Hz and from 0.02 to 0.05 Hz for the DPD and NDPD patients, respectively. Furthermore, compared with HC, the most significant inter-group difference across five brain oscillations was found in the basal ganglia (0.01 to 0.05 Hz) and paralimbic-limbic network (0.02 to 0.22 Hz) for the DPD patients, and in the visual cortex (0.02 to 0.05 Hz) for the NDPD patients. Compared with NDPD, the DPD patients showed reduced efficiency of nodes in the basal ganglia network (0.01 to 0.05 Hz). Our results demonstrated that DPD is characterized by a disrupted topological organization in large-scale brain functional networks. Moreover, the CEEMD analysis suggested a prominent dissociation in the topological organization of brain networks between DPD and NDPD in both space and frequency domains. Our findings indicated that these characteristic oscillatory activities in different functional circuits may contribute to distinct motor and non-motor components of clinical impairments in Parkinson's disease.

Insensitive dependence of delay-induced oscillation death on complex networks

NASA Astrophysics Data System (ADS)

Zou, Wei; Zheng, Xing; Zhan, Meng

2011-06-01

Oscillation death (also called amplitude death), a phenomenon of coupling induced stabilization of an unstable equilibrium, is studied for an arbitrary symmetric complex network with delay-coupled oscillators, and the critical conditions for its linear stability are explicitly obtained. All cases including one oscillator, a pair of oscillators, regular oscillator networks, and complex oscillator networks with delay feedback coupling, can be treated in a unified form. For an arbitrary symmetric network, we find that the corresponding smallest eigenvalue of the Laplacian λN (0 >λN ≥ -1) completely determines the death island, and as λN is located within the insensitive parameter region for nearly all complex networks, the death island keeps nearly the largest and does not sensitively depend on the complex network structures. This insensitivity effect has been tested for many typical complex networks including Watts-Strogatz (WS) and Newman-Watts (NW) small world networks, general scale-free (SF) networks, Erdos-Renyi (ER) random networks, geographical networks, and networks with community structures and is expected to be helpful for our understanding of dynamics on complex networks.

Title: Chimeras in small, globally coupled networks: Experiments and stability analysis

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

Since the initial observation of chimera states, there has been much discussion of the conditions under which these states emerge. The emphasis thus far has mainly been to analyze large networks of coupled oscillators; however, recent studies have begun to focus on the opposite limit: what is the smallest system of coupled oscillators in which chimeras can exist? We experimentally observe chimeras and other partially synchronous patterns in a network of four globally-coupled chaotic opto-electronic oscillators. By examining the equations of motion, we demonstrate that symmetries in the network topology allow a variety of synchronous states to exist, including cluster synchronous states and a chimera state. Using the group theoretical approach recently developed for analyzing cluster synchronization, we show how to derive the variational equations for these synchronous patterns and calculate their linear stability. The stability analysis gives good agreement with our experimental results. Both experiments and simulations suggest that these chimera states often appear in regions of multistability between global, cluster, and desynchronized states.

Distinct collective states due to trade-off between attractive and repulsive couplings

NASA Astrophysics Data System (ADS)

Sathiyadevi, K.; Chandrasekar, V. K.; Senthilkumar, D. V.; Lakshmanan, M.

2018-03-01

We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follow the same transition route in the entire coupling range. Depending upon distinct coupling ranges, the system displays different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power-law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.

Emergence of amplitude death scenario in a network of oscillators under repulsive delay interaction

NASA Astrophysics Data System (ADS)

Bera, Bidesh K.; Hens, Chittaranjan; Ghosh, Dibakar

2016-07-01

We report the existence of amplitude death in a network of identical oscillators under repulsive mean coupling. Amplitude death appears in a globally coupled network of identical oscillators with instantaneous repulsive mean coupling only when the number of oscillators is more than two. We further investigate that, amplitude death may emerge even in two coupled oscillators as well as network of oscillators if we introduce delay time in the repulsive mean coupling. We have analytically derived the region of amplitude death island and find out how strength of delay controls the death regime in two coupled or a large network of coupled oscillators. We have verified our results on network of delayed Mackey-Glass systems where parameters are set in hyperchaotic regime. We have also tested our coupling approach in two paradigmatic limit cycle oscillators: Stuart-Landau and Van der Pol oscillators.

Emergent Oscillations in Networks of Stochastic Spiking Neurons

PubMed Central

van Drongelen, Wim; Cowan, Jack D.

2011-01-01

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework. PMID:21573105

Collective Dynamics in Physical and Social Networks

NASA Astrophysics Data System (ADS)

Isakov, Alexander

We study four systems where individual units come together to display a range of collective behavior. First, we consider a physical system of phase oscillators on a network that expands the Kuramoto model to include oscillator-network interactions and the presence of noise: using a Hebbian-like learning rule, oscillators that synchronize in turn strengthen their connections to each other. We find that the average degree of connectivity strongly affects rates of flipping between aligned and anti-aligned states, and that this result persists to the case of complex networks. Turning to a fully multi-player, multi-strategy evolutionary dynamics model of cooperating bacteria that change who they give resources to and take resources from, we find several regimes that give rise to high levels of collective structure in the resulting networks. In this setting, we also explore the conditions in which an intervention that affects cooperation itself (e.g. "seeding the network with defectors") can lead to wiping out an infection. We find a non-monotonic connection between the percent of disabled cooperation and cure rate, suggesting that in some regimes a limited perturbation can lead to total population collapse. At a larger scale, we study how the locomotor system recovers after amputation in fruit flies. Through experiment and a theoretical model of multi-legged motion controlled by neural oscillators, we find that proprioception plays a role in the ability of flies to control leg forces appropriately to recover from a large initial turning bias induced by the injury. Finally, at the human scale, we consider a social network in a traditional society in Africa to understand how social ties lead to group formation for collective action (stealth raids). We identify critical and distinct roles for both leadership (important for catalyzing a group) and friendship (important for final composition). We conclude with prospects for future work.

Relationships among classes of self-oscillating transistor parallel inverters. [for power conditioning applications

NASA Technical Reports Server (NTRS)

Wilson, T. G.; Lee, F. C. Y.; Burns, W. W., III; Owen, H. A., Jr.

1975-01-01

It recently has been shown in the literature that many dc-to-square-wave parallel inverters which are widely used in power-conditioning applications can be grouped into one of two families. Each family is characterized by an equivalent RLC network. Based on this approach, a classification procedure is presented for self-oscillating parallel inverters which makes evident natural relationships which exist between various inverter configurations. By utilizing concepts from the basic theory of negative resistance oscillators and the principle of duality as applied to nonlinear networks, a chain of relationships is established which enables a methodical transfer of knowledge gained about one family of inverters to any of the other families in the classification array.

Robustness and fragility in coupled oscillator networks under targeted attacks.

PubMed

Yuan, Tianyu; Aihara, Kazuyuki; Tanaka, Gouhei

2017-01-01

The dynamical tolerance of coupled oscillator networks against local failures is studied. As the fraction of failed oscillator nodes gradually increases, the mean oscillation amplitude in the entire network decreases and then suddenly vanishes at a critical fraction as a phase transition. This critical fraction, widely used as a measure of the network robustness, was analytically derived for random failures but not for targeted attacks so far. Here we derive the general formula for the critical fraction, which can be applied to both random failures and targeted attacks. We consider the effects of targeting oscillator nodes based on their degrees. First we deal with coupled identical oscillators with homogeneous edge weights. Then our theory is applied to networks with heterogeneous edge weights and to those with nonidentical oscillators. The analytical results are validated by numerical experiments. Our results reveal the key factors governing the robustness and fragility of oscillator networks.

Creation and perturbation of planar networks of chemical oscillators

PubMed Central

Tompkins, Nathan; Cambria, Matthew Carl; Wang, Adam L.; Heymann, Michael; Fraden, Seth

2015-01-01

Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay. PMID:26117136

Oscillations in interconnected complex networks under intentional attack

NASA Astrophysics Data System (ADS)

Zhang, Wen-Ping; Xia, Yongxiang; Tan, Fei

2016-01-01

Many real-world networks are interconnected with each other. In this paper, we study the traffic dynamics in interconnected complex networks under an intentional attack. We find that with the shortest time delay routing strategy, the traffic dynamics can show the stable state, periodic, quasi-periodic and chaotic oscillations, when the capacity redundancy parameter changes. Moreover, compared with isolated complex networks, oscillations always take place in interconnected networks more easily. Thirdly, in interconnected networks, oscillations are affected strongly by the coupling probability and coupling preference.

Programs & Related Items | CTIO

Science.gov Websites

Telescope (University of Michigan Astronomy) GONG (Global Oscillation Network Group) LCOGT (Las Cumbres Telescopes) SARA (Southeastern Research Association for Research in Astronomy) SSI Airglow WHAM (Wisconsin H

Network properties of interstitial cells of Cajal affect intestinal pacemaker activity and motor patterns, according to a mathematical model of weakly coupled oscillators.

PubMed

Wei, Ruihan; Parsons, Sean P; Huizinga, Jan D

2017-03-01

What is the central question of this study? What are the effects of interstitial cells of Cajal (ICC) network perturbations on intestinal pacemaker activity and motor patterns? What is the main finding and its importance? Two-dimensional modelling of the ICC pacemaker activity according to a phase model of weakly coupled oscillators showed that network properties (coupling strength between oscillators, frequency gradient and frequency noise) strongly influence pacemaker network activity and subsequent motor patterns. The model explains motor patterns observed in physiological conditions and provides predictions and testable hypotheses for effects of ICC loss and frequency modulation on the motor patterns. Interstitial cells of Cajal (ICC) are the pacemaker cells of gut motility and are associated with motility disorders. Interstitial cells of Cajal form a network, but the contributions of its network properties to gut physiology and dysfunction are poorly understood. We modelled an ICC network as a two-dimensional network of weakly coupled oscillators with a frequency gradient and showed changes over time in video and graphical formats. Model parameters were obtained from slow-wave-driven contraction patterns in the mouse intestine and pacemaker slow-wave activities from the cat intestine. Marked changes in propagating oscillation patterns (including changes from propagation to non-propagating) were observed by changing network parameters (coupling strength between oscillators, the frequency gradient and frequency noise), which affected synchronization, propagation velocity and occurrence of dislocations (termination of an oscillation). Complete uncoupling of a circumferential ring of oscillators caused the proximal and distal section to desynchronize, but complete synchronization was maintained with only a single oscillator connecting the sections with high enough coupling. The network of oscillators could withstand loss; even with 40% of oscillators lost randomly within the network, significant synchronization and anterograde propagation remained. A local increase in pacemaker frequency diminished anterograde propagation; the effects were strongly dependent on location, frequency gradient and coupling strength. In summary, the model puts forth the hypothesis that fundamental changes in oscillation patterns (ICC slow-wave activity or circular muscle contractions) can occur through physiological modulation of network properties. Strong evidence is provided to accept the ICC network as a system of coupled oscillators. © 2016 The Authors. Experimental Physiology © 2016 The Physiological Society.

Gamma oscillations in a nonlinear regime: a minimal model approach using heterogeneous integrate-and-fire networks.

PubMed

Bathellier, Brice; Carleton, Alan; Gerstner, Wulfram

2008-12-01

Fast oscillations and in particular gamma-band oscillation (20-80 Hz) are commonly observed during brain function and are at the center of several neural processing theories. In many cases, mathematical analysis of fast oscillations in neural networks has been focused on the transition between irregular and oscillatory firing viewed as an instability of the asynchronous activity. But in fact, brain slice experiments as well as detailed simulations of biological neural networks have produced a large corpus of results concerning the properties of fully developed oscillations that are far from this transition point. We propose here a mathematical approach to deal with nonlinear oscillations in a network of heterogeneous or noisy integrate-and-fire neurons connected by strong inhibition. This approach involves limited mathematical complexity and gives a good sense of the oscillation mechanism, making it an interesting tool to understand fast rhythmic activity in simulated or biological neural networks. A surprising result of our approach is that under some conditions, a change of the strength of inhibition only weakly influences the period of the oscillation. This is in contrast to standard theoretical and experimental models of interneuron network gamma oscillations (ING), where frequency tightly depends on inhibition strength, but it is similar to observations made in some in vitro preparations in the hippocampus and the olfactory bulb and in some detailed network models. This result is explained by the phenomenon of suppression that is known to occur in strongly coupled oscillating inhibitory networks but had not yet been related to the behavior of oscillation frequency.

Coexistence of Stochastic Oscillations and Self-Organized Criticality in a Neuronal Network: Sandpile Model Application.

PubMed

Saeedi, Alireza; Jannesari, Mostafa; Gharibzadeh, Shahriar; Bakouie, Fatemeh

2018-04-01

Self-organized criticality (SOC) and stochastic oscillations (SOs) are two theoretically contradictory phenomena that are suggested to coexist in the brain. Recently it has been shown that an accumulation-release process like sandpile dynamics can generate SOC and SOs simultaneously. We considered the effect of the network structure on this coexistence and showed that the sandpile dynamics on a small-world network can produce two power law regimes along with two groups of SOs-two peaks in the power spectrum of the generated signal simultaneously. We also showed that external stimuli in the sandpile dynamics do not affect the coexistence of SOC and SOs but increase the frequency of SOs, which is consistent with our knowledge of the brain.

Checkpoints couple transcription network oscillator dynamics to cell-cycle progression.

PubMed

Bristow, Sara L; Leman, Adam R; Simmons Kovacs, Laura A; Deckard, Anastasia; Harer, John; Haase, Steven B

2014-09-05

The coupling of cyclin dependent kinases (CDKs) to an intrinsically oscillating network of transcription factors has been proposed to control progression through the cell cycle in budding yeast, Saccharomyces cerevisiae. The transcription network regulates the temporal expression of many genes, including cyclins, and drives cell-cycle progression, in part, by generating successive waves of distinct CDK activities that trigger the ordered program of cell-cycle events. Network oscillations continue autonomously in mutant cells arrested by depletion of CDK activities, suggesting the oscillator can be uncoupled from cell-cycle progression. It is not clear what mechanisms, if any, ensure that the network oscillator is restrained when progression in normal cells is delayed or arrested. A recent proposal suggests CDK acts as a master regulator of cell-cycle processes that have the potential for autonomous oscillatory behavior. Here we find that mitotic CDK is not sufficient for fully inhibiting transcript oscillations in arrested cells. We do find that activation of the DNA replication and spindle assembly checkpoints can fully arrest the network oscillator via overlapping but distinct mechanisms. Further, we demonstrate that the DNA replication checkpoint effector protein, Rad53, acts to arrest a portion of transcript oscillations in addition to its role in halting cell-cycle progression. Our findings indicate that checkpoint mechanisms, likely via phosphorylation of network transcription factors, maintain coupling of the network oscillator to progression during cell-cycle arrest.

Oscillatory network with self-organized dynamical connections for synchronization-based image segmentation.

PubMed

Kuzmina, Margarita; Manykin, Eduard; Surina, Irina

2004-01-01

An oscillatory network of columnar architecture located in 3D spatial lattice was recently designed by the authors as oscillatory model of the brain visual cortex. Single network oscillator is a relaxational neural oscillator with internal dynamics tunable by visual image characteristics - local brightness and elementary bar orientation. It is able to demonstrate either activity state (stable undamped oscillations) or "silence" (quickly damped oscillations). Self-organized nonlocal dynamical connections of oscillators depend on oscillator activity levels and orientations of cortical receptive fields. Network performance consists in transfer into a state of clusterized synchronization. At current stage grey-level image segmentation tasks are carried out by 2D oscillatory network, obtained as a limit version of the source model. Due to supplemented network coupling strength control the 2D reduced network provides synchronization-based image segmentation. New results on segmentation of brightness and texture images presented in the paper demonstrate accurate network performance and informative visualization of segmentation results, inherent in the model.

Altered modulation of gamma oscillation frequency by speed of visual motion in children with autism spectrum disorders.

PubMed

Stroganova, Tatiana A; Butorina, Anna V; Sysoeva, Olga V; Prokofyev, Andrey O; Nikolaeva, Anastasia Yu; Tsetlin, Marina M; Orekhova, Elena V

2015-01-01

Recent studies link autism spectrum disorders (ASD) with an altered balance between excitation and inhibition (E/I balance) in cortical networks. The brain oscillations in high gamma-band (50-120 Hz) are sensitive to the E/I balance and may appear useful biomarkers of certain ASD subtypes. The frequency of gamma oscillations is mediated by level of excitation of the fast-spiking inhibitory basket cells recruited by increasing strength of excitatory input. Therefore, the experimental manipulations affecting gamma frequency may throw light on inhibitory networks dysfunction in ASD. Here, we used magnetoencephalography (MEG) to investigate modulation of visual gamma oscillation frequency by speed of drifting annular gratings (1.2, 3.6, 6.0 °/s) in 21 boys with ASD and 26 typically developing boys aged 7-15 years. Multitaper method was used for analysis of spectra of gamma power change upon stimulus presentation and permutation test was applied for statistical comparisons. We also assessed in our participants visual orientation discrimination thresholds, which are thought to depend on excitability of inhibitory networks in the visual cortex. Although frequency of the oscillatory gamma response increased with increasing velocity of visual motion in both groups of participants, the velocity effect was reduced in a substantial proportion of children with ASD. The range of velocity-related gamma frequency modulation correlated inversely with the ability to discriminate oblique line orientation in the ASD group, while no such correlation has been observed in the group of typically developing participants. Our findings suggest that abnormal velocity-related gamma frequency modulation in ASD may constitute a potential biomarker for reduced excitability of fast-spiking inhibitory neurons in a subset of children with ASD.

Network-induced oscillatory behavior in material flow networks and irregular business cycles

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefen; Witt, Ulrich; Brenner, Thomas

2004-11-01

Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of supply networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most supply networks display damped oscillations, even when their units—and linear chains of these units—behave in a nonoscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a different interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments.

Synchronization in oscillator networks with delayed coupling: a stability criterion.

PubMed

Earl, Matthew G; Strogatz, Steven H

2003-03-01

We derive a stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling. The criterion applies to any network (whether regular or random, low dimensional or high dimensional, directed or undirected) in which each oscillator receives delayed signals from k others, where k is uniform for all oscillators.

Oscillations contribute to memory consolidation by changing criticality and stability in the brain

NASA Astrophysics Data System (ADS)

Wu, Jiaxing; Skilling, Quinton; Ognjanovski, Nicolette; Aton, Sara; Zochowski, Michal

Oscillations are a universal feature of every level of brain dynamics and have been shown to contribute to many brain functions. To investigate the fundamental mechanism underpinning oscillatory activity, the properties of heterogeneous networks are compared in situations with and without oscillations. Our results show that both network criticality and stability are changed in the presence of oscillations. Criticality describes the network state of neuronal avalanche, a cascade of bursts of action potential firing in neural network. Stability measures how stable the spike timing relationship between neuron pairs is over time. Using a detailed spiking model, we found that the branching parameter σ changes relative to oscillation and structural network properties, corresponding to transmission among different critical states. Also, analysis of functional network structures shows that the oscillation helps to stabilize neuronal representation of memory. Further, quantitatively similar results are observed in biological data recorded in vivo. In summary, we have observed that, by regulating the neuronal firing pattern, oscillations affect both criticality and stability properties of the network, and thus contribute to memory formation.

Collective signaling behavior in a networked-oscillator model

NASA Astrophysics Data System (ADS)

Liu, Z.-H.; Hui, P. M.

2007-09-01

We propose and study the collective behavior of a model of networked signaling objects that incorporates several ingredients of real-life systems. These ingredients include spatial inhomogeneity with grouping of signaling objects, signal attenuation with distance, and delayed and impulsive coupling between non-identical signaling objects. Depending on the coupling strength and/or time-delay effect, the model exhibits completely, partially, and locally collective signaling behavior. In particular, a correlated signaling (CS) behavior is observed in which there exist time durations when nearly a constant fraction of oscillators in the system are in the signaling state. These time durations are much longer than the duration of a spike when a single oscillator signals, and they are separated by regular intervals in which nearly all oscillators are silent. Such CS behavior is similar to that observed in biological systems such as fireflies, cicadas, crickets, and frogs. The robustness of the CS behavior against noise is also studied. It is found that properly adjusting the coupling strength and noise level could enhance the correlated behavior.

Global competition and local cooperation in a network of neural oscillators

NASA Astrophysics Data System (ADS)

Terman, David; Wang, DeLiang

An architecture of locally excitatory, globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation. The model for each oscillator corresponds to a standard relaxation oscillator with two time scales. Oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling, and each oscillator also inhibits other oscillators through a common inhibitor. Oscillators are driven to be oscillatory by external stimulation. The network exhibits a mechanism of selective gating, whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern, while preventing the other oscillators from jumping up. We show analytically that with the selective gating mechanism, the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks. Computer simulations demonstrate the model's promising ability for segmenting multiple input patterns in real time. This model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure/ ground segregation.

Rapid cell-free forward engineering of novel genetic ring oscillators

PubMed Central

Niederholtmeyer, Henrike; Sun, Zachary Z; Hori, Yutaka; Yeung, Enoch; Verpoorte, Amanda; Murray, Richard M; Maerkl, Sebastian J

2015-01-01

While complex dynamic biological networks control gene expression in all living organisms, the forward engineering of comparable synthetic networks remains challenging. The current paradigm of characterizing synthetic networks in cells results in lengthy design-build-test cycles, minimal data collection, and poor quantitative characterization. Cell-free systems are appealing alternative environments, but it remains questionable whether biological networks behave similarly in cell-free systems and in cells. We characterized in a cell-free system the ‘repressilator’, a three-node synthetic oscillator. We then engineered novel three, four, and five-gene ring architectures, from characterization of circuit components to rapid analysis of complete networks. When implemented in cells, our novel 3-node networks produced population-wide oscillations and 95% of 5-node oscillator cells oscillated for up to 72 hr. Oscillation periods in cells matched the cell-free system results for all networks tested. An alternate forward engineering paradigm using cell-free systems can thus accurately capture cellular behavior. DOI: http://dx.doi.org/10.7554/eLife.09771.001 PMID:26430766

Heteroclinic switching between chimeras

NASA Astrophysics Data System (ADS)

Bick, Christian

2018-05-01

Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator networks: Higher-order network interactions give rise to metastable chimeras—localized frequency synchrony patterns—which are joined by heteroclinic connections. Moreover, we illuminate the mechanisms that underly the switching dynamics in these experimentally accessible networks.

Metastability and Inter-Band Frequency Modulation in Networks of Oscillating Spiking Neuron Populations

PubMed Central

Bhowmik, David; Shanahan, Murray

2013-01-01

Groups of neurons firing synchronously are hypothesized to underlie many cognitive functions such as attention, associative learning, memory, and sensory selection. Recent theories suggest that transient periods of synchronization and desynchronization provide a mechanism for dynamically integrating and forming coalitions of functionally related neural areas, and that at these times conditions are optimal for information transfer. Oscillating neural populations display a great amount of spectral complexity, with several rhythms temporally coexisting in different structures and interacting with each other. This paper explores inter-band frequency modulation between neural oscillators using models of quadratic integrate-and-fire neurons and Hodgkin-Huxley neurons. We vary the structural connectivity in a network of neural oscillators, assess the spectral complexity, and correlate the inter-band frequency modulation. We contrast this correlation against measures of metastable coalition entropy and synchrony. Our results show that oscillations in different neural populations modulate each other so as to change frequency, and that the interaction of these fluctuating frequencies in the network as a whole is able to drive different neural populations towards episodes of synchrony. Further to this, we locate an area in the connectivity space in which the system directs itself in this way so as to explore a large repertoire of synchronous coalitions. We suggest that such dynamics facilitate versatile exploration, integration, and communication between functionally related neural areas, and thereby supports sophisticated cognitive processing in the brain. PMID:23614040

Locally excitatory, globally inhibitory oscillator networks: theory and application to scene segmentation

NASA Astrophysics Data System (ADS)

Wang, DeLiang; Terman, David

1995-01-01

A novel class of locally excitatory, globally inhibitory oscillator networks (LEGION) is proposed and investigated analytically and by computer simulation. The model of each oscillator corresponds to a standard relaxation oscillator with two time scales. The network exhibits a mechanism of selective gating, whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern, while preventing other oscillators from jumping up. We show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks. Computer simulations demonstrate LEGION's promising ability for segmenting multiple input patterns in real time. This model lays a physical foundation for the oscillatory correlation theory of feature binding, and may provide an effective computational framework for scene segmentation and figure/ground segregation.

On controlling networks of limit-cycle oscillators

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Arenas, Alex

2016-09-01

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

Clusters in nonsmooth oscillator networks

NASA Astrophysics Data System (ADS)

Nicks, Rachel; Chambon, Lucie; Coombes, Stephen

2018-03-01

For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in biology, physics, and engineering that can be described by PWL oscillators.

Dependence of synchronization on frequency mismatch and network configuration in chemo-mechanical oscillators

NASA Astrophysics Data System (ADS)

Kumar, Pawan; Parmananda, P.

2018-04-01

In this paper, synchronization among the mercury beating heart (MBH) oscillators is studied. In the first set of experiments, two MBH oscillators were taken. Frequency of one oscillator is kept constant and that of the other is increased monotonically. These were then coupled using bidirectional and unidirectional coupling mechanisms separately. Dependence of synchronization on the frequency difference between the two oscillators is investigated. For the second set of experiments involving unidirectional coupling, an ensemble of fifteen oscillators was taken and different configurations of these oscillators were considered. These include an all-to-all network and fractionally distributed master slave configurations. The effect of both the extent of coupling and network configuration on synchronization among these oscillators was investigated.

Shunting inhibition improves robustness of gamma oscillations in hippocampal interneuron networks by homogenizing firing rates.

PubMed

Vida, Imre; Bartos, Marlene; Jonas, Peter

2006-01-05

Networks of GABAergic neurons are key elements in the generation of gamma oscillations in the brain. Computational studies suggested that the emergence of coherent oscillations requires hyperpolarizing inhibition. Here, we show that GABA(A) receptor-mediated inhibition in mature interneurons of the hippocampal dentate gyrus is shunting rather than hyperpolarizing. Unexpectedly, when shunting inhibition is incorporated into a structured interneuron network model with fast and strong synapses, coherent oscillations emerge. In comparison to hyperpolarizing inhibition, networks with shunting inhibition show several advantages. First, oscillations are generated with smaller tonic excitatory drive. Second, network frequencies are tuned to the gamma band. Finally, robustness against heterogeneity in the excitatory drive is markedly improved. In single interneurons, shunting inhibition shortens the interspike interval for low levels of drive but prolongs it for high levels, leading to homogenization of neuronal firing rates. Thus, shunting inhibition may confer increased robustness to gamma oscillations in the brain.

Brain rhythms and neural syntax: implications for efficient coding of cognitive content and neuropsychiatric disease.

PubMed Central

Buzsáki, György; Watson, Brendon O.

2012-01-01

The perpetual activity of the cerebral cortex is largely supported by the variety of oscillations the brain generates, spanning a number of frequencies and anatomical locations, as well as behavioral correlates. First, we review findings from animal studies showing that most forms of brain rhythms are inhibition-based, producing rhythmic volleys of inhibitory inputs to principal cell populations, thereby providing alternating temporal windows of relatively reduced and enhanced excitability in neuronal networks. These inhibition-based mechanisms offer natural temporal frames to group or “chunk” neuronal activity into cell assemblies and sequences of assemblies, with more complex multi-oscillation interactions creating syntactical rules for the effective exchange of information among cortical networks. We then review recent studies in human psychiatric patients demonstrating a variety alterations in neural oscillations across all major psychiatric diseases, and suggest possible future research directions and treatment approaches based on the fundamental properties of brain rhythms. PMID:23393413

Reviving oscillations in coupled nonlinear oscillators.

PubMed

Zou, Wei; Senthilkumar, D V; Zhan, Meng; Kurths, Jürgen

2013-07-05

By introducing a processing delay in the coupling, we find that it can effectively annihilate the quenching of oscillation, amplitude death (AD), in a network of coupled oscillators by switching the stability of AD. It revives the oscillation in the AD regime to retain sustained rhythmic functioning of the networks, which is in sharp contrast to the propagation delay with the tendency to induce AD. This processing delay-induced phenomenon occurs both with and without the propagation delay. Further this effect is rather general from two coupled to networks of oscillators in all known scenarios that can exhibit AD, and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

Dynamics of a network of phase oscillators with plastic couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nekorkin, V. I.; Kasatkin, D. V.; Moscow Institute of Physics and Technology

The processes of synchronization and phase cluster formation are investigated in a complex network of dynamically coupled phase oscillators. Coupling weights evolve dynamically depending on the phase relations between the oscillators. It is shown that the network exhibits several types of behavior: the globally synchronized state, two-cluster and multi-cluster states, different synchronous states with a fixed phase relationship between the oscillators and chaotic desynchronized state.

Load capacity improvements in nucleic acid based systems using partially open feedback control.

PubMed

Kulkarni, Vishwesh; Kharisov, Evgeny; Hovakimyan, Naira; Kim, Jongmin

2014-08-15

Synthetic biology is facilitating novel methods and components to build in vivo and in vitro circuits to better understand and re-engineer biological networks. Recently, Kim and Winfree have synthesized a remarkably elegant network of transcriptional oscillators in vitro using a modular architecture of synthetic gene analogues and a few enzymes that, in turn, could be used to drive a variety of downstream circuits and nanodevices. However, these oscillators are sensitive to initial conditions and downstream load processes. Furthermore, the oscillations are not sustained since the inherently closed design suffers from enzyme deactivation, NTP fuel exhaustion, and waste product build up. In this paper, we show that a partially open architecture in which an [Symbol: see text]1 adaptive controller, implemented inside an in silico computer that resides outside the wet-lab apparatus, can ensure sustained tunable oscillations in two specific designs of the Kim-Winfree oscillator networks. We consider two broad cases of operation: (1) the oscillator network operating in isolation and (2) the oscillator network driving a DNA tweezer subject to a variable load. In both scenarios, our simulation results show a significant improvement in the tunability and robustness of these oscillator networks. Our approach can be easily adopted to improve the loading capacity of a wide range of synthetic biological devices.

Synchronization and spatiotemporal patterns in coupled phase oscillators on a weighted planar network

NASA Astrophysics Data System (ADS)

Kagawa, Yuki; Takamatsu, Atsuko

2009-04-01

To reveal the relation between network structures found in two-dimensional biological systems, such as protoplasmic tube networks in the plasmodium of true slime mold, and spatiotemporal oscillation patterns emerged on the networks, we constructed coupled phase oscillators on weighted planar networks and investigated their dynamics. Results showed that the distribution of edge weights in the networks strongly affects (i) the propensity for global synchronization and (ii) emerging ratios of oscillation patterns, such as traveling and concentric waves, even if the total weight is fixed. In-phase locking, traveling wave, and concentric wave patterns were, respectively, observed most frequently in uniformly weighted, center weighted treelike, and periphery weighted ring-shaped networks. Controlling the global spatiotemporal patterns with the weight distribution given by the local weighting (coupling) rules might be useful in biological network systems including the plasmodial networks and neural networks in the brain.

Complex Dynamics of Delay-Coupled Neural Networks

NASA Astrophysics Data System (ADS)

Mao, Xiaochen

2016-09-01

This paper reveals the complicated dynamics of a delay-coupled system that consists of a pair of sub-networks and multiple bidirectional couplings. Time delays are introduced into the internal connections and network-couplings, respectively. The stability and instability of the coupled network are discussed. The sufficient conditions for the existence of oscillations are given. Case studies of numerical simulations are given to validate the analytical results. Interesting and complicated neuronal activities are observed numerically, such as rest states, periodic oscillations, multiple switches of rest states and oscillations, and the coexistence of different types of oscillations.

Synchronization in complex oscillator networks and smart grids.

PubMed

Dörfler, Florian; Chertkov, Michael; Bullo, Francesco

2013-02-05

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.

Generation of oscillating gene regulatory network motifs

NASA Astrophysics Data System (ADS)

van Dorp, M.; Lannoo, B.; Carlon, E.

2013-07-01

Using an improved version of an evolutionary algorithm originally proposed by François and Hakim [Proc. Natl. Acad. Sci. USAPNASA60027-842410.1073/pnas.0304532101 101, 580 (2004)], we generated small gene regulatory networks in which the concentration of a target protein oscillates in time. These networks may serve as candidates for oscillatory modules to be found in larger regulatory networks and protein interaction networks. The algorithm was run for 105 times to produce a large set of oscillating modules, which were systematically classified and analyzed. The robustness of the oscillations against variations of the kinetic rates was also determined, to filter out the least robust cases. Furthermore, we show that the set of evolved networks can serve as a database of models whose behavior can be compared to experimentally observed oscillations. The algorithm found three smallest (core) oscillators in which nonlinearities and number of components are minimal. Two of those are two-gene modules: the mixed feedback loop, already discussed in the literature, and an autorepressed gene coupled with a heterodimer. The third one is a single gene module which is competitively regulated by a monomer and a dimer. The evolutionary algorithm also generated larger oscillating networks, which are in part extensions of the three core modules and in part genuinely new modules. The latter includes oscillators which do not rely on feedback induced by transcription factors, but are purely of post-transcriptional type. Analysis of post-transcriptional mechanisms of oscillation may provide useful information for circadian clock research, as recent experiments showed that circadian rhythms are maintained even in the absence of transcription.

Interactions between neural networks: a mechanism for tuning chaos and oscillations.

PubMed

Wang, Lipo

2007-06-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.

Interaction of oscillations, and their suppression via deep brain stimulation, in a model of the cortico-basal ganglia network.

PubMed

Kang, Guiyeom; Lowery, Madeleine M

2013-03-01

Growing evidence suggests that synchronized neural oscillations in the cortico-basal ganglia network may play a critical role in the pathophysiology of Parkinson's disease. In this study, a new model of the closed loop network is used to explore the generation and interaction of network oscillations and their suppression through deep brain stimulation (DBS). Under simulated dopamine depletion conditions, increased gain through the hyperdirect pathway resulted in the interaction of neural oscillations at different frequencies in the cortex and subthalamic nucleus (STN), leading to the emergence of synchronized oscillations at a new intermediate frequency. Further increases in synaptic gain resulted in the cortex driving synchronous oscillatory activity throughout the network. When DBS was added to the model a progressive reduction in STN power at the tremor and beta frequencies was observed as the frequency of stimulation was increased, with resonance effects occurring for low frequency DBS (40 Hz) in agreement with experimental observations. The results provide new insights into the mechanisms by which synchronous oscillations can arise within the network and how DBS may suppress unwanted oscillatory activity.

Interactions between neural networks: a mechanism for tuning chaos and oscillations

PubMed Central

2007-01-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability. PMID:19003511

Local complexity predicts global synchronization of hierarchically networked oscillators

NASA Astrophysics Data System (ADS)

Xu, Jin; Park, Dong-Ho; Jo, Junghyo

2017-07-01

We study the global synchronization of hierarchically-organized Stuart-Landau oscillators, where each subsystem consists of three oscillators with activity-dependent couplings. We considered all possible coupling signs between the three oscillators, and found that they can generate different numbers of phase attractors depending on the network motif. Here, the subsystems are coupled through mean activities of total oscillators. Under weak inter-subsystem couplings, we demonstrate that the synchronization between subsystems is highly correlated with the number of attractors in uncoupled subsystems. Among the network motifs, perfect anti-symmetric ones are unique to generate both single and multiple attractors depending on the activities of oscillators. The flexible local complexity can make global synchronization controllable.

Real Time Distributed Embedded Oscillator Operating Frequency Monitoring

NASA Technical Reports Server (NTRS)

Pollock, Julie (Inventor); Oliver, Brett D. (Inventor); Brickner, Christopher (Inventor)

2013-01-01

A method for clock monitoring in a network is provided. The method comprises receiving a first network clock signal at a network device and comparing the first network clock signal to a local clock signal from a primary oscillator coupled to the network device.

Coordinated Speed Oscillations in Schooling Killifish Enrich Social Communication

NASA Astrophysics Data System (ADS)

Swain, Daniel T.; Couzin, Iain D.; Leonard, Naomi Ehrich

2015-10-01

We examine the spatial dynamics of individuals in small schools of banded killifish ( Fundulus diaphanus) that exhibit rhythmic, oscillating speed, typically with sustained, coordinated, out-of-phase speed oscillations as they move around a shallow water tank. We show that the relative motion among the fish yields a periodically time-varying network of social interactions that enriches visually driven social communication. The oscillations lead to the regular making and breaking of occlusions, which we term "switching." We show that the rate of convergence to consensus (biologically, the capacity for individuals in groups to achieve effective coordinated motion) governed by the switching outperforms static alternatives, and performs as well as the less practical case of every fish sensing every other fish. We show further that the oscillations in speed yield oscillations in relative bearing between fish over a range that includes the angles previously predicted to be optimal for a fish to detect changes in heading and speed of its neighbors. To investigate systematically, we derive and analyze a dynamic model of interacting agents that move with oscillatory speed. We show that coordinated circular motion of the school leads to systematic cycling of spatial ordering of agents and possibilities for enriched spatial density of measurements of the external environment. Our results highlight the potential benefits of dynamic communication topologies in collective animal behavior, and suggest new, useful control laws for the distributed coordination of mobile robotic networks.

VOLTAGE-CONTROLLED TRANSISTOR OSCILLATOR

DOEpatents

Scheele, P.F.

1958-09-16

This patent relates to transistor oscillators and in particular to those transistor oscillators whose frequencies vary according to controlling voltages. A principal feature of the disclosed transistor oscillator circuit resides in the temperature compensation of the frequency modulating stage by the use of a resistorthermistor network. The resistor-thermistor network components are selected to have the network resistance, which is in series with the modulator transistor emitter circuit, vary with temperature to compensate for variation in the parameters of the transistor due to temperature change.

Dynamics of the solar chromosphere. I - Long-period network oscillations

NASA Technical Reports Server (NTRS)

Lites, B. W.; Rutten, R. J.; Kalkofen, W.

1993-01-01

We analyze differences in solar oscillations between the chromospheric network and internetwork regions from a 1 hr sequence of spectrograms of a quiet region near disk center. The spectrograms contain Ca II H, Ca I 422.7 nm, and various Fe I blends in the Ca II H wing. They permit vertical tracing of oscillations throughout the photosphere and into the low chromosphere. We find that the rms amplitude of Ca II H line center Doppler fluctuations is about 1.5 km/s for both network and internetwork, but that the character of the oscillations differs markedly in these two regions. Within internetwork areas the chromospheric velocity power spectrum is dominated by oscillations with frequencies at and above the acoustic cutoff frequency. They are well correlated with the oscillations in the underlying photosphere, but they are much reduced in the network. In contrast, the network Ca II H line center velocity and intensity power spectra are dominated by low-frequency oscillations with periods of 5-20 min. Their signature is much clearer in our Ca II H line center measurements than in previously used diagnostics which are contaminated by signals from deeper layers. We find that these long-period oscillations are not correlated with underlying photospheric disturbances, and we discuss their nature.

GONG Catalog of Solar Filament Oscillations Near Solar Maximum

NASA Astrophysics Data System (ADS)

Luna, M.; Karpen, J.; Ballester, J. L.; Muglach, K.; Terradas, J.; Kucera, T.; Gilbert, H.

2018-06-01

We have cataloged 196 filament oscillations from the Global Oscillation Network Group Hα network data during several months near the maximum of solar cycle 24 (2014 January–June). Selected examples from the catalog are described in detail, along with our statistical analyses of all events. Oscillations were classified according to their velocity amplitude: 106 small-amplitude oscillations (SAOs), with velocities <10 {km} {{{s}}}-1, and 90 large-amplitude oscillations (LAOs), with velocities >10 {km} {{{s}}}-1. Both SAOs and LAOs are common, with one event of each class every two days on the visible side of the Sun. For nearly half of the events, we identified their apparent trigger. The period distribution has a mean value of 58 ± 15 minutes for both types of oscillations. The distribution of the damping time per period peaks at τ/P = 1.75 and 1.25 for SAOs and LAOs, respectively. We confirmed that LAO damping rates depend nonlinearly on the oscillation velocity. The angle between the direction of motion and the filament spine has a distribution centered at 27° for all filament types. This angle agrees with the observed direction of filament-channel magnetic fields, indicating that most of the cataloged events are longitudinal (i.e., undergo field-aligned motions). We applied seismology to determine the average radius of curvature in the magnetic dips, R ≈ 89 Mm, and the average minimum magnetic field strength, B ≈ 16 G. The catalog is available to the community online and is intended to be expanded to cover at least 1 solar cycle.

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

PubMed Central

Lowet, Eric; Roberts, Mark J.; Bonizzi, Pietro; Karel, Joël; De Weerd, Peter

2016-01-01

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks. PMID:26745498

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Zhiwei; Sun, Yong; University of the Chinese Academy of Sciences, Beijing 100049

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weakmore » coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.« less

On influences of global and local cues on the rate of synchronization of oscillator networks

PubMed Central

Wang, Yongqiang; Doyle, Francis J.

2011-01-01

Synchronization of connected oscillator networks under global and local cues is ubiquitous in both science and engineering. Over the last few decades, enormous attention has been paid to study synchronization conditions of connected oscillators in chemistry, physics, mechanics, and particularly in biology. However, the influences of global and local cues on the rate of synchronization have not been fully studied. It is widespread that synchronization is achieved in the simultaneous presence of both global and local cues, such as intercellular coupling signals and external entrainment signals in terms of biological oscillators, and inter-neighbor coupling signals between follower nodes and central guiding signals in terms of groups of mobile autonomous agents. We prove in this paper that strength of the global cue is the only determinant of the rate of synchronization. More specifically, we prove that a stronger global cue means a faster rate of synchronization whereas a stronger local cue does not necessarily make the synchronization rate faster. Our results not only apply to the noise free case, but also apply to the case that the oscillator natural frequencies are subject to white noise. The analysis does not require the interplay to be symmetric or balanced. Simulation results are given to illustrate the proposed results. PMID:21607201

Interplay of intrinsic and synaptic conductances in the generation of high-frequency oscillations in interneuronal networks with irregular spiking.

PubMed

Baroni, Fabiano; Burkitt, Anthony N; Grayden, David B

2014-05-01

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.

Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking

PubMed Central

Baroni, Fabiano; Burkitt, Anthony N.; Grayden, David B.

2014-01-01

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks. PMID:24784237

How heart rate variability affects emotion regulation brain networks.

PubMed

Mather, Mara; Thayer, Julian

2018-02-01

Individuals with high heart rate variability tend to have better emotional well-being than those with low heart rate variability, but the mechanisms of this association are not yet clear. In this paper, we propose the novel hypothesis that by inducing oscillatory activity in the brain, high amplitude oscillations in heart rate enhance functional connectivity in brain networks associated with emotion regulation. Recent studies using daily biofeedback sessions to increase the amplitude of heart rate oscillations suggest that high amplitude physiological oscillations have a causal impact on emotional well-being. Because blood flow timing helps determine brain network structure and function, slow oscillations in heart rate have the potential to strengthen brain network dynamics, especially in medial prefrontal regulatory regions that are particularly sensitive to physiological oscillations.

Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

NASA Astrophysics Data System (ADS)

Leiser, Randolph J.; Rotstein, Horacio G.

2017-08-01

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

Network synchronization in hippocampal neurons.

PubMed

Penn, Yaron; Segal, Menahem; Moses, Elisha

2016-03-22

Oscillatory activity is widespread in dynamic neuronal networks. The main paradigm for the origin of periodicity consists of specialized pacemaking elements that synchronize and drive the rest of the network; however, other models exist. Here, we studied the spontaneous emergence of synchronized periodic bursting in a network of cultured dissociated neurons from rat hippocampus and cortex. Surprisingly, about 60% of all active neurons were self-sustained oscillators when disconnected, each with its own natural frequency. The individual neuron's tendency to oscillate and the corresponding oscillation frequency are controlled by its excitability. The single neuron intrinsic oscillations were blocked by riluzole, and are thus dependent on persistent sodium leak currents. Upon a gradual retrieval of connectivity, the synchrony evolves: Loose synchrony appears already at weak connectivity, with the oscillators converging to one common oscillation frequency, yet shifted in phase across the population. Further strengthening of the connectivity causes a reduction in the mean phase shifts until zero-lag is achieved, manifested by synchronous periodic network bursts. Interestingly, the frequency of network bursting matches the average of the intrinsic frequencies. Overall, the network behaves like other universal systems, where order emerges spontaneously by entrainment of independent rhythmic units. Although simplified with respect to circuitry in the brain, our results attribute a basic functional role for intrinsic single neuron excitability mechanisms in driving the network's activity and dynamics, contributing to our understanding of developing neural circuits.

Transition from amplitude to oscillation death in a network of oscillators

NASA Astrophysics Data System (ADS)

Nandan, Mauparna; Hens, C. R.; Pal, Pinaki; Dana, Syamal K.

2014-12-01

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.

Transition from amplitude to oscillation death in a network of oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandan, Mauparna; Department of Mathematics, National Institute of Technology, Durgapur 713209; Hens, C. R.

2014-12-01

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determinemore » the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.« less

Spatio-temporal specialization of GABAergic septo-hippocampal neurons for rhythmic network activity.

PubMed

Unal, Gunes; Crump, Michael G; Viney, Tim J; Éltes, Tímea; Katona, Linda; Klausberger, Thomas; Somogyi, Peter

2018-03-03

Medial septal GABAergic neurons of the basal forebrain innervate the hippocampus and related cortical areas, contributing to the coordination of network activity, such as theta oscillations and sharp wave-ripple events, via a preferential innervation of GABAergic interneurons. Individual medial septal neurons display diverse activity patterns, which may be related to their termination in different cortical areas and/or to the different types of innervated interneurons. To test these hypotheses, we extracellularly recorded and juxtacellularly labeled single medial septal neurons in anesthetized rats in vivo during hippocampal theta and ripple oscillations, traced their axons to distant cortical target areas, and analyzed their postsynaptic interneurons. Medial septal GABAergic neurons exhibiting different hippocampal theta phase preferences and/or sharp wave-ripple related activity terminated in restricted hippocampal regions, and selectively targeted a limited number of interneuron types, as established on the basis of molecular markers. We demonstrate the preferential innervation of bistratified cells in CA1 and of basket cells in CA3 by individual axons. One group of septal neurons was suppressed during sharp wave-ripples, maintained their firing rate across theta and non-theta network states and mainly fired along the descending phase of CA1 theta oscillations. In contrast, neurons that were active during sharp wave-ripples increased their firing significantly during "theta" compared to "non-theta" states, with most firing during the ascending phase of theta oscillations. These results demonstrate that specialized septal GABAergic neurons contribute to the coordination of network activity through parallel, target area- and cell type-selective projections to the hippocampus.

One central oscillatory drive is compatible with experimental motor unit behaviour in essential and Parkinsonian tremor

NASA Astrophysics Data System (ADS)

Dideriksen, Jakob L.; Gallego, Juan A.; Holobar, Ales; Rocon, Eduardo; Pons, Jose L.; Farina, Dario

2015-08-01

Objective. Pathological tremors are symptomatic to several neurological disorders that are difficult to differentiate and the way by which central oscillatory networks entrain tremorogenic contractions is unknown. We considered the alternative hypotheses that tremor arises from one oscillator (at the tremor frequency) or, as suggested by recent findings from the superimposition of two separate inputs (at the tremor frequency and twice that frequency). Approach. Assuming one central oscillatory network we estimated analytically the relative amplitude of the harmonics of the tremor frequency in the motor neuron output for different temporal behaviors of the oscillator. Next, we analyzed the bias in the relative harmonics amplitude introduced by superimposing oscillations at twice the tremor frequency. These findings were validated using experimental measurements of wrist angular velocity and surface electromyography (EMG) from 22 patients (11 essential tremor, 11 Parkinson’s disease). The ensemble motor unit action potential trains identified from the EMG represented the neural drive to the muscles. Main results. The analytical results showed that the relative power of the tremor harmonics in the analytical models of the neural drive was determined by the variability and duration of the tremor bursts and the presence of the second oscillator biased this power towards higher values. The experimental findings accurately matched the analytical model assuming one oscillator, indicating a negligible functional role of secondary oscillatory inputs. Furthermore, a significant difference in the relative power of harmonics in the neural drive was found across the patient groups, suggesting a diagnostic value of this measure (classification accuracy: 86%). This diagnostic power decreased substantially when estimated from limb acceleration or the EMG. Signficance. The results indicate that the neural drive in pathological tremor is compatible with one central network providing neural oscillations at the tremor frequency. Moreover, the regularity of this neural oscillation varies across tremor pathologies, making the relative amplitude of tremor harmonics a potential biomarker for diagnostic use.

One central oscillatory drive is compatible with experimental motor unit behaviour in essential and Parkinsonian tremor.

PubMed

Dideriksen, Jakob L; Gallego, Juan A; Holobar, Ales; Rocon, Eduardo; Pons, Jose L; Farina, Dario

2015-08-01

Pathological tremors are symptomatic to several neurological disorders that are difficult to differentiate and the way by which central oscillatory networks entrain tremorogenic contractions is unknown. We considered the alternative hypotheses that tremor arises from one oscillator (at the tremor frequency) or, as suggested by recent findings from the superimposition of two separate inputs (at the tremor frequency and twice that frequency). Assuming one central oscillatory network we estimated analytically the relative amplitude of the harmonics of the tremor frequency in the motor neuron output for different temporal behaviors of the oscillator. Next, we analyzed the bias in the relative harmonics amplitude introduced by superimposing oscillations at twice the tremor frequency. These findings were validated using experimental measurements of wrist angular velocity and surface electromyography (EMG) from 22 patients (11 essential tremor, 11 Parkinson's disease). The ensemble motor unit action potential trains identified from the EMG represented the neural drive to the muscles. The analytical results showed that the relative power of the tremor harmonics in the analytical models of the neural drive was determined by the variability and duration of the tremor bursts and the presence of the second oscillator biased this power towards higher values. The experimental findings accurately matched the analytical model assuming one oscillator, indicating a negligible functional role of secondary oscillatory inputs. Furthermore, a significant difference in the relative power of harmonics in the neural drive was found across the patient groups, suggesting a diagnostic value of this measure (classification accuracy: 86%). This diagnostic power decreased substantially when estimated from limb acceleration or the EMG. SIGNFICANCE: The results indicate that the neural drive in pathological tremor is compatible with one central network providing neural oscillations at the tremor frequency. Moreover, the regularity of this neural oscillation varies across tremor pathologies, making the relative amplitude of tremor harmonics a potential biomarker for diagnostic use.

Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks

PubMed Central

Solanka, Lukas; van Rossum, Mark CW; Nolan, Matthew F

2015-01-01

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength. DOI: http://dx.doi.org/10.7554/eLife.06444.001 PMID:26146940

Oscillations emerging from noise-driven steady state in networks with electrical synapses and subthreshold resonance

PubMed Central

Tchumatchenko, Tatjana; Clopath, Claudia

2014-01-01

Oscillations play a critical role in cognitive phenomena and have been observed in many brain regions. Experimental evidence indicates that classes of neurons exhibit properties that could promote oscillations, such as subthreshold resonance and electrical gap junctions. Typically, these two properties are studied separately but it is not clear which is the dominant determinant of global network rhythms. Our aim is to provide an analytical understanding of how these two effects destabilize the fluctuation-driven state, in which neurons fire irregularly, and lead to an emergence of global synchronous oscillations. Here we show how the oscillation frequency is shaped by single neuron resonance, electrical and chemical synapses.The presence of both gap junctions and subthreshold resonance are necessary for the emergence of oscillations. Our results are in agreement with several experimental observations such as network responses to oscillatory inputs and offer a much-needed conceptual link connecting a collection of disparate effects observed in networks. PMID:25405458

Spatiotemporal dynamics in excitable homogeneous random networks composed of periodically self-sustained oscillation.

PubMed

Qian, Yu; Liu, Fei; Yang, Keli; Zhang, Ge; Yao, Chenggui; Ma, Jun

2017-09-19

The collective behaviors of networks are often dependent on the network connections and bifurcation parameters, also the local kinetics plays an important role in contributing the consensus of coupled oscillators. In this paper, we systematically investigate the influence of network structures and system parameters on the spatiotemporal dynamics in excitable homogeneous random networks (EHRNs) composed of periodically self-sustained oscillation (PSO). By using the dominant phase-advanced driving (DPAD) method, the one-dimensional (1D) Winfree loop is exposed as the oscillation source supporting the PSO, and the accurate wave propagation pathways from the oscillation source to the whole network are uncovered. Then, an order parameter is introduced to quantitatively study the influence of network structures and system parameters on the spatiotemporal dynamics of PSO in EHRNs. Distinct results induced by the network structures and the system parameters are observed. Importantly, the corresponding mechanisms are revealed. PSO influenced by the network structures are induced not only by the change of average path length (APL) of network, but also by the invasion of 1D Winfree loop from the outside linking nodes. Moreover, PSO influenced by the system parameters are determined by the excitation threshold and the minimum 1D Winfree loop. Finally, we confirmed that the excitation threshold and the minimum 1D Winfree loop determined PSO will degenerate as the system size is expanded.

Endogenous Cortical Oscillations Constrain Neuromodulation by Weak Electric Fields

PubMed Central

Schmidt, Stephen L.; Iyengar, Apoorva K.; Foulser, A. Alban; Boyle, Michael R.; Fröhlich, Flavio

2014-01-01

Background Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation modality that may modulate cognition by enhancing endogenous neocortical oscillations with the application of sine-wave electric fields. Yet, the role of endogenous network activity in enabling and shaping the effects of tACS has remained unclear. Objective We combined optogenetic stimulation and multichannel slice electrophysiology to elucidate how the effect of weak sine-wave electric field depends on the ongoing cortical oscillatory activity. We hypothesized that the structure of the response to stimulation depended on matching the stimulation frequency to the endogenous cortical oscillation. Methods We studied the effect of weak sine-wave electric fields on oscillatory activity in mouse neocortical slices. Optogenetic control of the network activity enabled the generation of in vivo like cortical oscillations for studying the temporal relationship between network activity and sine-wave electric field stimulation. Results Weak electric fields enhanced endogenous oscillations but failed to induce a frequency shift of the ongoing oscillation for stimulation frequencies that were not matched to the endogenous oscillation. This constraint on the effect of electric field stimulation imposed by endogenous network dynamics was limited to the case of weak electric fields targeting in vivo-like network dynamics. Together, these results suggest that the key mechanism of tACS may be enhancing but not overriding of intrinsic network dynamics. Conclusion Our results contribute to understanding the inconsistent tACS results from human studies and propose that stimulation precisely adjusted in frequency to the endogenous oscillations is key to rational design of non-invasive brain stimulation paradigms. PMID:25129402

Control of coupled oscillator networks with application to microgrid technologies.

PubMed

Skardal, Per Sebastian; Arenas, Alex

2015-08-01

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.

Control of coupled oscillator networks with application to microgrid technologies

PubMed Central

Skardal, Per Sebastian; Arenas, Alex

2015-01-01

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions—a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself. PMID:26601231

Control of coupled oscillator networks with application to microgrid technologies

NASA Astrophysics Data System (ADS)

Arenas, Alex

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn- chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.

Explosive synchronization transitions in complex neural networks.

PubMed

Chen, Hanshuang; He, Gang; Huang, Feng; Shen, Chuansheng; Hou, Zhonghuai

2013-09-01

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

Explosive synchronization transitions in complex neural networks

NASA Astrophysics Data System (ADS)

Chen, Hanshuang; He, Gang; Huang, Feng; Shen, Chuansheng; Hou, Zhonghuai

2013-09-01

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

NASA Astrophysics Data System (ADS)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

Reconfiguration of a Multi-oscillator Network by Light in the Drosophila Circadian Clock.

PubMed

Chatterjee, Abhishek; Lamaze, Angélique; De, Joydeep; Mena, Wilson; Chélot, Elisabeth; Martin, Béatrice; Hardin, Paul; Kadener, Sebastian; Emery, Patrick; Rouyer, François

2018-06-07

The brain clock that drives circadian rhythms of locomotor activity relies on a multi-oscillator neuronal network. In addition to synchronizing the clock with day-night cycles, light also reformats the clock-driven daily activity pattern. How changes in lighting conditions modify the contribution of the different oscillators to remodel the daily activity pattern remains largely unknown. Our data in Drosophila indicate that light readjusts the interactions between oscillators through two different modes. We show that a morning s-LNv > DN1p circuit works in series, whereas two parallel evening circuits are contributed by LNds and other DN1ps. Based on the photic context, the master pacemaker in the s-LNv neurons swaps its enslaved partner-oscillator-LNd in the presence of light or DN1p in the absence of light-to always link up with the most influential phase-determining oscillator. When exposure to light further increases, the light-activated LNd pacemaker becomes independent by decoupling from the s-LNvs. The calibration of coupling by light is layered on a clock-independent network interaction wherein light upregulates the expression of the PDF neuropeptide in the s-LNvs, which inhibits the behavioral output of the DN1p evening oscillator. Thus, light modifies inter-oscillator coupling and clock-independent output-gating to achieve flexibility in the network. It is likely that the light-induced changes in the Drosophila brain circadian network could reveal general principles of adapting to varying environmental cues in any neuronal multi-oscillator system. Copyright © 2018 Elsevier Ltd. All rights reserved.

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks.

PubMed

Cybulski, Olgierd; Jakiela, Slawomir; Garstecki, Piotr

2015-12-01

The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies that assumed a constant cross section of the channels along their length have shown that the sequence of droplets entering the left (L) or right (R) arm of the loop can present either a uniform distribution of choices (e.g., RLRLRL...) or long sequences of repeated choices (RRR...LLL), with all the intermediate permutations being dynamically equivalent and virtually equally probable to be observed. We use experiments and computer simulations to show that even small variation of the cross section along channels completely shifts the dynamics either into the strong preference for highly grouped patterns (RRR...LLL) that generate system-size oscillations in flow or just the opposite-to patterns that distribute the droplets homogeneously between the arms of the loop. We also show the importance of noise in the process of self-organization of the spatiotemporal patterns of droplets. Our results provide guidelines for rational design of systems that reproducibly produce either grouped or homogeneous sequences of droplets flowing in microfluidic networks.

Numerical and analytical investigation of the chimera state excitation conditions in the Kuramoto-Sakaguchi oscillator network

NASA Astrophysics Data System (ADS)

Frolov, Nikita S.; Goremyko, Mikhail V.; Makarov, Vladimir V.; Maksimenko, Vladimir A.; Hramov, Alexander E.

2017-03-01

In this paper we study the conditions of chimera states excitation in ensemble of non-locally coupled Kuramoto-Sakaguchi (KS) oscillators. In the framework of current research we analyze the dynamics of the homogeneous network containing identical oscillators. We show the chimera state formation process is sensitive to the parameters of coupling kernel and to the KS network initial state. To perform the analysis we have used the Ott-Antonsen (OA) ansatz to consider the behavior of infinitely large KS network.

Analysis of structural patterns in the brain with the complex network approach

NASA Astrophysics Data System (ADS)

Maksimenko, Vladimir A.; Makarov, Vladimir V.; Kharchenko, Alexander A.; Pavlov, Alexey N.; Khramova, Marina V.; Koronovskii, Alexey A.; Hramov, Alexander E.

2015-03-01

In this paper we study mechanisms of the phase synchronization in a model network of Van der Pol oscillators and in the neural network of the brain by consideration of macroscopic parameters of these networks. As the macroscopic characteristics of the model network we consider a summary signal produced by oscillators. Similar to the model simulations, we study EEG signals reflecting the macroscopic dynamics of neural network. We show that the appearance of the phase synchronization leads to an increased peak in the wavelet spectrum related to the dynamics of synchronized oscillators. The observed correlation between the phase relations of individual elements and the macroscopic characteristics of the whole network provides a way to detect phase synchronization in the neural networks in the cases of normal and pathological activity.

Power oscillator

DOEpatents

Gitsevich, Aleksandr

2001-01-01

An oscillator includes an amplifier having an input and an output, and an impedance transformation network connected between the input of the amplifier and the output of the amplifier, wherein the impedance transformation network is configured to provide suitable positive feedback from the output of the amplifier to the input of the amplifier to initiate and sustain an oscillating condition, and wherein the impedance transformation network is configured to protect the input of the amplifier from a destructive feedback signal. One example of the oscillator is a single active element device capable of providing over 70 watts of power at over 70% efficiency. Various control circuits may be employed to match the driving frequency of the oscillator to a plurality of tuning states of the lamp.

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

NASA Astrophysics Data System (ADS)

Hua, Da-Yin; Gao, Ke

2011-06-01

We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading in Watts—Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on the spatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.

One node driving synchronisation

NASA Astrophysics Data System (ADS)

Wang, Chengwei; Grebogi, Celso; Baptista, Murilo S.

2015-12-01

Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with heterogeneous coupling strengths. The synchronisation of phase-oscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phase-oscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phase-angles for the synchronous oscillators.

One node driving synchronisation

PubMed Central

Wang, Chengwei; Grebogi, Celso; Baptista, Murilo S.

2015-01-01

Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with heterogeneous coupling strengths. The synchronisation of phase-oscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phase-oscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phase-angles for the synchronous oscillators. PMID:26656718

Third Advances in Solar Physics Euroconference: Magnetic Fields and Oscillations

NASA Astrophysics Data System (ADS)

Schmieder, B.; Hofmann, A.; Staude, J.

The third Advances in Solar Physics Euroconference (ASPE) "Magnetic Fields and Oscillations"concluded a series of three Euroconferences sponsored by the European Union. The meeting took place in Caputh near Potsdam, Germany, on September 22-25, 1998, followed by the JOSO (Joint Organization for Solar Observations) 30th Annual Board Meeting on September 26, 1998. The ASPE formula is attractive and compares well with other meetings with "show-and-tell" character. This meeting had 122 participants coming from 26 countries; 36 participants came from countries formerly behind the Iron Curtain; a "politically incorrect" estimate says that 48 participants were below 35 years of age, with an unusually large female-to-male ratio. This characteristic of youngness is the more striking since solar physics is a perhaps overly established field exhibiting an overly senior age profile. It was a good opportunity to train this young generation in Solar Physics. The conference topic "Magnetic Fields and Oscillations" obviously was wide enough to cater to many an interest. These proceedings are organized according to the structure of the meeting. They include the topics 'High resolution spectropolarimetry and magnetometry', 'Flux-tube dynamics', 'Modelling of the 3-D magnetic field structure', 'Mass motions and magnetic fields in sunspot penumbral structures', 'Sunspot oscillations', 'Oscillations in active regions - diagnostics and seismology', 'Network and intranetwork structure and dynamics', and 'Waves in magnetic structures'. These topics covered the first 2.5 days of the conference. The reviews, oral contributions, and poster presentations were by no means all of the meeting. The ASPE formula also adds extensive plenary sessions of JOSO Working groups on topics that involve planning of Europe-wide collaboration. At this meeting these concerned solar observing techniques, solar data bases, coordination between SOHO and ground-based observing, and preparations for August 11, 1999 when more Europeans will be eclipsed than ever before. The contributions to these sessions have been included into the present volume as well. The participants of the EU-TMR Research Network 'Solar Magnetometry Network' came together to discuss in a special working group session questions of their future collaboration.

A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network

NASA Astrophysics Data System (ADS)

Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien

2017-03-01

With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.

Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states

NASA Astrophysics Data System (ADS)

Picallo, Clara B.; Riecke, Hermann

2011-03-01

Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.

A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network.

PubMed

Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien

2017-03-21

With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices' non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.

A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network

PubMed Central

Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien

2017-01-01

With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing. PMID:28322262

Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors.

PubMed

Fang, Yan; Yashin, Victor V; Dickerson, Samuel J; Balazs, Anna C

2018-05-01

We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.

Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors

NASA Astrophysics Data System (ADS)

Fang, Yan; Yashin, Victor V.; Dickerson, Samuel J.; Balazs, Anna C.

2018-05-01

We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.

Gap junction plasticity as a mechanism to regulate network-wide oscillations

PubMed Central

Nicola, Wilten; Clopath, Claudia

2018-01-01

Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap junction coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be modified in an activity-dependent manner, similar to chemical synapses. We hypothesized that activity-dependent gap junction plasticity acts as a mechanism to regulate oscillations in the cortex. We developed a computational model of gap junction plasticity in a recurrent cortical network based on recent experimental findings. We showed that gap junction plasticity can serve as a homeostatic mechanism for oscillations by maintaining a tight balance between two network states: asynchronous irregular activity and synchronized oscillations. This homeostatic mechanism allows for robust communication between neuronal assemblies through two different mechanisms: transient oscillations and frequency modulation. This implies a direct functional role for gap junction plasticity in information transmission in cortex. PMID:29529034

Predicting neural network firing pattern from phase resetting curve

NASA Astrophysics Data System (ADS)

Oprisan, Sorinel; Oprisan, Ana

2007-04-01

Autonomous neural networks called central pattern generators (CPG) are composed of endogenously bursting neurons and produce rhythmic activities, such as flying, swimming, walking, chewing, etc. Simplified CPGs for quadrupedal locomotion and swimming are modeled by a ring of neural oscillators such that the output of one oscillator constitutes the input for the subsequent neural oscillator. The phase response curve (PRC) theory discards the detailed conductance-based description of the component neurons of a network and reduces them to ``black boxes'' characterized by a transfer function, which tabulates the transient change in the intrinsic period of a neural oscillator subject to external stimuli. Based on open-loop PRC, we were able to successfully predict the phase-locked period and relative phase between neurons in a half-center network. We derived existence and stability criteria for heterogeneous ring neural networks that are in good agreement with experimental data.

A neural mass model of basal ganglia nuclei simulates pathological beta rhythm in Parkinson's disease

NASA Astrophysics Data System (ADS)

Liu, Fei; Wang, Jiang; Liu, Chen; Li, Huiyan; Deng, Bin; Fietkiewicz, Chris; Loparo, Kenneth A.

2016-12-01

An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.

Indirect synchronization control in a starlike network of phase oscillators

NASA Astrophysics Data System (ADS)

Kuptsov, Pavel V.; Kuptsova, Anna V.

2018-04-01

A starlike network of non-identical phase oscillators is considered that contains the hub and tree rays each having a single node. In such network effect of indirect synchronization control is reported: changing the natural frequency and the coupling strength of one of the peripheral oscillators one can switch on an off the synchronization of the others. The controlling oscillator at that is not synchronized with them and has a frequency that is approximately four time higher then the frequency of the synchronization. The parameter planes showing a corresponding synchronization tongue are represented and time dependencies of phase differences are plotted for points within and outside of the tongue.

Synchronization of networked chaotic oscillators under external periodic driving.

PubMed

Yang, Wenchao; Lin, Weijie; Wang, Xingang; Huang, Liang

2015-03-01

The dynamical responses of a complex system to external perturbations are of both fundamental interest and practical significance. Here, by the model of networked chaotic oscillators, we investigate how the synchronization behavior of a complex network is influenced by an externally added periodic driving. Interestingly, it is found that by a slight change of the properties of the external driving, e.g., the frequency or phase lag between its intrinsic oscillation and external driving, the network synchronizability could be significantly modified. We demonstrate this phenomenon by different network models and, based on the method of master stability function, give an analysis on the underlying mechanisms. Our studies highlight the importance of external perturbations on the collective behaviors of complex networks, and also provide an alternate approach for controlling network synchronization.

The thalamic low-threshold Ca2+ potential: a key determinant of the local and global dynamics of the slow (<1 Hz) sleep oscillation in thalamocortical networks

PubMed Central

Crunelli, Vincenzo; Errington, Adam C.; Hughes, Stuart W.; Tóth, Tibor I.

2011-01-01

During non-rapid eye movement sleep and certain types of anaesthesia, neurons in the neocortex and thalamus exhibit a distinctive slow (<1 Hz) oscillation that consists of alternating UP and DOWN membrane potential states and which correlates with a pronounced slow (<1 Hz) rhythm in the electroencephalogram. While several studies have claimed that the slow oscillation is generated exclusively in neocortical networks and then transmitted to other brain areas, substantial evidence exists to suggest that the full expression of the slow oscillation in an intact thalamocortical (TC) network requires the balanced interaction of oscillator systems in both the neocortex and thalamus. Within such a scenario, we have previously argued that the powerful low-threshold Ca2+ potential (LTCP)-mediated burst of action potentials that initiates the UP states in individual TC neurons may be a vital signal for instigating UP states in related cortical areas. To investigate these issues we constructed a computational model of the TC network which encompasses the important known aspects of the slow oscillation that have been garnered from earlier in vivo and in vitro experiments. Using this model we confirm that the overall expression of the slow oscillation is intricately reliant on intact connections between the thalamus and the cortex. In particular, we demonstrate that UP state-related LTCP-mediated bursts in TC neurons are proficient in triggering synchronous UP states in cortical networks, thereby bringing about a synchronous slow oscillation in the whole network. The importance of LTCP-mediated action potential bursts in the slow oscillation is also underlined by the observation that their associated dendritic Ca2+ signals are the only ones that inform corticothalamic synapses of the TC neuron output, since they, but not those elicited by tonic action potential firing, reach the distal dendritic sites where these synapses are located. PMID:21893530

Noise-assisted energy transport in electrical oscillator networks with off-diagonal dynamical disorder.

PubMed

León-Montiel, Roberto de J; Quiroz-Juárez, Mario A; Quintero-Torres, Rafael; Domínguez-Juárez, Jorge L; Moya-Cessa, Héctor M; Torres, Juan P; Aragón, José L

2015-11-27

Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing-assisted transport. Here, we report on the experimental observation of such effect in a network of coupled electrical oscillators. We demonstrate that by introducing stochastic fluctuations in one of the couplings of the network, a relative enhancement in the energy transport efficiency of 22.5 ± 3.6% can be observed.

Emergence of self-sustained oscillations in excitable Erdös-Rényi random networks.

PubMed

Qian, Yu

2014-09-01

We investigate the emergence of self-sustained oscillations in excitable Erdös-Rényi random networks (EERRNs). Interestingly, periodical self-sustained oscillations have been found at a moderate connection probability P. For smaller or larger P, the system evolves into a homogeneous rest state with distinct mechanisms. One-dimensional Winfree loops are discovered as the sources to maintain the oscillations. Moreover, by analyzing these oscillation sources, we propose two criteria to explain the spatiotemporal dynamics obtained in EERRNs. Finally, the two critical connection probabilities for which self-sustained oscillations can emerge are approximately predicted based on these two criteria.

Analysis of the characteristics of the synchronous clusters in the adaptive Kuramoto network and neural network of the epileptic brain

NASA Astrophysics Data System (ADS)

Hramov, Alexander E.; Kharchenko, Alexander A.; Makarov, Vladimir V.; Khramova, Marina V.; Koronovskii, Alexey A.; Pavlov, Alexey N.; Dana, Syamal K.

2016-04-01

In the paper we study the mechanisms of phase synchronization in the adaptive model network of Kuramoto oscillators and the neural network of brain by consideration of the integral characteristics of the observed networks signals. As the integral characteristics of the model network we consider the summary signal produced by the oscillators. Similar to the model situation we study the ECoG signal as the integral characteristic of neural network of the brain. We show that the establishment of the phase synchronization results in the increase of the peak, corresponding to synchronized oscillators, on the wavelet energy spectrum of the integral signals. The observed correlation between the phase relations of the elements and the integral characteristics of the whole network open the way to detect the size of synchronous clusters in the neural networks of the epileptic brain before and during seizure.

Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators

NASA Astrophysics Data System (ADS)

Papadopoulos, Lia; Kim, Jason Z.; Kurths, Jürgen; Bassett, Danielle S.

2017-07-01

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule—which preserves connections between more out-of-phase oscillators while rewiring connections between more in-phase oscillators—can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree-frequency and frequency-neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules.

Chaos in generically coupled phase oscillator networks with nonpairwise interactions.

PubMed

Bick, Christian; Ashwin, Peter; Rodrigues, Ana

2016-09-01

The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.

Chaos in generically coupled phase oscillator networks with nonpairwise interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bick, Christian; Ashwin, Peter; Rodrigues, Ana

The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamicsmore » in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.« less

Region-Specific Slowing of Alpha Oscillations is Associated with Visual-Perceptual Abilities in Children Born Very Preterm

PubMed Central

Doesburg, Sam M.; Moiseev, Alexander; Herdman, Anthony T.; Ribary, Urs; Grunau, Ruth E.

2013-01-01

Children born very preterm (≤32 weeks gestational age) without major intellectual or neurological impairments often express selective deficits in visual-perceptual abilities. The alterations in neurophysiological development underlying these problems, however, remain poorly understood. Recent research has indicated that spontaneous alpha oscillations are slowed in children born very preterm, and that atypical alpha-mediated functional network connectivity may underlie selective developmental difficulties in visual-perceptual ability in this group. The present study provides the first source-resolved analysis of slowing of spontaneous alpha oscillations in very preterm children, indicating alterations in a distributed set of brain regions concentrated in areas of posterior parietal and inferior temporal regions associated with visual perception, as well as prefrontal cortical regions and thalamus. We also uniquely demonstrate that slowing of alpha oscillations is associated with selective difficulties in visual-perceptual ability in very preterm children. These results indicate that region-specific slowing of alpha oscillations contribute to selective developmental difficulties prevalent in this population. PMID:24298250

Slow oscillations orchestrating fast oscillations and memory consolidation.

PubMed

Mölle, Matthias; Born, Jan

2011-01-01

Slow-wave sleep (SWS) facilitates the consolidation of hippocampus-dependent declarative memory. Based on the standard two-stage memory model, we propose that memory consolidation during SWS represents a process of system consolidation which is orchestrated by the neocortical <1Hz electroencephalogram (EEG) slow oscillation and involves the reactivation of newly encoded representations and their subsequent redistribution from temporary hippocampal to neocortical long-term storage sites. Indeed, experimental induction of slow oscillations during non-rapid eye movement (non-REM) sleep by slowly alternating transcranial current stimulation distinctly improves consolidation of declarative memory. The slow oscillations temporally group neuronal activity into up-states of strongly enhanced neuronal activity and down-states of neuronal silence. In a feed-forward efferent action, this grouping is induced not only in the neocortex but also in other structures relevant to consolidation, namely the thalamus generating 10-15Hz spindles, and the hippocampus generating sharp wave-ripples, with the latter well known to accompany a replay of newly encoded memories taking place in hippocampal circuitries. The feed-forward synchronizing effect of the slow oscillation enables the formation of spindle-ripple events where ripples and accompanying reactivated hippocampal memory information become nested into the single troughs of spindles. Spindle-ripple events thus enable reactivated memory-related hippocampal information to be fed back to neocortical networks in the excitable slow oscillation up-state where they can induce enduring plastic synaptic changes underlying the effective formation of long-term memories. Copyright © 2011 Elsevier B.V. All rights reserved.

Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinha, Mohit; Dorfler, Florian; Johnson, Brian B.

2016-08-01

This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation ofmore » a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.« less

Minimum Winfree loop determines self-sustained oscillations in excitable Erdös-Rényi random networks.

PubMed

Qian, Yu; Cui, Xiaohua; Zheng, Zhigang

2017-07-18

The investigation of self-sustained oscillations in excitable complex networks is very important in understanding various activities in brain systems, among which the exploration of the key determinants of oscillations is a challenging task. In this paper, by investigating the influence of system parameters on self-sustained oscillations in excitable Erdös-Rényi random networks (EERRNs), the minimum Winfree loop (MWL) is revealed to be the key factor in determining the emergence of collective oscillations. Specifically, the one-to-one correspondence between the optimal connection probability (OCP) and the MWL length is exposed. Moreover, many important quantities such as the lower critical connection probability (LCCP), the OCP, and the upper critical connection probability (UCCP) are determined by the MWL. Most importantly, they can be approximately predicted by the network structure analysis, which have been verified in numerical simulations. Our results will be of great importance to help us in understanding the key factors in determining persistent activities in biological systems.

Oscillator networks with tissue-specific circadian clocks in plants.

PubMed

Inoue, Keisuke; Araki, Takashi; Endo, Motomu

2017-09-08

Many organisms rely on circadian clocks to synchronize their biological processes with the 24-h rotation of the earth. In mammals, the circadian clock consists of a central clock in the suprachiasmatic nucleus and peripheral clocks in other tissues. The central clock is tightly coupled to synchronize rhythmicity and can organize peripheral clocks through neural and hormonal signals. In contrast to mammals, it has long been assumed that the circadian clocks in each plant cell is able to be entrained by external light, and they are only weakly coupled to each other. Recently, however, several reports have demonstrated that plants have unique oscillator networks with tissue-specific circadian clocks. Here, we introduce our current view regarding tissue-specific properties and oscillator networks of plant circadian clocks. Accumulating evidence suggests that plants have multiple oscillators, which show distinct properties and reside in different tissues. A direct tissue-isolation technique and micrografting have clearly demonstrated that plants have hierarchical oscillator networks consisting of multiple tissue-specific clocks. Copyright © 2017. Published by Elsevier Ltd.

Pyramidal cell-interneuron interactions underlie hippocampal ripple oscillations.

PubMed

Stark, Eran; Roux, Lisa; Eichler, Ronny; Senzai, Yuta; Royer, Sebastien; Buzsáki, György

2014-07-16

High-frequency ripple oscillations, observed most prominently in the hippocampal CA1 pyramidal layer, are associated with memory consolidation. The cellular and network mechanisms underlying the generation, frequency control, and spatial coherence of the rhythm are poorly understood. Using multisite optogenetic manipulations in freely behaving rodents, we found that depolarization of a small group of nearby pyramidal cells was sufficient to induce high-frequency oscillations, whereas closed-loop silencing of pyramidal cells or activation of parvalbumin- (PV) or somatostatin-immunoreactive interneurons aborted spontaneously occurring ripples. Focal pharmacological blockade of GABAA receptors abolished ripples. Localized PV interneuron activation paced ensemble spiking, and simultaneous induction of high-frequency oscillations at multiple locations resulted in a temporally coherent pattern mediated by phase-locked interneuron spiking. These results constrain competing models of ripple generation and indicate that temporally precise local interactions between excitatory and inhibitory neurons support ripple generation in the intact hippocampus. Copyright © 2014 Elsevier Inc. All rights reserved.

Pyramidal Cell-Interneuron Interactions Underlie Hippocampal Ripple Oscillations

PubMed Central

Stark, Eran; Roux, Lisa; Eichler, Ronny; Senzai, Yuta; Royer, Sebastien; Buzsáki, György

2015-01-01

SUMMARY High-frequency ripple oscillations, observed most prominently in the hippocampal CA1 pyramidal layer, are associated with memory consolidation. The cellular and network mechanisms underlying the generation, frequency control, and spatial coherence of the rhythm are poorly understood. Using multisite optogenetic manipulations in freely behaving rodents, we found that depolarization of a small group of nearby pyramidal cells was sufficient to induce high-frequency oscillations, whereas closed-loop silencing of pyramidal cells or activation of parvalbumin-(PV) or somatostatin-immunoreactive interneurons aborted spontaneously occurring ripples. Focal pharmacological blockade of GABAA receptors abolished ripples. Localized PV inter-neuron activation paced ensemble spiking, and simultaneous induction of high-frequency oscillations at multiple locations resulted in a temporally coherent pattern mediated by phase-locked inter-neuron spiking. These results constrain competing models of ripple generation and indicate that temporally precise local interactions between excitatory and inhibitory neurons support ripple generation in the intact hippocampus. PMID:25033186

Ketamine: differential neurophysiological dynamics in functional networks in the rat brain

PubMed Central

Ahnaou, A; Huysmans, H; Biermans, R; Manyakov, N V; Drinkenburg, W H I M

2017-01-01

Recently, the N-methyl-d-aspartate-receptor (NMDAR) antagonist ketamine has emerged as a fast-onset mechanism to achieve antidepressant activity, whereas its psychomimetic, dissociative and amnestic effects have been well documented to pharmacologically model schizophrenia features in rodents. Sleep–wake architecture, neuronal oscillations and network connectivity are key mechanisms supporting brain plasticity and cognition, which are disrupted in mood disorders such as depression and schizophrenia. In rats, we investigated the dynamic effects of acute and chronic subcutaneous administration of ketamine (2.5, 5 and 10 mg kg−1) on sleep–wake cycle, multichannels network interactions assessed by coherence and phase–amplitude cross-frequency coupling, locomotor activity (LMA), cognitive information processing as reflected by the mismatch negativity-like (MMN) component of event-related brain potentials (ERPs). Acute ketamine elicited a short, lasting inhibition of rapid eye movement (REM) sleep, increased coherence in higher gamma frequency oscillations independent of LMA, altered theta-gamma phase–amplitude coupling, increased MMN peak-amplitude response and evoked higher gamma oscillations. In contrast, chronic ketamine reduced large-scale communication among cortical regions by decreasing oscillations and coherent activity in the gamma frequency range, shifted networks activity towards slow alpha rhythm, decreased MMN peak response and enhanced aberrant higher gamma neuronal network oscillations. Altogether, our data show that acute and chronic ketamine elicited differential changes in network connectivity, ERPs and event-related oscillations (EROs), supporting possible underlying alterations in NMDAR–GABAergic signaling. The findings underscore the relevance of intermittent dosing of ketamine to accurately maintain the functional integrity of neuronal networks for long-term plastic changes and therapeutic effect. PMID:28926001

Impossibility of asymptotic synchronization for pulse-coupled oscillators with delayed excitatory coupling.

PubMed

Wu, Wei; Chen, Tianping

2009-12-01

Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.

Modeling spike-wave discharges by a complex network of neuronal oscillators.

PubMed

Medvedeva, Tatiana M; Sysoeva, Marina V; van Luijtelaar, Gilles; Sysoev, Ilya V

2018-02-01

The organization of neural networks and the mechanisms, which generate the highly stereotypical for absence epilepsy spike-wave discharges (SWDs) is heavily debated. Here we describe such a model which can both reproduce the characteristics of SWDs and dynamics of coupling between brain regions, relying mainly on properties of hierarchically organized networks of a large number of neuronal oscillators. We used a two level mesoscale model. The first level consists of three structures: the nervus trigeminus serving as an input, the thalamus and the somatosensory cortex; the second level of a group of nearby situated neurons belonging to one of three modeled structures. The model reproduces the main features of the transition from normal to epileptiformic activity and its spontaneous abortion: an increase in the oscillation amplitude, the emergence of the main frequency and its higher harmonics, and the ability to generate trains of seizures. The model was stable with respect to variations in the structure of couplings and to scaling. The analyzes of the interactions between model structures from their time series using Granger causality method showed that the model reproduced the preictal coupling increase detected previously from experimental data. SWDs can be generated by changes in network organization. It is proposed that a specific pathological architecture of couplings in the brain is necessary to allow the transition from normal to epileptiformic activity, next to by others modeled and reported factors referring to complex, intrinsic, and synaptic mechanisms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Multi-load Groups Coordinated Load Control Strategy Considering Power Network Constraints

NASA Astrophysics Data System (ADS)

Liu, Meng; Zhao, Binchao; Wang, Jun; Zhang, Guohui; Wang, Xin

2017-05-01

Loads with energy storage property can actively participate in power balance for power systems, this paper takes air conditioner as a controllable load example, proposing a multi-load groups coordinated load control strategy considering power network constraints. Firstly, two load control modes considering recovery of load diversity are designed, blocking power oscillation of aggregated air conditioners. As the same time, air conditioner temperature setpoint recovery control strategy is presented to avoid power recovery peak. Considering inherent characteristics of two load control modes, an coordinated load control mode is designed by combining the both. Basing on this, a multi-load groups coordinated load control strategy is proposed. During the implementing of load control, power network constraints should be satisfied. An indice which can reflect the security of power system operating is defined. By minimizing its value through optimization, the change of air conditioning loads’ aggregated power on each load bus can be calculated. Simulations are conducted on an air conditioners group and New England 10-generator 39-bus system, verifying the effectiveness of the proposed multi-load groups coordinated load control strategy considering power network constraints.

Modulation of dynamic modes by interplay between positive and negative feedback loops in gene regulatory networks

NASA Astrophysics Data System (ADS)

Wang, Liu-Suo; Li, Ning-Xi; Chen, Jing-Jia; Zhang, Xiao-Peng; Liu, Feng; Wang, Wei

2018-04-01

A positive and a negative feedback loop can induce bistability and oscillation, respectively, in biological networks. Nevertheless, they are frequently interlinked to perform more elaborate functions in many gene regulatory networks. Coupled positive and negative feedback loops may exhibit either oscillation or bistability depending on the intensity of the stimulus in some particular networks. It is less understood how the transition between the two dynamic modes is modulated by the positive and negative feedback loops. We developed an abstract model of such systems, largely based on the core p53 pathway, to explore the mechanism for the transformation of dynamic behaviors. Our results show that enhancing the positive feedback may promote or suppress oscillations depending on the strength of both feedback loops. We found that the system oscillates with low amplitudes in response to a moderate stimulus and switches to the on state upon a strong stimulus. When the positive feedback is activated much later than the negative one in response to a strong stimulus, the system exhibits long-term oscillations before switching to the on state. We explain this intriguing phenomenon using quasistatic approximation. Moreover, early switching to the on state may occur when the system starts from a steady state in the absence of stimuli. The interplay between the positive and negative feedback plays a key role in the transitions between oscillation and bistability. Of note, our conclusions should be applicable only to some specific gene regulatory networks, especially the p53 network, in which both oscillation and bistability exist in response to a certain type of stimulus. Our work also underscores the significance of transient dynamics in determining cellular outcome.

Noise-assisted energy transport in electrical oscillator networks with off-diagonal dynamical disorder

PubMed Central

León-Montiel, Roberto de J.; Quiroz-Juárez, Mario A.; Quintero-Torres, Rafael; Domínguez-Juárez, Jorge L.; Moya-Cessa, Héctor M.; Torres, Juan P.; Aragón, José L.

2015-01-01

Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing-assisted transport. Here, we report on the experimental observation of such effect in a network of coupled electrical oscillators. We demonstrate that by introducing stochastic fluctuations in one of the couplings of the network, a relative enhancement in the energy transport efficiency of 22.5 ± 3.6% can be observed. PMID:26610864

Associative memory in phasing neuron networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nair, Niketh S; Bochove, Erik J.; Braiman, Yehuda

2014-01-01

We studied pattern formation in a network of coupled Hindmarsh-Rose model neurons and introduced a new model for associative memory retrieval using networks of Kuramoto oscillators. Hindmarsh-Rose Neural Networks can exhibit a rich set of collective dynamics that can be controlled by their connectivity. Specifically, we showed an instance of Hebb's rule where spiking was correlated with network topology. Based on this, we presented a simple model of associative memory in coupled phase oscillators.

Relationships among classes of self-oscillating transistor parallel inverters. [dc to square wave converter circuits for power conditioning

NASA Technical Reports Server (NTRS)

Wilson, T. G.; Lee, F. C. Y.; Burns, W. W., III; Owen, H. A., Jr.

1974-01-01

A procedure is developed for classifying dc-to-square-wave two-transistor parallel inverters used in power conditioning applications. The inverters are reduced to equivalent RLC networks and are then grouped with other inverters with the same basic equivalent circuit. Distinction between inverter classes is based on the topology characteristics of the equivalent circuits. Information about one class can then be extended to another class using the basic oscillation theory and the concept of duality. Oscillograms from test circuits confirm the validity of the procedure adopted.

Cortical networks dynamically emerge with the interplay of slow and fast oscillations for memory of a natural scene.

PubMed

Mizuhara, Hiroaki; Sato, Naoyuki; Yamaguchi, Yoko

2015-05-01

Neural oscillations are crucial for revealing dynamic cortical networks and for serving as a possible mechanism of inter-cortical communication, especially in association with mnemonic function. The interplay of the slow and fast oscillations might dynamically coordinate the mnemonic cortical circuits to rehearse stored items during working memory retention. We recorded simultaneous EEG-fMRI during a working memory task involving a natural scene to verify whether the cortical networks emerge with the neural oscillations for memory of the natural scene. The slow EEG power was enhanced in association with the better accuracy of working memory retention, and accompanied cortical activities in the mnemonic circuits for the natural scene. Fast oscillation showed a phase-amplitude coupling to the slow oscillation, and its power was tightly coupled with the cortical activities for representing the visual images of natural scenes. The mnemonic cortical circuit with the slow neural oscillations would rehearse the distributed natural scene representations with the fast oscillation for working memory retention. The coincidence of the natural scene representations could be obtained by the slow oscillation phase to create a coherent whole of the natural scene in the working memory. Copyright © 2015 Elsevier Inc. All rights reserved.

A Quantitative Analysis of Solar Flare Characteristics as Observed in the Solar Observing Optical Network and the Global Oscillation Network Group

DTIC Science & Technology

2012-03-01

due to their possible threat to operations. Because of their importance, event-level flares are given extra consideration in this report. (AFWA...In the impulsive phase (3 to 10 minutes), as this reconnection takes place, electrons and ions with large energies are accelerated and released...right, correspond to the horizontal lines with large red dashes. The flash and gradual phases are bound by the vertical dashed lines. 13 variable in

Circadian desynchronization

PubMed Central

Granada, Adrián E.; Cambras, Trinitat; Díez-Noguera, Antoni; Herzel, Hanspeter

2011-01-01

The suprachiasmatic nucleus (SCN) coordinates via multiple outputs physiological and behavioural circadian rhythms. The SCN is composed of a heterogeneous network of coupled oscillators that entrain to the daily light–dark cycles. Outside the physiological entrainment range, rich locomotor patterns of desynchronized rhythms are observed. Previous studies interpreted these results as the output of different SCN neural subpopulations. We find, however, that even a single periodically driven oscillator can induce such complex desynchronized locomotor patterns. Using signal analysis, we show how the observed patterns can be consistently clustered into two generic oscillatory interaction groups: modulation and superposition. In seven of 17 rats undergoing forced desynchronization, we find a theoretically predicted third spectral component. Combining signal analysis with the theory of coupled oscillators, we provide a framework for the study of circadian desynchronization. PMID:22419981

The Edge of Stability: Response Times and Delta Oscillations in Balanced Networks

PubMed Central

Gillary, Grant; Niebur, Ernst

2016-01-01

The standard architecture of neocortex is a network with excitation and inhibition in closely maintained balance. These networks respond fast and with high precision to their inputs and they allow selective amplification of patterned signals. The stability of such networks is known to depend on balancing the strengths of positive and negative feedback. We here show that a second condition is required for stability which depends on the relative strengths and time courses of fast (AMPA) and slow (NMDA) currents in the excitatory projections. This condition also determines the response time of the network. We show that networks which respond quickly to an input are necessarily close to an oscillatory instability which resonates in the delta range. This instability explains the existence of neocortical delta oscillations and the emergence of absence epilepsy. Although cortical delta oscillations are a network-level phenomenon, we show that in non-pathological networks, individual neurons receive sufficient information to keep the network in the fast-response regime without sliding into the instability. PMID:27689361

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Entraining the topology and the dynamics of a network of phase oscillators

NASA Astrophysics Data System (ADS)

Sendiña-Nadal, I.; Leyva, I.; Buldú, J. M.; Almendral, J. A.; Boccaletti, S.

2009-04-01

We show that the topology and dynamics of a network of unsynchronized Kuramoto oscillators can be simultaneously controlled by means of a forcing mechanism which yields a phase locking of the oscillators to that of an external pacemaker in connection with the reshaping of the network’s degree distribution. The entrainment mechanism is based on the addition, at regular time intervals, of unidirectional links from oscillators that follow the dynamics of a pacemaker to oscillators in the pristine graph whose phases hold a prescribed phase relationship. Such a dynamically based rule in the attachment process leads to the emergence of a power-law shape in the final degree distribution of the graph whenever the network is entrained to the dynamics of the pacemaker. We show that the arousal of a scale-free distribution in connection with the success of the entrainment process is a robust feature, characterizing different networks’ initial configurations and parameters.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Cell Type-specific Intrinsic Perithreshold Oscillations in Hippocampal GABAergic Interneurons.

PubMed

Kang, Young-Jin; Lewis, Hannah Elisabeth Smashey; Young, Mason William; Govindaiah, Gubbi; Greenfield, Lazar John; Garcia-Rill, Edgar; Lee, Sang-Hun

2018-04-15

The hippocampus plays a critical role in learning, memory, and spatial processing through coordinated network activity including theta and gamma oscillations. Recent evidence suggests that hippocampal subregions (e.g., CA1) can generate these oscillations at the network level, at least in part, through GABAergic interneurons. However, it is unclear whether specific GABAergic interneurons generate intrinsic theta and/or gamma oscillations at the single-cell level. Since major types of CA1 interneurons (i.e., parvalbumin-positive basket cells (PVBCs), cannabinoid type 1 receptor-positive basket cells (CB 1 BCs), Schaffer collateral-associated cells (SCAs), neurogliaform cells and ivy cells) are thought to play key roles in network theta and gamma oscillations in the hippocampus, we tested the hypothesis that these cells generate intrinsic perithreshold oscillations at the single-cell level. We performed whole-cell patch-clamp recordings from GABAergic interneurons in the CA1 region of the mouse hippocampus in the presence of synaptic blockers to identify intrinsic perithreshold membrane potential oscillations. The majority of PVBCs (83%), but not the other interneuron subtypes, produced intrinsic perithreshold gamma oscillations if the membrane potential remained above -45 mV. In contrast, CB 1 BCs, SCAs, neurogliaform cells, ivy cells, and the remaining PVBCs (17%) produced intrinsic theta, but not gamma, oscillations. These oscillations were prevented by blockers of persistent sodium current. These data demonstrate that the major types of hippocampal interneurons produce distinct frequency bands of intrinsic perithreshold membrane oscillations. Copyright © 2018 IBRO. Published by Elsevier Ltd. All rights reserved.

Neurodynamic oscillators

NASA Technical Reports Server (NTRS)

Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz

1995-01-01

Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.

Desynchronization of slow oscillations in the basal ganglia during natural sleep.

PubMed

Mizrahi-Kliger, Aviv D; Kaplan, Alexander; Israel, Zvi; Bergman, Hagai

2018-05-01

Slow oscillations of neuronal activity alternating between firing and silence are a hallmark of slow-wave sleep (SWS). These oscillations reflect the default activity present in all mammalian species, and are ubiquitous to anesthesia, brain slice preparations, and neuronal cultures. In all these cases, neuronal firing is highly synchronous within local circuits, suggesting that oscillation-synchronization coupling may be a governing principle of sleep physiology regardless of anatomical connectivity. To investigate whether this principle applies to overall brain organization, we recorded the activity of individual neurons from basal ganglia (BG) structures and the thalamocortical (TC) network over 70 full nights of natural sleep in two vervet monkeys. During SWS, BG neurons manifested slow oscillations (∼0.5 Hz) in firing rate that were as prominent as in the TC network. However, in sharp contrast to any neural substrate explored thus far, the slow oscillations in all BG structures were completely desynchronized between individual neurons. Furthermore, whereas in the TC network single-cell spiking was locked to slow oscillations in the local field potential (LFP), the BG LFP exhibited only weak slow oscillatory activity and failed to entrain nearby cells. We thus show that synchrony is not inherent to slow oscillations, and propose that the BG desynchronization of slow oscillations could stem from its unique anatomy and functional connectivity. Finally, we posit that BG slow-oscillation desynchronization may further the reemergence of slow-oscillation traveling waves from multiple independent origins in the frontal cortex, thus significantly contributing to normal SWS.

Nonequilibrium landscape theory of neural networks.

PubMed

Yan, Han; Zhao, Lei; Hu, Liang; Wang, Xidi; Wang, Erkang; Wang, Jin

2013-11-05

The brain map project aims to map out the neuron connections of the human brain. Even with all of the wirings mapped out, the global and physical understandings of the function and behavior are still challenging. Hopfield quantified the learning and memory process of symmetrically connected neural networks globally through equilibrium energy. The energy basins of attractions represent memories, and the memory retrieval dynamics is determined by the energy gradient. However, the realistic neural networks are asymmetrically connected, and oscillations cannot emerge from symmetric neural networks. Here, we developed a nonequilibrium landscape-flux theory for realistic asymmetrically connected neural networks. We uncovered the underlying potential landscape and the associated Lyapunov function for quantifying the global stability and function. We found the dynamics and oscillations in human brains responsible for cognitive processes and physiological rhythm regulations are determined not only by the landscape gradient but also by the flux. We found that the flux is closely related to the degrees of the asymmetric connections in neural networks and is the origin of the neural oscillations. The neural oscillation landscape shows a closed-ring attractor topology. The landscape gradient attracts the network down to the ring. The flux is responsible for coherent oscillations on the ring. We suggest the flux may provide the driving force for associations among memories. We applied our theory to rapid-eye movement sleep cycle. We identified the key regulation factors for function through global sensitivity analysis of landscape topography against wirings, which are in good agreements with experiments.

Nonequilibrium landscape theory of neural networks

PubMed Central

Yan, Han; Zhao, Lei; Hu, Liang; Wang, Xidi; Wang, Erkang; Wang, Jin

2013-01-01

The brain map project aims to map out the neuron connections of the human brain. Even with all of the wirings mapped out, the global and physical understandings of the function and behavior are still challenging. Hopfield quantified the learning and memory process of symmetrically connected neural networks globally through equilibrium energy. The energy basins of attractions represent memories, and the memory retrieval dynamics is determined by the energy gradient. However, the realistic neural networks are asymmetrically connected, and oscillations cannot emerge from symmetric neural networks. Here, we developed a nonequilibrium landscape–flux theory for realistic asymmetrically connected neural networks. We uncovered the underlying potential landscape and the associated Lyapunov function for quantifying the global stability and function. We found the dynamics and oscillations in human brains responsible for cognitive processes and physiological rhythm regulations are determined not only by the landscape gradient but also by the flux. We found that the flux is closely related to the degrees of the asymmetric connections in neural networks and is the origin of the neural oscillations. The neural oscillation landscape shows a closed-ring attractor topology. The landscape gradient attracts the network down to the ring. The flux is responsible for coherent oscillations on the ring. We suggest the flux may provide the driving force for associations among memories. We applied our theory to rapid-eye movement sleep cycle. We identified the key regulation factors for function through global sensitivity analysis of landscape topography against wirings, which are in good agreements with experiments. PMID:24145451

Organization of Anti-Phase Synchronization Pattern in Neural Networks: What are the Key Factors?

PubMed Central

Li, Dong; Zhou, Changsong

2011-01-01

Anti-phase oscillation has been widely observed in cortical neural network. Elucidating the mechanism underlying the organization of anti-phase pattern is of significance for better understanding more complicated pattern formations in brain networks. In dynamical systems theory, the organization of anti-phase oscillation pattern has usually been considered to relate to time delay in coupling. This is consistent to conduction delays in real neural networks in the brain due to finite propagation velocity of action potentials. However, other structural factors in cortical neural network, such as modular organization (connection density) and the coupling types (excitatory or inhibitory), could also play an important role. In this work, we investigate the anti-phase oscillation pattern organized on a two-module network of either neuronal cell model or neural mass model, and analyze the impact of the conduction delay times, the connection densities, and coupling types. Our results show that delay times and coupling types can play key roles in this organization. The connection densities may have an influence on the stability if an anti-phase pattern exists due to the other factors. Furthermore, we show that anti-phase synchronization of slow oscillations can be achieved with small delay times if there is interaction between slow and fast oscillations. These results are significant for further understanding more realistic spatiotemporal dynamics of cortico-cortical communications. PMID:22232576

Animal-to-animal variability in the phasing of the crustacean cardiac motor pattern: an experimental and computational analysis

PubMed Central

Williams, Alex H.; Kwiatkowski, Molly A.; Mortimer, Adam L.; Marder, Eve; Zeeman, Mary Lou

2013-01-01

The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: “small cells” (SCs) and “large cells” (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintained. To determine both the consequences of this variability and how CG phasing is controlled, we modeled the CG as a pair of Morris-Lecar oscillators coupled by electrical and excitatory synapses and constructed a database of 15,000 simulated networks using random parameter sets. These simulations, like our experimental results, displayed variable phase relationships, with the bursts beginning together but ending at variable phases. The model suggests that the variable phasing of the pattern has important implications for the functional role of the excitatory synapses. In networks in which the two oscillators had similar duty cycles, the excitatory coupling functioned to increase cycle frequency. In networks with disparate duty cycles, it functioned to decrease network frequency. Overall, we suggest that the phasing of the CG may vary without compromising appropriate motor output and that this variability may critically determine how the network behaves in response to manipulations. PMID:23446690

Affective Monitoring: A Generic Mechanism for Affect Elicitation

PubMed Central

Phaf, R. Hans; Rotteveel, Mark

2012-01-01

In this paper we sketch a new framework for affect elicitation, which is based on previous evolutionary and connectionist modeling and experimental work from our group. Affective monitoring is considered a local match–mismatch process within a module of the neural network. Negative affect is raised instantly by mismatches, incongruency, disfluency, novelty, incoherence, and dissonance, whereas positive affect follows from matches, congruency, fluency, familiarity, coherence, and resonance, at least when an initial mismatch can be solved quickly. Affective monitoring is considered an evolutionary-early conflict and change detection process operating at the same level as, for instance, attentional selection. It runs in parallel and imparts affective flavor to emotional behavior systems, which involve evolutionary-prepared stimuli and action tendencies related to for instance defensive, exploratory, attachment, or appetitive behavior. Positive affect is represented in the networks by high-frequency oscillations, presumably in the gamma band. Negative affect corresponds to more incoherent lower-frequency oscillations, presumably in the theta band. For affect to become conscious, large-scale synchronization of the oscillations over the network and the construction of emotional experiences are required. These constructions involve perceptions of bodily states and action tendencies, but also appraisals as well as efforts to regulate the emotion. Importantly, affective monitoring accompanies every kind of information processing, but conscious emotions, which result from the later integration of affect in a cognitive context, are much rarer events. PMID:22403557

Time-Distance Sunspot Seismology with GONG Data

NASA Astrophysics Data System (ADS)

Braun, D. C.

1997-09-01

We present time-distance analyses of several active regions and a region of quiet Sun observed with the Global Oscillation Network Group (GONG). Analyzing temporal correlations between the p-mode oscillation signal observed within the sunspots with the signals integrated within surrounding annuli, we confirm the recent finding of Duvall and his colleagues that travel times (τ+) for outward propagating p-modes are smaller by approximately 1 minute than corresponding inward travel times (τ-). We also analyze correlations of the oscillation signal integrated within annuli of different radii. By varying the radius of the inner annulus (that which is closer to the target) we show that the radial extent of the region giving rise to the travel time perturbations is coincident with the outer boundary of the sunspot penumbrae. A comparison of independent methods designed to determine the mean travel time perturbations of p-modes passing through the sunspots is made. We find the surprising result that time-distance correlations that do not utilize the signal within the sunspot itself (employing ``two-skip'' trajectories) yield mean travel times that differ substantially from the average of τ+ and τ- and that are significantly closer in agreement with times predicted from scattering phase shifts measured by Hankel decomposition techniques. These observations suggest that it unlikely that Doppler shifts caused by subsurface flows are responsible for the travel time differences determined from center-annuli correlations targeted on sunspots. This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, a Division of the National Optical Astronomy Observatories, which is operated by AURA, Inc., under a cooperative agreement with the National Science Foundation.

Complex Dynamical Networks Constructed with Fully Controllable Nonlinear Nanomechanical Oscillators.

PubMed

Fon, Warren; Matheny, Matthew H; Li, Jarvis; Krayzman, Lev; Cross, Michael C; D'Souza, Raissa M; Crutchfield, James P; Roukes, Michael L

2017-10-11

Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks that provide dynamical control of individual nodes and edges, has remained elusive. Given the vast hierarchy of time scales involved, it also proves challenging to measure a complex network's full internal dynamics. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. Here, we demonstrate an experimental system that satisfies these requirements. It is based upon modular, fully controllable, nonlinear radio frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges of arbitrary topology. The dynamics of these oscillators and their surrounding network are analog and continuous-valued and can be fully interrogated in real time. They comprise a piezoelectric nanomechanical membrane resonator, which serves as the frequency-determining element within an electrical feedback circuit. This embodiment permits network interconnections entirely within the electrical domain and provides unprecedented node and edge control over a vast region of parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities. We demonstrate the operation of this platform through the real-time capture of the dynamics of a three-node ring network as it evolves from the uncoupled state to full synchronization.

Fast effects of glucocorticoids on memory-related network oscillations in the mouse hippocampus.

PubMed

Weiss, E K; Krupka, N; Bähner, F; Both, M; Draguhn, A

2008-05-01

Transient or lasting increases in glucocorticoids accompany deficits in hippocampus-dependent memory formation. Recent data indicate that the formation and consolidation of declarative and spatial memory are mechanistically related to different patterns of hippocampal network oscillations. These include gamma oscillations during memory acquisition and the faster ripple oscillations (approximately 200 Hz) during subsequent memory consolidation. We therefore analysed the effects of acutely applied glucocorticoids on network activity in mouse hippocampal slices. Evoked field population spikes and paired-pulse responses were largely unaltered by corticosterone or cortisol, respectively, despite a slight increase in maximal population spike amplitude by 10 microm corticosterone. Several characteristics of sharp waves and superimposed ripple oscillations were affected by glucocorticoids, most prominently the frequency of spontaneously occurring sharp waves. At 0.1 microm, corticosterone increased this frequency, whereas maximal (10 microm) concentrations led to a reduction. In addition, gamma oscillations became slightly faster and less regular in the presence of high doses of corticosteroids. The present study describes acute effects of glucocorticoids on sharp wave-ripple complexes and gamma oscillations in mouse hippocampal slices, revealing a potential background for memory deficits in the presence of elevated levels of these hormones.

Symmetries of Chimera States

NASA Astrophysics Data System (ADS)

Kemeth, Felix P.; Haugland, Sindre W.; Krischer, Katharina

2018-05-01

Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different setwise symmetries in the incoherent oscillators, and in particular, some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.

High frequency inductive lamp and power oscillator

DOEpatents

Kirkpatrick, Douglas A.; Gitsevich, Aleksandr

2005-09-27

An oscillator includes an amplifier having an input and an output, a feedback network connected between the input of the amplifier and the output of the amplifier, the feedback network being configured to provide suitable positive feedback from the output of the amplifier to the input of the amplifier to initiate and sustain an oscillating condition, and a tuning circuit connected to the input of the amplifier, wherein the tuning circuit is continuously variable and consists of solid state electrical components with no mechanically adjustable devices including a pair of diodes connected to each other at their respective cathodes with a control voltage connected at the junction of the diodes. Another oscillator includes an amplifier having an input and an output, a feedback network connected between the input of the amplifier and the output of the amplifier, the feedback network being configured to provide suitable positive feedback from the output of the amplifier to the input of the amplifier to initiate and sustain an oscillating condition, and transmission lines connected to the input of the amplifier with an input pad and a perpendicular transmission line extending from the input pad and forming a leg of a resonant "T", and wherein the feedback network is coupled to the leg of the resonant "T".

Distributed Bandpass Filtering and Signal Demodulation in Cortical Network Models

NASA Astrophysics Data System (ADS)

McDonnell, Mark D.

Experimental recordings of cortical activity often exhibit narrowband oscillations, at various center frequencies ranging in the order of 1-200 Hz. Many neuronal mechanisms are known to give rise to oscillations, but here we focus on a population effect known as sparsely synchronised oscillations. In this effect, individual neurons in a cortical network fire irregularly at slow average spike rates (1-10 Hz), but the population spike rate oscillates at gamma frequencies (greater than 40 Hz) in response to spike bombardment from the thalamus. These cortical networks form recurrent (feedback) synapses. Here we describe a model of sparsely synchronized population oscillations using the language of feedback control engineering, where we treat spiking as noisy feedback. We show, using a biologically realistic model of synaptic current that includes a delayed response to inputs, that the collective behavior of the neurons in the network is like a distributed bandpass filter acting on the network inputs. Consequently, the population response has the character of narrowband random noise, and therefore has an envelope and instantaneous frequency with lowpass characteristics. Given that there exist biologically plausible neuronal mechanisms for demodulating the envelope and instantaneous frequency, we suggest there is potential for similar effects to be exploited in nanoscale electronics implementations of engineered communications receivers.

Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems

NASA Astrophysics Data System (ADS)

Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato

Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.

The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells.

PubMed

Gosak, Marko; Stožer, Andraž; Markovič, Rene; Dolenšek, Jurij; Marhl, Marko; Rupnik, Marjan Slak; Perc, Matjaž

2015-07-01

Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue.

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus.

PubMed

Fan, Denggui; Wang, Qingyun; Su, Jianzhong; Xi, Hongguang

2017-12-01

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

An efficient approach to suppress the negative role of contrarian oscillators in synchronization

NASA Astrophysics Data System (ADS)

Zhang, Xiyun; Ruan, Zhongyuan; Liu, Zonghua

2013-09-01

It has been found that contrarian oscillators usually take a negative role in the collective behaviors formed by conformist oscillators. However, experiments revealed that it is also possible to achieve a strong coherence even when there are contrarians in the system such as neuron networks with both excitable and inhibitory neurons. To understand the underlying mechanism of this abnormal phenomenon, we here consider a complex network of coupled Kuramoto oscillators with mixed positive and negative couplings and present an efficient approach, i.e., tit-for-tat strategy, to suppress the negative role of contrarian oscillators in synchronization and thus increase the order parameter of synchronization. Two classes of contrarian oscillators are numerically studied and a brief theoretical analysis is provided to explain the numerical results.

Inferring phase equations from multivariate time series.

PubMed

Tokuda, Isao T; Jain, Swati; Kiss, István Z; Hudson, John L

2007-08-10

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast with previous methods it does not require measurements in isolated single or two-oscillator setups. This noninvasive technique can be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data are taken from the nonsynchronized regime. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the obtained phase model is utilized to predict the synchronization diagram of the system.

SYNCHRONIZATION OF HETEROGENEOUS OSCILLATORS UNDER NETWORK MODIFICATIONS: PERTURBATION AND OPTIMIZATION OF THE SYNCHRONY ALIGNMENT FUNCTION

PubMed Central

Taylor, Dane; Skardal, Per Sebastian; Sun, Jie

2016-01-01

Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications—for which proper functionality depends sensitively on the extent of synchronization—there remains a lack of understanding for how systems can best evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system’s ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments. PMID:27872501

Complex and unexpected dynamics in simple genetic regulatory networks

NASA Astrophysics Data System (ADS)

Borg, Yanika; Ullner, Ekkehard; Alagha, Afnan; Alsaedi, Ahmed; Nesbeth, Darren; Zaikin, Alexey

2014-03-01

One aim of synthetic biology is to construct increasingly complex genetic networks from interconnected simpler ones to address challenges in medicine and biotechnology. However, as systems increase in size and complexity, emergent properties lead to unexpected and complex dynamics due to nonlinear and nonequilibrium properties from component interactions. We focus on four different studies of biological systems which exhibit complex and unexpected dynamics. Using simple synthetic genetic networks, small and large populations of phase-coupled quorum sensing repressilators, Goodwin oscillators, and bistable switches, we review how coupled and stochastic components can result in clustering, chaos, noise-induced coherence and speed-dependent decision making. A system of repressilators exhibits oscillations, limit cycles, steady states or chaos depending on the nature and strength of the coupling mechanism. In large repressilator networks, rich dynamics can also be exhibited, such as clustering and chaos. In populations of Goodwin oscillators, noise can induce coherent oscillations. In bistable systems, the speed with which incoming external signals reach steady state can bias the network towards particular attractors. These studies showcase the range of dynamical behavior that simple synthetic genetic networks can exhibit. In addition, they demonstrate the ability of mathematical modeling to analyze nonlinearity and inhomogeneity within these systems.

Dynamics of alpha control: Preparatory suppression of posterior alpha oscillations by frontal modulators revealed with combined EEG and event-related optical signal (EROS)

PubMed Central

Mathewson, Kyle E.; Beck, Diane M.; Ro, Tony; Maclin, Edward L.; Low, Kathy A.; Fabiani, Monica; Gratton, Gabriele

2015-01-01

We investigated the dynamics of brain processes facilitating conscious experience of external stimuli. Previously we proposed that alpha (8-12 Hz) oscillations, which fluctuate with both sustained and directed attention, represent a pulsed inhibition of ongoing sensory brain activity. Here we tested the prediction that inhibitory alpha oscillations in visual cortex are modulated by top-down signals from frontoparietal attention networks. We measured modulations in phase-coherent alpha oscillations from superficial frontal, parietal, and occipital cortices using the event-related optical signal (EROS), a measure of neuronal activity affording high spatiotemporal resolution, along with concurrently-recorded electroencephalogram (EEG), while subjects performed a visual target-detection task. The pre-target alpha oscillations measured with EEG and EROS from posterior areas were larger for subsequently undetected targets, supporting alpha's inhibitory role. Using EROS, we localized brain correlates of these awareness-related alpha oscillations measured at the scalp to the cuneus and precuneus. Crucially, EROS alpha suppression correlated with posterior EEG alpha power across subjects. Sorting the EROS data based on EEG alpha power quartiles to investigate alpha modulators revealed that suppression of posterior alpha was preceded by increased activity in regions of the dorsal attention network, and decreased activity in regions of the cingulo-opercular network. Cross-correlations revealed the temporal dynamics of activity within these preparatory networks prior to posterior alpha modulation. The novel combination of EEG and EROS afforded localization of the sources and correlates of alpha oscillations and their temporal relationships, supporting our proposal that top-down control from attention networks modulates both posterior alpha and awareness of visual stimuli. PMID:24702458

A fast, robust and tunable synthetic gene oscillator.

PubMed

Stricker, Jesse; Cookson, Scott; Bennett, Matthew R; Mather, William H; Tsimring, Lev S; Hasty, Jeff

2008-11-27

One defining goal of synthetic biology is the development of engineering-based approaches that enable the construction of gene-regulatory networks according to 'design specifications' generated from computational modelling. This approach provides a systematic framework for exploring how a given regulatory network generates a particular phenotypic behaviour. Several fundamental gene circuits have been developed using this approach, including toggle switches and oscillators, and these have been applied in new contexts such as triggered biofilm development and cellular population control. Here we describe an engineered genetic oscillator in Escherichia coli that is fast, robust and persistent, with tunable oscillatory periods as fast as 13 min. The oscillator was designed using a previously modelled network architecture comprising linked positive and negative feedback loops. Using a microfluidic platform tailored for single-cell microscopy, we precisely control environmental conditions and monitor oscillations in individual cells through multiple cycles. Experiments reveal remarkable robustness and persistence of oscillations in the designed circuit; almost every cell exhibited large-amplitude fluorescence oscillations throughout observation runs. The oscillatory period can be tuned by altering inducer levels, temperature and the media source. Computational modelling demonstrates that the key design principle for constructing a robust oscillator is a time delay in the negative feedback loop, which can mechanistically arise from the cascade of cellular processes involved in forming a functional transcription factor. The positive feedback loop increases the robustness of the oscillations and allows for greater tunability. Examination of our refined model suggested the existence of a simplified oscillator design without positive feedback, and we construct an oscillator strain confirming this computational prediction.

Impaired Long Distance Functional Connectivity and Weighted Network Architecture in Alzheimer's Disease

PubMed Central

Liu, Yong; Yu, Chunshui; Zhang, Xinqing; Liu, Jieqiong; Duan, Yunyun; Alexander-Bloch, Aaron F.; Liu, Bing; Jiang, Tianzi; Bullmore, Ed

2014-01-01

Alzheimer's disease (AD) is increasingly recognized as a disconnection syndrome, which leads to cognitive impairment due to the disruption of functional activity across large networks or systems of interconnected brain regions. We explored abnormal functional magnetic resonance imaging (fMRI) resting-state dynamics, functional connectivity, and weighted functional networks, in a sample of patients with severe AD (N = 18) and age-matched healthy volunteers (N = 21). We found that patients had reduced amplitude and regional homogeneity of low-frequency fMRI oscillations, and reduced the strength of functional connectivity, in several regions previously described as components of the default mode network, for example, medial posterior parietal cortex and dorsal medial prefrontal cortex. In patients with severe AD, functional connectivity was particularly attenuated between regions that were separated by a greater physical distance; and loss of long distance connectivity was associated with less efficient global and nodal network topology. This profile of functional abnormality in severe AD was consistent with the results of a comparable analysis of data on 2 additional groups of patients with mild AD (N = 17) and amnestic mild cognitive impairment (MCI; N = 18). A greater degree of cognitive impairment, measured by the mini-mental state examination across all patient groups, was correlated with greater attenuation of functional connectivity, particularly over long connection distances, for example, between anterior and posterior components of the default mode network, and greater reduction of global and nodal network efficiency. These results indicate that neurodegenerative disruption of fMRI oscillations and connectivity in AD affects long-distance connections to hub nodes, with the consequent loss of network efficiency. This profile was evident also to a lesser degree in the patients with less severe cognitive impairment, indicating that the potential of resting-state fMRI measures as biomarkers or predictors of disease progression in AD. PMID:23314940

New type of chimera structures in a ring of bistable FitzHugh-Nagumo oscillators with nonlocal interaction

NASA Astrophysics Data System (ADS)

Shepelev, I. A.; Vadivasova, T. E.; Bukh, A. V.; Strelkova, G. I.; Anishchenko, V. S.

2017-04-01

We study the spatiotemporal dynamics of a ring of nonlocally coupled FitzHugh-Nagumo oscillators in the bistable regime. A new type of chimera patterns has been found in the noise-free network and when isolated elements do not oscillate. The region of existence of these structures has been explored when the coupling range and the coupling strength between the network elements are varied.

Robustness of chimera states in complex dynamical systems

PubMed Central

Yao, Nan; Huang, Zi-Gang; Lai, Ying-Cheng; Zheng, Zhi-Gang

2013-01-01

The remarkable phenomenon of chimera state in systems of non-locally coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interests. In such a state, different groups of oscillators can exhibit characteristically distinct types of dynamical behaviors, in spite of identity of the oscillators. But how robust are chimera states against random perturbations to the structure of the underlying network? We address this fundamental issue by studying the effects of random removal of links on the probability for chimera states. Using direct numerical calculations and two independent theoretical approaches, we find that the likelihood of chimera state decreases with the probability of random-link removal. A striking finding is that, even when a large number of links are removed so that chimera states are deemed not possible, in the state space there are generally both coherent and incoherent regions. The regime of chimera state is a particular case in which the oscillators in the coherent region happen to be synchronized or phase-locked. PMID:24343533

Experimental observation of chimera and cluster states in a minimal globally coupled network

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

2016-09-01

A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.

Influences of adding negative couplings between cliques of Kuramoto-like oscillators

NASA Astrophysics Data System (ADS)

Yang, Li-xin; Lin, Xiao-lin; Jiang, Jun

2018-06-01

We study the dynamics in a clustered network of coupled oscillators by considering positive and negative coupling schemes. Second order oscillators can be interpreted as a model of consumers and generators working in a power network. Numerical results indicate that coupling strategies play an important role in the synchronizability of the clustered power network. It is found that the synchronizability can be enhanced as the positive intragroup connections increase. Meanwhile, when the intragroup interactions are positive and the probability p that two nodes belonging to different clusters are connected is increased, the synchronization has better performance. Besides, when the intragroup connections are negative, it is observed that the power network has poor synchronizability as the probability p increases. Our simulation results can help us understand the collective behavior of the power network with positive and negative couplings.

Beta and gamma oscillatory activities associated with olfactory memory tasks: different rhythms for different functional networks?

PubMed Central

Martin, Claire; Ravel, Nadine

2014-01-01

Olfactory processing in behaving animals, even at early stages, is inextricable from top down influences associated with odor perception. The anatomy of the olfactory network (olfactory bulb, piriform, and entorhinal cortices) and its unique direct access to the limbic system makes it particularly attractive to study how sensory processing could be modulated by learning and memory. Moreover, olfactory structures have been early reported to exhibit oscillatory population activities easy to capture through local field potential recordings. An attractive hypothesis is that neuronal oscillations would serve to “bind” distant structures to reach a unified and coherent perception. In relation to this hypothesis, we will assess the functional relevance of different types of oscillatory activity observed in the olfactory system of behaving animals. This review will focus primarily on two types of oscillatory activities: beta (15–40 Hz) and gamma (60–100 Hz). While gamma oscillations are dominant in the olfactory system in the absence of odorant, both beta and gamma rhythms have been reported to be modulated depending on the nature of the olfactory task. Studies from the authors of the present review and other groups brought evidence for a link between these oscillations and behavioral changes induced by olfactory learning. However, differences in studies led to divergent interpretations concerning the respective role of these oscillations in olfactory processing. Based on a critical reexamination of those data, we propose hypotheses on the functional involvement of beta and gamma oscillations for odor perception and memory. PMID:25002840

Chimera states in two-dimensional networks of locally coupled oscillators

NASA Astrophysics Data System (ADS)

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Chimera states in two-dimensional networks of locally coupled oscillators.

PubMed

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K; Ghosh, Dibakar; Lakshmanan, M

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Synchronization properties of network motifs: Influence of coupling delay and symmetry

NASA Astrophysics Data System (ADS)

D'Huys, O.; Vicente, R.; Erneux, T.; Danckaert, J.; Fischer, I.

2008-09-01

We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.

Design principles for robust oscillatory behavior.

PubMed

Castillo-Hair, Sebastian M; Villota, Elizabeth R; Coronado, Alberto M

2015-09-01

Oscillatory responses are ubiquitous in regulatory networks of living organisms, a fact that has led to extensive efforts to study and replicate the circuits involved. However, to date, design principles that underlie the robustness of natural oscillators are not completely known. Here we study a three-component enzymatic network model in order to determine the topological requirements for robust oscillation. First, by simulating every possible topological arrangement and varying their parameter values, we demonstrate that robust oscillators can be obtained by augmenting the number of both negative feedback loops and positive autoregulations while maintaining an appropriate balance of positive and negative interactions. We then identify network motifs, whose presence in more complex topologies is a necessary condition for obtaining oscillatory responses. Finally, we pinpoint a series of simple architectural patterns that progressively render more robust oscillators. Together, these findings can help in the design of more reliable synthetic biomolecular networks and may also have implications in the understanding of other oscillatory systems.

Design and progress report for compact cryocooled sapphire oscillator 'VCSO'

NASA Technical Reports Server (NTRS)

Dick, G. John; Wang, Rabi T.; Tjoelker, Robert L.

2005-01-01

We report on the development of a compact cryocooled sapphiere oscillator 'VCSO', designed as a higher-performance replacement for ultra-stable quartz oscillators in local oscillator, cleanup, and flywheel applications in the frequency generation and distribution subsystems of NASA's Deep Space Network (DSN).

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

Delay decomposition approach to [Formula: see text] filtering analysis of genetic oscillator networks with time-varying delays.

PubMed

Revathi, V M; Balasubramaniam, P

2016-04-01

In this paper, the [Formula: see text] filtering problem is treated for N coupled genetic oscillator networks with time-varying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov-Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed [Formula: see text] performance. Second, based on the above analysis, the existence of the designed [Formula: see text] filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.

Interaction of chimera states in a multilayered network of nonlocally coupled oscillators

NASA Astrophysics Data System (ADS)

Goremyko, M. V.; Maksimenko, V. A.; Makarov, V. V.; Ghosh, D.; Bera, B.; Dana, S. K.; Hramov, A. E.

2017-08-01

The processes of formation and evolution of chimera states in the model of a multilayered network of nonlinear elements with complex coupling topology are studied. A two-layered network of nonlocally intralayer-coupled Kuramoto-Sakaguchi phase oscillators is taken as the object of investigation. Different modes implemented in this system upon variation of the degree of interlayer interaction are demonstrated.

Thermodynamic characterization of synchronization-optimized oscillator networks

NASA Astrophysics Data System (ADS)

Yanagita, Tatsuo; Ichinomiya, Takashi

2014-12-01

We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1 000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.

Neural Oscillations and Synchrony in Brain Dysfunction and Neuropsychiatric Disorders: It's About Time.

PubMed

Mathalon, Daniel H; Sohal, Vikaas S

2015-08-01

Neural oscillations are rhythmic fluctuations over time in the activity or excitability of single neurons, local neuronal populations or "assemblies," and/or multiple regionally distributed neuronal assemblies. Synchronized oscillations among large numbers of neurons are evident in electrocorticographic, electroencephalographic, magnetoencephalographic, and local field potential recordings and are generally understood to depend on inhibition that paces assemblies of excitatory neurons to produce alternating temporal windows of reduced and increased excitability. Synchronization of neural oscillations is supported by the extensive networks of local and long-range feedforward and feedback bidirectional connections between neurons. Here, we review some of the major methods and measures used to characterize neural oscillations, with a focus on gamma oscillations. Distinctions are drawn between stimulus-independent oscillations recorded during resting states or intervals between task events, stimulus-induced oscillations that are time locked but not phase locked to stimuli, and stimulus-evoked oscillations that are both time and phase locked to stimuli. Synchrony of oscillations between recording sites, and between the amplitudes and phases of oscillations of different frequencies (cross-frequency coupling), is described and illustrated. Molecular mechanisms underlying gamma oscillations are also reviewed. Ultimately, understanding the temporal organization of neuronal network activity, including interactions between neural oscillations, is critical for elucidating brain dysfunction in neuropsychiatric disorders.

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions.

PubMed

Semenov, Sergey N; Kraft, Lewis J; Ainla, Alar; Zhao, Mengxia; Baghbanzadeh, Mostafa; Campbell, Victoria E; Kang, Kyungtae; Fox, Jerome M; Whitesides, George M

2016-09-29

Networks of organic chemical reactions are important in life and probably played a central part in its origin. Network dynamics regulate cell division, circadian rhythms, nerve impulses and chemotaxis, and guide the development of organisms. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics such as spontaneous pattern formation, bistability and periodic oscillations, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes and DNA) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions), the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

NASA Astrophysics Data System (ADS)

Semenov, Sergey N.; Kraft, Lewis J.; Ainla, Alar; Zhao, Mengxia; Baghbanzadeh, Mostafa; Campbell, Victoria E.; Kang, Kyungtae; Fox, Jerome M.; Whitesides, George M.

2016-09-01

Networks of organic chemical reactions are important in life and probably played a central part in its origin. Network dynamics regulate cell division, circadian rhythms, nerve impulses and chemotaxis, and guide the development of organisms. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics such as spontaneous pattern formation, bistability and periodic oscillations, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes and DNA) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions), the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.

Selective Coupling between Theta Phase and Neocortical Fast Gamma Oscillations during REM-Sleep in Mice

PubMed Central

Scheffzük, Claudia; Kukushka, Valeriy I.; Vyssotski, Alexei L.; Draguhn, Andreas

2011-01-01

Background The mammalian brain expresses a wide range of state-dependent network oscillations which vary in frequency and spatial extension. Such rhythms can entrain multiple neurons into coherent patterns of activity, consistent with a role in behaviour, cognition and memory formation. Recent evidence suggests that locally generated fast network oscillations can be systematically aligned to long-range slow oscillations. It is likely that such cross-frequency coupling supports specific tasks including behavioural choice and working memory. Principal Findings We analyzed temporal coupling between high-frequency oscillations and EEG theta activity (4–12 Hz) in recordings from mouse parietal neocortex. Theta was exclusively present during active wakefulness and REM-sleep. Fast oscillations occurred in two separate frequency bands: gamma (40–100 Hz) and fast gamma (120–160 Hz). Theta, gamma and fast gamma were more prominent during active wakefulness as compared to REM-sleep. Coupling between theta and the two types of fast oscillations, however, was more pronounced during REM-sleep. This state-dependent cross-frequency coupling was particularly strong for theta-fast gamma interaction which increased 9-fold during REM as compared to active wakefulness. Theta-gamma coupling increased only by 1.5-fold. Significance State-dependent cross-frequency-coupling provides a new functional characteristic of REM-sleep and establishes a unique property of neocortical fast gamma oscillations. Interactions between defined patterns of slow and fast network oscillations may serve selective functions in sleep-dependent information processing. PMID:22163023

Regulating Cortical Oscillations in an Inhibition-Stabilized Network.

PubMed

Jadi, Monika P; Sejnowski, Terrence J

2014-04-21

Understanding the anatomical and functional architecture of the brain is essential for designing neurally inspired intelligent systems. Theoretical and empirical studies suggest a role for narrowband oscillations in shaping the functional architecture of the brain through their role in coding and communication of information. Such oscillations are ubiquitous signals in the electrical activity recorded from the brain. In the cortex, oscillations detected in the gamma range (30-80 Hz) are modulated by behavioral states and sensory features in complex ways. How is this regulation achieved? Although several underlying principles for the genesis of these oscillations have been proposed, a unifying account for their regulation has remained elusive. In a network of excitatory and inhibitory neurons operating in an inhibition-stabilized regime, we show that strongly superlinear responses of inhibitory neurons facilitate bidirectional regulation of oscillation frequency and power. In such a network, the balance of drives to the excitatory and inhibitory populations determines how the power and frequency of oscillations are modulated. The model accounts for the puzzling increase in their frequency with the salience of visual stimuli, and a decrease with their size. Oscillations in our model grow stronger as the mean firing level is reduced, accounting for the size dependence of visually evoked gamma rhythms, and suggesting a role for oscillations in improving the signal-to-noise ratio (SNR) of signals in the brain. Empirically testing such predictions is still challenging, and implementing the proposed coding and communication strategies in neuromorphic systems could assist in our understanding of the biological system.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

PubMed

Liu, Wei; Huang, Jie

2018-03-01

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Entrainment of a Bacterial Synthetic Gene Oscillator through Proteolytic Queueing.

PubMed

Butzin, Nicholas C; Hochendoner, Philip; Ogle, Curtis T; Mather, William H

2017-03-17

Internal chemical oscillators (chemical clocks) direct the behavior of numerous biological systems, and maintenance of a given period and phase among many such oscillators may be important for their proper function. However, both environmental variability and fundamental molecular noise can cause biochemical oscillators to lose coherence. One solution to maintaining coherence is entrainment, where an external signal provides a cue that resets the phase of the oscillators. In this work, we study the entrainment of gene networks by a queueing interaction established by competition between proteins for a common proteolytic pathway. Principles of queueing entrainment are investigated for an established synthetic oscillator in Escherichia coli. We first explore this theoretically using a standard chemical reaction network model and a map-based model, both of which suggest that queueing entrainment can be achieved through pulsatile production of an additional protein competing for a common degradation pathway with the oscillator proteins. We then use a combination of microfluidics and fluorescence microscopy to verify that pulse trains modulating the production rate of a fluorescent protein targeted to the same protease (ClpXP) as the synthetic oscillator can entrain the oscillator.

Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together

NASA Astrophysics Data System (ADS)

Zhang, Yuanzhao; Motter, Adilson E.

2018-01-01

An outstanding problem in the study of networks of heterogeneous dynamical units concerns the development of rigorous methods to probe the stability of synchronous states when the differences between the units are not small. Here, we address this problem by presenting a generalization of the master stability formalism that can be applied to heterogeneous oscillators with large mismatches. Our approach is based on the simultaneous block diagonalization of the matrix terms in the variational equation, and it leads to dimension reduction that simplifies the original equation significantly. This new formalism allows the systematic investigation of scenarios in which the oscillators need to be nonidentical in order to reach an identical state, where all oscillators are completely synchronized. In the case of networks of identically coupled oscillators, this corresponds to breaking the symmetry of the system as a means to preserve the symmetry of the dynamical state— a recently discovered effect termed asymmetry-induced synchronization (AISync). Our framework enables us to identify communication delay as a new and potentially common mechanism giving rise to AISync, which we demonstrate using networks of delay-coupled Stuart-Landau oscillators. The results also have potential implications for control, as they reveal oscillator heterogeneity as an attribute that may be manipulated to enhance the stability of synchronous states.

The effect of aging on EEG brain oscillations related to sensory and sensorimotor functions.

PubMed

Dushanova, Juliana; Christov, Mario

2014-03-01

The question of the present study is whether the brain as a system with gradually decreasing resources maximizes its performance by reorganizing neural networks for greater efficiency. Auditory event-related low frequency oscillations (delta δ - [2, 4]Hz; theta θ - [4.5, 7]Hz; alpha α - [7.5, 12]Hz) were examined during an auditory discrimination motor task (low-frequency tone - right hand movement, high-frequency tone - left hand movement) between two groups with mean age 26.3 and 55 years. The amplitudes of the phase-locked δ, θ and α activity were more pronounced with a progressive increase in age during the sensory processing, independent of tone type. The difference between the groups with respect to scalp distribution was tone-independent for delta/theta oscillations, but not for the alpha activity. Age-related and tone-dependent changes in α band activity were focused at frontal and sensorimotor areas. Neither functional brain specificity was observed for the amplitudes of the low-frequency (δ, θ, α) oscillations during the cognitive processing, which diminished with increasing age. The cognitive brain oscillatory specificity diminished with increasing age. Copyright © 2014 Medical University of Bialystok. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved.

Impact of environmental inputs on reverse-engineering approach to network structures.

PubMed

Wu, Jianhua; Sinfield, James L; Buchanan-Wollaston, Vicky; Feng, Jianfeng

2009-12-04

Uncovering complex network structures from a biological system is one of the main topic in system biology. The network structures can be inferred by the dynamical Bayesian network or Granger causality, but neither techniques have seriously taken into account the impact of environmental inputs. With considerations of natural rhythmic dynamics of biological data, we propose a system biology approach to reveal the impact of environmental inputs on network structures. We first represent the environmental inputs by a harmonic oscillator and combine them with Granger causality to identify environmental inputs and then uncover the causal network structures. We also generalize it to multiple harmonic oscillators to represent various exogenous influences. This system approach is extensively tested with toy models and successfully applied to a real biological network of microarray data of the flowering genes of the model plant Arabidopsis Thaliana. The aim is to identify those genes that are directly affected by the presence of the sunlight and uncover the interactive network structures associating with flowering metabolism. We demonstrate that environmental inputs are crucial for correctly inferring network structures. Harmonic causal method is proved to be a powerful technique to detect environment inputs and uncover network structures, especially when the biological data exhibit periodic oscillations.

Experimental observation of chimera and cluster states in a minimal globally coupled network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, Joseph D.; Department of Physics, University of Maryland, College Park, Maryland 20742; Bansal, Kanika

A “chimera state” is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belongingmore » to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.« less

Sustained Activity in Hierarchical Modular Neural Networks: Self-Organized Criticality and Oscillations

PubMed Central

Wang, Sheng-Jun; Hilgetag, Claus C.; Zhou, Changsong

2010-01-01

Cerebral cortical brain networks possess a number of conspicuous features of structure and dynamics. First, these networks have an intricate, non-random organization. In particular, they are structured in a hierarchical modular fashion, from large-scale regions of the whole brain, via cortical areas and area subcompartments organized as structural and functional maps to cortical columns, and finally circuits made up of individual neurons. Second, the networks display self-organized sustained activity, which is persistent in the absence of external stimuli. At the systems level, such activity is characterized by complex rhythmical oscillations over a broadband background, while at the cellular level, neuronal discharges have been observed to display avalanches, indicating that cortical networks are at the state of self-organized criticality (SOC). We explored the relationship between hierarchical neural network organization and sustained dynamics using large-scale network modeling. Previously, it was shown that sparse random networks with balanced excitation and inhibition can sustain neural activity without external stimulation. We found that a hierarchical modular architecture can generate sustained activity better than random networks. Moreover, the system can simultaneously support rhythmical oscillations and SOC, which are not present in the respective random networks. The mechanism underlying the sustained activity is that each dense module cannot sustain activity on its own, but displays SOC in the presence of weak perturbations. Therefore, the hierarchical modular networks provide the coupling among subsystems with SOC. These results imply that the hierarchical modular architecture of cortical networks plays an important role in shaping the ongoing spontaneous activity of the brain, potentially allowing the system to take advantage of both the sensitivity of critical states and the predictability and timing of oscillations for efficient information processing. PMID:21852971

Explosive death of conjugate coupled Van der Pol oscillators on networks

NASA Astrophysics Data System (ADS)

Zhao, Nannan; Sun, Zhongkui; Yang, Xiaoli; Xu, Wei

2018-06-01

Explosive death phenomenon has been gradually gaining attention of researchers due to the research boom of explosive synchronization, and it has been observed recently for the identical or nonidentical coupled systems in all-to-all network. In this work, we investigate the emergence of explosive death in networked Van der Pol (VdP) oscillators with conjugate variables coupling. It is demonstrated that the network structures play a crucial role in identifying the types of explosive death behaviors. We also observe that the damping coefficient of the VdP system not only can determine whether the explosive death state is generated but also can adjust the forward transition point. We further show that the backward transition point is independent of the network topologies and the damping coefficient, which is well confirmed by theoretical analysis. Our results reveal the generality of explosive death phenomenon in different network topologies and are propitious to promote a better comprehension for the oscillation quenching behaviors.

Basin stability measure of different steady states in coupled oscillators

NASA Astrophysics Data System (ADS)

Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar

2017-04-01

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.

Frequency adjustment and synchrony in networks of delayed pulse-coupled oscillators

NASA Astrophysics Data System (ADS)

Nishimura, Joel

2015-01-01

We introduce a system of pulse-coupled oscillators that can change both their phases and frequencies and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on strongly connected graphs with time delays. The analysis involves decomposing the network into a forest of tree-like structures that capture causality. These results provide a robust method of sensor net synchronization as well as demonstrate a new avenue of possible pulse-coupled oscillator research.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

Collective stochastic coherence in recurrent neuronal networks

NASA Astrophysics Data System (ADS)

Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi

2016-09-01

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.

Basal Ganglia Beta Oscillations Accompany Cue Utilization

PubMed Central

Leventhal, Daniel K.; Gage, Gregory J.; Schmidt, Robert; Pettibone, Jeffrey R.; Case, Alaina C.; Berke, Joshua D.

2012-01-01

SUMMARY Beta oscillations in cortical-basal ganglia (BG) circuits have been implicated in normal movement suppression and motor impairment in Parkinson’s disease. To dissect the functional correlates of these rhythms we compared neural activity during four distinct variants of a cued choice task in rats. Brief beta (~20 Hz) oscillations occurred simultaneously throughout the cortical-BG network, both spontaneously and at precise moments of task performance. Beta phase was rapidly reset in response to salient cues, yet increases in beta power were not rigidly linked to cues, movements, or movement suppression. Rather, beta power was enhanced after cues were used to determine motor output. We suggest that beta oscillations reflect a postdecision stabilized state of cortical-BG networks, which normally reduces interference from alternative potential actions. The abnormally strong beta seen in Parkinson’s Disease may reflect overstabilization of these networks, producing pathological persistence of the current motor state. PMID:22325204

Designing synthetic networks in silico: a generalised evolutionary algorithm approach.

PubMed

Smith, Robert W; van Sluijs, Bob; Fleck, Christian

2017-12-02

Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes). The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction. In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.

Solar filament material oscillations and drainage before eruption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bi, Yi; Jiang, Yunchun; Yang, Jiayan

Both large-amplitude longitudinal (LAL) oscillations and material drainage in a solar filament are associated with the flow of material along the filament axis, often followed by an eruption. However, the relationship between these two motions and a subsequent eruption event is poorly understood. We analyze a filament eruption using EUV imaging data captured by the Atmospheric Imaging Array on board the Solar Dynamics Observatory and the Hα images from the Global Oscillation Network Group. Hours before the eruption, the filament was activated, with one of its legs undergoing a slow rising motion. The asymmetric activation inclined the filament relative tomore » the solar surface. After the active phase, LAL oscillations were observed in the inclined filament. The oscillation period increased slightly over time, which may suggest that the magnetic fields supporting the filament evolve to be flatter during the slow rising phase. After the oscillations, a significant amount of filament material was drained toward one filament endpoint, followed immediately by the violent eruption of the filament. The material drainage may further support the change in magnetic topology prior to the eruption. Moreover, we suggest that the filament material drainage could play a role in the transition from a slow to a fast rise of the erupting filament.« less

The Drosophila Circadian Pacemaker Circuit: Pas de Deux or Tarantella?

PubMed Central

Sheeba, Vasu; Kaneko, Maki; Sharma, Vijay Kumar; Holmes, Todd C.

2008-01-01

Molecular genetic analysis of the fruit fly Drosophila melanogaster has revolutionized our understanding of the transcription/translation loop mechanisms underlying the circadian molecular oscillator. More recently, Drosophila has been used to understand how different neuronal groups within the circadian pacemaker circuit interact to regulate the overall behavior of the fly in response to daily cyclic environmental cues as well as seasonal changes. Our present understanding of circadian timekeeping at the molecular and circuit level is discussed with a critical evaluation of the strengths and weaknesses of present models. Two models for circadian neural circuits are compared: one that posits that two anatomically distinct oscillators control the synchronization to the two major daily morning and evening transitions, versus a distributed network model that posits that many cell-autonomous oscillators are coordinated in a complex fashion and respond via plastic mechanisms to changes in environmental cues. PMID:18307108

Nonlinear analysis of a family of LC tuned inverters

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1975-01-01

Four widely used self-oscillating dc-to-square-wave parallel inverters which employ an inductor-capacitor tuned network to determine the oscillation frequency are reduced to a common equivalent RLC network, The techniques of singular-point analysis and state-plane interpretations are employed to describe the steady-state and transient behavior of these circuits and to elucidate the three possible modes of operation: quasi-harmonic, relaxation, and discontinuous. Design guidelines are provided through a study of the influence of circuit parameter variations on the characteristics of oscillation and on frequency stability. Several examples are provided to illustrate the usefulness of this analysis when studying such problems as transistor emitter-to-base junction breakdown during oscillations and the design of starting circuits to insure self-excited oscillations in these inverters.

Autonomous Modeling, Statistical Complexity and Semi-annealed Treatment of Boolean Networks

NASA Astrophysics Data System (ADS)

Gong, Xinwei

This dissertation presents three studies on Boolean networks. Boolean networks are a class of mathematical systems consisting of interacting elements with binary state variables. Each element is a node with a Boolean logic gate, and the presence of interactions between any two nodes is represented by directed links. Boolean networks that implement the logic structures of real systems are studied as coarse-grained models of the real systems. Large random Boolean networks are studied with mean field approximations and used to provide a baseline of possible behaviors of large real systems. This dissertation presents one study of the former type, concerning the stable oscillation of a yeast cell-cycle oscillator, and two studies of the latter type, respectively concerning the statistical complexity of large random Boolean networks and an extension of traditional mean field techniques that accounts for the presence of short loops. In the cell-cycle oscillator study, a novel autonomous update scheme is introduced to study the stability of oscillations in small networks. A motif that corrects pulse-growing perturbations and a motif that grows pulses are identified. A combination of the two motifs is capable of sustaining stable oscillations. Examining a Boolean model of the yeast cell-cycle oscillator using an autonomous update scheme yields evidence that it is endowed with such a combination. Random Boolean networks are classified as ordered, critical or disordered based on their response to small perturbations. In the second study, random Boolean networks are taken as prototypical cases for the evaluation of two measures of complexity based on a criterion for optimal statistical prediction. One measure, defined for homogeneous systems, does not distinguish between the static spatial inhomogeneity in the ordered phase and the dynamical inhomogeneity in the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical phases and for highly disordered networks, peaking somewhere in the disordered phase. Individual nodes with high complexity have, on average, a larger influence on the system dynamics. Lastly, a semi-annealed approximation that preserves the correlation between states at neighboring nodes is introduced to study a social game-inspired network model in which all links are bidirectional and all nodes have a self-input. The technique developed here is shown to yield accurate predictions of distribution of players' states, and accounts for some nontrivial collective behavior of game theoretic interest.

Duality in Phase Space and Complex Dynamics of an Integrated Pest Management Network Model

NASA Astrophysics Data System (ADS)

Yuan, Baoyin; Tang, Sanyi; Cheke, Robert A.

Fragmented habitat patches between which plants and animals can disperse can be modeled as networks with varying degrees of connectivity. A predator-prey model with network structures is proposed for integrated pest management (IPM) with impulsive control actions. The model was analyzed using numerical methods to investigate how factors such as the impulsive period, the releasing constant of natural enemies and the mode of connections between the patches affect pest outbreak patterns and the success or failure of pest control. The concept of the cluster as defined by Holland and Hastings is used to describe variations in results ranging from global synchrony when all patches have identical fluctuations to n-cluster solutions with all patches having different dynamics. Heterogeneity in the initial densities of either pest or natural enemy generally resulted in a variety of cluster oscillations. Surprisingly, if n > 1, the clusters fall into two groups one with low amplitude fluctuations and the other with high amplitude fluctuations (i.e. duality in phase space), implying that control actions radically alter the system's characteristics by inducing duality and more complex dynamics. When the impulsive period is small enough, i.e. the control strategy is undertaken frequently, the pest can be eradicated. As the period increases, the pest's dynamics shift from a steady state to become chaotic with periodic windows and more multicluster oscillations arise for heterogenous initial density distributions. Period-doubling bifurcation and periodic halving cascades occur as the releasing constant of the natural enemy increases. For the same ecological system with five differently connected networks, as the randomness of the connectedness increases, the transient duration becomes smaller and the probability of multicluster oscillations appearing becomes higher.

Synchrony-optimized networks of Kuramoto oscillators with inertia

NASA Astrophysics Data System (ADS)

Pinto, Rafael S.; Saa, Alberto

2016-12-01

We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a hill climb scheme in which the edges of the network are swapped in order to enhance its synchronization capacity. We show that the synchrony-optimized networks generated by our algorithm have some interesting topological and dynamical properties. In particular, they typically exhibit an anticipation of the synchronization onset and are more robust against certain types of perturbations. We consider synthetic random networks and also a network with a topology based on an approximated model of the (high voltage) power grid of Spain, since networks of Kuramoto oscillators with inertia have been used recently as simplified models for power grids, for which synchronization is obviously a crucial issue. Despite the extreme simplifications adopted in these models, our results, among others recently obtained in the literature, may provide interesting principles to guide the future growth and development of real-world grids, specially in the case of a change of the current paradigm of centralized towards distributed generation power grids.

Investigating Synchronous Oscillation and Deep Brain Stimulation Treatment in A Model of Cortico-Basal Ganglia Network.

PubMed

Lu, Meili; Wei, Xile; Loparo, Kenneth A

2017-11-01

Altered firing properties and increased pathological oscillations in the basal ganglia have been proven to be hallmarks of Parkinson's disease (PD). Increasing evidence suggests that abnormal synchronous oscillations and suppression in the cortex may also play a critical role in the pathogenic process and treatment of PD. In this paper, a new closed-loop network including the cortex and basal ganglia using the Izhikevich models is proposed to investigate the synchrony and pathological oscillations in motor circuits and their modulation by deep brain stimulation (DBS). Results show that more coherent dynamics in the cortex may cause stronger effects on the synchrony and pathological oscillations of the subthalamic nucleus (STN). The pathological beta oscillations of the STN can both be efficiently suppressed with DBS applied directly to the STN or to cortical neurons, respectively, but the underlying mechanisms by which DBS suppresses the beta oscillations are different. This research helps to understand the dynamics of pathological oscillations in PD-related motor regions and supports the therapeutic potential of stimulation of cortical neurons.

Bifurcation of synchronous oscillations into torus in a system of two reciprocally inhibitory silicon neurons: experimental observation and modeling.

PubMed

Bondarenko, Vladimir E; Cymbalyuk, Gennady S; Patel, Girish; Deweerth, Stephen P; Calabrese, Ronald L

2004-12-01

Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed.

Intrinsic evolution of controllable oscillators in FPTA-2

NASA Technical Reports Server (NTRS)

Sekanina, Lukas; Zebulum, Ricardo S.

2005-01-01

Simple one- and two-bit controllable oscillators were intrinsically evolved using only four cells of Field Programmable Transistor Array (FPTA-2). These oscillators can produce different oscillations for different setting of control signals. Therefore, they could be used, in principle, to compose complex networks of oscillators that could exhibit rich dynamical behavior in order to perform a computation or to model a desired system.

Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons.

PubMed

Ratas, Irmantas; Pyragas, Kestutis

2016-09-01

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.

Macroscopic and microscopic spectral properties of brain networks during local and global synchronization

NASA Astrophysics Data System (ADS)

Maksimenko, Vladimir A.; Lüttjohann, Annika; Makarov, Vladimir V.; Goremyko, Mikhail V.; Koronovskii, Alexey A.; Nedaivozov, Vladimir; Runnova, Anastasia E.; van Luijtelaar, Gilles; Hramov, Alexander E.; Boccaletti, Stefano

2017-07-01

We introduce a practical and computationally not demanding technique for inferring interactions at various microscopic levels between the units of a network from the measurements and the processing of macroscopic signals. Starting from a network model of Kuramoto phase oscillators, which evolve adaptively according to homophilic and homeostatic adaptive principles, we give evidence that the increase of synchronization within groups of nodes (and the corresponding formation of synchronous clusters) causes also the defragmentation of the wavelet energy spectrum of the macroscopic signal. Our methodology is then applied to getting a glance into the microscopic interactions occurring in a neurophysiological system, namely, in the thalamocortical neural network of an epileptic brain of a rat, where the group electrical activity is registered by means of multichannel EEG. We demonstrate that it is possible to infer the degree of interaction between the interconnected regions of the brain during different types of brain activities and to estimate the regions' participation in the generation of the different levels of consciousness.

Spatial Attention and the Effects of Frontoparietal Alpha Band Stimulation

PubMed Central

van Schouwenburg, Martine R.; Zanto, Theodore P.; Gazzaley, Adam

2017-01-01

A frontoparietal network has long been implicated in top-down control of attention. Recent studies have suggested that this network might communicate through coherence in the alpha band. Here we aimed to test the effect of coherent alpha (8–12 Hz) stimulation on the frontoparietal network. To this end, we recorded behavioral performance and electroencephalography (EEG) data while participants were engaged in a spatial attention task. Furthermore, participants received transcranial alternating current stimulation (tACS) over the right frontal and parietal cortex, which oscillated coherently in-phase within the alpha band. Compared to a group of participants that received sham stimulation, we found that coherent frontoparietal alpha band stimulation altered a behavioral spatial attention bias. Neurally, the groups showed hemispheric-specific differences in alpha coherence between the frontal and parietal-occipital cortex. These results provide preliminary evidence that alpha coherence in the frontoparietal network might play a role in top-down control of spatial attention. PMID:28174529

Network structure, topology, and dynamics in generalized models of synchronization

NASA Astrophysics Data System (ADS)

Lerman, Kristina; Ghosh, Rumi

2012-08-01

Network structure is a product of both its topology and interactions between its nodes. We explore this claim using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state, nodes synchronize in stages, revealing the network's underlying community structure. Traditional models of synchronization assume that interactions between nodes are mediated by a conservative process similar to diffusion. However, social and biological processes are often nonconservative. We propose a model of synchronization in a network of oscillators coupled via nonconservative processes. We study the dynamics of synchronization of a synthetic and real-world networks and show that the traditional and nonconservative models of synchronization reveal different structures within the same network.

Robust autoassociative memory with coupled networks of Kuramoto-type oscillators

NASA Astrophysics Data System (ADS)

Heger, Daniel; Krischer, Katharina

2016-08-01

Uncertain recognition success, unfavorable scaling of connection complexity, or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a network architecture of coupled oscillators for pattern recognition which shows none of the mentioned flaws. Furthermore we illustrate the recognition process with simulation results and analyze the dynamics analytically: Possible output patterns are isolated attractors of the system. Additionally, simple criteria for recognition success are derived from a lower bound on the basins of attraction.

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats

PubMed Central

Chicoli, Amanda; Paley, Derek A.

2016-01-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion. PMID:27907996

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats

NASA Astrophysics Data System (ADS)

Chicoli, Amanda; Paley, Derek A.

2016-11-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats.

PubMed

Chicoli, Amanda; Paley, Derek A

2016-11-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.

Network recruitment to coherent oscillations in a hippocampal computer model

PubMed Central

Krieger, Abba; Litt, Brian

2011-01-01

Coherent neural oscillations represent transient synchronization of local neuronal populations in both normal and pathological brain activity. These oscillations occur at or above gamma frequencies (>30 Hz) and often are propagated to neighboring tissue under circumstances that are both normal and abnormal, such as gamma binding or seizures. The mechanisms that generate and propagate these oscillations are poorly understood. In the present study we demonstrate, via a detailed computational model, a mechanism whereby physiological noise and coupling initiate oscillations and then recruit neighboring tissue, in a manner well described by a combination of stochastic resonance and coherence resonance. We develop a novel statistical method to quantify recruitment using several measures of network synchrony. This measurement demonstrates that oscillations spread via preexisting network connections such as interneuronal connections, recurrent synapses, and gap junctions, provided that neighboring cells also receive sufficient inputs in the form of random synaptic noise. “Epileptic” high-frequency oscillations (HFOs), produced by pathologies such as increased synaptic activity and recurrent connections, were superior at recruiting neighboring tissue. “Normal” HFOs, associated with fast firing of inhibitory cells and sparse pyramidal cell firing, tended to suppress surrounding cells and showed very limited ability to recruit. These findings point to synaptic noise and physiological coupling as important targets for understanding the generation and propagation of both normal and pathological HFOs, suggesting potential new diagnostic and therapeutic approaches to human disorders such as epilepsy. PMID:21273309

Neuromorphic computing with nanoscale spintronic oscillators

PubMed Central

Torrejon, Jacob; Riou, Mathieu; Araujo, Flavio Abreu; Tsunegi, Sumito; Khalsa, Guru; Querlioz, Damien; Bortolotti, Paolo; Cros, Vincent; Fukushima, Akio; Kubota, Hitoshi; Yuasa, Shinji; Stiles, M. D.; Grollier, Julie

2017-01-01

Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information1. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge numbers of nanoscale non-linear oscillators. Indeed, a simple estimation indicates that, in order to fit a hundred million oscillators organized in a two-dimensional array inside a chip the size of a thumb, their lateral dimensions must be smaller than one micrometer. However, despite multiple theoretical proposals2–5, and several candidates such as memristive6 or superconducting7 oscillators, there is no proof of concept today of neuromorphic computing with nano-oscillators. Indeed, nanoscale devices tend to be noisy and to lack the stability required to process data in a reliable way. Here, we show experimentally that a nanoscale spintronic oscillator8,9 can achieve spoken digit recognition with accuracies similar to state of the art neural networks. We pinpoint the regime of magnetization dynamics leading to highest performance. These results, combined with the exceptional ability of these spintronic oscillators to interact together, their long lifetime, and low energy consumption, open the path to fast, parallel, on-chip computation based on networks of oscillators. PMID:28748930

Seizure-induced alterations in fast-spiking basket cell GABA currents modulate frequency and coherence of gamma oscillation in network simulations

NASA Astrophysics Data System (ADS)

Proddutur, Archana; Yu, Jiandong; Elgammal, Fatima S.; Santhakumar, Vijayalakshmi

2013-12-01

Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shift in GABA reversal potential (EGABA). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (gGABA-extra) and experimentally identified, seizure-induced changes in gGABA-extra and EGABA influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40-100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30-40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing gGABA-extra reduced the frequency and coherence of FS-BC firing when EGABA was shunting (-74 mV), but failed to alter average FS-BC frequency when EGABA was depolarizing (-54 mV). When FS-BCs were activated by biologically based dendritic synaptic inputs, enhancing gGABA-extra reduced the frequency and coherence of FS-BC firing when EGABA was shunting and increased average FS-BC firing when EGABA was depolarizing. Shifting EGABA from shunting to depolarizing potentials consistently increased network frequency to and above high gamma frequencies (>80 Hz). Since gamma oscillations may contribute to learning and memory processing [Fell et al., Nat. Neurosci. 4, 1259 (2001); Jutras et al., J. Neurosci. 29, 12521 (2009); Wang, Physiol. Rev. 90, 1195 (2010)], our demonstration that network oscillations are modulated by extrasynaptic inhibition in FS-BCs suggests that neuroactive compounds that act on extrasynaptic GABA receptors could impact memory formation by modulating hippocampal gamma oscillations. The simulation results indicate that the depolarized FS-BC GABA reversal, observed after experimental seizures, together with enhanced spillover extrasynaptic GABA currents are likely to promote generation of focal high frequency activity associated with epileptic networks.

Neuronal Oscillations Indicate Sleep-dependent Changes in the Cortical Memory Trace.

PubMed

Köster, Moritz; Finger, Holger; Kater, Maren-Jo; Schenk, Christoph; Gruber, Thomas

2017-04-01

Sleep promotes the consolidation of newly acquired associative memories. Here we used neuronal oscillations in the human EEG to investigate sleep-dependent changes in the cortical memory trace. The retrieval activity for object-color associations was assessed immediately after encoding and after 3 hr of sleep or wakefulness. Sleep had beneficial effects on memory performance and led to reduced event-related theta and gamma power during the retrieval of associative memories. Furthermore, event-related alpha suppression was attenuated in the wake group for memorized and novel stimuli. There were no sleep-dependent changes in retrieval activity for missed items or items retrieved without color. Thus, the sleep-dependent reduction in theta and gamma oscillations was specific for the retrieval of associative memories. In line with theoretical accounts on sleep-dependent memory consolidation, decreased theta may indicate reduced mediotemporal activity because of a transfer of information into neocortical networks during sleep, whereas reduced parietal gamma may reflect effects of synaptic downscaling. Changes in alpha suppression in the wake group possibly index reduced attentional resources that may also contribute to a lower memory performance in this group. These findings indicate that the consolidation of associative memories during sleep is associated with profound changes in the cortical memory trace and relies on multiple neuronal processes working in concert.

Smallest chimera states

NASA Astrophysics Data System (ADS)

Maistrenko, Yuri; Brezetsky, Serhiy; Jaros, Patrycja; Levchenko, Roman; Kapitaniak, Tomasz

2017-01-01

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e., rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks relevant to various real-world systems.

The CRYPTOCHROME photoreceptor gates PDF neuropeptide signaling to set circadian network hierarchy in Drosophila.

PubMed

Zhang, Luoying; Lear, Bridget C; Seluzicki, Adam; Allada, Ravi

2009-12-15

Circadian clocks in the brain are organized as coupled oscillators that integrate seasonal cues such as light and temperature to time daily behaviors. In Drosophila, the PIGMENT DISPERSING FACTOR (PDF) neuropeptide-expressing morning (M) and non-PDF evening (E) cells are coupled cell groups important for morning and evening behavior, respectively. Depending on day length, either M cells (short days) or E cells (long days) dictate both the morning and the evening phase, a phenomenon that we term network hierarchy. To examine the role of PDF in light-dark conditions, we examined flies lacking both the PDF receptor (PDFR) and the circadian photoreceptor CRYPTOCHROME (CRY). We found that subsets of E cells exhibit molecular oscillations antiphase to those of wild-type flies, single cry mutants, or single Pdfr mutants, demonstrating a potent role for PDF in light-mediated entrainment, specifically in the absence of CRY. Moreover, we find that the evening behavioral phase is more strongly reset by PDF(+) M cells in the absence of CRY. On the basis of our findings, we propose that CRY can gate PDF signaling to determine behavioral phase and network hierarchy.

Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons.

PubMed

Oh, Myongkeun; Matveev, Victor

2009-04-01

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris-Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation in the firing order of the two cells, as reported recently by Maran and Canavier (J Comput Nerosci, 2008) for a network of Wang-Buzsáki model neurons. Although alternating-order firing has been previously reported as a near-synchronous state, we show that the stable phase difference between the spikes of the two Morris-Lecar cells can constitute as much as 70% of the unperturbed oscillation period. Further, we examine the generality of this phenomenon for a class of type-I oscillators that are close to their excitation thresholds, and provide an intuitive geometric description of such "leap-frog" dynamics. In the Morris-Lecar model network, the alternation in the firing order arises under the condition of fast closing of K( + ) channels at hyperpolarized potentials, which leads to slow dynamics of membrane potential upon synaptic inhibition, allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation. Further, we show that non-zero synaptic decay time is crucial for the existence of leap-frog firing in networks of phase oscillators. However, we demonstrate that leap-frog spiking can also be obtained in pulse-coupled inhibitory networks of one-dimensional oscillators with a multi-branched phase domain, for instance in a network of quadratic integrate-and-fire model cells. Finally, for the case of a homogeneous network, we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternating-order spiking, complementing the analysis of Goel and Ermentrout (Physica D 163:191-216, 2002) of the order-preserving phase transition map.

Spontaneous oscillations in microfluidic networks

NASA Astrophysics Data System (ADS)

Case, Daniel; Angilella, Jean-Regis; Motter, Adilson

2017-11-01

Precisely controlling flows within microfluidic systems is often difficult which typically results in systems being heavily reliant on numerous external pumps and computers. Here, I present a simple microfluidic network that exhibits flow rate switching, bistablity, and spontaneous oscillations controlled by a single pressure. That is, by solely changing the driving pressure, it is possible to switch between an oscillating and steady flow state. Such functionality does not rely on external hardware and may even serve as an on-chip memory or timing mechanism. I use an analytic model and rigorous fluid dynamics simulations to show these results.

Input-dependent frequency modulation of cortical gamma oscillations shapes spatial synchronization and enables phase coding.

PubMed

Lowet, Eric; Roberts, Mark; Hadjipapas, Avgis; Peter, Alina; van der Eerden, Jan; De Weerd, Peter

2015-02-01

Fine-scale temporal organization of cortical activity in the gamma range (∼25-80Hz) may play a significant role in information processing, for example by neural grouping ('binding') and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.

Input-Dependent Frequency Modulation of Cortical Gamma Oscillations Shapes Spatial Synchronization and Enables Phase Coding

PubMed Central

Lowet, Eric; Roberts, Mark; Hadjipapas, Avgis; Peter, Alina; van der Eerden, Jan; De Weerd, Peter

2015-01-01

Fine-scale temporal organization of cortical activity in the gamma range (∼25–80Hz) may play a significant role in information processing, for example by neural grouping (‘binding’) and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity. PMID:25679780

Neuromorphic computing with nanoscale spintronic oscillators.

PubMed

Torrejon, Jacob; Riou, Mathieu; Araujo, Flavio Abreu; Tsunegi, Sumito; Khalsa, Guru; Querlioz, Damien; Bortolotti, Paolo; Cros, Vincent; Yakushiji, Kay; Fukushima, Akio; Kubota, Hitoshi; Yuasa, Shinji; Stiles, Mark D; Grollier, Julie

2017-07-26

Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 10 8 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

Solitary states for coupled oscillators with inertia.

PubMed

Jaros, Patrycja; Brezetsky, Serhiy; Levchenko, Roman; Dudkowski, Dawid; Kapitaniak, Tomasz; Maistrenko, Yuri

2018-01-01

Networks of identical oscillators with inertia can display remarkable spatiotemporal patterns in which one or a few oscillators split off from the main synchronized cluster and oscillate with different averaged frequency. Such "solitary states" are impossible for the classical Kuramoto model with sinusoidal coupling. However, if inertia is introduced, these states represent a solid part of the system dynamics, where each solitary state is characterized by the number of isolated oscillators and their disposition in space. We present system parameter regions for the existence of solitary states in the case of local, non-local, and global network couplings and show that they preserve in both thermodynamic and conservative limits. We give evidence that solitary states arise in a homoclinic bifurcation of a saddle-type synchronized state and die eventually in a crisis bifurcation after essential variation of the parameters.

Solitary states for coupled oscillators with inertia

NASA Astrophysics Data System (ADS)

Jaros, Patrycja; Brezetsky, Serhiy; Levchenko, Roman; Dudkowski, Dawid; Kapitaniak, Tomasz; Maistrenko, Yuri

2018-01-01

Networks of identical oscillators with inertia can display remarkable spatiotemporal patterns in which one or a few oscillators split off from the main synchronized cluster and oscillate with different averaged frequency. Such "solitary states" are impossible for the classical Kuramoto model with sinusoidal coupling. However, if inertia is introduced, these states represent a solid part of the system dynamics, where each solitary state is characterized by the number of isolated oscillators and their disposition in space. We present system parameter regions for the existence of solitary states in the case of local, non-local, and global network couplings and show that they preserve in both thermodynamic and conservative limits. We give evidence that solitary states arise in a homoclinic bifurcation of a saddle-type synchronized state and die eventually in a crisis bifurcation after essential variation of the parameters.

Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control.

PubMed

He, Ding-Xin; Ling, Guang; Guan, Zhi-Hong; Hu, Bin; Liao, Rui-Quan

2018-02-01

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

The Slow Oscillation in Cortical and Thalamic Networks: Mechanisms and Functions

PubMed Central

Neske, Garrett T.

2016-01-01

During even the most quiescent behavioral periods, the cortex and thalamus express rich spontaneous activity in the form of slow (<1 Hz), synchronous network state transitions. Throughout this so-called slow oscillation, cortical and thalamic neurons fluctuate between periods of intense synaptic activity (Up states) and almost complete silence (Down states). The two decades since the original characterization of the slow oscillation in the cortex and thalamus have seen considerable advances in deciphering the cellular and network mechanisms associated with this pervasive phenomenon. There are, nevertheless, many questions regarding the slow oscillation that await more thorough illumination, particularly the mechanisms by which Up states initiate and terminate, the functional role of the rhythmic activity cycles in unconscious or minimally conscious states, and the precise relation between Up states and the activated states associated with waking behavior. Given the substantial advances in multineuronal recording and imaging methods in both in vivo and in vitro preparations, the time is ripe to take stock of our current understanding of the slow oscillation and pave the way for future investigations of its mechanisms and functions. My aim in this Review is to provide a comprehensive account of the mechanisms and functions of the slow oscillation, and to suggest avenues for further exploration. PMID:26834569

The vertical propagation of waves in the solar atmosphere. II Phase delays in the quiet chromosphere and cell-network distinctions

NASA Technical Reports Server (NTRS)

Lites, B. W.; Chipman, E. G.; White, O. R.

1982-01-01

The differences in the phase of the velocity oscillations between a pair of chromospheric Ca II lines was measured using the Vacuum Tower Telescope at the Sacramento Peak Observatory. The observed phase differences indicate that the acoustic modes are trapped or envanescent, rather than propagating, in the chromosphere. Systematic distinctions are found in the phase delays between quiet network and cell interior regions for both intensity and velocity oscillations in photospheric and chromospheric lines. The theory of linear perturbations in an isothermal atmosphere is invoked to interpret these differences. From this analysis it is found that one or more of the following explanations is possible: (1) the radiative damping is more effective in the network than in the cell interior; (2) the network features exclude oscillations of large horizontal wavenumber; or (3) the scale height of the chromosphere is larger in the network than in the cell interior.

Layer-specific optogenetic activation of pyramidal neurons causes beta–gamma entrainment of neonatal networks

PubMed Central

Bitzenhofer, Sebastian H; Ahlbeck, Joachim; Wolff, Amy; Wiegert, J. Simon; Gee, Christine E.; Oertner, Thomas G.; Hanganu-Opatz, Ileana L.

2017-01-01

Coordinated activity patterns in the developing brain may contribute to the wiring of neuronal circuits underlying future behavioural requirements. However, causal evidence for this hypothesis has been difficult to obtain owing to the absence of tools for selective manipulation of oscillations during early development. We established a protocol that combines optogenetics with electrophysiological recordings from neonatal mice in vivo to elucidate the substrate of early network oscillations in the prefrontal cortex. We show that light-induced activation of layer II/III pyramidal neurons that are transfected by in utero electroporation with a high-efficiency channelrhodopsin drives frequency-specific spiking and boosts network oscillations within beta–gamma frequency range. By contrast, activation of layer V/VI pyramidal neurons causes nonspecific network activation. Thus, entrainment of neonatal prefrontal networks in fast rhythms relies on the activation of layer II/III pyramidal neurons. This approach used here may be useful for further interrogation of developing circuits, and their behavioural readout. PMID:28216627

Parvalbumin-expressing interneurons coordinate hippocampal network dynamics required for memory consolidation

NASA Astrophysics Data System (ADS)

Ognjanovski, Nicolette; Schaeffer, Samantha; Wu, Jiaxing; Mofakham, Sima; Maruyama, Daniel; Zochowski, Michal; Aton, Sara J.

2017-04-01

Activity in hippocampal area CA1 is essential for consolidating episodic memories, but it is unclear how CA1 activity patterns drive memory formation. We find that in the hours following single-trial contextual fear conditioning (CFC), fast-spiking interneurons (which typically express parvalbumin (PV)) show greater firing coherence with CA1 network oscillations. Post-CFC inhibition of PV+ interneurons blocks fear memory consolidation. This effect is associated with loss of two network changes associated with normal consolidation: (1) augmented sleep-associated delta (0.5-4 Hz), theta (4-12 Hz) and ripple (150-250 Hz) oscillations; and (2) stabilization of CA1 neurons' functional connectivity patterns. Rhythmic activation of PV+ interneurons increases CA1 network coherence and leads to a sustained increase in the strength and stability of functional connections between neurons. Our results suggest that immediately following learning, PV+ interneurons drive CA1 oscillations and reactivation of CA1 ensembles, which directly promotes network plasticity and long-term memory formation.

Transition to subthreshold activity with the use of phase shifting in a model thalamic network

NASA Astrophysics Data System (ADS)

Thomas, Elizabeth; Grisar, Thierry

1997-05-01

Absence epilepsy involves a state of low frequency synchronous oscillations by the involved neuronal networks. These oscillations may be either above or subthreshold. In this investigation, we studied the methods which could be utilized to transform the threshold activity of neurons in the network to a subthreshold state. A model thalamic network was constructed using the Hodgkin Huxley framework. Subthreshold activity was achieved by the application of stimuli to the network which caused phase shifts in the oscillatory activity of selected neurons in the network. In some instances the stimulus was a periodic pulse train of low frequency to the reticular thalamic neurons of the network while in others, it was a constant hyperpolarizing current applied to the thalamocortical neurons.

Synchronization Dynamics of Coupled Chemical Oscillators

NASA Astrophysics Data System (ADS)

Tompkins, Nathan

The synchronization dynamics of complex networks have been extensively studied over the past few decades due to their ubiquity in the natural world. Prominent examples include cardiac rhythms, circadian rhythms, the flashing of fireflies, predator/prey population dynamics, mammalian gait, human applause, pendulum clocks, the electrical grid, and of the course the brain. Detailed experiments have been done to map the topology of many of these systems and significant advances have been made to describe the mathematics of these networks. Compared to these bodies of work relatively little has been done to directly test the role of topology in the synchronization dynamics of coupled oscillators. This Dissertation develops technology to examine the dynamics due to topology within networks of discrete oscillatory components. The oscillatory system used here consists of the photo-inhibitable Belousov-Zhabotinsky (BZ) reaction water-in-oil emulsion where the oscillatory drops are diffusively coupled to one another and the topology is defined by the geometry of the diffusive connections. Ring networks are created from a close-packed 2D array of drops using the Programmable Illumination Microscope (PIM) in order to test Turing's theory of morphogenesis directly. Further technology is developed to create custom planar networks of BZ drops in more complicated topologies which can be individually perturbed using illumination from the PIM. The work presented here establishes the validity of using the BZ emulsion system with a PIM to study the topology induced effects on the synchronization dynamics of coupled chemical oscillators, tests the successes and limitations of Turing's theory of morphogenesis, and develops new technology to further probe the effects of network topology on a system of coupled oscillators. Finally, this Dissertation concludes by describing ongoing experiments which utilize this new technology to examine topology induced transitions of synchronization dynamics of diffusively coupled chemical oscillators.

Modeling the emergence of circadian rhythms in a clock neuron network.

PubMed

Diambra, Luis; Malta, Coraci P

2012-01-01

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.

Downstream effects of hippocampal sharp wave ripple oscillations on medial entorhinal cortex layer V neurons in vitro.

PubMed

Roth, Fabian C; Beyer, Katinka M; Both, Martin; Draguhn, Andreas; Egorov, Alexei V

2016-12-01

The entorhinal cortex (EC) is a critical component of the medial temporal lobe (MTL) memory system. Local networks within the MTL express a variety of state-dependent network oscillations that are believed to organize neuronal activity during memory formation. The peculiar pattern of sharp wave-ripple complexes (SPW-R) entrains neurons by a very fast oscillation at ∼200 Hz in the hippocampal areas CA3 and CA1 and then propagates through the "output loop" into the EC. The precise mechanisms of SPW-R propagation and the resulting cellular input patterns in the mEC are, however, largely unknown. We therefore investigated the activity of layer V (LV) principal neurons of the medial EC (mEC) during SPW-R oscillations in horizontal mouse brain slices. Intracellular recordings in the mEC were combined with extracellular monitoring of propagating network activity. SPW-R in CA1 were regularly followed by negative field potential deflections in the mEC. Propagation of SPW-R activity from CA1 to the mEC was mostly monosynaptic and excitatory, such that synaptic input to mEC LV neurons directly reflected unit activity in CA1. Comparison with propagating network activity from CA3 to CA1 revealed a similar role of excitatory long-range connections for both regions. However, SPW-R-induced activity in CA1 involved strong recruitment of rhythmic synaptic inhibition and corresponding fast field oscillations, in contrast to the mEC. These differences between features of propagating SPW-R emphasize the differential processing of network activity by each local network of the hippocampal output loop. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Synchronization in neural nets

NASA Technical Reports Server (NTRS)

Vidal, Jacques J.; Haggerty, John

1988-01-01

The paper presents an artificial neural network concept (the Synchronizable Oscillator Networks) where the instants of individual firings in the form of point processes constitute the only form of information transmitted between joining neurons. In the model, neurons fire spontaneously and regularly in the absence of perturbation. When interaction is present, the scheduled firings are advanced or delayed by the firing of neighboring neurons. Networks of such neurons become global oscillators which exhibit multiple synchronizing attractors. From arbitrary initial states, energy minimization learning procedures can make the network converge to oscillatory modes that satisfy multi-dimensional constraints. Such networks can directly represent routing and scheduling problems that consist of ordering sequences of events.

Synchronization of heteroclinic circuits through learning in coupled neural networks

NASA Astrophysics Data System (ADS)

Selskii, Anton; Makarov, Valeri A.

2016-01-01

The synchronization of oscillatory activity in neural networks is usually implemented by coupling the state variables describing neuronal dynamics. Here we study another, but complementary mechanism based on a learning process with memory. A driver network, acting as a teacher, exhibits winner-less competition (WLC) dynamics, while a driven network, a learner, tunes its internal couplings according to the oscillations observed in the teacher. We show that under appropriate training the learner can "copy" the coupling structure and thus synchronize oscillations with the teacher. The replication of the WLC dynamics occurs for intermediate memory lengths only, consequently, the learner network exhibits a phenomenon of learning resonance.

Local Optogenetic Induction of Fast (20-40 Hz) Pyramidal-Interneuron Network Oscillations in the In Vitro and In Vivo CA1 Hippocampus: Modulation by CRF and Enforcement of Perirhinal Theta Activity.

PubMed

Dine, Julien; Genewsky, Andreas; Hladky, Florian; Wotjak, Carsten T; Deussing, Jan M; Zieglgänsberger, Walter; Chen, Alon; Eder, Matthias

2016-01-01

The neurophysiological processes that can cause theta-to-gamma frequency range (4-80 Hz) network oscillations in the rhinal cortical-hippocampal system and the potential connectivity-based interactions of such forebrain rhythms are a topic of intensive investigation. Here, using selective Channelrhodopsin-2 (ChR2) expression in mouse forebrain glutamatergic cells, we were able to locally, temporally precisely, and reliably induce fast (20-40 Hz) field potential oscillations in hippocampal area CA1 in vitro (at 25°C) and in vivo (i.e., slightly anesthetized NEX-Cre-ChR2 mice). As revealed by pharmacological analyses and patch-clamp recordings from pyramidal cells and GABAergic interneurons in vitro, these light-triggered oscillations can exclusively arise from sustained suprathreshold depolarization (~200 ms or longer) and feedback inhibition of CA1 pyramidal neurons, as being mandatory for prototypic pyramidal-interneuron network (P-I) oscillations. Consistently, the oscillations comprised rhythmically occurring population spikes (generated by pyramidal cells) and their frequency increased with increasing spectral power. We further demonstrate that the optogenetically driven CA1 oscillations, which remain stable over repeated evocations, are impaired by the stress hormone corticotropin-releasing factor (CRF, 125 nM) in vitro and, even more remarkably, found that they are accompanied by concurrent states of enforced theta activity in the memory-associated perirhinal cortex (PrC) in vivo. The latter phenomenon most likely derives from neurotransmission via a known, but poorly studied excitatory CA1→PrC pathway. Collectively, our data provide evidence for the existence of a prototypic (CRF-sensitive) P-I gamma rhythm generator in area CA1 and suggest that CA1 P-I oscillations can rapidly up-regulate theta activity strength in hippocampus-innervated rhinal networks, at least in the PrC.

Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks

NASA Astrophysics Data System (ADS)

Luo, Chao; Zhang, Xiaolin; Zheng, YuanJie

2017-06-01

In this article, the evolution of prisoner's dilemma game with volunteering on interdependent networks is investigated. Different from the traditional two-strategy game, voluntary participation as an additional strategy is involved in repeated game, that can introduce more complex evolutionary dynamics. And, interdependent networks provide a more generalized network architecture to study the intricate variability of dynamics. We have showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks. We further discussed the influence of interdependent strength on the densities of different strategies and found that an intermediate interdependence would play a bigger role on the evolution of dynamics. Subsequently, the critical values of the defection temptation for phase transitions under different conditions have been studied. Moreover, the global oscillations induced by the circle of dominance of three strategies on interdependent networks have been quantitatively investigated. Counter-intuitively, the oscillations of strategy densities are not periodic or stochastic, but have rich dynamical behaviors. By means of various analysis tools, we have demonstrated the global oscillations of strategy densities possessed chaotic characteristics.

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

PubMed

Brunel, N; Hakim, V

1999-10-01

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Robustness of Oscillatory Behavior in Correlated Networks

PubMed Central

Sasai, Takeyuki; Morino, Kai; Tanaka, Gouhei; Almendral, Juan A.; Aihara, Kazuyuki

2015-01-01

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity. PMID:25894574

Recognition of abstract objects via neural oscillators: interaction among topological organization, associative memory and gamma band synchronization.

PubMed

Ursino, Mauro; Magosso, Elisa; Cuppini, Cristiano

2009-02-01

Synchronization of neural activity in the gamma band is assumed to play a significant role not only in perceptual processing, but also in higher cognitive functions. Here, we propose a neural network of Wilson-Cowan oscillators to simulate recognition of abstract objects, each represented as a collection of four features. Features are ordered in topological maps of oscillators connected via excitatory lateral synapses, to implement a similarity principle. Experience on previous objects is stored in long-range synapses connecting the different topological maps, and trained via timing dependent Hebbian learning (previous knowledge principle). Finally, a downstream decision network detects the presence of a reliable object representation, when all features are oscillating in synchrony. Simulations performed giving various simultaneous objects to the network (from 1 to 4), with some missing and/or modified properties suggest that the network can reconstruct objects, and segment them from the other simultaneously present objects, even in case of deteriorated information, noise, and moderate correlation among the inputs (one common feature). The balance between sensitivity and specificity depends on the strength of the Hebbian learning. Achieving a correct reconstruction in all cases, however, requires ad hoc selection of the oscillation frequency. The model represents an attempt to investigate the interactions among topological maps, autoassociative memory, and gamma-band synchronization, for recognition of abstract objects.

Modeling carbachol-induced hippocampal network synchronization using hidden Markov models

NASA Astrophysics Data System (ADS)

Dragomir, Andrei; Akay, Yasemin M.; Akay, Metin

2010-10-01

In this work we studied the neural state transitions undergone by the hippocampal neural network using a hidden Markov model (HMM) framework. We first employed a measure based on the Lempel-Ziv (LZ) estimator to characterize the changes in the hippocampal oscillation patterns in terms of their complexity. These oscillations correspond to different modes of hippocampal network synchronization induced by the cholinergic agonist carbachol in the CA1 region of mice hippocampus. HMMs are then used to model the dynamics of the LZ-derived complexity signals as first-order Markov chains. Consequently, the signals corresponding to our oscillation recordings can be segmented into a sequence of statistically discriminated hidden states. The segmentation is used for detecting transitions in neural synchronization modes in data recorded from wild-type and triple transgenic mice models (3xTG) of Alzheimer's disease (AD). Our data suggest that transition from low-frequency (delta range) continuous oscillation mode into high-frequency (theta range) oscillation, exhibiting repeated burst-type patterns, occurs always through a mode resembling a mixture of the two patterns, continuous with burst. The relatively random patterns of oscillation during this mode may reflect the fact that the neuronal network undergoes re-organization. Further insight into the time durations of these modes (retrieved via the HMM segmentation of the LZ-derived signals) reveals that the mixed mode lasts significantly longer (p < 10-4) in 3xTG AD mice. These findings, coupled with the documented cholinergic neurotransmission deficits in the 3xTG mice model, may be highly relevant for the case of AD.

Periodic fluctuations in correlation-based connectivity density time series: Application to wind speed-monitoring network in Switzerland

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Telesca, Luciano; Kanevski, Mikhail

2018-02-01

In this paper, we study the periodic fluctuations of connectivity density time series of a wind speed-monitoring network in Switzerland. By using the correlogram-based robust periodogram annual periodic oscillations were found in the correlation-based network. The intensity of such annual periodic oscillations is larger for lower correlation thresholds and smaller for higher. The annual periodicity in the connectivity density seems reasonably consistent with the seasonal meteo-climatic cycle.

Inhibition delay increases neural network capacity through Stirling transform.

PubMed

Nogaret, Alain; King, Alastair

2018-03-01

Inhibitory neural networks are found to encode high volumes of information through delayed inhibition. We show that inhibition delay increases storage capacity through a Stirling transform of the minimum capacity which stabilizes locally coherent oscillations. We obtain both the exact and asymptotic formulas for the total number of dynamic attractors. Our results predict a (ln2)^{-N}-fold increase in capacity for an N-neuron network and demonstrate high-density associative memories which host a maximum number of oscillations in analog neural devices.

Inhibition delay increases neural network capacity through Stirling transform

NASA Astrophysics Data System (ADS)

Nogaret, Alain; King, Alastair

2018-03-01

Inhibitory neural networks are found to encode high volumes of information through delayed inhibition. We show that inhibition delay increases storage capacity through a Stirling transform of the minimum capacity which stabilizes locally coherent oscillations. We obtain both the exact and asymptotic formulas for the total number of dynamic attractors. Our results predict a (ln2) -N-fold increase in capacity for an N -neuron network and demonstrate high-density associative memories which host a maximum number of oscillations in analog neural devices.

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Some properties of asymmetric Hopfield neural networks with finite time of transition between states

NASA Astrophysics Data System (ADS)

Suleimenov, Ibragim; Mun, Grigoriy; Panchenko, Sergey; Pak, Ivan

2016-11-01

There were implemented samples of asymmetric Hopfield neural networks which have finite time of transition from one state to another. It was shown that in such systems, various oscillation modes could occur. It was revealed that the oscillation of the output signal of certain neuron could be treated as extra logical variable, which describes the state of the neuron. Asymmetric Hopfield neural networks are described in terms of ternary logic. Such logic may be employed in image recognition procedure.

Cluster dynamics of pulse coupled oscillators

NASA Astrophysics Data System (ADS)

O'Keeffe, Kevin; Strogatz, Steven; Krapivsky, Paul

2015-03-01

We study the dynamics of networks of pulse coupled oscillators. Much attention has been devoted to the ultimate fate of the system: which conditions lead to a steady state in which all the oscillators are firing synchronously. But little is known about how synchrony builds up from an initially incoherent state. The current work addresses this question. Oscillators start to synchronize by forming clusters of different sizes that fire in unison. First pairs of oscillators, then triplets and so on. These clusters progressively grow by coalescing with others, eventually resulting in the fully synchronized state. We study the mean field model in which the coupling between oscillators is all to all. We use probabilistic arguments to derive a recursive set of evolution equations for these clusters. Using a generating function formalism, we derive simple equations for the moments of these clusters. Our results are in good agreement simulation. We then numerically explore the effects of non-trivial connectivity. Our results have potential application to ultra-low power ``impulse radio'' & sensor networks.

Voluntary control of intracortical oscillations for reconfiguration of network activity

PubMed Central

Corlier, Juliana; Valderrama, Mario; Navarrete, Miguel; Lehongre, Katia; Hasboun, Dominique; Adam, Claude; Belaid, Hayat; Clémenceau, Stéphane; Baulac, Michel; Charpier, Stéphane; Navarro, Vincent; Le Van Quyen, Michel

2016-01-01

Voluntary control of oscillatory activity represents a key target in the self-regulation of brain function. Using a real-time closed-loop paradigm and simultaneous macro- and micro-electrode recordings, we studied the effects of self-induced intracortical oscillatory activity (4–8 Hz) in seven neurosurgical patients. Subjects learned to robustly and specifically induce oscillations in the target frequency, confirmed by increased oscillatory event density. We have found that the session-to-session variability in performance was explained by the functional long-range decoupling of the target area suggesting a training-induced network reorganization. Downstream effects on more local activities included progressive cross-frequency-coupling with gamma oscillations (30–120 Hz), and the dynamic modulation of neuronal firing rates and spike timing, indicating an improved temporal coordination of local circuits. These findings suggest that effects of voluntary control of intracortical oscillations can be exploited to specifically target plasticity processes to reconfigure network activity, with a particular relevance for memory function or skill acquisition. PMID:27808225

Endogenously generated gamma-band oscillations in early visual cortex: A neurofeedback study.

PubMed

Merkel, Nina; Wibral, Michael; Bland, Gareth; Singer, Wolf

2018-04-26

Human subjects were trained with neurofeedback (NFB) to enhance the power of narrow-band gamma oscillations in circumscribed regions of early visual cortex. To select the region and the oscillation frequency for NFB training, gamma oscillations were induced with locally presented drifting gratings. The source and frequency of these induced oscillations were determined using beamforming methods. During NFB training the power of narrow band gamma oscillations was continuously extracted from this source with online beamforming and converted into the pitch of a tone signal. We found that seven out of ten subjects were able to selectively increase the amplitude of gamma oscillations in the absence of visual stimulation. One subject however failed completely and two subjects succeeded to manipulate the feedback signal by contraction of muscles. In all subjects the attempts to enhance visual gamma oscillations were associated with an increase of beta oscillations over precentral/frontal regions. Only successful subjects exhibited an additional marked increase of theta oscillations over precentral/prefrontal and temporal regions whereas unsuccessful subjects showed an increase of alpha band oscillations over occipital regions. We argue that spatially confined networks in early visual cortex can be entrained to engage in narrow band gamma oscillations not only by visual stimuli but also by top down signals. We interpret the concomitant increase in beta oscillations as indication for an engagement of the fronto-parietal attention network and the increase of theta oscillations as a correlate of imagery. Our finding support the application of NFB in disease conditions associated with impaired gamma synchronization. © 2018 Wiley Periodicals, Inc.

Sensory-driven and spontaneous gamma oscillations engage distinct cortical circuitry

PubMed Central

2015-01-01

Gamma oscillations are a robust component of sensory responses but are also part of the background spontaneous activity of the brain. To determine whether the properties of gamma oscillations in cortex are specific to their mechanism of generation, we compared in mouse visual cortex in vivo the laminar geometry and single-neuron rhythmicity of oscillations produced during sensory representation with those occurring spontaneously in the absence of stimulation. In mouse visual cortex under anesthesia (isoflurane and xylazine), visual stimulation triggered oscillations mainly between 20 and 50 Hz, which, because of their similar functional significance to gamma oscillations in higher mammals, we define here as gamma range. Sensory representation in visual cortex specifically increased gamma oscillation amplitude in the supragranular (L2/3) and granular (L4) layers and strongly entrained putative excitatory and inhibitory neurons in infragranular layers, while spontaneous gamma oscillations were distributed evenly through the cortical depth and primarily entrained putative inhibitory neurons in the infragranular (L5/6) cortical layers. The difference in laminar distribution of gamma oscillations during the two different conditions may result from differences in the source of excitatory input to the cortex. In addition, modulation of superficial gamma oscillation amplitude did not result in a corresponding change in deep-layer oscillations, suggesting that superficial and deep layers of cortex may utilize independent but related networks for gamma generation. These results demonstrate that stimulus-driven gamma oscillations engage cortical circuitry in a manner distinct from spontaneous oscillations and suggest multiple networks for the generation of gamma oscillations in cortex. PMID:26719085

The Drosophila Clock Neuron Network Features Diverse Coupling Modes and Requires Network-wide Coherence for Robust Circadian Rhythms.

PubMed

Yao, Zepeng; Bennett, Amelia J; Clem, Jenna L; Shafer, Orie T

2016-12-13

In animals, networks of clock neurons containing molecular clocks orchestrate daily rhythms in physiology and behavior. However, how various types of clock neurons communicate and coordinate with one another to produce coherent circadian rhythms is not well understood. Here, we investigate clock neuron coupling in the brain of Drosophila and demonstrate that the fly's various groups of clock neurons display unique and complex coupling relationships to core pacemaker neurons. Furthermore, we find that coordinated free-running rhythms require molecular clock synchrony not only within the well-characterized lateral clock neuron classes but also between lateral clock neurons and dorsal clock neurons. These results uncover unexpected patterns of coupling in the clock neuron network and reveal that robust free-running behavioral rhythms require a coherence of molecular oscillations across most of the fly's clock neuron network. Copyright © 2016 The Author(s). Published by Elsevier Inc. All rights reserved.

Mapping and mining interictal pathological gamma (30–100 Hz) oscillations with clinical intracranial EEG in patients with epilepsy

PubMed Central

Smart, Otis; Maus, Douglas; Marsh, Eric; Dlugos, Dennis; Litt, Brian; Meador, Kimford

2012-01-01

Localizing an epileptic network is essential for guiding neurosurgery and antiepileptic medical devices as well as elucidating mechanisms that may explain seizure-generation and epilepsy. There is increasing evidence that pathological oscillations may be specific to diseased networks in patients with epilepsy and that these oscillations may be a key biomarker for generating and indentifying epileptic networks. We present a semi-automated method that detects, maps, and mines pathological gamma (30–100 Hz) oscillations (PGOs) in human epileptic brain to possibly localize epileptic networks. We apply the method to standard clinical iEEG (<100 Hz) with interictal PGOs and seizures from six patients with medically refractory epilepsy. We demonstrate that electrodes with consistent PGO discharges do not always coincide with clinically determined seizure onset zone (SOZ) electrodes but at times PGO-dense electrodes include secondary seizure-areas (SS) or even areas without seizures (NS). In 4/5 patients with epilepsy surgery, we observe poor (Engel Class 4) post-surgical outcomes and identify more PGO-activity in SS or NS than in SOZ. Additional studies are needed to further clarify the role of PGOs in epileptic brain. PMID:23105174

Interneuron-mediated inhibition synchronizes neuronal activity during slow oscillation.

PubMed

Chen, Jen-Yung; Chauvette, Sylvain; Skorheim, Steven; Timofeev, Igor; Bazhenov, Maxim

2012-08-15

The signature of slow-wave sleep in the electroencephalogram (EEG) is large-amplitude fluctuation of the field potential, which reflects synchronous alternation of activity and silence across cortical neurons. While initiation of the active cortical states during sleep slow oscillation has been intensively studied, the biological mechanisms which drive the network transition from an active state to silence remain poorly understood. In the current study, using a combination of in vivo electrophysiology and thalamocortical network simulation, we explored the impact of intrinsic and synaptic inhibition on state transition during sleep slow oscillation. We found that in normal physiological conditions, synaptic inhibition controls the duration and the synchrony of active state termination. The decline of interneuron-mediated inhibition led to asynchronous downward transition across the cortical network and broke the regular slow oscillation pattern. Furthermore, in both in vivo experiment and computational modelling, we revealed that when the level of synaptic inhibition was reduced significantly, it led to a recovery of synchronized oscillations in the form of seizure-like bursting activity. In this condition, the fast active state termination was mediated by intrinsic hyperpolarizing conductances. Our study highlights the significance of both intrinsic and synaptic inhibition in manipulating sleep slow rhythms.

Interneuron-mediated inhibition synchronizes neuronal activity during slow oscillation

PubMed Central

Chen, Jen-Yung; Chauvette, Sylvain; Skorheim, Steven; Timofeev, Igor; Bazhenov, Maxim

2012-01-01

The signature of slow-wave sleep in the electroencephalogram (EEG) is large-amplitude fluctuation of the field potential, which reflects synchronous alternation of activity and silence across cortical neurons. While initiation of the active cortical states during sleep slow oscillation has been intensively studied, the biological mechanisms which drive the network transition from an active state to silence remain poorly understood. In the current study, using a combination of in vivo electrophysiology and thalamocortical network simulation, we explored the impact of intrinsic and synaptic inhibition on state transition during sleep slow oscillation. We found that in normal physiological conditions, synaptic inhibition controls the duration and the synchrony of active state termination. The decline of interneuron-mediated inhibition led to asynchronous downward transition across the cortical network and broke the regular slow oscillation pattern. Furthermore, in both in vivo experiment and computational modelling, we revealed that when the level of synaptic inhibition was reduced significantly, it led to a recovery of synchronized oscillations in the form of seizure-like bursting activity. In this condition, the fast active state termination was mediated by intrinsic hyperpolarizing conductances. Our study highlights the significance of both intrinsic and synaptic inhibition in manipulating sleep slow rhythms. PMID:22641778

System for adjusting frequency of electrical output pulses derived from an oscillator

DOEpatents

Bartholomew, David B.

2006-11-14

A system for setting and adjusting a frequency of electrical output pulses derived from an oscillator in a network is disclosed. The system comprises an accumulator module configured to receive pulses from an oscillator and to output an accumulated value. An adjustor module is configured to store an adjustor value used to correct local oscillator drift. A digital adder adds values from the accumulator module to values stored in the adjustor module and outputs their sums to the accumulator module, where they are stored. The digital adder also outputs an electrical pulse to a logic module. The logic module is in electrical communication with the adjustor module and the network. The logic module may change the value stored in the adjustor module to compensate for local oscillator drift or change the frequency of output pulses. The logic module may also keep time and calculate drift.

Common medial frontal mechanisms of adaptive control in humans and rodents

PubMed Central

Frank, Michael J.; Laubach, Mark

2013-01-01

In this report, we describe how common brain networks within the medial frontal cortex facilitate adaptive behavioral control in rodents and humans. We demonstrate that low frequency oscillations below 12 Hz are dramatically modulated after errors in humans over mid-frontal cortex and in rats within prelimbic and anterior cingulate regions of medial frontal cortex. These oscillations were phase-locked between medial frontal cortex and motor areas in both rats and humans. In rats, single neurons that encoded prior behavioral outcomes were phase-coherent with low-frequency field oscillations particularly after errors. Inactivating medial frontal regions in rats led to impaired behavioral adjustments after errors, eliminated the differential expression of low frequency oscillations after errors, and increased low-frequency spike-field coupling within motor cortex. Our results describe a novel mechanism for behavioral adaptation via low-frequency oscillations and elucidate how medial frontal networks synchronize brain activity to guide performance. PMID:24141310

Gamma and Beta Oscillations Define a Sequence of Neurocognitive Modes Present in Odor Processing

PubMed Central

Frederick, Donald E.; Brown, Austin; Brim, Elizabeth; Mehta, Nisarg; Vujovic, Mark

2016-01-01

Olfactory system beta (15–35 Hz) and gamma (40–110 Hz) oscillations of the local field potential in mammals have both been linked to odor learning and discrimination. Gamma oscillations represent the activity of a local network within the olfactory bulb, and beta oscillations represent engagement of a systemwide network. Here, we test whether beta and gamma oscillations represent different cognitive modes using the different demands of go/no-go and two-alternative choice tasks that previously were suggested to favor beta or gamma oscillations, respectively. We reconcile previous studies and show that both beta and gamma oscillations occur in both tasks, with gamma dominating the early odor sampling period (2–4 sniffs) and beta dominating later. The relative power and coherence of both oscillations depend separately on multiple factors within both tasks without categorical differences across tasks. While the early/gamma-associated period occurs in all trials, rats can perform above chance without the later/beta-associated period. Longer sampling, which includes beta oscillations, is associated with better performance. Gamma followed by beta oscillations therefore represents a sequence of cognitive and neural states during odor discrimination, which can be separately modified depending on the demands of a task and odor discrimination. Additionally, fast (85 Hz) and slow (70 Hz) olfactory bulb gamma oscillation sub-bands have been hypothesized to represent tufted and mitral cell networks, respectively (Manabe and Mori, 2013). We find that fast gamma favors the early and slow gamma the later (beta-dominated) odor-sampling period and that the relative contributions of these oscillations are consistent across tasks. SIGNIFICANCE STATEMENT Olfactory system gamma (40–110 Hz) and beta (15–35 Hz) oscillations of the local field potential indicate different neural firing statistics and functional circuits. We show that gamma and beta oscillations occur in stereotyped sequence during odor sampling in associative tasks, with local gamma dominating the first 250 ms of odor sniffing, followed by systemwide beta as behavioral responses are prepared. Oscillations and coupling strength between brain regions are modulated by task, odor, and learning, showing that task features can dramatically adjust the dynamics of a cortical sensory system, which changes state every ∼250 ms. Understanding cortical circuits, even at the biophysical level, depends on careful use of multiple behavioral contexts and stimuli. PMID:27445151

Gamma and Beta Oscillations Define a Sequence of Neurocognitive Modes Present in Odor Processing.

PubMed

Frederick, Donald E; Brown, Austin; Brim, Elizabeth; Mehta, Nisarg; Vujovic, Mark; Kay, Leslie M

2016-07-20

Olfactory system beta (15-35 Hz) and gamma (40-110 Hz) oscillations of the local field potential in mammals have both been linked to odor learning and discrimination. Gamma oscillations represent the activity of a local network within the olfactory bulb, and beta oscillations represent engagement of a systemwide network. Here, we test whether beta and gamma oscillations represent different cognitive modes using the different demands of go/no-go and two-alternative choice tasks that previously were suggested to favor beta or gamma oscillations, respectively. We reconcile previous studies and show that both beta and gamma oscillations occur in both tasks, with gamma dominating the early odor sampling period (2-4 sniffs) and beta dominating later. The relative power and coherence of both oscillations depend separately on multiple factors within both tasks without categorical differences across tasks. While the early/gamma-associated period occurs in all trials, rats can perform above chance without the later/beta-associated period. Longer sampling, which includes beta oscillations, is associated with better performance. Gamma followed by beta oscillations therefore represents a sequence of cognitive and neural states during odor discrimination, which can be separately modified depending on the demands of a task and odor discrimination. Additionally, fast (85 Hz) and slow (70 Hz) olfactory bulb gamma oscillation sub-bands have been hypothesized to represent tufted and mitral cell networks, respectively (Manabe and Mori, 2013). We find that fast gamma favors the early and slow gamma the later (beta-dominated) odor-sampling period and that the relative contributions of these oscillations are consistent across tasks. Olfactory system gamma (40-110 Hz) and beta (15-35 Hz) oscillations of the local field potential indicate different neural firing statistics and functional circuits. We show that gamma and beta oscillations occur in stereotyped sequence during odor sampling in associative tasks, with local gamma dominating the first 250 ms of odor sniffing, followed by systemwide beta as behavioral responses are prepared. Oscillations and coupling strength between brain regions are modulated by task, odor, and learning, showing that task features can dramatically adjust the dynamics of a cortical sensory system, which changes state every ∼250 ms. Understanding cortical circuits, even at the biophysical level, depends on careful use of multiple behavioral contexts and stimuli. Copyright © 2016 the authors 0270-6474/16/367750-18$15.00/0.

The Logic of Circadian Organization in Drosophila

PubMed Central

Dissel, Stephane; Hansen, Celia N.; Özkaya, Özge; Hemsley, Matthew; Kyriacou, Charalambos P.; Rosato, Ezio

2014-01-01

Summary Background In the fruit fly Drosophila melanogaster, interlocked negative transcription/translation feedback loops provide the core of the circadian clock that generates rhythmic phenotypes. Although the current molecular model portrays the oscillator as cell autonomous, cross-talk among clock neurons is essential for robust cycling behavior. Nevertheless, the functional organization of the neuronal network remains obscure. Results Here we show that shortening or lengthening of the circadian period of locomotor activity can be obtained either by targeting different groups of clock cells with the same genetic manipulation or by challenging the same group of cells with activators and repressors of neuronal excitability. Conclusions Based on these observations we interpret circadian rhythmicity as an emerging property of the circadian network and we propose an initial model for its architectural design. PMID:25220056

Seizure-induced alterations in fast-spiking basket cell GABA currents modulate frequency and coherence of gamma oscillation in network simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proddutur, Archana; Yu, Jiandong; Elgammal, Fatima S.

2013-12-15

Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shiftmore » in GABA reversal potential (E{sub GABA}). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (g{sub GABA-extra}) and experimentally identified, seizure-induced changes in g{sub GABA-extra} and E{sub GABA} influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40–100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30–40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing g{sub GABA-extra} reduced the frequency and coherence of FS-BC firing when E{sub GABA} was shunting (−74 mV), but failed to alter average FS-BC frequency when E{sub GABA} was depolarizing (−54 mV). When FS-BCs were activated by biologically based dendritic synaptic inputs, enhancing g{sub GABA-extra} reduced the frequency and coherence of FS-BC firing when E{sub GABA} was shunting and increased average FS-BC firing when E{sub GABA} was depolarizing. Shifting E{sub GABA} from shunting to depolarizing potentials consistently increased network frequency to and above high gamma frequencies (>80 Hz). Since gamma oscillations may contribute to learning and memory processing [Fell et al., Nat. Neurosci. 4, 1259 (2001); Jutras et al., J. Neurosci. 29, 12521 (2009); Wang, Physiol. Rev. 90, 1195 (2010)], our demonstration that network oscillations are modulated by extrasynaptic inhibition in FS-BCs suggests that neuroactive compounds that act on extrasynaptic GABA receptors could impact memory formation by modulating hippocampal gamma oscillations. The simulation results indicate that the depolarized FS-BC GABA reversal, observed after experimental seizures, together with enhanced spillover extrasynaptic GABA currents are likely to promote generation of focal high frequency activity associated with epileptic networks.« less

Symmetries and stability of chimera states in small, globally-coupled networks

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

It has recently been demonstrated that symmetries in a network's topology can help predict the patterns of synchronized clusters that can emerge in a network of coupled oscillators. This and related discoveries have led to increased interest in both network symmetries and cluster synchronization. In parallel with these discoveries, interest in chimera states-dynamical patterns in which a network separates into coherent and incoherent portions-has grown, and chimeras have now been observed in a variety of experimental systems. We present an opto-electronic experiment in which both chimera states and synchronized clusters are observed in a small, globally-coupled network. We show that the symmetries and sub-symmetries of the network permit the formation of the chimera and cluster states. A recently developed group theoretical approach enables us to predict the stability of the observed chimera and cluster states, and highlights the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization.

Disruption to control network function correlates with altered dynamic connectivity in the wider autism spectrum.

PubMed

de Lacy, N; Doherty, D; King, B H; Rachakonda, S; Calhoun, V D

2017-01-01

Autism is a common developmental condition with a wide, variable range of co-occurring neuropsychiatric symptoms. Contrasting with most extant studies, we explored whole-brain functional organization at multiple levels simultaneously in a large subject group reflecting autism's clinical diversity, and present the first network-based analysis of transient brain states, or dynamic connectivity , in autism. Disruption to inter-network and inter-system connectivity, rather than within individual networks, predominated. We identified coupling disruption in the anterior-posterior default mode axis, and among specific control networks specialized for task start cues and the maintenance of domain-independent task positive status, specifically between the right fronto-parietal and cingulo-opercular networks and default mode network subsystems. These appear to propagate downstream in autism, with significantly dampened subject oscillations between brain states, and dynamic connectivity configuration differences. Our account proposes specific motifs that may provide candidates for neuroimaging biomarkers within heterogeneous clinical populations in this diverse condition.

Heteroclinic dynamics of coupled semiconductor lasers with optoelectronic feedback.

PubMed

Shahin, S; Vallini, F; Monifi, F; Rabinovich, M; Fainman, Y

2016-11-15

Generalized Lotka-Volterra (GLV) equations are important equations used in various areas of science to describe competitive dynamics among a population of N interacting nodes in a network topology. In this Letter, we introduce a photonic network consisting of three optoelectronically cross-coupled semiconductor lasers to realize a GLV model. In such a network, the interaction of intensity and carrier inversion rates, as well as phases of laser oscillator nodes, result in various dynamics. We study the influence of asymmetric coupling strength and frequency detuning between semiconductor lasers and show that inhibitory asymmetric coupling is required to achieve consecutive amplitude oscillations of the laser nodes. These studies were motivated primarily by the dynamical models used to model brain cognitive activities and their correspondence with dynamics obtained among coupled laser oscillators.

Generating macroscopic chaos in a network of globally coupled phase oscillators

PubMed Central

So, Paul; Barreto, Ernest

2011-01-01

We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662

Revealing determinants of two-phase dynamics of P53 network under gamma irradiation based on a reduced 2D relaxation oscillator model.

PubMed

Demirkıran, Gökhan; Kalaycı Demir, Güleser; Güzeliş, Cüneyt

2018-02-01

This study proposes a two-dimensional (2D) oscillator model of p53 network, which is derived via reducing the multidimensional two-phase dynamics model into a model of ataxia telangiectasia mutated (ATM) and Wip1 variables, and studies the impact of p53-regulators on cell fate decision. First, the authors identify a 6D core oscillator module, then reduce this module into a 2D oscillator model while preserving the qualitative behaviours. The introduced 2D model is shown to be an excitable relaxation oscillator. This oscillator provides a mechanism that leads diverse modes underpinning cell fate, each corresponding to a cell state. To investigate the effects of p53 inhibitors and the intrinsic time delay of Wip1 on the characteristics of oscillations, they introduce also a delay differential equation version of the 2D oscillator. They observe that the suppression of p53 inhibitors decreases the amplitudes of p53 oscillation, though the suppression increases the sustained level of p53. They identify Wip1 and P53DINP1 as possible targets for cancer therapies considering their impact on the oscillator, supported by biological findings. They model some mutations as critical changes of the phase space characteristics. Possible cancer therapeutic strategies are then proposed for preventing these mutations' effects using the phase space approach.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

γ-Aminobutyric Acid Type A Receptor Potentiation Inhibits Learning in a Computational Network Model.

PubMed

Storer, Kingsley P; Reeke, George N

2018-04-17

Propofol produces memory impairment at concentrations well below those abolishing consciousness. Episodic memory, mediated by the hippocampus, is most sensitive. Two potentially overlapping scenarios may explain how γ-aminobutyric acid receptor type A (GABAA) potentiation by propofol disrupts episodic memory-the first mediated by shifting the balance from excitation to inhibition while the second involves disruption of rhythmic oscillations. We use a hippocampal network model to explore these scenarios. The basis for these experiments is the proposal that the brain represents memories as groups of anatomically dispersed strongly connected neurons. A neuronal network with connections modified by synaptic plasticity was exposed to patterned stimuli, after which spiking output demonstrated evidence of stimulus-related neuronal group development analogous to memory formation. The effect of GABAA potentiation on this memory model was studied in 100 unique networks. GABAA potentiation consistent with moderate propofol effects reduced neuronal group size formed in response to a patterned stimulus by around 70%. Concurrently, accuracy of a Bayesian classifier in identifying learned patterns in the network output was reduced. Greater potentiation led to near total failure of group formation. Theta rhythm variations had no effect on group size or classifier accuracy. Memory formation is widely thought to depend on changes in neuronal connection strengths during learning that enable neuronal groups to respond with greater facility to familiar stimuli. This experiment suggests the ability to form such groups is sensitive to alteration in the balance between excitation and inhibition such as that resulting from administration of a γ-aminobutyric acid-mediated anesthetic agent.

Center for Neural Engineering: applications of pulse-coupled neural networks

NASA Astrophysics Data System (ADS)

Malkani, Mohan; Bodruzzaman, Mohammad; Johnson, John L.; Davis, Joel

1999-03-01

Pulsed-Coupled Neural Network (PCNN) is an oscillatory model neural network where grouping of cells and grouping among the groups that form the output time series (number of cells that fires in each input presentation also called `icon'). This is based on the synchronicity of oscillations. Recent work by Johnson and others demonstrated the functional capabilities of networks containing such elements for invariant feature extraction using intensity maps. PCNN thus presents itself as a more biologically plausible model with solid functional potential. This paper will present the summary of several projects and their results where we successfully applied PCNN. In project one, the PCNN was applied for object recognition and classification through a robotic vision system. The features (icons) generated by the PCNN were then fed into a feedforward neural network for classification. In project two, we developed techniques for sensory data fusion. The PCNN algorithm was implemented and tested on a B14 mobile robot. The PCNN-based features were extracted from the images taken from the robot vision system and used in conjunction with the map generated by data fusion of the sonar and wheel encoder data for the navigation of the mobile robot. In our third project, we applied the PCNN for speaker recognition. The spectrogram image of speech signals are fed into the PCNN to produce invariant feature icons which are then fed into a feedforward neural network for speaker identification.

Synchronization of mobile chaotic oscillator networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp; Kurths, Jürgen; Díaz-Guilera, Albert

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to themore » transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.« less

Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.

PubMed

Mall, Susmita; Chakraverty, S

2016-08-01

Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

Kainate-induced network activity in the anterior cingulate cortex.

PubMed

Shinozaki, R; Hojo, Y; Mukai, H; Hashizume, M; Murakoshi, T

2016-06-14

Anterior cingulate cortex (ACC) plays a pivotal role in higher order processing of cognition, attention and emotion. The network oscillation is considered an essential means for integration of these CNS functions. The oscillation power and coherence among related areas are often dis-regulated in several psychiatric and pathological conditions with a hemispheric asymmetric manner. Here we describe the network-based activity of field potentials recorded from the superficial layer of the mouse ACC in vitro using submerged type recordings. A short activation by kainic acid administration to the preparation induced populational activities ranging over several frequency bands including theta (3-8Hz), alpha (8-12Hz), beta (13-30Hz), low gamma (30-50Hz) and high gamma (50-80Hz). These responses were repeatable and totally abolished by tetrodotoxin, and greatly diminished by inhibitors of ionotropic and metabotropic glutamate receptors, GABAA receptor or gap-junctions. These observations suggest that the kainate-induced network activity can be a useful model of the network oscillation in the ACC circuit. Copyright © 2016 IBRO. Published by Elsevier Ltd. All rights reserved.

Signal Processing in Periodically Forced Gradient Frequency Neural Networks

PubMed Central

Kim, Ji Chul; Large, Edward W.

2015-01-01

Oscillatory instability at the Hopf bifurcation is a dynamical phenomenon that has been suggested to characterize active non-linear processes observed in the auditory system. Networks of oscillators poised near Hopf bifurcation points and tuned to tonotopically distributed frequencies have been used as models of auditory processing at various levels, but systematic investigation of the dynamical properties of such oscillatory networks is still lacking. Here we provide a dynamical systems analysis of a canonical model for gradient frequency neural networks driven by a periodic signal. We use linear stability analysis to identify various driven behaviors of canonical oscillators for all possible ranges of model and forcing parameters. The analysis shows that canonical oscillators exhibit qualitatively different sets of driven states and transitions for different regimes of model parameters. We classify the parameter regimes into four main categories based on their distinct signal processing capabilities. This analysis will lead to deeper understanding of the diverse behaviors of neural systems under periodic forcing and can inform the design of oscillatory network models of auditory signal processing. PMID:26733858

Role of local network oscillations in resting-state functional connectivity.

PubMed

Cabral, Joana; Hugues, Etienne; Sporns, Olaf; Deco, Gustavo

2011-07-01

Spatio-temporally organized low-frequency fluctuations (<0.1 Hz), observed in BOLD fMRI signal during rest, suggest the existence of underlying network dynamics that emerge spontaneously from intrinsic brain processes. Furthermore, significant correlations between distinct anatomical regions-or functional connectivity (FC)-have led to the identification of several widely distributed resting-state networks (RSNs). This slow dynamics seems to be highly structured by anatomical connectivity but the mechanism behind it and its relationship with neural activity, particularly in the gamma frequency range, remains largely unknown. Indeed, direct measurements of neuronal activity have revealed similar large-scale correlations, particularly in slow power fluctuations of local field potential gamma frequency range oscillations. To address these questions, we investigated neural dynamics in a large-scale model of the human brain's neural activity. A key ingredient of the model was a structural brain network defined by empirically derived long-range brain connectivity together with the corresponding conduction delays. A neural population, assumed to spontaneously oscillate in the gamma frequency range, was placed at each network node. When these oscillatory units are integrated in the network, they behave as weakly coupled oscillators. The time-delayed interaction between nodes is described by the Kuramoto model of phase oscillators, a biologically-based model of coupled oscillatory systems. For a realistic setting of axonal conduction speed, we show that time-delayed network interaction leads to the emergence of slow neural activity fluctuations, whose patterns correlate significantly with the empirically measured FC. The best agreement of the simulated FC with the empirically measured FC is found for a set of parameters where subsets of nodes tend to synchronize although the network is not globally synchronized. Inside such clusters, the simulated BOLD signal between nodes is found to be correlated, instantiating the empirically observed RSNs. Between clusters, patterns of positive and negative correlations are observed, as described in experimental studies. These results are found to be robust with respect to a biologically plausible range of model parameters. In conclusion, our model suggests how resting-state neural activity can originate from the interplay between the local neural dynamics and the large-scale structure of the brain. Copyright © 2011 Elsevier Inc. All rights reserved.

Maintaining network activity in submerged hippocampal slices: importance of oxygen supply.

PubMed

Hájos, Norbert; Ellender, Tommas J; Zemankovics, Rita; Mann, Edward O; Exley, Richard; Cragg, Stephanie J; Freund, Tamás F; Paulsen, Ole

2009-01-01

Studies in brain slices have provided a wealth of data on the basic features of neurons and synapses. In the intact brain, these properties may be strongly influenced by ongoing network activity. Although physiologically realistic patterns of network activity have been successfully induced in brain slices maintained in interface-type recording chambers, they have been harder to obtain in submerged-type chambers, which offer significant experimental advantages, including fast exchange of pharmacological agents, visually guided patch-clamp recordings, and imaging techniques. Here, we investigated conditions for the emergence of network oscillations in submerged slices prepared from the hippocampus of rats and mice. We found that the local oxygen level is critical for generation and propagation of both spontaneously occurring sharp wave-ripple oscillations and cholinergically induced fast oscillations. We suggest three ways to improve the oxygen supply to slices under submerged conditions: (i) optimizing chamber design for laminar flow of superfusion fluid; (ii) increasing the flow rate of superfusion fluid; and (iii) superfusing both surfaces of the slice. These improvements to the recording conditions enable detailed studies of neurons under more realistic conditions of network activity, which are essential for a better understanding of neuronal network operation.

Learning characteristics of a space-time neural network as a tether skiprope observer

NASA Technical Reports Server (NTRS)

Lea, Robert N.; Villarreal, James A.; Jani, Yashvant; Copeland, Charles

1993-01-01

The Software Technology Laboratory at the Johnson Space Center is testing a Space Time Neural Network (STNN) for observing tether oscillations present during retrieval of a tethered satellite. Proper identification of tether oscillations, known as 'skiprope' motion, is vital to safe retrieval of the tethered satellite. Our studies indicate that STNN has certain learning characteristics that must be understood properly to utilize this type of neural network for the tethered satellite problem. We present our findings on the learning characteristics including a learning rate versus momentum performance table.

Learning characteristics of a space-time neural network as a tether skiprope observer

NASA Technical Reports Server (NTRS)

Lea, Robert N.; Villarreal, James A.; Jani, Yashvant; Copeland, Charles

1992-01-01

The Software Technology Laboratory at JSC is testing a Space Time Neural Network (STNN) for observing tether oscillations present during retrieval of a tethered satellite. Proper identification of tether oscillations, known as 'skiprope' motion, is vital to safe retrieval of the tethered satellite. Our studies indicate that STNN has certain learning characteristics that must be understood properly to utilize this type of neural network for the tethered satellite problem. We present our findings on the learning characteristics including a learning rate versus momentum performance table.

Increased Amplitude of Thalamocortical Low-Frequency Oscillations in Patients with Migraine

PubMed Central

Wilcox, Sophie L.; Veggeberg, Rosanna; Noseda, Rodrigo; Burstein, Rami; Borsook, David; Becerra, Lino

2016-01-01

For many years, neurobiological theories have emphasized the importance of neuronal oscillations in the emergence of brain function. At the same time, clinical studies have shown that disturbances or irregularities in brain rhythms may relate to various common neurological conditions, including migraine. Increasing evidence suggests that the CNS plays a fundamental role in the predisposition to develop different forms of headache. Here, we present human imaging data that strongly support the presence of abnormal low-frequency oscillations (LFOs) in thalamocortical networks of patients in the interictal phase of migraine. Our results show that the main source of arrhythmic activity was localized to the higher-order thalamic relays of the medial dorsal nucleus. In addition, spontaneous LFOs in the thalamus were selectively associated with the headache attack frequency, meaning that the varying amplitude of dysrhythmia could predispose patients to recurrent attacks. Rhythmic cortical feedback to the thalamus is a major factor in the amplification of thalamocortical oscillations, making it a strong candidate for influencing neuronal excitability. We further speculate that the intrinsic dynamics of thalamocortical network oscillations are crucial for early sensory processing and therefore could underlie important pathophysiological processes involved in multisensory integration. SIGNIFICANCE STATEMENT In many cases, migraine attacks are thought to begin centrally. A major obstacle to studying intrinsic brain activity has been the identification of the precise anatomical structures and functional networks that are involved in migraine. Here, we present imaging data that strongly support the presence of abnormal low-frequency oscillations in thalamocortical networks of patients in the interictal phase of migraine. This arrhythmic activity was localized to the higher-order thalamic relays of the medial dorsal nucleus and was selectively associated with headache attack frequency. Rhythmic cortical feedback to the thalamus is a major factor in the amplification of thalamocortical oscillations, making it a strong candidate for influencing neuronal excitability and higher-level processes involved in multisensory integration. PMID:27466345

The Energy Coding of a Structural Neural Network Based on the Hodgkin-Huxley Model.

PubMed

Zhu, Zhenyu; Wang, Rubin; Zhu, Fengyun

2018-01-01

Based on the Hodgkin-Huxley model, the present study established a fully connected structural neural network to simulate the neural activity and energy consumption of the network by neural energy coding theory. The numerical simulation result showed that the periodicity of the network energy distribution was positively correlated to the number of neurons and coupling strength, but negatively correlated to signal transmitting delay. Moreover, a relationship was established between the energy distribution feature and the synchronous oscillation of the neural network, which showed that when the proportion of negative energy in power consumption curve was high, the synchronous oscillation of the neural network was apparent. In addition, comparison with the simulation result of structural neural network based on the Wang-Zhang biophysical model of neurons showed that both models were essentially consistent.

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Optogenetically induced spatiotemporal gamma oscillations and neuronal spiking activity in primate motor cortex.

PubMed

Lu, Yao; Truccolo, Wilson; Wagner, Fabien B; Vargas-Irwin, Carlos E; Ozden, Ilker; Zimmermann, Jonas B; May, Travis; Agha, Naubahar S; Wang, Jing; Nurmikko, Arto V

2015-06-01

Transient gamma-band (40-80 Hz) spatiotemporal patterns are hypothesized to play important roles in cortical function. Here we report the direct observation of gamma oscillations as spatiotemporal waves induced by targeted optogenetic stimulation, recorded by intracortical multichannel extracellular techniques in macaque monkeys during their awake resting states. Microelectrode arrays integrating an optical fiber at their center were chronically implanted in primary motor (M1) and ventral premotor (PMv) cortices of two subjects. Targeted brain tissue was transduced with the red-shifted opsin C1V1(T/T). Constant (1-s square pulses) and ramp stimulation induced narrowband gamma oscillations during awake resting states. Recordings across 95 microelectrodes (4 × 4-mm array) enabled us to track the transient gamma spatiotemporal patterns manifested, e.g., as concentric expanding and spiral waves. Gamma oscillations were induced well beyond the light stimulation volume, via network interactions at distal electrode sites, depending on optical power. Despite stimulation-related modulation in spiking rates, neuronal spiking remained highly asynchronous during induced gamma oscillations. In one subject we examined stimulation effects during preparation and execution of a motor task and observed that movement execution largely attenuated optically induced gamma oscillations. Our findings demonstrate that, beyond previously reported induced gamma activity under periodic drive, a prolonged constant stimulus above a certain threshold may carry primate motor cortex network dynamics into gamma oscillations, likely via a Hopf bifurcation. More broadly, the experimental capability in combining microelectrode array recordings and optogenetic stimulation provides an important approach for probing spatiotemporal dynamics in primate cortical networks during various physiological and behavioral conditions.

Optogenetically induced spatiotemporal gamma oscillations and neuronal spiking activity in primate motor cortex

PubMed Central

Lu, Yao; Truccolo, Wilson; Wagner, Fabien B.; Vargas-Irwin, Carlos E.; Ozden, Ilker; Zimmermann, Jonas B.; May, Travis; Agha, Naubahar S.; Wang, Jing

2015-01-01

Transient gamma-band (40–80 Hz) spatiotemporal patterns are hypothesized to play important roles in cortical function. Here we report the direct observation of gamma oscillations as spatiotemporal waves induced by targeted optogenetic stimulation, recorded by intracortical multichannel extracellular techniques in macaque monkeys during their awake resting states. Microelectrode arrays integrating an optical fiber at their center were chronically implanted in primary motor (M1) and ventral premotor (PMv) cortices of two subjects. Targeted brain tissue was transduced with the red-shifted opsin C1V1(T/T). Constant (1-s square pulses) and ramp stimulation induced narrowband gamma oscillations during awake resting states. Recordings across 95 microelectrodes (4 × 4-mm array) enabled us to track the transient gamma spatiotemporal patterns manifested, e.g., as concentric expanding and spiral waves. Gamma oscillations were induced well beyond the light stimulation volume, via network interactions at distal electrode sites, depending on optical power. Despite stimulation-related modulation in spiking rates, neuronal spiking remained highly asynchronous during induced gamma oscillations. In one subject we examined stimulation effects during preparation and execution of a motor task and observed that movement execution largely attenuated optically induced gamma oscillations. Our findings demonstrate that, beyond previously reported induced gamma activity under periodic drive, a prolonged constant stimulus above a certain threshold may carry primate motor cortex network dynamics into gamma oscillations, likely via a Hopf bifurcation. More broadly, the experimental capability in combining microelectrode array recordings and optogenetic stimulation provides an important approach for probing spatiotemporal dynamics in primate cortical networks during various physiological and behavioral conditions. PMID:25761956

Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach

NASA Astrophysics Data System (ADS)

Pinto, Rafael S.; Saa, Alberto

2015-12-01

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function ωTL ω , where ω stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix. Many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition. A computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.

Dynamical Bayesian inference of time-evolving interactions: from a pair of coupled oscillators to networks of oscillators.

PubMed

Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V E; Stefanovska, Aneta

2012-12-01

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. [Phys. Rev. Lett. 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Amplitude death induced by mixed attractive and repulsive coupling in the relay system

NASA Astrophysics Data System (ADS)

Zhao, Nannan; Sun, Zhongkui; Xu, Wei

2018-01-01

The amplitude death (AD) phenomenon is found in the relay system in the presence of the mixed couplings composed of attractive coupling and repulsive coupling. The generation mechanism of AD is revealed and shows that the middle oscillator achieving AD is a prerequisite to further suppress oscillation of the outermost oscillators for the paradigmatic Stuart-Landau and Rössler models. Moreover, regarding the Stuart-Landau relay system as a small motif of star network, we also observe that the mixed couplings can facilitate AD state of the whole network system. Particularly, the threshold of coupling strength is invariable with the change of network size. Our findings may shed a new insight to explore the effects of hybrid coupling on complex systems, also provide a new strategy to control dynamic behaviors in engineering science and neuroscience fields.

Rational design of functional and tunable oscillating enzymatic networks

NASA Astrophysics Data System (ADS)

Semenov, Sergey N.; Wong, Albert S. Y.; van der Made, R. Martijn; Postma, Sjoerd G. J.; Groen, Joost; van Roekel, Hendrik W. H.; de Greef, Tom F. A.; Huck, Wilhelm T. S.

2015-02-01

Life is sustained by complex systems operating far from equilibrium and consisting of a multitude of enzymatic reaction networks. The operating principles of biology's regulatory networks are known, but the in vitro assembly of out-of-equilibrium enzymatic reaction networks has proved challenging, limiting the development of synthetic systems showing autonomous behaviour. Here, we present a strategy for the rational design of programmable functional reaction networks that exhibit dynamic behaviour. We demonstrate that a network built around autoactivation and delayed negative feedback of the enzyme trypsin is capable of producing sustained oscillating concentrations of active trypsin for over 65 h. Other functions, such as amplification, analog-to-digital conversion and periodic control over equilibrium systems, are obtained by linking multiple network modules in microfluidic flow reactors. The methodology developed here provides a general framework to construct dissipative, tunable and robust (bio)chemical reaction networks.

A 16 element quasi-optical FET oscillator power combining array with external injection locking

NASA Astrophysics Data System (ADS)

Birkeland, Joel; Itoh, Tatsuo

1992-03-01

The authors present analysis, design and experimental results of a 16 element planar oscillator array for quasi-optical power combining. Each element in the array consists of a single FET oscillator with an input port for injection of the locking signal, and an output port which is connected to a patch radiator. The array is synchronized using a 16-way power dividing network which distributes the locking signal to the oscillating elements. The array is constructed using a two-sided microstrip configuration, with the oscillators and feed network on one side of a ground plane, and the patch radiators on the opposite side. An effective radiated power (ERP) of 28.2 W CW with an isotropic conversion gain of 9.9 dB was measured at 6 GHz. For an injected power of 10.3 dBm, a locking range of 453 MHz at a center frequency of 6.015 GHz was obtained; a bandwidth of 7.5 percent. Because of the simple nature of the individual oscillator elements, this approach is well suited to MMIC implementation.

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

NASA Astrophysics Data System (ADS)

Zhao, Liyun; Zhou, Jin; Wu, Quanjun

2016-01-01

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.

Stochastic Noise and Synchronisation during Dictyostelium Aggregation Make cAMP Oscillations Robust

PubMed Central

Kim, Jongrae; Heslop-Harrison, Pat; Postlethwaite, Ian; Bates, Declan G

2007-01-01

Stable and robust oscillations in the concentration of adenosine 3′, 5′-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca2+ oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high. PMID:17997595

BLOCKING OSCILLATOR DOUBLE PULSE GENERATOR CIRCUIT

DOEpatents

Haase, J.A.

1961-01-24

A double-pulse generator, particuiarly a double-pulse generator comprising a blocking oscillator utilizing a feedback circuit to provide means for producing a second pulse within the recovery time of the blocking oscillator, is described. The invention utilized a passive network which permits adjustment of the spacing between the original pulses derived from the blocking oscillator and further utilizes the original pulses to trigger a circuit from which other pulses are initiated. These other pulses are delayed and then applied to the input of the blocking oscillator, with the result that the output from the oscillator circuit contains twice the number of pulses originally initiated by the blocking oscillator itself.

From quiescence to proliferation: Cdk oscillations drive the mammalian cell cycle

PubMed Central

Gérard, Claude; Goldbeter, Albert

2012-01-01

We recently proposed a detailed model describing the dynamics of the network of cyclin-dependent kinases (Cdks) driving the mammalian cell cycle (Gérard and Goldbeter, 2009). The model contains four modules, each centered around one cyclin/Cdk complex. Cyclin D/Cdk4–6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2 ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings about the G2/M transition. This model shows that in the presence of sufficient amounts of growth factor the Cdk network is capable of temporal self-organization in the form of sustained oscillations, which correspond to the ordered, sequential activation of the various cyclin/Cdk complexes that control the successive phases of the cell cycle. The results suggest that the switch from cellular quiescence to cell proliferation corresponds to the transition from a stable steady state to sustained oscillations in the Cdk network. The transition depends on a finely tuned balance between factors that promote or hinder progression in the cell cycle. We show that the transition from quiescence to proliferation can occur in multiple ways that alter this balance. By resorting to bifurcation diagrams, we analyze the mechanism of oscillations in the Cdk network. Finally, we show that the complexity of the detailed model can be greatly reduced, without losing its key dynamical properties, by considering a skeleton model for the Cdk network. Using such a skeleton model for the mammalian cell cycle we show that positive feedback (PF) loops enhance the amplitude and the robustness of Cdk oscillations with respect to molecular noise. We compare the relative merits of the detailed and skeleton versions of the model for the Cdk network driving the mammalian cell cycle. PMID:23130001

A Neurophysiological Perspective on a Preventive Treatment against Schizophrenia Using Transcranial Electric Stimulation of the Corticothalamic Pathway

PubMed Central

Pinault, Didier

2017-01-01

Schizophrenia patients are waiting for a treatment free of detrimental effects. Psychotic disorders are devastating mental illnesses associated with dysfunctional brain networks. Ongoing brain network gamma frequency (30–80 Hz) oscillations, naturally implicated in integrative function, are excessively amplified during hallucinations, in at-risk mental states for psychosis and first-episode psychosis. So, gamma oscillations represent a bioelectrical marker for cerebral network disorders with prognostic and therapeutic potential. They accompany sensorimotor and cognitive deficits already present in prodromal schizophrenia. Abnormally amplified gamma oscillations are reproduced in the corticothalamic systems of healthy humans and rodents after a single systemic administration, at a psychotomimetic dose, of the glutamate N-methyl-d-aspartate receptor antagonist ketamine. These translational ketamine models of prodromal schizophrenia are thus promising to work out a preventive noninvasive treatment against first-episode psychosis and chronic schizophrenia. In the present essay, transcranial electric stimulation (TES) is considered an appropriate preventive therapeutic modality because it can influence cognitive performance and neural oscillations. Here, I highlight clinical and experimental findings showing that, together, the corticothalamic pathway, the thalamus, and the glutamatergic synaptic transmission form an etiopathophysiological backbone for schizophrenia and represent a potential therapeutic target for preventive TES of dysfunctional brain networks in at-risk mental state patients against psychotic disorders. PMID:28350371

A Neurophysiological Perspective on a Preventive Treatment against Schizophrenia Using Transcranial Electric Stimulation of the Corticothalamic Pathway.

PubMed

Pinault, Didier

2017-03-28

Schizophrenia patients are waiting for a treatment free of detrimental effects. Psychotic disorders are devastating mental illnesses associated with dysfunctional brain networks. Ongoing brain network gamma frequency (30-80 Hz) oscillations, naturally implicated in integrative function, are excessively amplified during hallucinations, in at-risk mental states for psychosis and first-episode psychosis. So, gamma oscillations represent a bioelectrical marker for cerebral network disorders with prognostic and therapeutic potential. They accompany sensorimotor and cognitive deficits already present in prodromal schizophrenia. Abnormally amplified gamma oscillations are reproduced in the corticothalamic systems of healthy humans and rodents after a single systemic administration, at a psychotomimetic dose, of the glutamate N - methyl -d-aspartate receptor antagonist ketamine. These translational ketamine models of prodromal schizophrenia are thus promising to work out a preventive noninvasive treatment against first-episode psychosis and chronic schizophrenia. In the present essay, transcranial electric stimulation (TES) is considered an appropriate preventive therapeutic modality because it can influence cognitive performance and neural oscillations. Here, I highlight clinical and experimental findings showing that, together, the corticothalamic pathway, the thalamus, and the glutamatergic synaptic transmission form an etiopathophysiological backbone for schizophrenia and represent a potential therapeutic target for preventive TES of dysfunctional brain networks in at-risk mental state patients against psychotic disorders.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br; Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de

2015-04-15

We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the fullmore » synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.« less

On synchronization in power-grids modelled as networks of second-order Kuramoto oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2016-11-01

This work concerns analytical results on the role of coupling strength in the phenomenon of onset of complete frequency locking in power-grids modelled as a network of second-order Kuramoto oscillators. Those results allow estimation of the coupling strength for the onset of complete frequency locking and to assess the features of network and oscillators that favor synchronization. The analytical results are evaluated using an order parameter defined as the normalized sum of absolute values of phase deviations of the oscillators over time. The investigation of the frequency synchronization within the subsets of the parameter space involved in the synchronization problem is also carried out. It is shown that the analytical results are in good agreement with those observed in the numerical simulations. In order to illustrate the methodology, a case study is presented, involving the Brazilian high-voltage transmission system under a load peak condition to study the effect of load on the syncronizability of the grid. The results show that both the load and the centralized generation might have concurred to the 2014 blackout.

All together now: Analogies between chimera state collapses and epileptic seizures

NASA Astrophysics Data System (ADS)

Andrzejak, Ralph G.; Rummel, Christian; Mormann, Florian; Schindler, Kaspar

2016-03-01

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena. A recent and not yet fully understood example is the collapse of coexisting synchronous and asynchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications.

Granule cell excitability regulates gamma and beta oscillations in a model of the olfactory bulb dendrodendritic microcircuit

PubMed Central

Osinski, Bolesław L.

2016-01-01

Odors evoke gamma (40–100 Hz) and beta (20–30 Hz) oscillations in the local field potential (LFP) of the mammalian olfactory bulb (OB). Gamma (and possibly beta) oscillations arise from interactions in the dendrodendritic microcircuit between excitatory mitral cells (MCs) and inhibitory granule cells (GCs). When cortical descending inputs to the OB are blocked, beta oscillations are extinguished whereas gamma oscillations become larger. Much of this centrifugal input targets inhibitory interneurons in the GC layer and regulates the excitability of GCs, which suggests a causal link between the emergence of beta oscillations and GC excitability. We investigate the effect that GC excitability has on network oscillations in a computational model of the MC-GC dendrodendritic network with Ca2+-dependent graded inhibition. Results from our model suggest that when GC excitability is low, the graded inhibitory current mediated by NMDA channels and voltage-dependent Ca2+ channels (VDCCs) is also low, allowing MC populations to fire in the gamma frequency range. When GC excitability is increased, the activation of NMDA receptors and other VDCCs is also increased, allowing the slow decay time constants of these channels to sustain beta-frequency oscillations. Our model argues that Ca2+ flow through VDCCs alone could sustain beta oscillations and that the switch between gamma and beta oscillations can be triggered by an increase in the excitability state of a subpopulation of GCs. PMID:27121582

Real-Time Distributed Embedded Oscillator Operating Frequency Monitoring

NASA Technical Reports Server (NTRS)

Pollock, Julie; Oliver, Brett; Brickner, Christopher

2012-01-01

A document discusses the utilization of embedded clocks inside of operating network data links as an auxiliary clock source to satisfy local oscillator monitoring requirements. Modem network interfaces, typically serial network links, often contain embedded clocking information of very tight precision to recover data from the link. This embedded clocking data can be utilized by the receiving device to monitor the local oscillator for tolerance to required specifications, often important in high-integrity fault-tolerant applications. A device can utilize a received embedded clock to determine if the local or the remote device is out of tolerance by using a single link. The local device can determine if it is failing, assuming a single fault model, with two or more active links. Network fabric components, containing many operational links, can potentially determine faulty remote or local devices in the presence of multiple faults. Two methods of implementation are described. In one method, a recovered clock can be directly used to monitor the local clock as a direct replacement of an external local oscillator. This scheme is consistent with a general clock monitoring function whereby clock sources are clocking two counters and compared over a fixed interval of time. In another method, overflow/underflow conditions can be used to detect clock relationships for monitoring. These network interfaces often provide clock compensation circuitry to allow data to be transferred from the received (network) clock domain to the internal clock domain. This circuit could be modified to detect overflow/underflow conditions of the buffering required and report a fast or slow receive clock, respectively.

A modeling comparison of projection neuron- and neuromodulator-elicited oscillations in a central pattern generating network.

PubMed

Kintos, Nickolas; Nusbaum, Michael P; Nadim, Farzan

2008-06-01

Many central pattern generating networks are influenced by synaptic input from modulatory projection neurons. The network response to a projection neuron is sometimes mimicked by bath applying the neuronally-released modulator, despite the absence of network interactions with the projection neuron. One interesting example occurs in the crab stomatogastric ganglion (STG), where bath applying the neuropeptide pyrokinin (PK) elicits a gastric mill rhythm which is similar to that elicited by the projection neuron modulatory commissural neuron 1 (MCN1), despite the absence of PK in MCN1 and the fact that MCN1 is not active during the PK-elicited rhythm. MCN1 terminals have fast and slow synaptic actions on the gastric mill network and are presynaptically inhibited by this network in the STG. These local connections are inactive in the PK-elicited rhythm, and the mechanism underlying this rhythm is unknown. We use mathematical and biophysically-realistic modeling to propose potential mechanisms by which PK can elicit a gastric mill rhythm that is similar to the MCN1-elicited rhythm. We analyze slow-wave network oscillations using simplified mathematical models and, in parallel, develop biophysically-realistic models that account for fast, action potential-driven oscillations and some spatial structure of the network neurons. Our results illustrate how the actions of bath-applied neuromodulators can mimic those of descending projection neurons through mathematically similar but physiologically distinct mechanisms.

Network models provide insights into how oriens–lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations

PubMed Central

Ferguson, Katie A.; Huh, Carey Y. L.; Amilhon, Bénédicte; Manseau, Frédéric; Williams, Sylvain; Skinner, Frances K.

2015-01-01

Hippocampal theta is a 4–12 Hz rhythm associated with episodic memory, and although it has been studied extensively, the cellular mechanisms underlying its generation are unclear. The complex interactions between different interneuron types, such as those between oriens–lacunosum-moleculare (OLM) interneurons and bistratified cells (BiCs), make their contribution to network rhythms difficult to determine experimentally. We created network models that are tied to experimental work at both cellular and network levels to explore how these interneuron interactions affect the power of local oscillations. Our cellular models were constrained with properties from patch clamp recordings in the CA1 region of an intact hippocampus preparation in vitro. Our network models are composed of three different types of interneurons: parvalbumin-positive (PV+) basket and axo-axonic cells (BC/AACs), PV+ BiCs, and somatostatin-positive OLM cells. Also included is a spatially extended pyramidal cell model to allow for a simplified local field potential representation, as well as experimentally-constrained, theta frequency synaptic inputs to the interneurons. The network size, connectivity, and synaptic properties were constrained with experimental data. To determine how the interactions between OLM cells and BiCs could affect local theta power, we explored how the number of OLM-BiC connections and connection strength affected local theta power. We found that our models operate in regimes that could be distinguished by whether OLM cells minimally or strongly affected the power of network theta oscillations due to balances that, respectively, allow compensatory effects or not. Inactivation of OLM cells could result in no change or even an increase in theta power. We predict that the dis-inhibitory effect of OLM cells to BiCs to pyramidal cell interactions plays a critical role in the resulting power of network theta oscillations. Overall, our network models reveal a dynamic interplay between different classes of interneurons in influencing local theta power. PMID:26300744

Excitatory motor neurons are local oscillators for backward locomotion

PubMed Central

Guan, Sihui Asuka; Fouad, Anthony D; Meng, Jun; Kawano, Taizo; Huang, Yung-Chi; Li, Yi; Alcaire, Salvador; Hung, Wesley; Lu, Yangning; Qi, Yingchuan Billy; Jin, Yishi; Alkema, Mark; Fang-Yen, Christopher

2018-01-01

Cell- or network-driven oscillators underlie motor rhythmicity. The identity of C. elegans oscillators remains unknown. Through cell ablation, electrophysiology, and calcium imaging, we show: (1) forward and backward locomotion is driven by different oscillators; (2) the cholinergic and excitatory A-class motor neurons exhibit intrinsic and oscillatory activity that is sufficient to drive backward locomotion in the absence of premotor interneurons; (3) the UNC-2 P/Q/N high-voltage-activated calcium current underlies A motor neuron’s oscillation; (4) descending premotor interneurons AVA, via an evolutionarily conserved, mixed gap junction and chemical synapse configuration, exert state-dependent inhibition and potentiation of A motor neuron’s intrinsic activity to regulate backward locomotion. Thus, motor neurons themselves derive rhythms, which are dually regulated by the descending interneurons to control the reversal motor state. These and previous findings exemplify compression: essential circuit properties are conserved but executed by fewer numbers and layers of neurons in a small locomotor network. PMID:29360035

Excitatory motor neurons are local oscillators for backward locomotion.

PubMed

Gao, Shangbang; Guan, Sihui Asuka; Fouad, Anthony D; Meng, Jun; Kawano, Taizo; Huang, Yung-Chi; Li, Yi; Alcaire, Salvador; Hung, Wesley; Lu, Yangning; Qi, Yingchuan Billy; Jin, Yishi; Alkema, Mark; Fang-Yen, Christopher; Zhen, Mei

2018-01-23

Cell- or network-driven oscillators underlie motor rhythmicity. The identity of C. elegans oscillators remains unknown. Through cell ablation, electrophysiology, and calcium imaging, we show: (1) forward and backward locomotion is driven by different oscillators; (2) the cholinergic and excitatory A-class motor neurons exhibit intrinsic and oscillatory activity that is sufficient to drive backward locomotion in the absence of premotor interneurons; (3) the UNC-2 P/Q/N high-voltage-activated calcium current underlies A motor neuron's oscillation; (4) descending premotor interneurons AVA, via an evolutionarily conserved, mixed gap junction and chemical synapse configuration, exert state-dependent inhibition and potentiation of A motor neuron's intrinsic activity to regulate backward locomotion. Thus, motor neurons themselves derive rhythms, which are dually regulated by the descending interneurons to control the reversal motor state. These and previous findings exemplify compression: essential circuit properties are conserved but executed by fewer numbers and layers of neurons in a small locomotor network. © 2017, Gao et al.

Theta and Alpha Oscillations Are Traveling Waves in the Human Neocortex.

PubMed

Zhang, Honghui; Watrous, Andrew J; Patel, Ansh; Jacobs, Joshua

2018-06-01

Human cognition requires the coordination of neural activity across widespread brain networks. Here, we describe a new mechanism for large-scale coordination in the human brain: traveling waves of theta and alpha oscillations. Examining direct brain recordings from neurosurgical patients performing a memory task, we found contiguous clusters of cortex in individual patients with oscillations at specific frequencies within 2 to 15 Hz. These oscillatory clusters displayed spatial phase gradients, indicating that they formed traveling waves that propagated at ∼0.25-0.75 m/s. Traveling waves were relevant behaviorally because their propagation correlated with task events and was more consistent when subjects performed the task well. Human traveling theta and alpha waves can be modeled by a network of coupled oscillators because the direction of wave propagation correlated with the spatial orientation of local frequency gradients. Our findings suggest that oscillations support brain connectivity by organizing neural processes across space and time. Copyright © 2018 Elsevier Inc. All rights reserved.

Locking of correlated neural activity to ongoing oscillations

PubMed Central

Helias, Moritz

2017-01-01

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks. Two distinct mechanisms cause time-dependent covariances: the modulation of the susceptibility of single neurons (via the external input and network feedback) and the time-varying variances of single unit activities. For some parameters, the effectively inhibitory recurrent feedback leads to resonant covariances even if mean activities show non-resonant behavior. Our analytical results open the question of time-modulated synchronous activity to a quantitative analysis. PMID:28604771

Interaction function of oscillating coupled neurons

PubMed Central

Dodla, Ramana; Wilson, Charles J.

2013-01-01

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210

Resting-state functional connectivity in multiple sclerosis: an examination of group differences and individual differences.

PubMed

Janssen, Alisha L; Boster, Aaron; Patterson, Beth A; Abduljalil, Amir; Prakash, Ruchika Shaurya

2013-11-01

Multiple sclerosis (MS) is a neurodegenerative, inflammatory disease of the central nervous system, resulting in physical and cognitive disturbances. The goal of the current study was to examine the association between network integrity and composite measures of cognition and disease severity in individuals with relapsing-remitting MS (RRMS), relative to healthy controls. All participants underwent a neuropsychological and neuroimaging session, where resting-state data was collected. Independent component analysis and dual regression were employed to examine network integrity in individuals with MS, relative to healthy controls. The MS sample exhibited less connectivity in the motor and visual networks, relative to healthy controls, after controlling for group differences in gray matter volume. However, no alterations were observed in the frontoparietal, executive control, or default-mode networks, despite previous evidence of altered neuronal patterns during tasks of exogenous processing. Whole-brain, voxel-wise regression analyses with disease severity and processing speed composites were also performed to elucidate the brain-behavior relationship with neuronal network integrity. Individuals with higher levels of disease severity demonstrated reduced intra-network connectivity of the motor network, and the executive control network, while higher disease burden was associated with greater inter-network connectivity between the medial visual network and areas involved in visuomotor learning. Our findings underscore the importance of examining resting-state oscillations in this population, both as a biomarker of disease progression and a potential target for therapeutic intervention. Copyright © 2013 Elsevier Ltd. All rights reserved.

Oscillator Neural Network Retrieving Sparsely Coded Phase Patterns

NASA Astrophysics Data System (ADS)

Aoyagi, Toshio; Nomura, Masaki

1999-08-01

Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case of sparsely coded patterns, it is biologically important to consider the timings of firings and to study how such consideration influences storage capacities and quality of recalled patterns. For this purpose, we propose a simple extended model of oscillator neural networks to allow for expression of a nonfiring state. Analyzing both equilibrium states and dynamical properties in recalling processes, we find that the system possesses good associative memory.

Resurgence of oscillation in coupled oscillators under delayed cyclic interaction

NASA Astrophysics Data System (ADS)

Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar

2017-07-01

This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.

Brain clock driven by neuropeptides and second messengers

NASA Astrophysics Data System (ADS)

Miro-Bueno, Jesus; Sosík, Petr

2014-09-01

The master circadian pacemaker in mammals is localized in a small portion of the brain called the suprachiasmatic nucleus (SCN). It is unclear how the SCN produces circadian rhythms. A common interpretation is that the SCN produces oscillations through the coupling of genetic oscillators in the neurons. The coupling is effected by a network of neuropeptides and second messengers. This network is crucial for the correct function of the SCN. However, models that study a possible oscillatory behavior of the network itself have received little attention. Here we propose and analyze a model to examine this oscillatory potential. We show that an intercellular oscillator emerges in the SCN as a result of the neuropeptide and second messenger dynamics. We find that this intercellular clock can produce circadian rhythms by itself with and without genetic clocks. We also found that the model is robust to perturbation of parameters and can be entrained by light-dark cycles.

Connection adaption for control of networked mobile chaotic agents.

PubMed

Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Xiao, Gaoxi; Boccaletti, S

2017-11-22

In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time.

Brain clock driven by neuropeptides and second messengers.

PubMed

Miro-Bueno, Jesus; Sosík, Petr

2014-09-01

The master circadian pacemaker in mammals is localized in a small portion of the brain called the suprachiasmatic nucleus (SCN). It is unclear how the SCN produces circadian rhythms. A common interpretation is that the SCN produces oscillations through the coupling of genetic oscillators in the neurons. The coupling is effected by a network of neuropeptides and second messengers. This network is crucial for the correct function of the SCN. However, models that study a possible oscillatory behavior of the network itself have received little attention. Here we propose and analyze a model to examine this oscillatory potential. We show that an intercellular oscillator emerges in the SCN as a result of the neuropeptide and second messenger dynamics. We find that this intercellular clock can produce circadian rhythms by itself with and without genetic clocks. We also found that the model is robust to perturbation of parameters and can be entrained by light-dark cycles.

Dynamical Bayesian inference of time-evolving interactions: From a pair of coupled oscillators to networks of oscillators

NASA Astrophysics Data System (ADS)

Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta

2012-12-01

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Neuronal plasticity and thalamocortical sleep and waking oscillations

PubMed Central

Timofeev, Igor

2011-01-01

Throughout life, thalamocortical (TC) network alternates between activated states (wake or rapid eye movement sleep) and slow oscillatory state dominating slow-wave sleep. The patterns of neuronal firing are different during these distinct states. I propose that due to relatively regular firing, the activated states preset some steady state synaptic plasticity and that the silent periods of slow-wave sleep contribute to a release from this steady state synaptic plasticity. In this respect, I discuss how states of vigilance affect short-, mid-, and long-term synaptic plasticity, intrinsic neuronal plasticity, as well as homeostatic plasticity. Finally, I suggest that slow oscillation is intrinsic property of cortical network and brain homeostatic mechanisms are tuned to use all forms of plasticity to bring cortical network to the state of slow oscillation. However, prolonged and profound shift from this homeostatic balance could lead to development of paroxysmal hyperexcitability and seizures as in the case of brain trauma. PMID:21854960

Direct heuristic dynamic programming for damping oscillations in a large power system.

PubMed

Lu, Chao; Si, Jennie; Xie, Xiaorong

2008-08-01

This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

Mind over chatter: plastic up-regulation of the fMRI salience network directly after EEG neurofeedback

PubMed Central

Ros, Tomas; Théberge, Jean; Frewen, Paul A.; Kluetsch, Rosemarie; Densmore, Maria; Calhoun, Vince D.; Lanius, Ruth A.

2016-01-01

Neurofeedback (NFB) involves a brain-computer interface that allows users to learn to voluntarily control their cortical oscillations, reflected in the electroencephalogram (EEG). Although NFB is being pioneered as a noninvasive tool for treating brain disorders, there is insufficient evidence on the mechanism of its impact on brain function. Furthermore, the dominant rhythm of the human brain is the alpha oscillation (8–12 Hz), yet its behavioral significance remains multifaceted and largely correlative. In this study with 34 healthy participants, we examined whether during the performance of an attentional task, the functional connectivity of distinct fMRI networks would be plastically altered after a 30-min session of voluntary reduction of alpha rhythm (n=17) versus a sham-feedback condition (n=17). We reveal that compared to sham-feedback, NFB induced an increase of connectivity within the salience network (dorsal anterior cingulate focus), which was detectable 30 minutes after termination of training. This increase in connectivity was negatively correlated with changes in 'on-task' mind-wandering as well as resting state alpha rhythm. Crucially, there was a causal dependence between alpha rhythm modulations during NFB and at subsequent resting state, not exhibited by the sham group. Our findings provide neurobehavioral evidence for a temporally direct, plastic impact of NFB on a key cognitive control network of the brain, suggesting a promising basis for its use to treat cognitive disorders under physiological conditions. PMID:23022326

How Fast Can Networks Synchronize? A Random Matrix Theory Approach

NASA Astrophysics Data System (ADS)

Timme, Marc; Wolf, Fred; Geisel, Theo

2004-03-01

Pulse-coupled oscillators constitute a paradigmatic class of dynamical systems interacting on networks because they model a variety of biological systems including flashing fireflies and chirping crickets as well as pacemaker cells of the heart and neural networks. Synchronization is one of the most simple and most prevailing kinds of collective dynamics on such networks. Here we study collective synchronization [1] of pulse-coupled oscillators interacting on asymmetric random networks. Using random matrix theory we analytically determine the speed of synchronization in such networks in dependence on the dynamical and network parameters [2]. The speed of synchronization increases with increasing coupling strengths. Surprisingly, however, it stays finite even for infinitely strong interactions. The results indicate that the speed of synchronization is limited by the connectivity of the network. We discuss the relevance of our findings to general equilibration processes on complex networks. [5mm] [1] M. Timme, F. Wolf, T. Geisel, Phys. Rev. Lett. 89:258701 (2002). [2] M. Timme, F. Wolf, T. Geisel, cond-mat/0306512 (2003).

Object segmentation and recovery via neural oscillators implementing the similarity and prior knowledge gestalt rules.

PubMed

Ursino, Mauro; Magosso, Elisa; La Cara, Giuseppe-Emiliano; Cuppini, Cristiano

2006-09-01

Object recognition requires the solution of the binding and segmentation problems, i.e., grouping different features to achieve a coherent representation. Synchronization of neural activity in the gamma-band, associated with gestalt perception, has often been proposed as a putative mechanism to solve these problems, not only as to low-level processing, but also in higher cortical functions. In the present work, a network of Wilson-Cowan oscillators is used to segment simultaneous objects, and recover an object from partial or corrupted information, by implementing two gestalt rules: similarity and prior knowledge. The network consists of H different areas, each devoted to representation of a particular feature of the object, according to a topological organization. The similarity law is realized via lateral intra-area connections, arranged as a "Mexican-hat". Prior knowledge is realized via inter-area connections, which link properties belonging to a previously memorized object. A global inhibitor allows segmentation of several objects avoiding interference. Simulation results, performed using three simultaneous input objects, show that the network is able to detect an object even in difficult conditions (i.e., when some features are absent or shifted with respect to the original one). Moreover, the trade-off between sensitivity (capacity to detect true positives) and specificity (capacity to reject false positives) can be controlled acting on the extension of lateral synapses (i.e., on the level of accepted similarity). Finally, the network can also deal with correlated objects, i.e., objects which have some common features. Simulations performed using a different number of objects (2, 3, 4 or 5) suggest that the network is able to segment and recall up to four objects, but the oscillation frequency must increase, the lower the number of objects simultaneously present. The model, although quite simpler compared with neurophysiology, may represent a theoretical framework for the analysis of the relationships between object representation, memory, learning, and gamma-band activity. In particular, it extends previous studies on autoassociative memory since it exploits not only oscillatory dynamics, but also a topological organization of features.

Relationships between hippocampal sharp waves, ripples and fast gamma oscillation: influence of dentate and entorhinal cortical activity

PubMed Central

Sullivan, David; Csicsvari, Jozsef; Mizuseki, Kenji; Montgomery, Sean; Diba, Kamran; Buzsáki, György

2011-01-01

Summary Hippocampal sharp waves (SPW) and associated fast (‘ripple’) oscillations in the CA1 region are among the most synchronous physiological patterns in the mammalian brain. Using two-dimensional arrays of electrodes for recording local field potentials and unit discharges in freely moving rats, we studied the emergence of ripple oscillations (140–220 Hz) and compared their origin and cellular-synaptic mechanisms with fast gamma oscillations (90–140 Hz). We show that (a) hippocampal SPW-Rs and fast gamma oscillations are quantitatively distinct patterns but involve the same networks and share similar mechanisms, (b) both the frequency and magnitude of fast oscillations is positively correlated with the magnitude of SPWs, (c) during both ripples and fast gamma oscillations the frequency of network oscillation is higher in CA1 than in CA3, (d) SPWs and associated firing of neurons are synchronous in the dorsal hippocampus and dorso-medial entorhinal cortex but ripples are confined to the CA1 pyramidal layer and its downstream targets and (e) the emergence of CA3 population bursts, a prerequisite for SPW-ripples, is biased by activity patterns in the dentate gyrus and entorhinal cortex, with highest probability of ripples associated with an ‘optimum’ level of dentate gamma power. We hypothesize that each hippocampal subnetwork possesses distinct resonant properties, tuned by the magnitude of the excitatory drive. PMID:21653864

Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation

PubMed Central

2017-01-01

The thalamus plays a critical role in the genesis of thalamocortical oscillations, yet the underlying mechanisms remain elusive. To understand whether the isolated thalamus can generate multiple distinct oscillations, we developed a biophysical thalamic model to test the hypothesis that generation of and transition between distinct thalamic oscillations can be explained as a function of neuromodulation by acetylcholine (ACh) and norepinephrine (NE) and afferent synaptic excitation. Indeed, the model exhibited four distinct thalamic rhythms (delta, sleep spindle, alpha and gamma oscillations) that span the physiological states corresponding to different arousal levels from deep sleep to focused attention. Our simulation results indicate that generation of these distinct thalamic oscillations is a result of both intrinsic oscillatory cellular properties and specific network connectivity patterns. We then systematically varied the ACh/NE and input levels to generate a complete map of the different oscillatory states and their transitions. Lastly, we applied periodic stimulation to the thalamic network and found that entrainment of thalamic oscillations is highly state-dependent. Our results support the hypothesis that ACh/NE modulation and afferent excitation define thalamic oscillatory states and their response to brain stimulation. Our model proposes a broader and more central role of the thalamus in the genesis of multiple distinct thalamo-cortical rhythms than previously assumed. PMID:29073146

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Bifurcation Analysis on Phase-Amplitude Cross-Frequency Coupling in Neural Networks with Dynamic Synapses

PubMed Central

Sase, Takumi; Katori, Yuichi; Komuro, Motomasa; Aihara, Kazuyuki

2017-01-01

We investigate a discrete-time network model composed of excitatory and inhibitory neurons and dynamic synapses with the aim at revealing dynamical properties behind oscillatory phenomena possibly related to brain functions. We use a stochastic neural network model to derive the corresponding macroscopic mean field dynamics, and subsequently analyze the dynamical properties of the network. In addition to slow and fast oscillations arising from excitatory and inhibitory networks, respectively, we show that the interaction between these two networks generates phase-amplitude cross-frequency coupling (CFC), in which multiple different frequency components coexist and the amplitude of the fast oscillation is modulated by the phase of the slow oscillation. Furthermore, we clarify the detailed properties of the oscillatory phenomena by applying the bifurcation analysis to the mean field model, and accordingly show that the intermittent and the continuous CFCs can be characterized by an aperiodic orbit on a closed curve and one on a torus, respectively. These two CFC modes switch depending on the coupling strength from the excitatory to inhibitory networks, via the saddle-node cycle bifurcation of a one-dimensional torus in map (MT1SNC), and may be associated with the function of multi-item representation. We believe that the present model might have potential for studying possible functional roles of phase-amplitude CFC in the cerebral cortex. PMID:28424606

The Intrinsic Electrophysiological Properties of Mammalian Neurons: Insights into Central Nervous System Function

NASA Astrophysics Data System (ADS)

Llinas, Rodolfo R.

1988-12-01

This article reviews the electroresponsive properties of single neurons in the mammalian central nervous system (CNS). In some of these cells the ionic conductances responsible for their excitability also endow them with autorhythmic electrical oscillatory properties. Chemical or electrical synaptic contacts between these neurons often result in network oscillations. In such networks, autorhytmic neurons may act as true oscillators (as pacemakers) or as resonators (responding preferentially to certain firing frequencies). Oscillations and resonance in the CNS are proposed to have diverse functional roles, such as (i) determining global functional states (for example, sleep-wakefulness or attention), (ii) timing in motor coordination, and (iii) specifying connectivity during development. Also, oscillation, especially in the thalamo-cortical circuits, may be related to certain neurological and psychiatric disorders. This review proposes that the autorhythmic electrical properties of central neurons and their connectivity form the basis for an intrinsic functional coordinate system that provides internal context to sensory input.

Analysis of dynamic brain oscillations: methodological advances.

PubMed

Le Van Quyen, Michel; Bragin, Anatol

2007-07-01

In recent years, new recording technologies have advanced such that, at high temporal and spatial resolutions, oscillations of neuronal networks can be identified from simultaneous, multisite recordings. However, because of the deluge of multichannel data generated by these experiments, achieving the full potential of parallel neuronal recordings also depends on the development of new mathematical methods that can extract meaningful information relating to time, frequency and space. Here, we aim to bridge this gap by focusing on up-to-date recording techniques for measurement of network oscillations and new analysis tools for their quantitative assessment. In particular, we emphasize how these methods can be applied, what property might be inferred from neuronal signals and potentially productive future directions. This review is part of the INMED and TINS special issue, Physiogenic and pathogenic oscillations: the beauty and the beast, derived from presentations at the annual INMED and TINS symposium (http://inmednet.com).

Phase dynamics of coupled oscillators reconstructed from data

NASA Astrophysics Data System (ADS)

Rosenblum, Michael; Kralemann, Bjoern; Pikovsky, Arkady

2013-03-01

We present a technique for invariant reconstruction of the phase dynamics equations for coupled oscillators from data. The invariant description is achieved by means of a transformation of phase estimates (protophases) obtained from general scalar observables to genuine phases. Staring from the bivariate data, we obtain the coupling functions in terms of these phases. We discuss the importance of the protophase-to-phase transformation for characterization of strength and directionality of interaction. To illustrate the technique we analyse the cardio-respiratory interaction on healthy humans. Our invariant approach is confirmed by high similarity of the coupling functions obtained from different observables of the cardiac system. Next, we generalize the technique to cover the case of small networks of coupled periodic units. We use the partial norms of the reconstructed coupling functions to quantify directed coupling between the oscillators. We illustrate the method by different network motifs for three coupled oscillators. We also discuss nonlinear effects in coupling.

Robustness of synthetic oscillators in growing and dividing cells

NASA Astrophysics Data System (ADS)

Paijmans, Joris; Lubensky, David K.; Rein ten Wolde, Pieter

2017-05-01

Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. Elowitz and Leibler [Nature (London) 403, 335 (2000), 10.1038/35002125] showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator. More recently, Stricker et al. [Nature (London) 456, 516 (2008), 10.1038/nature07389] presented another synthetic oscillator, called the dual-feedback oscillator, which is more stable. Detailed studies have been carried out to determine how the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle [Paijmans et al., Proc. Natl. Acad. Sci. (USA) 113, 4063 (2016), 10.1073/pnas.1507291113], but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.

Simulation of cortico-basal ganglia oscillations and their suppression by closed loop deep brain stimulation.

PubMed

Grant, Peadar F; Lowery, Madeleine M

2013-07-01

A new model of deep brain stimulation (DBS) is presented that integrates volume conduction effects with a neural model of pathological beta-band oscillations in the cortico-basal ganglia network. The model is used to test the clinical hypothesis that closed-loop control of the amplitude of DBS may be possible, based on the average rectified value of beta-band oscillations in the local field potential. Simulation of closed-loop high-frequency DBS was shown to yield energy savings, with the magnitude of the energy saved dependent on the strength of coupling between the subthalamic nucleus and the remainder of the cortico-basal ganglia network. When closed-loop DBS was applied to a strongly coupled cortico-basal ganglia network, the stimulation energy delivered over a 480 s period was reduced by up to 42%. Greater energy reductions were observed for weakly coupled networks, as the stimulation amplitude reduced to zero once the initial desynchronization had occurred. The results provide support for the application of closed-loop high-frequency DBS based on electrophysiological biomarkers.

Coarse-Grained Descriptions of Dynamics for Networks with Both Intrinsic and Structural Heterogeneities

PubMed Central

Bertalan, Tom; Wu, Yan; Laing, Carlo; Gear, C. William; Kevrekidis, Ioannis G.

2017-01-01

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and ultimately design. Here, we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables—variables successfully summarizing the detailed state of such networks. Finding such variables can naturally lead to successful reduced dynamic models for the networks. The main premise enabling our approach is the assumption that the behavior of a node in the network depends (after a short initial transient) on the node identity: a set of descriptors that quantify the node properties, whether intrinsic (e.g., parameters in the node evolution equations) or structural (imparted to the node by its connectivity in the particular network structure). The approach creates a natural link with modeling and “computational enabling technology” developed in the context of Uncertainty Quantification. In our case, however, we will not focus on ensembles of different realizations of a problem, each with parameters randomly selected from a distribution. We will instead study many coupled heterogeneous units, each characterized by randomly assigned (heterogeneous) parameter value(s). One could then coin the term Heterogeneity Quantification for this approach, which we illustrate through a model dynamic network consisting of coupled oscillators with one intrinsic heterogeneity (oscillator individual frequency) and one structural heterogeneity (oscillator degree in the undirected network). The computational implementation of the approach, its shortcomings and possible extensions are also discussed. PMID:28659781

Functional network inference of the suprachiasmatic nucleus

PubMed Central

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel; St. John, Peter C.; Wang, Thomas J.; Bales, Benjamin B.; Doyle, Francis J.; Herzog, Erik D.; Petzold, Linda R.

2016-01-01

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure. PMID:27044085

The visual cognitive network, but not the visual sensory network, is affected in amnestic mild cognitive impairment: a study of brain oscillatory responses.

PubMed

Yener, Görsev G; Emek-Savaş, Derya Durusu; Güntekin, Bahar; Başar, Erol

2014-10-17

Mild Cognitive Impairment (MCI) is considered in many as prodromal stage of Alzheimer's disease (AD). Event-related oscillations (ERO) reflect cognitive responses of brain whereas sensory-evoked oscillations (SEO) inform about sensory responses. For this study, we compared visual SEO and ERO responses in MCI to explore brain dynamics (BACKGROUND). Forty-three patients with MCI (mean age=74.0 year) and 41 age- and education-matched healthy-elderly controls (HC) (mean age=71.1 year) participated in the study. The maximum peak-to-peak amplitudes for each subject's averaged delta response (0.5-3.0 Hz) were measured from two conditions (simple visual stimulation and classical visual oddball paradigm target stimulation) (METHOD). Overall, amplitudes of target ERO responses were higher than SEO amplitudes. The preferential location for maximum amplitude values was frontal lobe for ERO and occipital lobe for SEO. The ANOVA for delta responses showed significant results for the group Xparadigm. Post-hoc tests indicated that (1) the difference between groups were significant for target delta responses, but not for SEO, (2) ERO elicited higher responses for HC than MCI patients, and (3) females had higher target ERO than males and this difference was pronounced in the control group (RESULTS). Overall, cognitive responses display almost double the amplitudes of sensory responses over frontal regions. The topography of oscillatory responses differs depending on stimuli: visualsensory responses are highest over occipitals and -cognitive responses over frontal regions. A group effect is observed in MCI indicating that visual sensory and cognitive circuits behave differently indicating preserved visual sensory responses, but decreased cognitive responses (CONCLUSION). Copyright © 2014 Elsevier B.V. All rights reserved.

Pattern recognition with "materials that compute".

PubMed

Fang, Yan; Yashin, Victor V; Levitan, Steven P; Balazs, Anna C

2016-09-01

Driven by advances in materials and computer science, researchers are attempting to design systems where the computer and material are one and the same entity. Using theoretical and computational modeling, we design a hybrid material system that can autonomously transduce chemical, mechanical, and electrical energy to perform a computational task in a self-organized manner, without the need for external electrical power sources. Each unit in this system integrates a self-oscillating gel, which undergoes the Belousov-Zhabotinsky (BZ) reaction, with an overlaying piezoelectric (PZ) cantilever. The chemomechanical oscillations of the BZ gels deflect the PZ layer, which consequently generates a voltage across the material. When these BZ-PZ units are connected in series by electrical wires, the oscillations of these units become synchronized across the network, where the mode of synchronization depends on the polarity of the PZ. We show that the network of coupled, synchronizing BZ-PZ oscillators can perform pattern recognition. The "stored" patterns are set of polarities of the individual BZ-PZ units, and the "input" patterns are coded through the initial phase of the oscillations imposed on these units. The results of the modeling show that the input pattern closest to the stored pattern exhibits the fastest convergence time to stable synchronization behavior. In this way, networks of coupled BZ-PZ oscillators achieve pattern recognition. Further, we show that the convergence time to stable synchronization provides a robust measure of the degree of match between the input and stored patterns. Through these studies, we establish experimentally realizable design rules for creating "materials that compute."

Pattern recognition with “materials that compute”

PubMed Central

Fang, Yan; Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.

2016-01-01

Driven by advances in materials and computer science, researchers are attempting to design systems where the computer and material are one and the same entity. Using theoretical and computational modeling, we design a hybrid material system that can autonomously transduce chemical, mechanical, and electrical energy to perform a computational task in a self-organized manner, without the need for external electrical power sources. Each unit in this system integrates a self-oscillating gel, which undergoes the Belousov-Zhabotinsky (BZ) reaction, with an overlaying piezoelectric (PZ) cantilever. The chemomechanical oscillations of the BZ gels deflect the PZ layer, which consequently generates a voltage across the material. When these BZ-PZ units are connected in series by electrical wires, the oscillations of these units become synchronized across the network, where the mode of synchronization depends on the polarity of the PZ. We show that the network of coupled, synchronizing BZ-PZ oscillators can perform pattern recognition. The “stored” patterns are set of polarities of the individual BZ-PZ units, and the “input” patterns are coded through the initial phase of the oscillations imposed on these units. The results of the modeling show that the input pattern closest to the stored pattern exhibits the fastest convergence time to stable synchronization behavior. In this way, networks of coupled BZ-PZ oscillators achieve pattern recognition. Further, we show that the convergence time to stable synchronization provides a robust measure of the degree of match between the input and stored patterns. Through these studies, we establish experimentally realizable design rules for creating “materials that compute.” PMID:27617290

Hydrodynamically induced oscillations and traffic dynamics in 1D microfludic networks

NASA Astrophysics Data System (ADS)

Bartolo, Denis; Jeanneret, Raphael

2011-03-01

We report on the traffic dynamics of particles driven through a minimal microfluidic network. Even in the minimal network consisting in a single loop, the traffic dynamics has proven to yield complex temporal patterns, including periodic, multi-periodic or chaotic sequences. This complex dynamics arises from the strongly nonlinear hydrodynamic interactions between the particles, that takes place at a junction. To better understand the consequences of this nontrivial coupling, we combined theoretical, numerical and experimental efforts and solved the 3-body problem in a 1D loop network. This apparently simple dynamical system revealed a rich and unexpected dynamics, including coherent spontaneous oscillations along closed orbits. Striking similarities between Hamiltonian systems and this driven dissipative system will be explained.

Input-output features of anatomically identified CA3 neurons during hippocampal sharp wave/ripple oscillation in vitro.

PubMed

Hájos, Norbert; Karlócai, Mária R; Németh, Beáta; Ulbert, István; Monyer, Hannah; Szabó, Gábor; Erdélyi, Ferenc; Freund, Tamás F; Gulyás, Attila I

2013-07-10

Hippocampal sharp waves and the associated ripple oscillations (SWRs) are implicated in memory processes. These network events emerge intrinsically in the CA3 network. To understand cellular interactions that generate SWRs, we detected first spiking activity followed by recording of synaptic currents in distinct types of anatomically identified CA3 neurons during SWRs that occurred spontaneously in mouse hippocampal slices. We observed that the vast majority of interneurons fired during SWRs, whereas only a small portion of pyramidal cells was found to spike. There were substantial differences in the firing behavior among interneuron groups; parvalbumin-expressing basket cells were one of the most active GABAergic cells during SWRs, whereas ivy cells were silent. Analysis of the synaptic currents during SWRs uncovered that the dominant synaptic input to the pyramidal cell was inhibitory, whereas spiking interneurons received larger synaptic excitation than inhibition. The discharge of all interneurons was primarily determined by the magnitude and the timing of synaptic excitation. Strikingly, we observed that the temporal structure of synaptic excitation and inhibition during SWRs significantly differed between parvalbumin-containing basket cells, axoaxonic cells, and type 1 cannabinoid receptor (CB1)-expressing basket cells, which might explain their distinct recruitment to these synchronous events. Our data support the hypothesis that the active current sources restricted to the stratum pyramidale during SWRs originate from the synaptic output of parvalbumin-expressing basket cells. Thus, in addition to gamma oscillation, these GABAergic cells play a central role in SWR generation.

Resonant Interneurons Can Increase Robustness of Gamma Oscillations.

PubMed

Tikidji-Hamburyan, Ruben A; Martínez, Joan José; White, John A; Canavier, Carmen C

2015-11-25

Gamma oscillations are believed to play a critical role in in information processing, encoding, and retrieval. Inhibitory interneuronal network gamma (ING) oscillations may arise from a coupled oscillator mechanism in which individual neurons oscillate or from a population oscillator in which individual neurons fire sparsely and stochastically. All ING mechanisms, including the one proposed herein, rely on alternating waves of inhibition and windows of opportunity for spiking. The coupled oscillator model implemented with Wang-Buzsáki model neurons is not sufficiently robust to heterogeneity in excitatory drive, and therefore intrinsic frequency, to account for in vitro models of ING. Similarly, in a tightly synchronized regime, the stochastic population oscillator model is often characterized by sparse firing, whereas interneurons both in vivo and in vitro do not fire sparsely during gamma, but rather on average every other cycle. We substituted so-called resonator neural models, which exhibit class 2 excitability and postinhibitory rebound (PIR), for the integrators that are typically used. This results in much greater robustness to heterogeneity that actually increases as the average participation in spikes per cycle approximates physiological levels. Moreover, dynamic clamp experiments that show autapse-induced firing in entorhinal cortical interneurons support the idea that PIR can serve as a network gamma mechanism. Furthermore, parvalbumin-positive (PV(+)) cells were much more likely to display both PIR and autapse-induced firing than GAD2(+) cells, supporting the view that PV(+) fast-firing basket cells are more likely to exhibit class 2 excitability than other types of inhibitory interneurons. Gamma oscillations are believed to play a critical role in information processing, encoding, and retrieval. Networks of inhibitory interneurons are thought to be essential for these oscillations. We show that one class of interneurons with an abrupt onset of firing at a threshold frequency may allow more robust synchronization in the presence of noise and heterogeneity. The mechanism for this robustness depends on the intrinsic resonance at this threshold frequency. Moreover, we show experimentally the feasibility of the proposed mechanism and suggest a way to distinguish between this mechanism and another proposed mechanism: that of a stochastic population oscillator independent of the dynamics of individual neurons. Copyright © 2015 the authors 0270-6474/15/3515682-14$15.00/0.

Experimental study of the robust global synchronization of Brockett oscillators

NASA Astrophysics Data System (ADS)

Ahmed, Hafiz; Ushirobira, Rosane; Efimov, Denis

2017-12-01

This article studies the experimental synchronization of a family of a recently proposed oscillator model, i.e. the Brockett oscillator [R. Brockett, Synchronization without periodicity, in Mathematical Systems Theory, A Volume in Honor of U. Helmke, edited by K. Huper, J. Trumpf (CreateSpace, Seattle, USA, 2013), pp. 65-74]. Due to its structural property, Brockett oscillator can be considered as a promising benchmark nonlinear model for investigating synchronization and the consensus phenomena. Our experimental setup consists of analog circuit realizations of a network of Brockett oscillators. Experimental results obtained in this work correspond to the prior theoretical findings.

Gap junction networks can generate both ripple-like and fast ripple-like oscillations

PubMed Central

Simon, Anna; Traub, Roger D.; Vladimirov, Nikita; Jenkins, Alistair; Nicholson, Claire; Whittaker, Roger G.; Schofield, Ian; Clowry, Gavin J.; Cunningham, Mark O.; Whittington, Miles A.

2014-01-01

Fast ripples (FRs) are network oscillations, defined variously as having frequencies of > 150 to > 250 Hz, with a controversial mechanism. FRs appear to indicate a propensity of cortical tissue to originate seizures. Here, we demonstrate field oscillations, at up to 400 Hz, in spontaneously epileptic human cortical tissue in vitro, and present a network model that could explain FRs themselves, and their relation to ‘ordinary’ (slower) ripples. We performed network simulations with model pyramidal neurons, having axons electrically coupled. Ripples (< 250 Hz) were favored when conduction of action potentials, axon to axon, was reliable. Whereas ripple population activity was periodic, firing of individual axons varied in relative phase. A switch from ripples to FRs took place when an ectopic spike occurred in a cell coupled to another cell, itself multiply coupled to others. Propagation could then start in one direction only, a condition suitable for re-entry. The resulting oscillations were > 250 Hz, were sustained or interrupted, and had little jitter in the firing of individual axons. The form of model FR was similar to spontaneously occurring FRs in excised human epileptic tissue. In vitro, FRs were suppressed by a gap junction blocker. Our data suggest that a given network can produce ripples, FRs, or both, via gap junctions, and that FRs are favored by clusters of axonal gap junctions. If axonal gap junctions indeed occur in epileptic tissue, and are mediated by connexin 26 (recently shown to mediate coupling between immature neocortical pyramidal cells), then this prediction is testable. PMID:24118191

Gap junction networks can generate both ripple-like and fast ripple-like oscillations.

PubMed

Simon, Anna; Traub, Roger D; Vladimirov, Nikita; Jenkins, Alistair; Nicholson, Claire; Whittaker, Roger G; Schofield, Ian; Clowry, Gavin J; Cunningham, Mark O; Whittington, Miles A

2014-01-01

Fast ripples (FRs) are network oscillations, defined variously as having frequencies of > 150 to > 250 Hz, with a controversial mechanism. FRs appear to indicate a propensity of cortical tissue to originate seizures. Here, we demonstrate field oscillations, at up to 400 Hz, in spontaneously epileptic human cortical tissue in vitro, and present a network model that could explain FRs themselves, and their relation to 'ordinary' (slower) ripples. We performed network simulations with model pyramidal neurons, having axons electrically coupled. Ripples (< 250 Hz) were favored when conduction of action potentials, axon to axon, was reliable. Whereas ripple population activity was periodic, firing of individual axons varied in relative phase. A switch from ripples to FRs took place when an ectopic spike occurred in a cell coupled to another cell, itself multiply coupled to others. Propagation could then start in one direction only, a condition suitable for re-entry. The resulting oscillations were > 250 Hz, were sustained or interrupted, and had little jitter in the firing of individual axons. The form of model FR was similar to spontaneously occurring FRs in excised human epileptic tissue. In vitro, FRs were suppressed by a gap junction blocker. Our data suggest that a given network can produce ripples, FRs, or both, via gap junctions, and that FRs are favored by clusters of axonal gap junctions. If axonal gap junctions indeed occur in epileptic tissue, and are mediated by connexin 26 (recently shown to mediate coupling between immature neocortical pyramidal cells), then this prediction is testable. © 2013 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Synchronization in Random Pulse Oscillator Networks

NASA Astrophysics Data System (ADS)

Brown, Kevin; Hermundstad, Ann

Motivated by synchronization phenomena in neural systems, we study synchronization of random networks of coupled pulse oscillators. We begin by considering binomial random networks whose nodes have intrinsic linear dynamics. We quantify order in the network spiking dynamics using a new measure: the normalized Lev-Zimpel complexity (LZC) of the nodes' spike trains. Starting from a globally-synchronized state, we see two broad classes of behaviors. In one (''temporally random''), the LZC is high and nodes spike independently with no coherent pattern. In another (''temporally regular''), the network does not globally synchronize but instead forms coherent, repeating population firing patterns with low LZC. No topological feature of the network reliably predicts whether an individual network will show temporally random or regular behavior; however, we find evidence that degree heterogeneity in binomial networks has a strong effect on the resulting state. To confirm these findings, we generate random networks with independently-adjustable degree mean and variance. We find that the likelihood of temporally-random behavior increases as degree variance increases. Our results indicate the subtle and complex relationship between network structure and dynamics.

Bursting endemic bubbles in an adaptive network

NASA Astrophysics Data System (ADS)

Sherborne, N.; Blyuss, K. B.; Kiss, I. Z.

2018-04-01

The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavioral change have found oscillations, but in an extremely narrow region of the parameter space, which contrasts with intuition and available data. In this paper we propose a simple susceptible-infected-susceptible epidemic model on an adaptive network with time-delayed rewiring, and show that oscillatory solutions are now present in a wide region of the parameter space. Altering the transmission or rewiring rates reveals the presence of an endemic bubble—an enclosed region of the parameter space where oscillations are observed.

Chimera states in complex networks: interplay of fractal topology and delay

NASA Astrophysics Data System (ADS)

Sawicki, Jakub; Omelchenko, Iryna; Zakharova, Anna; Schöll, Eckehard

2017-06-01

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.

Oscillation, Conduction Delays, and Learning Cooperate to Establish Neural Competition in Recurrent Networks

PubMed Central

Kato, Hideyuki; Ikeguchi, Tohru

2016-01-01

Specific memory might be stored in a subnetwork consisting of a small population of neurons. To select neurons involved in memory formation, neural competition might be essential. In this paper, we show that excitable neurons are competitive and organize into two assemblies in a recurrent network with spike timing-dependent synaptic plasticity (STDP) and axonal conduction delays. Neural competition is established by the cooperation of spontaneously induced neural oscillation, axonal conduction delays, and STDP. We also suggest that the competition mechanism in this paper is one of the basic functions required to organize memory-storing subnetworks into fine-scale cortical networks. PMID:26840529

Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

NASA Astrophysics Data System (ADS)

Hoff, Anderson; dos Santos, Juliana V.; Manchein, Cesar; Albuquerque, Holokx A.

2014-07-01

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also presents multistability shown in the planes of the basin of attractions.

Alterations of cortical GABA neurons and network oscillations in schizophrenia.

PubMed

Gonzalez-Burgos, Guillermo; Hashimoto, Takanori; Lewis, David A

2010-08-01

The hypothesis that alterations of cortical inhibitory gamma-aminobutyric acid (GABA) neurons are a central element in the pathology of schizophrenia has emerged from a series of postmortem studies. How such abnormalities may contribute to the clinical features of schizophrenia has been substantially informed by a convergence with basic neuroscience studies revealing complex details of GABA neuron function in the healthy brain. Importantly, activity of the parvalbumin-containing class of GABA neurons has been linked to the production of cortical network oscillations. Furthermore, growing knowledge supports the concept that gamma band oscillations (30-80 Hz) are an essential mechanism for cortical information transmission and processing. Herein we review recent studies further indicating that inhibition from parvalbumin-positive GABA neurons is necessary to produce gamma oscillations in cortical circuits; provide an update on postmortem studies documenting that deficits in the expression of glutamic acid decarboxylase67, which accounts for most GABA synthesis in the cortex, are widely observed in schizophrenia; and describe studies using novel, noninvasive approaches directly assessing potential relations between alterations in GABA, oscillations, and cognitive function in schizophrenia.

Resource-Competing Oscillator Network as a Model of Amoeba-Based Neurocomputer

NASA Astrophysics Data System (ADS)

Aono, Masashi; Hirata, Yoshito; Hara, Masahiko; Aihara, Kazuyuki

An amoeboid organism, Physarum, exhibits rich spatiotemporal oscillatory behavior and various computational capabilities. Previously, the authors created a recurrent neurocomputer incorporating the amoeba as a computing substrate to solve optimization problems. In this paper, considering the amoeba to be a network of oscillators coupled such that they compete for constant amounts of resources, we present a model of the amoeba-based neurocomputer. The model generates a number of oscillation modes and produces not only simple behavior to stabilize a single mode but also complex behavior to spontaneously switch among different modes, which reproduces well the experimentally observed behavior of the amoeba. To explore the significance of the complex behavior, we set a test problem used to compare computational performances of the oscillation modes. The problem is a kind of optimization problem of how to allocate a limited amount of resource to oscillators such that conflicts among them can be minimized. We show that the complex behavior enables to attain a wider variety of solutions to the problem and produces better performances compared with the simple behavior.

Induction of θ-frequency oscillations in the rat medial septal diagonal band slice by metabotropic glutamate receptor agonists.

PubMed

Lu, C B; Ouyang, G; Henderson, Z; Li, X

2011-03-17

The aim of this study was to examine the role of metabotropic glutamate receptors (mGluR) in the generation of oscillatory field activity at theta frequency (4-12 Hz) in the medial septal slice prepared from rat brain. Bath application of mGluR agonists and antagonists showed that activation of mGluR1-type receptors produces persistent theta frequency oscillations in a dose-responsive manner. This activity, induced by the group I mGluR agonist (RS)-3,5-dihydroxyphenylglycine (DHPG), was reduced by ionotropic glutamate receptor antagonists and abolished by further addition of a GABAA receptor antagonist. However, addition of a GABAA receptor antagonist on its own converted the DHPG-induced oscillations to intermittent episodes of accentuated theta frequency activity following a burst. In a proportion of slices, DHPG induced large amplitude field population spiking activity (100-300 μV) which is correlated linearly with the field theta oscillations and is sensitive to glutamate receptor antagonists, suggesting a role of this type of spikes in theta generation induced by DHPG. These data demonstrate that DHPG-sensitive neuronal networks within medial septum generate theta rhythmic activity and are differentially modulated by excitatory and inhibitory ionotropic neurotransmissions. Copyright © 2011 IBRO. Published by Elsevier Ltd. All rights reserved.

Star-type oscillatory networks with generic Kuramoto-type coupling: A model for "Japanese drums synchrony"

NASA Astrophysics Data System (ADS)

Vlasov, Vladimir; Pikovsky, Arkady; Macau, Elbert E. N.

2015-12-01

We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, which gives full analytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra.

Order parameter analysis of synchronization transitions on star networks

NASA Astrophysics Data System (ADS)

Chen, Hong-Bin; Sun, Yu-Ting; Gao, Jian; Xu, Can; Zheng, Zhi-Gang

2017-12-01

The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.

Optimal design of tweezer control for chimera states

NASA Astrophysics Data System (ADS)

Omelchenko, Iryna; Omel'chenko, Oleh E.; Zakharova, Anna; Schöll, Eckehard

2018-01-01

Chimera states are complex spatio-temporal patterns which consist of coexisting domains of spatially coherent and incoherent dynamics in systems of coupled oscillators. In small networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. A tweezer feedback control scheme can stabilize and fix the position of chimera states. We analyze the action of the tweezer control in small nonlocally coupled networks of Van der Pol and FitzHugh-Nagumo oscillators, and determine the ranges of optimal control parameters. We demonstrate that the tweezer control scheme allows for stabilization of chimera states with different shapes, and can be used as an instrument for controlling the coherent domains size, as well as the maximum average frequency difference of the oscillators.

Influence of slow oscillation on hippocampal activity and ripples through cortico-hippocampal synaptic interactions, analyzed by a cortical-CA3-CA1 network model.

PubMed

Taxidis, Jiannis; Mizuseki, Kenji; Mason, Robert; Owen, Markus R

2013-01-01

Hippocampal sharp wave-ripple complexes (SWRs) involve the synchronous discharge of thousands of cells throughout the CA3-CA1-subiculum-entorhinal cortex axis. Their strong transient output affects cortical targets, rendering SWRs a possible means for memory transfer from the hippocampus to the neocortex for long-term storage. Neurophysiological observations of hippocampal activity modulation by the cortical slow oscillation (SO) during deep sleep and anesthesia, and correlations between ripples and UP states, support the role of SWRs in memory consolidation through a cortico-hippocampal feedback loop. We couple a cortical network exhibiting SO with a hippocampal CA3-CA1 computational network model exhibiting SWRs, in order to model such cortico-hippocampal correlations and uncover important parameters and coupling mechanisms controlling them. The cortical oscillatory output entrains the CA3 network via connections representing the mossy fiber input, and the CA1 network via the temporoammonic pathway (TA). The spiking activity in CA3 and CA1 is shown to depend on the excitation-to-inhibition ratio, induced by combining the two hippocampal inputs, with mossy fiber input controlling the UP-state correlation of CA3 population bursts and corresponding SWRs, whereas the temporoammonic input affects the overall CA1 spiking activity. Ripple characteristics and pyramidal spiking participation to SWRs are shaped by the strength of the Schaffer collateral drive. A set of in vivo recordings from the rat hippocampus confirms a model-predicted segregation of pyramidal cells into subgroups according to the SO state where they preferentially fire and their response to SWRs. These groups can potentially play distinct functional roles in the replay of spike sequences.

Simultaneous Transverse and Longitudinal Oscillations in a Quiescent Prominence Triggered by a Coronal Jet

NASA Astrophysics Data System (ADS)

Zhang, Q. M.; Li, D.; Ning, Z. J.

2017-12-01

In this paper, we report our multiwavelength observations of the simultaneous transverse and longitudinal oscillations in a quiescent prominence. The prominence was observed by the Global Oscillation Network Group and by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory on 2015 June 29. A GOES C2.4 flare took place in NOAA active region 12373, which was associated with a pair of short ribbons and a remote ribbon. During the impulsive phase of the flare, a coronal jet spurted out of the primary flare site and propagated in the northwest direction at an apparent speed of ∼224 km s‑1. Part of the jet stopped near the remote ribbon. The remaining part continued moving forward before stopping to the east of the prominence. Once the jet encountered the prominence, it pushed the prominence to oscillate periodically. The transverse oscillation of the eastern part (EP) of prominence can be divided into two phases. In phase I, the initial amplitude, velocity, period, and damping timescale are ∼4.5 Mm, ∼20 km s‑1, ∼25 minutes, and ∼7.5 hr, respectively. The oscillation lasted for two cycles. In phase II, the initial amplitude increases to ∼11.3 Mm, while the initial velocity halves to ∼10 km s‑1. The period increases by a factor of ∼3.5. With a damping timescale of ∼4.4 hr, the oscillation lasted for about three cycles. The western part of prominence also experienced transverse oscillation. The initial amplitude is only ∼2 Mm and the velocity is less than 10 km s‑1. The period (∼27 minutes) is slightly longer than that of the EP in phase I. The oscillation lasted for about four cycles with the shortest damping timescale (∼1.7 hr). To the east of prominence, a handful of horizontal threads experienced longitudinal oscillation. The initial amplitude, velocity, period, and damping timescale are ∼52 Mm, ∼50 km s‑1, ∼99 minutes, and 2.5 hr, respectively. To our knowledge, this is the first report of simultaneous transverse and longitudinal prominence oscillations triggered by a coronal jet.

Large-amplitude Longitudinal Oscillations in a Solar Filament

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Q. M.; Su, Y. N.; Ji, H. S.

In this paper, we report our multiwavelength observations of the large-amplitude longitudinal oscillations of a filament observed on 2015 May 3. Located next to active region 12335, the sigmoidal filament was observed by the ground-based H α telescopes from the Global Oscillation Network Group and by the Atmospheric Imaging Assembly instrument on board the Solar Dynamics Observatory . The filament oscillations were most probably triggered by the magnetic reconnection in the filament channel, which is characterized by the bidirectional flows, brightenings in EUV and soft X-ray, and magnetic cancellation in the photosphere. The directions of oscillations have angles of 4°–36°more » with respect to the filament axis. The whole filament did not oscillate in phase as a rigid body. Meanwhile, the oscillation periods (3100–4400 s) have a spatial dependence, implying that the curvature radii ( R ) of the magnetic dips are different at different positions. The values of R are estimated to be 69.4–133.9 Mm, and the minimum transverse magnetic field of the dips is estimated to be 15 G. The amplitudes of S5-S8 grew with time, while the amplitudes of S9-S14 damped with time. The oscillation amplitudes range from a few to ten Mm, and the maximum velocity can reach 30 km s{sup −1}. Interestingly, the filament experienced mass drainage southward at a speed of ∼27 km s{sup −1}. The oscillations continued after the mass drainage and lasted for more than 11 hr. After the mass drainage, the oscillation phases did not change much. The periods of S5-S8 decreased, while the periods of S9-S14 increased. The amplitudes of S5-S8 damped with time, while the amplitudes of S9-S14 grew. Most of the damping (growing) ratios are between −9 and 14. We offer a schematic cartoon to explain the complex behaviors of oscillations by introducing thread-thread interaction.« less

Hemispheric Coherence in ASD with and without Comorbid ADHD and Anxiety.

PubMed

Saunders, A; Kirk, I J; Waldie, K E

2016-01-01

There is a growing body of evidence suggesting that altered brain connectivity may be a defining feature of disorders such as autism spectrum disorder (ASD), anxiety, and ADHD. This study investigated whether resting state functional connectivity, measured by 128-channel EEG oscillation coherence, differs between developmental disorders. Analyses were conducted separately on groups with and without comorbid conditions. Analyses revealed increased coherence across central electrodes over the primary motor cortex and decreased coherence in the frontal lobe networks in those with ASD compared to neurotypical controls. There was increased coherence in occipital lobe networks in the ADHD group compared to other groups. Symptoms of generalised anxiety were positively correlated with both frontal-occipital intrahemispheric (alpha only) coherence and occipital interhemispheric coherence (alpha, approaching theta band). The patterns of coherence in the ASD pure group were different when comorbid conditions were included in the analyses, suggesting that aberrant coherence in the frontal and central areas of the brain is specifically associated with ASD. Our findings support the idea that comorbid conditions are additive, rather than being symptoms of the same disorder.

Hemispheric Coherence in ASD with and without Comorbid ADHD and Anxiety

PubMed Central

Saunders, A.; Kirk, I. J.; Waldie, K. E.

2016-01-01

There is a growing body of evidence suggesting that altered brain connectivity may be a defining feature of disorders such as autism spectrum disorder (ASD), anxiety, and ADHD. This study investigated whether resting state functional connectivity, measured by 128-channel EEG oscillation coherence, differs between developmental disorders. Analyses were conducted separately on groups with and without comorbid conditions. Analyses revealed increased coherence across central electrodes over the primary motor cortex and decreased coherence in the frontal lobe networks in those with ASD compared to neurotypical controls. There was increased coherence in occipital lobe networks in the ADHD group compared to other groups. Symptoms of generalised anxiety were positively correlated with both frontal-occipital intrahemispheric (alpha only) coherence and occipital interhemispheric coherence (alpha, approaching theta band). The patterns of coherence in the ASD pure group were different when comorbid conditions were included in the analyses, suggesting that aberrant coherence in the frontal and central areas of the brain is specifically associated with ASD. Our findings support the idea that comorbid conditions are additive, rather than being symptoms of the same disorder. PMID:27127785

Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emenheiser, Jeffrey; Department of Physics, University of California, Davis, California 95616; Chapman, Airlie

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cyclesmore » at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.« less

Membrane Properties and the Balance between Excitation and Inhibition Control Gamma-Frequency Oscillations Arising from Feedback Inhibition

PubMed Central

Economo, Michael N.; White, John A.

2012-01-01

Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30–80 Hz gamma rhythm in which network oscillations arise through ‘stochastic synchrony’ capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs. PMID:22275859

The motor cortex: a network tuned to 7-14 Hz

PubMed Central

Castro-Alamancos, Manuel A.

2013-01-01

The neocortex or six layer cortex consists of at least 52 cytoarchitectonically distinct areas in humans, and similar areas can be distinguished in rodents. Each of these areas has a defining set of extrinsic connections, identifiable functional roles, a distinct laminar arrangement, etc. Thus, neocortex is extensively subdivided into areas of anatomical and functional specialization, but less is known about the specialization of cellular and network physiology across areas. The motor cortex appears to have a distinct propensity to oscillate in the 7–14 Hz frequency range. Augmenting responses, normal mu and beta oscillations, and abnormal oscillations or after discharges caused by enhancing excitation or suppressing inhibition are all expressed around this frequency range. The substrate for this activity may be an excitatory network that is unique to the motor cortex or that is more strongly suppressed in other areas, such as somatosensory cortex. Interestingly, augmenting responses are dependent on behavioral state. They are abolished during behavioral arousal. Here, I briefly review this evidence. PMID:23439785

Strong feedback limit of the Goodwin circadian oscillator

NASA Astrophysics Data System (ADS)

Woller, Aurore; Gonze, Didier; Erneux, Thomas

2013-03-01

The three-variable Goodwin model constitutes a prototypical oscillator based on a negative feedback loop. It was used as a minimal model for circadian oscillations. Other core models for circadian clocks are variants of the Goodwin model. The Goodwin oscillator also appears in many studies of coupled oscillator networks because of its relative simplicity compared to other biophysical models involving a large number of variables and parameters. Because the synchronization properties of Goodwin oscillators still remain difficult to explore mathematically, further simplifications of the Goodwin model have been sought. In this paper, we investigate the strong negative feedback limit of Goodwin equations by using asymptotic techniques. We find that Goodwin oscillations approach a sequence of decaying exponentials that can be described in terms of a single-variable leaky integrated-and-fire model.

Analysis of remote synchronization in complex networks

NASA Astrophysics Data System (ADS)

Gambuzza, Lucia Valentina; Cardillo, Alessio; Fiasconaro, Alessandro; Fortuna, Luigi; Gómez-Gardeñes, Jesus; Frasca, Mattia

2013-12-01

A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs [Bergner et al., Phys. Rev. E 85, 026208 (2012)]. We show the existence of a more general dynamical state of remote synchronization in arbitrary networks of coupled oscillators. This state is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes. This phenomenon is almost negligible in networks of phase oscillators as its underlying mechanism is the modulation of the amplitude of those intermediary nodes between the remotely synchronized units. Our findings thus show the ubiquity and robustness of these states and bridge the gap from their recent observation in simple toy graphs to complex networks.

Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns.

PubMed

Lezon, Timothy R; Banavar, Jayanth R; Cieplak, Marek; Maritan, Amos; Fedoroff, Nina V

2006-12-12

We describe a method based on the principle of entropy maximization to identify the gene interaction network with the highest probability of giving rise to experimentally observed transcript profiles. In its simplest form, the method yields the pairwise gene interaction network, but it can also be extended to deduce higher-order interactions. Analysis of microarray data from genes in Saccharomyces cerevisiae chemostat cultures exhibiting energy metabolic oscillations identifies a gene interaction network that reflects the intracellular communication pathways that adjust cellular metabolic activity and cell division to the limiting nutrient conditions that trigger metabolic oscillations. The success of the present approach in extracting meaningful genetic connections suggests that the maximum entropy principle is a useful concept for understanding living systems, as it is for other complex, nonequilibrium systems.

Chimera states in bipartite networks of FitzHugh-Nagumo oscillators

NASA Astrophysics Data System (ADS)

Wu, Zhi-Min; Cheng, Hong-Yan; Feng, Yuee; Li, Hai-Hong; Dai, Qiong-Lin; Yang, Jun-Zhong

2018-04-01

Chimera states consisting of spatially coherent and incoherent domains have been observed in different topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh-Nagumo (FHN) oscillators in which the units are allocated evenly to two layers, and FHN units interact with each other only when they are in different layers. We report the existence of chimera states in bipartite networks. Owing to the interplay between chimera states in the two layers, many types of chimera states such as in-phase chimera states, antiphase chimera states, and out-of-phase chimera states are classified. Stability diagrams of several typical chimera states in the coupling strength-coupling radius plane, which show strong multistability of chimera states, are explored.

Stabilizing Motifs in Autonomous Boolean Networks and the Yeast Cell Cycle Oscillator

NASA Astrophysics Data System (ADS)

Sevim, Volkan; Gong, Xinwei; Socolar, Joshua

2009-03-01

Synchronously updated Boolean networks are widely used to model gene regulation. Some properties of these model networks are known to be artifacts of the clocking in the update scheme. Autonomous updating is a less artificial scheme that allows one to introduce small timing perturbations and study stability of the attractors. We argue that the stabilization of a limit cycle in an autonomous Boolean network requires a combination of motifs such as feed-forward loops and auto-repressive links that can correct small fluctuations in the timing of switching events. A recently published model of the transcriptional cell-cycle oscillator in yeast contains the motifs necessary for stability under autonomous updating [1]. [1] D. A. Orlando, et al. Nature (London), 4530 (7197):0 944--947, 2008.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

NASA Astrophysics Data System (ADS)

Costa, Ariadne; Brochini, Ludmila; Kinouchi, Osame

2017-08-01

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

Neural computational modeling reveals a major role of corticospinal gating of central oscillations in the generation of essential tremor.

PubMed

Qu, Hong-En; Niu, Chuanxin M; Li, Si; Hao, Man-Zhao; Hu, Zi-Xiang; Xie, Qing; Lan, Ning

2017-12-01

Essential tremor, also referred to as familial tremor, is an autosomal dominant genetic disease and the most common movement disorder. It typically involves a postural and motor tremor of the hands, head or other part of the body. Essential tremor is driven by a central oscillation signal in the brain. However, the corticospinal mechanisms involved in the generation of essential tremor are unclear. Therefore, in this study, we used a neural computational model that includes both monosynaptic and multisynaptic corticospinal pathways interacting with a propriospinal neuronal network. A virtual arm model is driven by the central oscillation signal to simulate tremor activity behavior. Cortical descending commands are classified as alpha or gamma through monosynaptic or multisynaptic corticospinal pathways, which converge respectively on alpha or gamma motoneurons in the spinal cord. Several scenarios are evaluated based on the central oscillation signal passing down to the spinal motoneurons via each descending pathway. The simulated behaviors are compared with clinical essential tremor characteristics to identify the corticospinal pathways responsible for transmitting the central oscillation signal. A propriospinal neuron with strong cortical inhibition performs a gating function in the generation of essential tremor. Our results indicate that the propriospinal neuronal network is essential for relaying the central oscillation signal and the production of essential tremor.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity

NASA Astrophysics Data System (ADS)

Sadilek, Maximilian; Thurner, Stefan

2015-05-01

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity.

PubMed

Sadilek, Maximilian; Thurner, Stefan

2015-05-21

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.

Fast oscillations in cortical-striatal networks switch frequency following rewarding events and stimulant drugs.

PubMed

Berke, J D

2009-09-01

Oscillations may organize communication between components of large-scale brain networks. Although gamma-band oscillations have been repeatedly observed in cortical-basal ganglia circuits, their functional roles are not yet clear. Here I show that, in behaving rats, distinct frequencies of ventral striatal local field potential oscillations show coherence with different cortical inputs. The approximately 50 Hz gamma oscillations that normally predominate in awake ventral striatum are coherent with piriform cortex, whereas approximately 80-100 Hz high-gamma oscillations are coherent with frontal cortex. Within striatum, entrainment to gamma rhythms is selective to fast-spiking interneurons, with distinct fast-spiking interneuron populations entrained to different gamma frequencies. Administration of the psychomotor stimulant amphetamine or the dopamine agonist apomorphine causes a prolonged decrease in approximately 50 Hz power and increase in approximately 80-100 Hz power. The same frequency switch is observed for shorter epochs spontaneously in awake, undrugged animals and is consistently provoked for < 1 s following reward receipt. Individual striatal neurons can participate in these brief high-gamma bursts with, or without, substantial changes in firing rate. Switching between discrete oscillatory states may allow different modes of information processing during decision-making and reinforcement-based learning, and may also be an important systems-level process by which stimulant drugs affect cognition and behavior.

Measurement of Long Baseline Neutrino Oscillations and Improvements from Deep Learning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Psihas, Fernanda

NOvA is a long-baseline neutrino oscillation experiment which measures the oscillation of muon neutrinos from the NuMI beam at Fermilab after they travel through the Earth for 810 km. In this dissertation I describe the operations and monitoring of the detectors which make it possible to record over 98% of the delivered neutrino beam. I also present reconstruction and identification techniques using deep convolutional neural networks (CNNs), which are applicable to multiple analyses. Lastly, I detail the oscillation analyses in themore » $$\

Emergence of Slow Collective Oscillations in Neural Networks with Spike-Timing Dependent Plasticity

NASA Astrophysics Data System (ADS)

Mikkelsen, Kaare; Imparato, Alberto; Torcini, Alessandro

2013-05-01

The collective dynamics of excitatory pulse coupled neurons with spike-timing dependent plasticity is studied. The introduction of spike-timing dependent plasticity induces persistent irregular oscillations between strongly and weakly synchronized states, reminiscent of brain activity during slow-wave sleep. We explain the oscillations by a mechanism, the Sisyphus Effect, caused by a continuous feedback between the synaptic adjustments and the coherence in the neural firing. Due to this effect, the synaptic weights have oscillating equilibrium values, and this prevents the system from relaxing into a stationary macroscopic state.

Shear properties of vocal fold mucosal tissues and their effect on vocal fold oscillation

NASA Astrophysics Data System (ADS)

Chan, Roger Wai Kai

Viscoelastic shear properties of vocal fold mucosal tissues and phonosurgical biomaterials were measured with a parallel-plate rotational rheometer. Elastic, viscous and damping properties were quantified as a function of frequency (0.01 Hz to 15 Hz) for human vocal fold mucosal tissues (N = 15), implantable biomaterials commonly used in the treatment of vocal fold paralysis (Teflon, gelatin, and collagen) (the non-mucosal group), and biomaterials currently or potentially useful in the treatment of vocal fold mucosal defects (adipose tissue or fat, hyaluronic acid, and fibronectin) (the mucosal group). It was found that intersubject differences as large as an order of magnitude were often observed for the shear properties of vocal fold mucosal tissues, part of which may be age- and gender-related. Shear properties of the non-mucosal group biomaterials were often much higher than those of the mucosal group biomaterials, which were relatively close to the shear properties of mucosal tissues. Viscoelastic and rheological modeling showed that shear properties of human vocal fold mucosa may be described by a quasi-linear viscoelastic theory and a statistical network theory, based upon which extrapolations to audio frequencies were possible. A theory of small-amplitude vocal fold oscillation was revisited to describe the effects of tissue shear properties on vocal fold oscillation and phonation threshold pressure, a measure of the 'ease' of phonation and an objective indication of vocal function. It was found that phonation threshold pressure is directly related to the viscous shear modulus or the 'effective damping modulus', a concept proposed to quantify the effective amount of damping in vocal fold oscillation. The mucosal group biomaterials were incorporated into the artificial vocal fold mucosa of a physical model in order to empirically assess their effects on phonation threshold pressure. Results showed that higher threshold pressures were consistently observed for higher concentrations of hyaluronic acid and for hyaluronic acid mixed with fibronectin, in correlation with their differences in viscous shear modulus and effective damping modulus. Implications for phonosurgery were discussed in terms of the choice of optimal biomaterials for the surgical management of vocal fold mucosal defects and lamina propria deficiencies.

Abnormal salience signaling in schizophrenia: The role of integrative beta oscillations.

PubMed

Liddle, Elizabeth B; Price, Darren; Palaniyappan, Lena; Brookes, Matthew J; Robson, Siân E; Hall, Emma L; Morris, Peter G; Liddle, Peter F

2016-04-01

Aberrant salience attribution and cerebral dysconnectivity both have strong evidential support as core dysfunctions in schizophrenia. Aberrant salience arising from an excess of dopamine activity has been implicated in delusions and hallucinations, exaggerating the significance of everyday occurrences and thus leading to perceptual distortions and delusional causal inferences. Meanwhile, abnormalities in key nodes of a salience brain network have been implicated in other characteristic symptoms, including the disorganization and impoverishment of mental activity. A substantial body of literature reports disruption to brain network connectivity in schizophrenia. Electrical oscillations likely play a key role in the coordination of brain activity at spatially remote sites, and evidence implicates beta band oscillations in long-range integrative processes. We used magnetoencephalography and a task designed to disambiguate responses to relevant from irrelevant stimuli to investigate beta oscillations in nodes of a network implicated in salience detection and previously shown to be structurally and functionally abnormal in schizophrenia. Healthy participants, as expected, produced an enhanced beta synchronization to behaviorally relevant, as compared to irrelevant, stimuli, while patients with schizophrenia showed the reverse pattern: a greater beta synchronization in response to irrelevant than to relevant stimuli. These findings not only support both the aberrant salience and disconnectivity hypotheses, but indicate a common mechanism that allows us to integrate them into a single framework for understanding schizophrenia in terms of disrupted recruitment of contextually appropriate brain networks. © 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Abnormal salience signaling in schizophrenia: The role of integrative beta oscillations

PubMed Central

Liddle, Elizabeth B.; Price, Darren; Palaniyappan, Lena; Brookes, Matthew J.; Robson, Siân E.; Hall, Emma L.; Morris, Peter G.

2016-01-01

Abstract Aberrant salience attribution and cerebral dysconnectivity both have strong evidential support as core dysfunctions in schizophrenia. Aberrant salience arising from an excess of dopamine activity has been implicated in delusions and hallucinations, exaggerating the significance of everyday occurrences and thus leading to perceptual distortions and delusional causal inferences. Meanwhile, abnormalities in key nodes of a salience brain network have been implicated in other characteristic symptoms, including the disorganization and impoverishment of mental activity. A substantial body of literature reports disruption to brain network connectivity in schizophrenia. Electrical oscillations likely play a key role in the coordination of brain activity at spatially remote sites, and evidence implicates beta band oscillations in long‐range integrative processes. We used magnetoencephalography and a task designed to disambiguate responses to relevant from irrelevant stimuli to investigate beta oscillations in nodes of a network implicated in salience detection and previously shown to be structurally and functionally abnormal in schizophrenia. Healthy participants, as expected, produced an enhanced beta synchronization to behaviorally relevant, as compared to irrelevant, stimuli, while patients with schizophrenia showed the reverse pattern: a greater beta synchronization in response to irrelevant than to relevant stimuli. These findings not only support both the aberrant salience and disconnectivity hypotheses, but indicate a common mechanism that allows us to integrate them into a single framework for understanding schizophrenia in terms of disrupted recruitment of contextually appropriate brain networks. Hum Brain Mapp 37:1361‐1374, 2016. © 2016 Wiley Periodicals, Inc. PMID:26853904

Synchronization in a chaotic neural network with time delay depending on the spatial distance between neurons

NASA Astrophysics Data System (ADS)

Tang, Guoning; Xu, Kesheng; Jiang, Luoluo

2011-10-01

The synchronization is investigated in a two-dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of time delay is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the neuronal network. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, the time delay induces the abnormal membrane potential oscillations in neurons. Specifically, the abnormal membrane potential oscillations for the symmetrically placed neurons form an antiphase, so that the large coupling strength and enlargement factor lead to the desynchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameters. The physical mechanism underlying these phenomena is analyzed.

On a Possible Relationship between Linguistic Expertise and EEG Gamma Band Phase Synchrony

PubMed Central

Reiterer, Susanne; Pereda, Ernesto; Bhattacharya, Joydeep

2011-01-01

Recent research has shown that extensive training in and exposure to a second language can modify the language organization in the brain by causing both structural and functional changes. However it is not yet known how these changes are manifested by the dynamic brain oscillations and synchronization patterns subserving the language networks. In search for synchronization correlates of proficiency and expertise in second language acquisition, multivariate EEG signals were recorded from 44 high and low proficiency bilinguals during processing of natural language in their first and second languages. Gamma band (30–45 Hz) phase synchronization (PS) was calculated mainly by two recently developed methods: coarse-graining of Markov chains (estimating global phase synchrony, measuring the degree of PS between one electrode and all other electrodes), and phase lag index (PLI; estimating bivariate phase synchrony, measuring the degree of PS between a pair of electrodes). On comparing second versus first language processing, global PS by coarse-graining Markov chains indicated that processing of the second language needs significantly higher synchronization strength than first language. On comparing the proficiency groups, bivariate PS measure (i.e., PLI) revealed that during second language processing the low proficiency group showed stronger and broader network patterns than the high proficiency group, with interconnectivities between a left fronto-parietal network. Mean phase coherence analysis also indicated that the network activity was globally stronger in the low proficiency group during second language processing. PMID:22125542

Synchrony-induced modes of oscillation of a neural field model

NASA Astrophysics Data System (ADS)

Esnaola-Acebes, Jose M.; Roxin, Alex; Avitabile, Daniele; Montbrió, Ernest

2017-11-01

We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

Synchrony-induced modes of oscillation of a neural field model.

PubMed

Esnaola-Acebes, Jose M; Roxin, Alex; Avitabile, Daniele; Montbrió, Ernest

2017-11-01

We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

Influence of parameter values on the oscillation sensitivities of two p53-Mdm2 models.

PubMed

Cuba, Christian E; Valle, Alexander R; Ayala-Charca, Giancarlo; Villota, Elizabeth R; Coronado, Alberto M

2015-09-01

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Activity patterns in networks stabilized by background oscillations.

PubMed

Hoppensteadt, Frank

2009-07-01

The brain operates in a highly oscillatory environment. We investigate here how such an oscillating background can create stable organized behavior in an array of neuro-oscillators that is not observable in the absence of oscillation, much like oscillating the support point of an inverted pendulum can stabilize its up position, which is unstable without the oscillation. We test this idea in an array of electronic circuits coming from neuroengineering: we show how the frequencies of the background oscillation create a partition of the state space into distinct basins of attraction. Thus, background signals can stabilize persistent activity that is otherwise not observable. This suggests that an image, represented as a stable firing pattern which is triggered by a voltage pulse and is sustained in synchrony or resonance with the background oscillation, can persist as a stable behavior long after the initial stimulus is removed. The background oscillations provide energy for organized behavior in the array, and these behaviors are categorized by the basins of attraction determined by the oscillation frequencies.

Frequency jumps in single chip microwave LC oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gualco, Gabriele; Grisi, Marco; Boero, Giovanni, E-mail: giovanni.boero@epfl.ch

2014-12-15

We report on the experimental observation of oscillation frequency jumps in microwave LC oscillators fabricated using standard complementary metal-oxide-semiconductor technologies. The LC oscillators, operating at a frequency of about 20 GHz, consist of a single turn planar coil, a metal-oxide-metal capacitor, and two cross-coupled metal-oxide-semiconductor field effect transistors used as negative resistance network. At 300 K as well as at 77 K, the oscillation frequency is a continuous function of the oscillator bias voltage. At 4 K, frequency jumps as large as 30 MHz are experimentally observed. This behavior is tentatively attributed to the emission and capture of single electrons from defects andmore » dopant atoms.« less

Distinct Dendritic Arborization and In Vivo Firing Patterns of Parvalbumin-Expressing Basket Cells in the Hippocampal Area CA3

PubMed Central

Tukker, John J.; Lasztóczi, Bálint; Katona, Linda; Roberts, J. David B.; Pissadaki, Eleftheria K.; Dalezios, Yannis; Márton, László; Zhang, Limei; Klausberger, Thomas; Somogyi, Peter

2015-01-01

Hippocampal CA3 area generates temporally structured network activity such as sharp waves and gamma and theta oscillations. Parvalbumin-expressing basket cells, making GABAergic synapses onto cell bodies and proximal dendrites of pyramidal cells, control pyramidal cell activity and participate in network oscillations in slice preparations, but their roles in vivo remain to be tested. We have recorded the spike timing of parvalbumin-expressing basket cells in areas CA2/3 of anesthetized rats in relation to CA3 putative pyramidal cell firing and activity locally and in area CA1. During theta oscillations, CA2/3 basket cells fired on the same phase as putative pyramidal cells, but, surprisingly, significantly later than downstream CA1 basket cells. This indicates a distinct modulation of CA3 and CA1 pyramidal cells by basket cells, which receive different inputs. We observed unexpectedly large dendritic arborization of CA2/3 basket cells in stratum lacunosum moleculare (33% of length, 29% surface, and 24% synaptic input from a total of ~35,000), different from the dendritic arborizations of CA1 basket cells. Area CA2/3 basket cells fired phase locked to both CA2/3 and CA1 gamma oscillations, and increased firing during CA1 sharp waves, thus supporting the role of CA3 networks in the generation of gamma oscillations and sharp waves. However, during ripples associated with sharp waves, firing of CA2/3 basket cells was phase locked only to local but not CA1 ripples, suggesting the independent generation of fast oscillations by basket cells in CA1 and CA2/3. The distinct spike timing of basket cells during oscillations in CA1 and CA2/3 suggests differences in synaptic inputs paralleled by differences in dendritic arborizations. PMID:23595740

Non-equilibrium physics of neural networks for leaning, memory and decision making: landscape and flux perspectives

NASA Astrophysics Data System (ADS)

Wang, Jin

Cognitive behaviors are determined by underlying neural networks. Many brain functions, such as learning and memory, can be described by attractor dynamics. We developed a theoretical framework for global dynamics by quantifying the landscape associated with the steady state probability distributions and steady state curl flux, measuring the degree of non-equilibrium through detailed balance breaking. We found the dynamics and oscillations in human brains responsible for cognitive processes and physiological rhythm regulations are determined not only by the landscape gradient but also by the flux. We found that the flux is closely related to the degrees of the asymmetric connections in neural networks and is the origin of the neural oscillations. The neural oscillation landscape shows a closed-ring attractor topology. The landscape gradient attracts the network down to the ring. The flux is responsible for coherent oscillations on the ring. We suggest the flux may provide the driving force for associations among memories. Both landscape and flux determine the kinetic paths and speed of decision making. The kinetics and global stability of decision making are explored by quantifying the landscape topography through the barrier heights and the mean first passage time. The theoretical predictions are in agreement with experimental observations: more errors occur under time pressure. We quantitatively explored two mechanisms of the speed-accuracy tradeoff with speed emphasis and further uncovered the tradeoffs among speed, accuracy, and energy cost. Our results show an optimal balance among speed, accuracy, and the energy cost in decision making. We uncovered possible mechanisms of changes of mind and how mind changes improve performance in decision processes. Our landscape approach can help facilitate an understanding of the underlying physical mechanisms of cognitive processes and identify the key elements in neural networks.

Functional network inference of the suprachiasmatic nucleus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel

2016-04-04

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data frommore » individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.« less

Gigahertz Electromagnetic Structures via Direct Ink Writing for Radio-Frequency Oscillator and Transmitter Applications.

PubMed

Zhou, Nanjia; Liu, Chengye; Lewis, Jennifer A; Ham, Donhee

2017-04-01

Radio-frequency (RF) electronics, which combine passive electromagnetic devices and active transistors to generate and process gigahertz (GHz) signals, provide a critical basis of ever-pervasive wireless networks. While transistors are best realized by top-down fabrication, relatively larger electromagnetic passives are within the reach of printing techniques. Here, direct writing of viscoelastic silver-nanoparticle inks is used to produce a broad array of RF passives operating up to 45 GHz. These include lumped devices such as inductors and capacitors, and wave-based devices such as transmission lines, their resonant networks, and antennas. Moreover, to demonstrate the utility of these printed RF passive structures in active RF electronic circuits, they are combined with discrete transistors to fabricate GHz self-sustained oscillators and synchronized oscillator arrays that provide RF references, and wireless transmitters clocked by the oscillators. This work demonstrates the synergy of direct ink writing and RF electronics for wireless applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Synchronization of three electrochemical oscillators: From local to global coupling

NASA Astrophysics Data System (ADS)

Liu, Yifan; Sebek, Michael; Mori, Fumito; Kiss, István Z.

2018-04-01

We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.

Mitigation of Subsynchronous Resonance with Fractional-order PI based UPFC controller

NASA Astrophysics Data System (ADS)

Raju, D. Koteswara; Umre, Bhimrao S.; Junghare, Anjali S.; Babu, B. Chitti

2017-02-01

Due to incorporation of series capacitor compensation in transmission line for stability improvement, subsynchronous oscillations are generated at turbine-generator shaft. These oscillations can damage the shaft system if these are not well suppressed. In order to damp out these oscillations, usually power system network should have sufficient damping and the increase of network damping is obtained by the injection of subsynchronous component of voltage and current into the line, which are extracted from the measured signal of the system. However, the effectiveness of damp out of these subsynchronous oscillations is possibly by incorporating UPFC in the transmission line network is of high interest and it should be further investigated. This research article proposes the mitigation of subsynchronous resonance (SSR) using fractional-order PI (FOPI) based unified power flow controller (UPFC). The robustness of the proposed controller is tested for 25%, 55% and 70% series compensation with a symmetrical fault (L-L-L fault). Further, Eigenvalue analysis and Fast Fourier Transform (FFT) analysis against operating point variations and uncertainties in the system are also examined. The IEEE first benchmark model is adopted for this study and the superiority of the FOPI based UPFC controller over PI based UPFC controller is discussed by comparing the results with various performance indices.

Impaired clock output by altered connectivity in the circadian network.

PubMed

Fernández, María de la Paz; Chu, Jessie; Villella, Adriana; Atkinson, Nigel; Kay, Steve A; Ceriani, María Fernanda

2007-03-27

Substantial progress has been made in elucidating the molecular processes that impart a temporal control to physiology and behavior in most eukaryotes. In Drosophila, dorsal and ventral neuronal networks act in concert to convey rhythmicity. Recently, the hierarchical organization among the different circadian clusters has been addressed, but how molecular oscillations translate into rhythmic behavior remains unclear. The small ventral lateral neurons can synchronize certain dorsal oscillators likely through the release of pigment dispersing factor (PDF), a neuropeptide central to the control of rhythmic rest-activity cycles. In the present study, we have taken advantage of flies exhibiting a distinctive arrhythmic phenotype due to mutation of the potassium channel slowpoke (slo) to examine the relevance of specific neuronal populations involved in the circadian control of behavior. We show that altered neuronal function associated with the null mutation specifically impaired PDF accumulation in the dorsal protocerebrum and, in turn, desynchronized molecular oscillations in the dorsal clusters. However, molecular oscillations in the small ventral lateral neurons are properly running in the null mutant, indicating that slo is acting downstream of these core pacemaker cells, most likely in the output pathway. Surprisingly, disrupted PDF signaling by slo dysfunction directly affects the structure of the underlying circuit. Our observations demonstrate that subtle structural changes within the circadian network are responsible for behavioral arrhythmicity.

Chimeralike states in a network of oscillators under attractive and repulsive global coupling.

PubMed

Mishra, Arindam; Hens, Chittaranjan; Bose, Mridul; Roy, Prodyot K; Dana, Syamal K

2015-12-01

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

Acupuncture analgesia involves modulation of pain-induced gamma oscillations and cortical network connectivity.

PubMed

Hauck, Michael; Schröder, Sven; Meyer-Hamme, Gesa; Lorenz, Jürgen; Friedrichs, Sunja; Nolte, Guido; Gerloff, Christian; Engel, Andreas K

2017-11-24

Recent studies support the view that cortical sensory, limbic and executive networks and the autonomic nervous system might interact in distinct manners under the influence of acupuncture to modulate pain. We performed a double-blind crossover design study to investigate subjective ratings, EEG and ECG following experimental laser pain under the influence of sham and verum acupuncture in 26 healthy volunteers. We analyzed neuronal oscillations and inter-regional coherence in the gamma band of 128-channel-EEG recordings as well as heart rate variability (HRV) on two experimental days. Pain ratings and pain-induced gamma oscillations together with vagally-mediated power in the high-frequency bandwidth (vmHF) of HRV decreased significantly stronger during verum than sham acupuncture. Gamma oscillations were localized in the prefrontal cortex (PFC), mid-cingulate cortex (MCC), primary somatosensory cortex and insula. Reductions of pain ratings and vmHF-power were significantly correlated with increase of connectivity between the insula and MCC. In contrast, connectivity between left and right PFC and between PFC and insula correlated positively with vmHF-power without a relationship to acupuncture analgesia. Overall, these findings highlight the influence of the insula in integrating activity in limbic-saliency networks with vagally mediated homeostatic control to mediate antinociception under the influence of acupuncture.

Mapping the core of the Arabidopsis circadian clock defines the network structure of the oscillator.

PubMed

Huang, W; Pérez-García, P; Pokhilko, A; Millar, A J; Antoshechkin, I; Riechmann, J L; Mas, P

2012-04-06

In many organisms, the circadian clock is composed of functionally coupled morning and evening oscillators. In Arabidopsis, oscillator coupling relies on a core loop in which the evening oscillator component TIMING OF CAB EXPRESSION 1 (TOC1) was proposed to activate a subset of morning-expressed oscillator genes. Here, we show that TOC1 does not function as an activator but rather as a general repressor of oscillator gene expression. Repression occurs through TOC1 rhythmic association to the promoters of the oscillator genes. Hormone-dependent induction of TOC1 and analysis of RNA interference plants show that TOC1 prevents the activation of morning-expressed genes at night. Our study overturns the prevailing model of the Arabidopsis circadian clock, showing that the morning and evening oscillator loops are connected through the repressing activity of TOC1.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

PubMed

Leistritz, L; Suesse, T; Haueisen, J; Hilgenfeld, B; Witte, H

2006-01-01

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Dynamics of delay-coupled FitzHugh-Nagumo neural rings.

PubMed

Mao, Xiaochen; Sun, Jianqiao; Li, Shaofan

2018-01-01

This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.

Dynamics of delay-coupled FitzHugh-Nagumo neural rings

NASA Astrophysics Data System (ADS)

Mao, Xiaochen; Sun, Jianqiao; Li, Shaofan

2018-01-01

This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.

Passive synchronization for Markov jump genetic oscillator networks with time-varying delays.

PubMed

Lu, Li; He, Bing; Man, Chuntao; Wang, Shun

2015-04-01

In this paper, the synchronization problem of coupled Markov jump genetic oscillator networks with time-varying delays and external disturbances is investigated. By introducing the drive-response concept, a novel mode-dependent control scheme is proposed, which guarantees that the synchronization can be achieved. By applying the Lyapunov-Krasovskii functional method and stochastic analysis, sufficient conditions are established based on passivity theory in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of our theoretical results. Copyright © 2015 Elsevier Inc. All rights reserved.

A flow-control mechanism for distributed systems

NASA Technical Reports Server (NTRS)

Maitan, J.

1991-01-01

A new approach to the rate-based flow control in store-and-forward networks is evaluated. Existing methods display oscillations in the presence of transport delays. The proposed scheme is based on the explicit use of an embedded dynamic model of a store-and-forward buffer in a controller's feedback loop. It is shown that the use of the model eliminates the oscillations caused by the transport delays. The paper presents simulation examples and assesses the applicability of the scheme in the new generation of high-speed photonic networks where transport delays must be considered.

Chaotic itinerancy in the oscillator neural network without Lyapunov functions.

PubMed

Uchiyama, Satoki; Fujisaka, Hirokazu

2004-09-01

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions. Copyright 2004 American Institute of Physics

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment

NASA Astrophysics Data System (ADS)

Zou, Wei; Sebek, Michael; Kiss, István Z.; Kurths, Jürgen

2017-06-01

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

Solution to the indexing problem of frequency domain simulation experiments

NASA Technical Reports Server (NTRS)

Mitra, Mousumi; Park, Stephen K.

1991-01-01

A frequency domain simulation experiment is one in which selected system parameters are oscillated sinusoidally to induce oscillations in one or more system statistics of interest. A spectral (Fourier) analysis of these induced oscillations is then performed. To perform this spectral analysis, all oscillation frequencies must be referenced to a common, independent variable - an oscillation index. In a discrete-event simulation, the global simulation clock is the most natural choice for the oscillation index. However, past efforts to reference all frequencies to the simulation clock generally yielded unsatisfactory results. The reason for these unsatisfactory results is explained in this paper and a new methodology which uses the simulation clock as the oscillation index is presented. Techniques for implementing this new methodology are demonstrated by performing a frequency domain simulation experiment for a network of queues.

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment.

PubMed

Zou, Wei; Sebek, Michael; Kiss, István Z; Kurths, Jürgen

2017-06-01

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms

PubMed Central

S, Shiju

2017-01-01

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to explain the morning and evening oscillators. The proposed dual oscillator model based on Daan's hypothesis supports per1 and per2 playing the role of morning and evening oscillators respectively and this may be the first step towards the understanding of the core molecular mechanism responsible for encoding the day length. PMID:28486525

Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms.

PubMed

S, Shiju; Sriram, K

2017-01-01

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to explain the morning and evening oscillators. The proposed dual oscillator model based on Daan's hypothesis supports per1 and per2 playing the role of morning and evening oscillators respectively and this may be the first step towards the understanding of the core molecular mechanism responsible for encoding the day length.

Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns

PubMed Central

Lezon, Timothy R.; Banavar, Jayanth R.; Cieplak, Marek; Maritan, Amos; Fedoroff, Nina V.

2006-01-01

We describe a method based on the principle of entropy maximization to identify the gene interaction network with the highest probability of giving rise to experimentally observed transcript profiles. In its simplest form, the method yields the pairwise gene interaction network, but it can also be extended to deduce higher-order interactions. Analysis of microarray data from genes in Saccharomyces cerevisiae chemostat cultures exhibiting energy metabolic oscillations identifies a gene interaction network that reflects the intracellular communication pathways that adjust cellular metabolic activity and cell division to the limiting nutrient conditions that trigger metabolic oscillations. The success of the present approach in extracting meaningful genetic connections suggests that the maximum entropy principle is a useful concept for understanding living systems, as it is for other complex, nonequilibrium systems. PMID:17138668

Aging transition in systems of oscillators with global distributed-delay coupling.

PubMed

Rahman, B; Blyuss, K B; Kyrychko, Y N

2017-09-01

We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.

Hysteretic transitions in the Kuramoto model with inertia.

PubMed

Olmi, Simona; Navas, Adrian; Boccaletti, Stefano; Torcini, Alessandro

2014-10-01

We report finite-size numerical investigations and mean-field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine, for a gaussian distribution of the frequencies, the transition from incoherence to coherence for increasingly large system size and inertia. For sufficiently large inertia the transition is hysteretic, and within the hysteretic region clusters of locked oscillators of various sizes and different levels of synchronization coexist. A modification of the mean-field theory developed by Tanaka, Lichtenberg, and Oishi [Physica D 100, 279 (1997)] allows us to derive the synchronization curve associated to each of these clusters. We have also investigated numerically the limits of existence of the coherent and of the incoherent solutions. The minimal coupling required to observe the coherent state is largely independent of the system size, and it saturates to a constant value already for moderately large inertia values. The incoherent state is observable up to a critical coupling whose value saturates for large inertia and for finite system sizes, while in the thermodinamic limit this critical value diverges proportionally to the mass. By increasing the inertia the transition becomes more complex, and the synchronization occurs via the emergence of clusters of whirling oscillators. The presence of these groups of coherently drifting oscillators induces oscillations in the order parameter. We have shown that the transition remains hysteretic even for randomly diluted networks up to a level of connectivity corresponding to a few links per oscillator. Finally, an application to the Italian high-voltage power grid is reported, which reveals the emergence of quasiperiodic oscillations in the order parameter due to the simultaneous presence of many competing whirling clusters.

Phase reduction approach to synchronisation of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Nakao, Hiroya

2016-04-01

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.

Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

PubMed Central

Burroni, Javier; Taylor, P.; Corey, Cassian; Vachnadze, Tengiz; Siegelmann, Hava T.

2017-01-01

Overview: We model energy constraints in a network of spiking neurons, while exploring general questions of resource limitation on network function abstractly. Background: Metabolic states like dietary ketosis or hypoglycemia have a large impact on brain function and disease outcomes. Glia provide metabolic support for neurons, among other functions. Yet, in computational models of glia-neuron cooperation, there have been no previous attempts to explore the effects of direct realistic energy costs on network activity in spiking neurons. Currently, biologically realistic spiking neural networks assume that membrane potential is the main driving factor for neural spiking, and do not take into consideration energetic costs. Methods: We define local energy pools to constrain a neuron model, termed Spiking Neuron Energy Pool (SNEP), which explicitly incorporates energy limitations. Each neuron requires energy to spike, and resources in the pool regenerate over time. Our simulation displays an easy-to-use GUI, which can be run locally in a web browser, and is freely available. Results: Energy dependence drastically changes behavior of these neural networks, causing emergent oscillations similar to those in networks of biological neurons. We analyze the system via Lotka-Volterra equations, producing several observations: (1) energy can drive self-sustained oscillations, (2) the energetic cost of spiking modulates the degree and type of oscillations, (3) harmonics emerge with frequencies determined by energy parameters, and (4) varying energetic costs have non-linear effects on energy consumption and firing rates. Conclusions: Models of neuron function which attempt biological realism may benefit from including energy constraints. Further, we assert that observed oscillatory effects of energy limitations exist in networks of many kinds, and that these findings generalize to abstract graphs and technological applications. PMID:28289370

Theta-Modulated Gamma-Band Synchronization Among Activated Regions During a Verb Generation Task

PubMed Central

Doesburg, Sam M.; Vinette, Sarah A.; Cheung, Michael J.; Pang, Elizabeth W.

2012-01-01

Expressive language is complex and involves processing within a distributed network of cortical regions. Functional MRI and magnetoencephalography (MEG) have identified brain areas critical for expressive language, but how these regions communicate across the network remains poorly understood. It is thought that synchronization of oscillations between neural populations, particularly at a gamma rate (>30 Hz), underlies functional integration within cortical networks. Modulation of gamma rhythms by theta-band oscillations (4–8 Hz) has been proposed as a mechanism for the integration of local cell coalitions into large-scale networks underlying cognition and perception. The present study tested the hypothesis that these oscillatory mechanisms of functional integration were present within the expressive language network. We recorded MEG while subjects performed a covert verb generation task. We localized activated cortical regions using beamformer analysis, calculated inter-regional phase locking between activated areas, and measured modulation of inter-regional gamma synchronization by theta phase. The results show task-dependent gamma-band synchronization among regions activated during the performance of the verb generation task, and we provide evidence that these transient and periodic instances of high-frequency connectivity were modulated by the phase of cortical theta oscillations. These findings suggest that oscillatory synchronization and cross-frequency interactions are mechanisms for functional integration among distributed brain areas supporting expressive language processing. PMID:22707946

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

PubMed

Chen, Bor-Sen; Hsu, Chih-Yuan

2012-10-26

Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

PubMed Central

2012-01-01

Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. Conclusion If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks. PMID:23101662

Relationships between cortical myeloarchitecture and electrophysiological networks

PubMed Central

Hunt, Benjamin A. E.; Tewarie, Prejaas K.; Mougin, Olivier E.; Geades, Nicolas; Singh, Krish D.; Morris, Peter G.; Gowland, Penny A.; Brookes, Matthew J.

2016-01-01

The human brain relies upon the dynamic formation and dissolution of a hierarchy of functional networks to support ongoing cognition. However, how functional connectivities underlying such networks are supported by cortical microstructure remains poorly understood. Recent animal work has demonstrated that electrical activity promotes myelination. Inspired by this, we test a hypothesis that gray-matter myelin is related to electrophysiological connectivity. Using ultra-high field MRI and the principle of structural covariance, we derive a structural network showing how myelin density differs across cortical regions and how separate regions can exhibit similar myeloarchitecture. Building upon recent evidence that neural oscillations mediate connectivity, we use magnetoencephalography to elucidate networks that represent the major electrophysiological pathways of communication in the brain. Finally, we show that a significant relationship exists between our functional and structural networks; this relationship differs as a function of neural oscillatory frequency and becomes stronger when integrating oscillations over frequency bands. Our study sheds light on the way in which cortical microstructure supports functional networks. Further, it paves the way for future investigations of the gray-matter structure/function relationship and its breakdown in pathology. PMID:27830650

Goal-directed control with cortical units that are gated by both top-down feedback and oscillatory coherence.

PubMed

Kerr, Robert R; Grayden, David B; Thomas, Doreen A; Gilson, Matthieu; Burkitt, Anthony N

2014-01-01

The brain is able to flexibly select behaviors that adapt to both its environment and its present goals. This cognitive control is understood to occur within the hierarchy of the cortex and relies strongly on the prefrontal and premotor cortices, which sit at the top of this hierarchy. Pyramidal neurons, the principal neurons in the cortex, have been observed to exhibit much stronger responses when they receive inputs at their soma/basal dendrites that are coincident with inputs at their apical dendrites. This corresponds to inputs from both lower-order regions (feedforward) and higher-order regions (feedback), respectively. In addition to this, coherence between oscillations, such as gamma oscillations, in different neuronal groups has been proposed to modulate and route communication in the brain. In this paper, we develop a simple, but novel, neural mass model in which cortical units (or ensembles) exhibit gamma oscillations when they receive coherent oscillatory inputs from both feedforward and feedback connections. By forming these units into circuits that can perform logic operations, we identify the different ways in which operations can be initiated and manipulated by top-down feedback. We demonstrate that more sophisticated and flexible top-down control is possible when the gain of units is modulated by not only top-down feedback but by coherence between the activities of the oscillating units. With these types of units, it is possible to not only add units to, or remove units from, a higher-level unit's logic operation using top-down feedback, but also to modify the type of role that a unit plays in the operation. Finally, we explore how different network properties affect top-down control and processing in large networks. Based on this, we make predictions about the likely connectivities between certain brain regions that have been experimentally observed to be involved in goal-directed behavior and top-down attention.

Goal-directed control with cortical units that are gated by both top-down feedback and oscillatory coherence

PubMed Central

Kerr, Robert R.; Grayden, David B.; Thomas, Doreen A.; Gilson, Matthieu; Burkitt, Anthony N.

2014-01-01

The brain is able to flexibly select behaviors that adapt to both its environment and its present goals. This cognitive control is understood to occur within the hierarchy of the cortex and relies strongly on the prefrontal and premotor cortices, which sit at the top of this hierarchy. Pyramidal neurons, the principal neurons in the cortex, have been observed to exhibit much stronger responses when they receive inputs at their soma/basal dendrites that are coincident with inputs at their apical dendrites. This corresponds to inputs from both lower-order regions (feedforward) and higher-order regions (feedback), respectively. In addition to this, coherence between oscillations, such as gamma oscillations, in different neuronal groups has been proposed to modulate and route communication in the brain. In this paper, we develop a simple, but novel, neural mass model in which cortical units (or ensembles) exhibit gamma oscillations when they receive coherent oscillatory inputs from both feedforward and feedback connections. By forming these units into circuits that can perform logic operations, we identify the different ways in which operations can be initiated and manipulated by top-down feedback. We demonstrate that more sophisticated and flexible top-down control is possible when the gain of units is modulated by not only top-down feedback but by coherence between the activities of the oscillating units. With these types of units, it is possible to not only add units to, or remove units from, a higher-level unit's logic operation using top-down feedback, but also to modify the type of role that a unit plays in the operation. Finally, we explore how different network properties affect top-down control and processing in large networks. Based on this, we make predictions about the likely connectivities between certain brain regions that have been experimentally observed to be involved in goal-directed behavior and top-down attention. PMID:25152715

Mechanisms of physiological and epileptic HFO generation

PubMed Central

Jefferys, John G.R.; de la Prida, Liset Menendez; Wendling, Fabrice; Bragin, Anatol; Avoli, Massimo; Timofeev, Igor; Lopes da Silva, Fernando H.

2016-01-01

High frequency oscillations (HFO) have a variety of characteristics: band-limited or broad-band, transient burst-like phenomenon or steady-state. HFOs may be encountered under physiological or under pathological conditions (pHFO). Here we review the underlying mechanisms of oscillations, at the level of cells and networks, investigated in a variety of experimental in vitro and in vivo models. Diverse mechanisms are described, from intrinsic membrane oscillations to network processes involving different types of synaptic interactions, gap junctions and ephaptic coupling. HFOs with similar frequency ranges can differ considerably in their physiological mechanisms. The fact that in most cases the combination of intrinsic neuronal membrane oscillations and synaptic circuits are necessary to sustain network oscillations is emphasized. Evidence for pathological HFOs, particularly fast ripples, in experimental models of epilepsy and in human epileptic patients is scrutinized. The underlying mechanisms of fast ripples are examined both in the light of animal observations, in vivo and in vitro, and in epileptic patients, with emphasis on single cell dynamics. Experimental observations and computational modeling have led to hypotheses for these mechanisms, several of which are considered here, namely the role of out-of-phase firing in neuronal clusters, the importance of strong excitatory AMPA-synaptic currents and recurrent inhibitory connectivity in combination with the fast time scales of IPSPs, ephaptic coupling and the contribution of interneuronal coupling through gap junctions. The statistical behaviour of fast ripple events can provide useful information on the underlying mechanism and can help to further improve classification of the diverse forms of HFOs. PMID:22420980

Coupling between Theta Oscillations and Cognitive Control Network during Cross-Modal Visual and Auditory Attention: Supramodal vs Modality-Specific Mechanisms.

PubMed

Wang, Wuyi; Viswanathan, Shivakumar; Lee, Taraz; Grafton, Scott T

2016-01-01

Cortical theta band oscillations (4-8 Hz) in EEG signals have been shown to be important for a variety of different cognitive control operations in visual attention paradigms. However the synchronization source of these signals as defined by fMRI BOLD activity and the extent to which theta oscillations play a role in multimodal attention remains unknown. Here we investigated the extent to which cross-modal visual and auditory attention impacts theta oscillations. Using a simultaneous EEG-fMRI paradigm, healthy human participants performed an attentional vigilance task with six cross-modal conditions using naturalistic stimuli. To assess supramodal mechanisms, modulation of theta oscillation amplitude for attention to either visual or auditory stimuli was correlated with BOLD activity by conjunction analysis. Negative correlation was localized to cortical regions associated with the default mode network and positively with ventral premotor areas. Modality-associated attention to visual stimuli was marked by a positive correlation of theta and BOLD activity in fronto-parietal area that was not observed in the auditory condition. A positive correlation of theta and BOLD activity was observed in auditory cortex, while a negative correlation of theta and BOLD activity was observed in visual cortex during auditory attention. The data support a supramodal interaction of theta activity with of DMN function, and modality-associated processes within fronto-parietal networks related to top-down theta related cognitive control in cross-modal visual attention. On the other hand, in sensory cortices there are opposing effects of theta activity during cross-modal auditory attention.

High frequency stimulation abolishes thalamic network oscillations: an electrophysiological and computational analysis

NASA Astrophysics Data System (ADS)

Lee, Kendall H.; Hitti, Frederick L.; Chang, Su-Youne; Lee, Dongchul C.; Roberts, David W.; McIntyre, Cameron C.; Leiter, James C.

2011-08-01

Deep brain stimulation (DBS) of the thalamus has been demonstrated to be effective for the treatment of epilepsy. To investigate the mechanism of action of thalamic DBS, we examined the effects of high frequency stimulation (HFS) on spindle oscillations in thalamic brain slices from ferrets. We recorded intracellular and extracellular electrophysiological activity in the nucleus reticularis thalami (nRt) and in thalamocortical relay (TC) neurons in the lateral geniculate nucleus, stimulated the slice using a concentric bipolar electrode, and recorded the level of glutamate within the slice. HFS (100 Hz) of TC neurons generated excitatory post-synaptic potentials, increased the number of action potentials in both TC and nRt neurons, reduced the input resistance, increased the extracellular glutamate concentration, and abolished spindle wave oscillations. HFS of the nRt also suppressed spindle oscillations. In both locations, HFS was associated with significant and persistent elevation in extracellular glutamate levels and suppressed spindle oscillations for many seconds after the cessation of stimulation. We simulated HFS within a computational model of the thalamic network, and HFS also disrupted spindle wave activity, but the suppression of spindle activity was short-lived. Simulated HFS disrupted spindle activity for prolonged periods of time only after glutamate release and glutamate-mediated activation of a hyperpolarization-activated current (Ih) was incorporated into the model. Our results suggest that the mechanism of action of thalamic DBS as used in epilepsy may involve the prolonged release of glutamate, which in turn modulates specific ion channels such as Ih, decreases neuronal input resistance, and abolishes thalamic network oscillatory activity.

Lamina-specific contribution of glutamatergic and GABAergic potentials to hippocampal sharp wave-ripple complexes.

PubMed

Schönberger, Jan; Draguhn, Andreas; Both, Martin

2014-01-01

The mammalian hippocampus expresses highly organized patterns of neuronal activity which form a neuronal correlate of spatial memories. These memory-encoding neuronal ensembles form on top of different network oscillations which entrain neurons in a state- and experience-dependent manner. The mechanisms underlying activation, timing and selection of participating neurons are incompletely understood. Here we studied the synaptic mechanisms underlying one prominent network pattern called sharp wave-ripple complexes (SPW-R) which are involved in memory consolidation during sleep. We recorded SPW-R with extracellular electrodes along the different layers of area CA1 in mouse hippocampal slices. Contribution of glutamatergic excitation and GABAergic inhibition, respectively, was probed by local application of receptor antagonists into s. radiatum, pyramidale and oriens. Laminar profiles of field potentials show that GABAergic potentials contribute substantially to sharp waves and superimposed ripple oscillations in s. pyramidale. Inhibitory inputs to s. pyramidale and s. oriens are crucial for action potential timing by ripple oscillations, as revealed by multiunit-recordings in the pyramidal cell layer. Glutamatergic afferents, on the other hand, contribute to sharp waves in s. radiatum where they also evoke a fast oscillation at ~200 Hz. Surprisingly, field ripples in s. radiatum are slightly slower than ripples in s. pyramidale, resulting in a systematic shift between dendritic and somatic oscillations. This complex interplay between dendritic excitation and perisomatic inhibition may be responsible for the precise timing of discharge probability during the time course of SPW-R. Together, our data illustrate a complementary role of spatially confined excitatory and inhibitory transmission during highly ordered network patterns in the hippocampus.

Solvable model for chimera states of coupled oscillators.

PubMed

Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

2008-08-22

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

How to Compress Sequential Memory Patterns into Periodic Oscillations: General Reduction Rules

PubMed Central

Zhang, Kechen

2017-01-01

A neural network with symmetric reciprocal connections always admits a Lyapunov function, whose minima correspond to the memory states stored in the network. Networks with suitable asymmetric connections can store and retrieve a sequence of memory patterns, but the dynamics of these networks cannot be characterized as readily as that of the symmetric networks due to the lack of established general methods. Here, a reduction method is developed for a class of asymmetric attractor networks that store sequences of activity patterns as associative memories, as in a Hopfield network. The method projects the original activity pattern of the network to a low-dimensional space such that sequential memory retrievals in the original network correspond to periodic oscillations in the reduced system. The reduced system is self-contained and provides quantitative information about the stability and speed of sequential memory retrievals in the original network. The time evolution of the overlaps between the network state and the stored memory patterns can also be determined from extended reduced systems. The reduction procedure can be summarized by a few reduction rules, which are applied to several network models, including coupled networks and networks with time-delayed connections, and the analytical solutions of the reduced systems are confirmed by numerical simulations of the original networks. Finally, a local learning rule that provides an approximation to the connection weights involving the pseudoinverse is also presented. PMID:24877729

Generalized synchronization between chimera states

NASA Astrophysics Data System (ADS)

Andrzejak, Ralph G.; Ruzzene, Giulia; Malvestio, Irene

2017-05-01

Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks.

Multimode and multistate ladder oscillator and frequency recognition device

NASA Technical Reports Server (NTRS)

Aumann, Herbert M. (Inventor)

1976-01-01

A ladder oscillator composed of capacitive and inductive impedances connected together to form a ladder network which has a chosen number N oscillation modes at N different frequencies. Each oscillation mode is characterized by a unique standing wave voltage pattern along the nodes of the ladder oscillator, with the mode in which the ladder oscillator is oscillating being determinable from the amplitudes or phase of the oscillations at the nodes. A logic circuit may be connected to the nodes of the oscillator to compare the phases of selected nodes and thereby determine which mode the oscillator is oscillating in. A ladder oscillator composed of passive capacitive and inductive impedances can be utilized as a frequency recognition device, since the passive ladder oscillator will display the characteristic standing wave patterns if an input signal impressed upon the ladder oscillator is close to one of the mode frequencies of the oscillator. A CL ladder oscillator having series capacitive impedances and shunt inductive impedances can exhibit sustained and autonomous oscillations if active nonlinear devices are connected in parallel with the shunt inductive impedances. The active CL ladder oscillator can be synchronized to input frequencies impressed upon the oscillator, and will continue to oscillate after the input signal has been removed at a mode frequency which is, in general, nearest to the input signal frequency. Autonomous oscillations may also be obtained as desired from the active CL ladder oscillator at the mode frequencies.

Impulse-induced localized control of chaos in starlike networks.

PubMed

Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

2016-06-01

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

Chimera states: Effects of different coupling topologies

NASA Astrophysics Data System (ADS)

Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar; Perc, Matjaž

2017-04-01

Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies as well as different types of coupling functions. Chimera states have recently received ample attention as a fascinating manifestation of collective behavior, in particular describing a symmetry breaking spatiotemporal pattern where synchronized and desynchronized states coexist in a network of coupled oscillators. In this perspective, we review the emergence of different chimera states, focusing on the effects of different coupling topologies that describe the interaction network connecting the oscillators. We cover chimera states that emerge in local, nonlocal and global coupling topologies, as well as in modular, temporal and multilayer networks. We also provide an outline of challenges and directions for future research.

A Realtime Active Feedback Control System For Coupled Nonlinear Chemical Oscillators

NASA Astrophysics Data System (ADS)

Tompkins, Nathan; Fraden, Seth

2012-02-01

We study the manipulation and control of oscillatory networks. As a model system we use an emulsion of Belousov-Zhabotinsky (BZ) oscillators packed on a hexagonal lattice. Each drop is observed and perturbed by a Programmable Illumination Microscope (PIM). The PIM allows us to track individual BZ oscillators, calculate the phase and order parameters of every drop, and selectively perturb specific drops with photo illumination, all in realtime. To date we have determined the native attractor patterns for drops in 1D arrays and 2D hexagonal packing as a function of coupling strength as well as determined methods to move the system from one attractor basin to another. Current work involves implementing these attractor control methods with our experimental system and future work will likely include implementing a model neural network for use with photo controllable BZ emulsions.

High voltage power supply

NASA Technical Reports Server (NTRS)

Ruitberg, A. P.; Young, K. M. (Inventor)

1985-01-01

A high voltage power supply is formed by three discrete circuits energized by a battery to provide a plurality of concurrent output signals floating at a high output voltage on the order of several tens of kilovolts. In the first two circuits, the regulator stages are pulse width modulated and include adjustable ressistances for varying the duty cycles of pulse trains provided to corresponding oscillator stages while the third regulator stage includes an adjustable resistance for varying the amplitude of a steady signal provided to a third oscillator stage. In the first circuit, the oscillator, formed by a constant current drive network and a tuned resonant network included a step up transformer, is coupled to a second step up transformer which, in turn, supplies an amplified sinusoidal signal to a parallel pair of complementary poled rectifying, voltage multiplier stages to generate the high output voltage.

Comodulation of dopamine and serotonin on prefrontal cortical rhythms: a theoretical study

PubMed Central

Wang, Da-Hui; Wong-Lin, KongFatt

2013-01-01

The prefrontal cortex (PFC) is implicated to play an important role in cognitive control. Abnormal PFC activities and rhythms have been observed in some neurological and neuropsychiatric disorders, and evidences suggest influences from the neuromodulators dopamine (DA) and serotonin (5-HT). Despite the high level of interest in these brain systems, the combined effects of DA and 5-HT modulation on PFC dynamics remain unknown. In this work, we build a mathematical model that incorporates available experimental findings to systematically study the comodulation of DA and 5-HT on the network behavior, focusing on beta and gamma band oscillations. Single neuronal model shows pyramidal cells with 5-HT1A and 2A receptors can be non-monotonically modulated by 5-HT. Two-population excitatory-inhibitory type network consisting of pyramidal cells with D1 receptors can provide rich repertoires of oscillatory behavior. In particular, 5-HT and DA can modulate the amplitude and frequency of the oscillations, which can emerge or cease, depending on receptor types. Certain receptor combinations are conducive for the robustness of the oscillatory regime, or the existence of multiple discrete oscillatory regimes. In a multi-population heterogeneous model that takes into account possible combination of receptors, we demonstrate that robust network oscillations require high DA concentration. We also show that selective D1 receptor antagonists (agonists) tend to suppress (enhance) network oscillations, increase the frequency from beta toward gamma band, while selective 5-HT1A antagonists (agonists) act in opposite ways. Selective D2 or 5-HT2A receptor antagonists (agonists) can lead to decrease (increase) in oscillation amplitude, but only 5-HT2A antagonists (agonists) can increase (decrease) the frequency. These results are comparable to some pharmacological effects. Our work illustrates the complex mechanisms of DA and 5-HT when operating simultaneously through multiple receptors. PMID:23935568

Generation of a tunable environment for electrical oscillator systems.

PubMed

León-Montiel, R de J; Svozilík, J; Torres, Juan P

2014-07-01

Many physical, chemical, and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally introduce, and control, noise effects due to a surrounding environment remains a subject of lively interest. Here, we experimentally demonstrate a setup that provides a unique tool to generate a fully tunable environment for classical electrical oscillator systems. We illustrate the operation of the setup by implementing the case of a damped random-frequency harmonic oscillator. The high degree of tunability and control of our scheme is demonstrated by gradually modifying the statistics of the oscillator's frequency fluctuations. This tunable system can readily be used to experimentally study interesting noise effects, such as noise-induced transitions in systems driven by multiplicative noise, and noise-induced transport, a phenomenon that takes place in quantum and classical coupled oscillator networks.

Dielectric Study of Alcohols Using Broadband Terahertz Time Domain Spectroscopy (THz-TDS).

NASA Astrophysics Data System (ADS)

Sarkar, Sohini; Saha, Debasis; Banerjee, Sneha; Mukherjee, Arnab; Mandal, Pankaj

2016-06-01

Broadband Terahertz-Time Domain Spectroscopy (THz-TDS) (1-10 THz) has been utilized to study the complex dielectric properties of methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, and 1-octanol. Previous reports on dielectric study of alcohols were limited to 5 THz. At THz (1 THz = 33.33 wn = 4 meV) frequency range (0.1 to 15 THz), the molecular reorientation and several intermolecular vibrations (local oscillation of dipoles) may coexist and contribute to the overall liquid dynamics. We find that the Debye type relaxations barely contribute beyond 1 THz, rather three harmonic oscillators dominate the entire spectral range. To get insights on the modes responsible for the observed absorption in THz frequency range, we performed all atom molecular dynamics (MD) using OPLS force field and ab initio quantum calculations. Combined experimental and theoretical study reveal that the complex dielectric functions of alcohols have contribution from a) alkyl group oscillation within H-bonded network ( 1 THz), b) intermolecular H-bond stretching ( 5 THz) , and c) librational motions in alcohols. The present work, therefore, complements all previous studies on alcohols at lower frequencies and provides a clear picture on them in a broad spectral range from microwave to 10 THz.

A Comparison of Solar p-Mode Parameters from MDI and Gong: Mode Frequencies and Structure Inversions

NASA Technical Reports Server (NTRS)

Basu, S.; Christensen-Dalsgaard, J.; Howe, R.; Schou, J.; Thompson, M. J.; Hill, F.; Komm, R.

2003-01-01

Helioseismic analysis of solar global oscillations allows investigation of the internal structure of the Sun. One important test of the reliability of the inferences from helioseismology is that the results from independent sets of contemporaneous data are consistent with one another. Here we compare mode frequencies from the Global Oscillation Network Group and Michelson Doppler Imager on board SOHO and resulting inversion results on the Sun's internal structure. The average relative differences between the data sets are typically less than 1 x 10(exp -5) substantially smaller than the formal errors in the differences; however, in some cases the frequency differences show a systematic behavior that might nonetheless influence the inversion results. We find that the differences in frequencies are not a result of instrumental effects but are almost entirely related to the data pipeline software. Inversion of the frequencies shows that their differences do not result in any significant effects on the resulting inferences on solar structure. We have also experimented with fitting asymmetric profiles to the oscillation power spectra and find that, compared with the symmetric fits, this causes no significant change in the inversion results.

Nanomechanical resonators based on group IV element monolayers

NASA Astrophysics Data System (ADS)

He, Ji-Dong; Sun, Jia-Sheng; Jiang, Jin-Wu

2018-04-01

We perform molecular dynamics simulations to investigate the energy dissipation of the resonant oscillation for the group IV monolayers of puckered configuration, in which the oscillation is driven with different actuation velocities. We find that, in the moderate actuation velocity regime, the nonlinear coupling between the resonant oscillation mode and other high-frequency modes will lead to the non-resonant motion of the system. For the larger actuation velocity, the effective strain generated during the resonant oscillating causes a structural transition from the puckered configuration into the planar configuration, which is a characteristic energy dissipation mechanism for the resonant oscillation of these group IV puckered monolayers. Our findings shed light on mechanical applications of the group IV monolayers in the nanomechanical resonator field.

Recent advances in symmetric and network dynamics

NASA Astrophysics Data System (ADS)

Golubitsky, Martin; Stewart, Ian

2015-09-01

We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.

Travelling Wave Pulse Coupled Oscillator (TWPCO) Using a Self-Organizing Scheme for Energy-Efficient Wireless Sensor Networks.

PubMed

Al-Mekhlafi, Zeyad Ghaleb; Hanapi, Zurina Mohd; Othman, Mohamed; Zukarnain, Zuriati Ahmad

2017-01-01

Recently, Pulse Coupled Oscillator (PCO)-based travelling waves have attracted substantial attention by researchers in wireless sensor network (WSN) synchronization. Because WSNs are generally artificial occurrences that mimic natural phenomena, the PCO utilizes firefly synchronization of attracting mating partners for modelling the WSN. However, given that sensor nodes are unable to receive messages while transmitting data packets (due to deafness), the PCO model may not be efficient for sensor network modelling. To overcome this limitation, this paper proposed a new scheme called the Travelling Wave Pulse Coupled Oscillator (TWPCO). For this, the study used a self-organizing scheme for energy-efficient WSNs that adopted travelling wave biologically inspired network systems based on phase locking of the PCO model to counteract deafness. From the simulation, it was found that the proposed TWPCO scheme attained a steady state after a number of cycles. It also showed superior performance compared to other mechanisms, with a reduction in the total energy consumption of 25%. The results showed that the performance improved by 13% in terms of data gathering. Based on the results, the proposed scheme avoids the deafness that occurs in the transmit state in WSNs and increases the data collection throughout the transmission states in WSNs.

Travelling Wave Pulse Coupled Oscillator (TWPCO) Using a Self-Organizing Scheme for Energy-Efficient Wireless Sensor Networks

PubMed Central

Hanapi, Zurina Mohd; Othman, Mohamed; Zukarnain, Zuriati Ahmad

2017-01-01

Recently, Pulse Coupled Oscillator (PCO)-based travelling waves have attracted substantial attention by researchers in wireless sensor network (WSN) synchronization. Because WSNs are generally artificial occurrences that mimic natural phenomena, the PCO utilizes firefly synchronization of attracting mating partners for modelling the WSN. However, given that sensor nodes are unable to receive messages while transmitting data packets (due to deafness), the PCO model may not be efficient for sensor network modelling. To overcome this limitation, this paper proposed a new scheme called the Travelling Wave Pulse Coupled Oscillator (TWPCO). For this, the study used a self-organizing scheme for energy-efficient WSNs that adopted travelling wave biologically inspired network systems based on phase locking of the PCO model to counteract deafness. From the simulation, it was found that the proposed TWPCO scheme attained a steady state after a number of cycles. It also showed superior performance compared to other mechanisms, with a reduction in the total energy consumption of 25%. The results showed that the performance improved by 13% in terms of data gathering. Based on the results, the proposed scheme avoids the deafness that occurs in the transmit state in WSNs and increases the data collection throughout the transmission states in WSNs. PMID:28056020

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

Synaptic State Matching: A Dynamical Architecture for Predictive Internal Representation and Feature Detection

PubMed Central

Tavazoie, Saeed

2013-01-01

Here we explore the possibility that a core function of sensory cortex is the generation of an internal simulation of sensory environment in real-time. A logical elaboration of this idea leads to a dynamical neural architecture that oscillates between two fundamental network states, one driven by external input, and the other by recurrent synaptic drive in the absence of sensory input. Synaptic strength is modified by a proposed synaptic state matching (SSM) process that ensures equivalence of spike statistics between the two network states. Remarkably, SSM, operating locally at individual synapses, generates accurate and stable network-level predictive internal representations, enabling pattern completion and unsupervised feature detection from noisy sensory input. SSM is a biologically plausible substrate for learning and memory because it brings together sequence learning, feature detection, synaptic homeostasis, and network oscillations under a single unifying computational framework. PMID:23991161

Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

NASA Astrophysics Data System (ADS)

Marandi, Alireza; Wang, Zhe; Takata, Kenta; Byer, Robert L.; Yamamoto, Yoshihisa

2014-12-01

Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch.

PubMed

Marucci, Lucia; Barton, David A W; Cantone, Irene; Ricci, Maria Aurelia; Cosma, Maria Pia; Santini, Stefania; di Bernardo, Diego; di Bernardo, Mario

2009-12-07

Systems and Synthetic Biology use computational models of biological pathways in order to study in silico the behaviour of biological pathways. Mathematical models allow to verify biological hypotheses and to predict new possible dynamical behaviours. Here we use the tools of non-linear analysis to understand how to change the dynamics of the genes composing a novel synthetic network recently constructed in the yeast Saccharomyces cerevisiae for In-vivo Reverse-engineering and Modelling Assessment (IRMA). Guided by previous theoretical results that make the dynamics of a biological network depend on its topological properties, through the use of simulation and continuation techniques, we found that the network can be easily turned into a robust and tunable synthetic oscillator or a bistable switch. Our results provide guidelines to properly re-engineering in vivo the network in order to tune its dynamics.

Chimeralike states in two distinct groups of identical populations of coupled Stuart-Landau oscillators

NASA Astrophysics Data System (ADS)

Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2017-02-01

We show the existence of chimeralike states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimeralike states occurs only for a small range of frequency difference between the two populations, and these states disappear for an increase of mismatch between the frequencies. Here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions. Perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states. An imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population I and synchronized oscillations in population II. Also the existence of chimera state is independent of the increase of frequency mismatch between the populations. We also find the coexistence of different dynamical states with respect to different initial conditions, which causes multistability in the globally coupled system. In the case of nonlocal coupling, the system does not show multistability except in the cluster state region.

Synchrony and entrainment properties of robust circadian oscillators

PubMed Central

Bagheri, Neda; Taylor, Stephanie R.; Meeker, Kirsten; Petzold, Linda R.; Doyle, Francis J.

2008-01-01

Systems theoretic tools (i.e. mathematical modelling, control, and feedback design) advance the understanding of robust performance in complex biological networks. We highlight phase entrainment as a key performance measure used to investigate dynamics of a single deterministic circadian oscillator for the purpose of generating insight into the behaviour of a population of (synchronized) oscillators. More specifically, the analysis of phase characteristics may facilitate the identification of appropriate coupling mechanisms for the ensemble of noisy (stochastic) circadian clocks. Phase also serves as a critical control objective to correct mismatch between the biological clock and its environment. Thus, we introduce methods of investigating synchrony and entrainment in both stochastic and deterministic frameworks, and as a property of a single oscillator or population of coupled oscillators. PMID:18426774

Synchronization of Oscillators: An Ideal Introduction to Phase Transitions

ERIC Educational Resources Information Center

English, L. Q.

2008-01-01

The spontaneous synchronization of phase-coupled, non-identical oscillators is explored numerically via the famous Kuramoto model. The conditions for synchronization are examined as a function of the coupling network. I argue that such a numerical exploration provides a feasible way to introduce the topic of phase transitions early in the physics…

A Network Model of Local Field Potential Activity in Essential Tremor and the Impact of Deep Brain Stimulation

PubMed Central

Mace, Michael; Pavese, Nicola; Borisyuk, Roman; Bain, Peter

2017-01-01

Essential tremor (ET), a movement disorder characterised by an uncontrollable shaking of the affected body part, is often professed to be the most common movement disorder, affecting up to one percent of adults over 40 years of age. The precise cause of ET is unknown, however pathological oscillations of a network of a number of brain regions are implicated in leading to the disorder. Deep brain stimulation (DBS) is a clinical therapy used to alleviate the symptoms of a number of movement disorders. DBS involves the surgical implantation of electrodes into specific nuclei in the brain. For ET the targeted region is the ventralis intermedius (Vim) nucleus of the thalamus. Though DBS is effective for treating ET, the mechanism through which the therapeutic effect is obtained is not understood. To elucidate the mechanism underlying the pathological network activity and the effect of DBS on such activity, we take a computational modelling approach combined with electrophysiological data. The pathological brain activity was recorded intra-operatively via implanted DBS electrodes, whilst simultaneously recording muscle activity of the affected limbs. We modelled the network hypothesised to underlie ET using the Wilson-Cowan approach. The modelled network exhibited oscillatory behaviour within the tremor frequency range, as did our electrophysiological data. By applying a DBS-like input we suppressed these oscillations. This study shows that the dynamics of the ET network support oscillations at the tremor frequency and the application of a DBS-like input disrupts this activity, which could be one mechanism underlying the therapeutic benefit. PMID:28068428

Subatmospheric pressure in the rabbit pleural lymphatic network

PubMed Central

Negrini, Daniela; Del Fabbro, Massimo

1999-01-01

Hydraulic pressure in intercostal and diaphragmatic lymphatic vessels was measured through the micropuncture technique in 23 anaesthetised paralysed rabbits. Pleural lymphatic vessels with diameters ranging from 55 to 950 μm were observed under stereomicroscope view about 3–4 h after intrapleural injection of 20 % fluorescent dextrans. Lymphatic pressure oscillated from a minimum (Pmin) to a maximum (Pmax) value, reflecting oscillations in phase with cardiac activity (cardiogenic oscillations) and lymphatic myogenic activity. With intact pleural space, Pmin in submesothelial diaphragmatic lymphatic vessels of the lateral apposition zone was −9.1 ± 4.2 mmHg, more subatmospheric than the simultaneously recorded pleural liquid pressure amounting to −3.9 ± 1.2 mmHg. In extrapleural intercostal lymphatic vessels Pmin averaged −1.3 ± 2.7 mmHg. Cardiogenic pressure oscillations (Pmax−Pmin), were observed in all recordings; their mean amplitude was about 5 mmHg and was not dependent upon frequency of cardiac contraction, nor lymphatic vessel diameter, nor the Pmin value. Intrinsic contractions of lymphatic vessel walls caused spontaneous pressure waves of about 7 mmHg in amplitude at a rate of 8 cycles min−1. These results demonstrated the ability of pleural lymphatic vessels to generate pressure oscillations driving fluid from the subatmospheric pleural space into the lymphatic network. PMID:10545142

Membrane Resonance Enables Stable and Robust Gamma Oscillations

PubMed Central

Moca, Vasile V.; Nikolić, Danko; Singer, Wolf; Mureşan, Raul C.

2014-01-01

Neuronal mechanisms underlying beta/gamma oscillations (20–80 Hz) are not completely understood. Here, we show that in vivo beta/gamma oscillations in the cat visual cortex sometimes exhibit remarkably stable frequency even when inputs fluctuate dramatically. Enhanced frequency stability is associated with stronger oscillations measured in individual units and larger power in the local field potential. Simulations of neuronal circuitry demonstrate that membrane properties of inhibitory interneurons strongly determine the characteristics of emergent oscillations. Exploration of networks containing either integrator or resonator inhibitory interneurons revealed that: (i) Resonance, as opposed to integration, promotes robust oscillations with large power and stable frequency via a mechanism called RING (Resonance INduced Gamma); resonance favors synchronization by reducing phase delays between interneurons and imposes bounds on oscillation cycle duration; (ii) Stability of frequency and robustness of the oscillation also depend on the relative timing of excitatory and inhibitory volleys within the oscillation cycle; (iii) RING can reproduce characteristics of both Pyramidal INterneuron Gamma (PING) and INterneuron Gamma (ING), transcending such classifications; (iv) In RING, robust gamma oscillations are promoted by slow but are impaired by fast inputs. Results suggest that interneuronal membrane resonance can be an important ingredient for generation of robust gamma oscillations having stable frequency. PMID:23042733

4 Hz oscillations synchronize prefrontal-amygdala circuits during fear behaviour

PubMed Central

Karalis, Nikolaos; Dejean, Cyril; Chaudun, Fabrice; Khoder, Suzana; Rozeske, Robert R.; Wurtz, Hélène; Bagur, Sophie; Benchenane, Karim; Sirota, Anton; Courtin, Julien; Herry, Cyril

2016-01-01

Fear expression relies on the coordinated activity of prefrontal and amygdala circuits, yet the mechanisms allowing long-range network synchronization during fear remain unknown. Using a combination of extracellular recordings, pharmacological, and optogenetic manipulations we report that freezing, a behavioural expression of fear, temporally coincides with the development of sustained, internally generated 4 Hz oscillations within prefrontal-amygdala circuits. 4 Hz oscillations predict freezing onset and offset and synchronize prefrontal-amygdala circuits. Optogenetic induction of prefrontal 4 Hz oscillations coordinates prefrontal-amygdala activity and elicits fear behaviour. These results unravel a novel sustained oscillatory mechanism mediating prefrontal-amygdala coupling during fear behaviour. PMID:26878674

Hippocampal Ripple Oscillations and Inhibition-First Network Models: Frequency Dynamics and Response to GABA Modulators.

PubMed

Donoso, José R; Schmitz, Dietmar; Maier, Nikolaus; Kempter, Richard

2018-03-21

Hippocampal ripples are involved in memory consolidation, but the mechanisms underlying their generation remain unclear. Models relying on interneuron networks in the CA1 region disagree on the predominant source of excitation to interneurons: either "direct," via the Schaffer collaterals that provide feedforward input from CA3 to CA1, or "indirect," via the local pyramidal cells in CA1, which are embedded in a recurrent excitatory-inhibitory network. Here, we used physiologically constrained computational models of basket-cell networks to investigate how they respond to different conditions of transient, noisy excitation. We found that direct excitation of interneurons could evoke ripples (140-220 Hz) that exhibited intraripple frequency accommodation and were frequency-insensitive to GABA modulators, as previously shown in in vitro experiments. In addition, the indirect excitation of the basket-cell network enabled the expression of intraripple frequency accommodation in the fast-gamma range (90-140 Hz), as in vivo In our model, intraripple frequency accommodation results from a hysteresis phenomenon in which the frequency responds differentially to the rising and descending phases of the transient excitation. Such a phenomenon predicts a maximum oscillation frequency occurring several milliseconds before the peak of excitation. We confirmed this prediction for ripples in brain slices from male mice. These results suggest that ripple and fast-gamma episodes are produced by the same interneuron network that is recruited via different excitatory input pathways, which could be supported by the previously reported intralaminar connectivity bias between basket cells and functionally distinct subpopulations of pyramidal cells in CA1. Together, our findings unify competing inhibition-first models of rhythm generation in the hippocampus. SIGNIFICANCE STATEMENT The hippocampus is a part of the brain of humans and other mammals that is critical for the acquisition and consolidation of memories. During deep sleep and resting periods, the hippocampus generates high-frequency (∼200 Hz) oscillations called ripples, which are important for memory consolidation. The mechanisms underlying ripple generation are not well understood. A prominent hypothesis holds that the ripples are generated by local recurrent networks of inhibitory neurons. Using computational models and experiments in brain slices from rodents, we show that the dynamics of interneuron networks clarify several previously unexplained characteristics of ripple oscillations, which advances our understanding of hippocampus-dependent memory consolidation. Copyright © 2018 the authors 0270-6474/18/383125-23$15.00/0.

Differences in MEG gamma oscillatory power during performance of a prosaccade task in adolescents with FASD

PubMed Central

Stephen, Julia M.; Coffman, Brian A.; Stone, David B.; Kodituwakku, Piyadasa

2013-01-01

Fetal alcohol spectrum disorder (FASD) is characterized by a broad range of behavioral and cognitive deficits that impact the long-term quality of life for affected individuals. However, the underlying changes in brain structure and function associated with these cognitive impairments are not well-understood. Previous studies identified deficits in behavioral performance of prosaccade tasks in children with FASD. In this study, we investigated group differences in gamma oscillations during performance of a prosaccade task. We collected magnetoencephalography (MEG) data from 15 adolescents with FASD and 20 age-matched healthy controls (HC) with a mean age of 15.9 ± 0.4 years during performance of a prosaccade task. Eye movement was recorded and synchronized to the MEG data using an MEG compatible eye-tracker. The MEG data were analyzed relative to the onset of the visual saccade. Time-frequency analysis was performed using Fieldtrip with a focus on group differences in gamma-band oscillations. Following left target presentation, we identified four clusters over right frontal, right parietal, and left temporal/occipital cortex, with significantly different gamma-band (30–50 Hz) power between FASD and HC. Furthermore, visual M100 latencies described in Coffman etal. (2012) corresponded with increased gamma power over right central cortex in FASD only. Gamma-band differences were not identified for stimulus-averaged responses implying that these gamma-band differences were related to differences in saccade network functioning. These differences in gamma-band power may provide indications of atypical development of cortical networks in individuals with FASD. PMID:24399957

Theory on the Dynamics of Oscillatory Loops in the Transcription Factor Networks

PubMed Central

Murugan, Rajamanickam

2014-01-01

We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes. PMID:25111803

Effects of frustration on explosive synchronization

NASA Astrophysics Data System (ADS)

Huang, Xia; Gao, Jian; Sun, Yu-Ting; Zheng, Zhi-Gang; Xu, Can

2016-12-01

In this study, we consider the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and frustration is included in the system. This assumption can enhance or delay the explosive transition to synchronization. Interestingly, a de-synchronization phenomenon occurs and the type of phase transition is also changed. Furthermore, we provide an analytical treatment based on a star graph, which resembles that obtained in scale-free networks. Finally, a self-consistent approach is implemented to study the de-synchronization regime. Our findings have important implications for controlling synchronization in complex networks because frustration is a controllable parameter in experiments and a discontinuous abrupt phase transition is always dangerous in engineering in the real world.

Oscillations and chaos in neural networks: an exactly solvable model.

PubMed Central

Wang, L P; Pichler, E E; Ross, J

1990-01-01

We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics. Images PMID:2251287

Cell Autonomy and Synchrony of Suprachiasmatic Nucleus Circadian Oscillators

PubMed Central

Mohawk, Jennifer A.; Takahashi, Joseph S.

2013-01-01

The suprachiasmatic nucleus (SCN) of the hypothalamus is the site of the master circadian pacemaker in mammals. The individual cells of the SCN are capable of functioning independently from one another and therefore must form a cohesive circadian network through intercellular coupling. The network properties of the SCN lead to coordination of circadian rhythms among its neurons and neuronal subpopulations. There is increasing evidence for multiple interconnected oscillators within the SCN, and in this Review, we will highlight recent advances in our understanding of the complex organization and function of the cellular and network-level SCN clock. Understanding the way in which synchrony is achieved between cells in the SCN will provide insight into the means by which this important nucleus orchestrates circadian rhythms throughout the organism. PMID:21665298

Membrane potential dynamics of grid cells

PubMed Central

Domnisoru, Cristina; Kinkhabwala, Amina A.; Tank, David W.

2014-01-01

During navigation, grid cells increase their spike rates in firing fields arranged on a strikingly regular triangular lattice, while their spike timing is often modulated by theta oscillations. Oscillatory interference models of grid cells predict theta amplitude modulations of membrane potential during firing field traversals, while competing attractor network models predict slow depolarizing ramps. Here, using in-vivo whole-cell recordings, we tested these models by directly measuring grid cell intracellular potentials in mice running along linear tracks in virtual reality. Grid cells had large and reproducible ramps of membrane potential depolarization that were the characteristic signature tightly correlated with firing fields. Grid cells also exhibited intracellular theta oscillations that influenced their spike timing. However, the properties of theta amplitude modulations were not consistent with the view that they determine firing field locations. Our results support cellular and network mechanisms in which grid fields are produced by slow ramps, as in attractor models, while theta oscillations control spike timing. PMID:23395984

Dysfunction of sensory oscillations in Autism Spectrum Disorder

PubMed Central

Simon, David M.; Wallace, Mark T.

2016-01-01

Autism Spectrum Disorder (ASD) is a highly prevalent developmental disability characterized by deficits in social communication and interaction, restricted interests, and repetitive behaviors. Recently, anomalous sensory and perceptual function has gained an increased level of recognition as an important feature of ASD. A specific impairment in the ability to integrate information across brain networks has been proposed to contribute to these disruptions. A crucial mechanism for these integrative processes is the rhythmic synchronization of neuronal excitability across neural populations; collectively known as oscillations. In ASD there is believed to be a deficit in the ability to efficiently couple functional neural networks using these oscillations. This review discusses evidence for disruptions in oscillatory synchronization in ASD, and how disturbance of this neural mechanism contributes to alterations in sensory and perceptual function. The review also frames oscillatory data from the perspective of prevailing neurobiologically-inspired theories of ASD. PMID:27451342

High-Frequency Network Oscillations in Cerebellar Cortex

PubMed Central

Middleton, Steven J.; Racca, Claudia; Cunningham, Mark O.; Traub, Roger D.; Monyer, Hannah; Knöpfel, Thomas; Schofield, Ian S.; Jenkins, Alistair; Whittington, Miles A.

2016-01-01

SUMMARY Both cerebellum and neocortex receive input from the somatosensory system. Interaction between these regions has been proposed to underpin the correct selection and execution of motor commands, but it is not clear how such interactions occur. In neocortex, inputs give rise to population rhythms, providing a spatiotemporal coding strategy for inputs and consequent outputs. Here, we show that similar patterns of rhythm generation occur in cerebellum during nicotinic receptor subtype activation. Both gamma oscillations (30–80 Hz) and very fast oscillations (VFOs, 80–160 Hz) were generated by intrinsic cerebellar cortical circuitry in the absence of functional glutamatergic connections. As in neocortex, gamma rhythms were dependent on GABAA receptor-mediated inhibition, whereas VFOs required only nonsynaptically connected intercellular networks. The ability of cerebellar cortex to generate population rhythms within the same frequency bands as neocortex suggests that they act as a common spatiotemporal code within which corticocerebellar dialog may occur. PMID:18549787

GABA neuron alterations, cortical circuit dysfunction and cognitive deficits in schizophrenia.

PubMed

Gonzalez-Burgos, Guillermo; Fish, Kenneth N; Lewis, David A

2011-01-01

Schizophrenia is a brain disorder associated with cognitive deficits that severely affect the patients' capacity for daily functioning. Whereas our understanding of its pathophysiology is limited, postmortem studies suggest that schizophrenia is associated with deficits of GABA-mediated synaptic transmission. A major role of GABA-mediated transmission may be producing synchronized network oscillations which are currently hypothesized to be essential for normal cognitive function. Therefore, cognitive deficits in schizophrenia may result from a GABA synapse dysfunction that disturbs neural synchrony. Here, we highlight recent studies further suggesting alterations of GABA transmission and network oscillations in schizophrenia. We also review current models for the mechanisms of GABA-mediated synchronization of neural activity, focusing on parvalbumin-positive GABA neurons, which are altered in schizophrenia and whose function has been strongly linked to the production of neural synchrony. Alterations of GABA signaling that impair gamma oscillations and, as a result, cognitive function suggest paths for novel therapeutic interventions.

Neural Network Analysis on the NOvA Experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Safford, Twymun K.; Himmel, Alex

NOνA is collaboration of 180 scientists and engineers from 28 institutions which plans to study neutrino oscillations using the existing NuMI neutrino beam at Fermilab. The NOνA experiment is designed to search for oscillations of muon neutrinos to electron neutrinos by comparing the electron neutrino event rate measured at the Fermilab site with the electron neutrino event rate measured at a location just south of International Falls, MN 810 kilometers distant from Fermilab. If oscillations occur, the far site will see the appearance of electrons in the muon neutrino beam produced at Fermilab. The presence of background radiation obscures themore » desired particles and trails to be observed. Using neural network analysis, the goal of the project was to implement machine learning to automate the removal of background radiation to render pixel maps of the particle trajectories.« less

Kinematic control of walking.

PubMed

Lacquaniti, F; Ivanenko, Y P; Zago, M

2002-10-01

The planar law of inter-segmental co-ordination we described may emerge from the coupling of neural oscillators between each other and with limb mechanical oscillators. Muscle contraction intervenes at variable times to re-excite the intrinsic oscillations of the system when energy is lost. The hypothesis that a law of coordinative control results from a minimal active tuning of the passive inertial and viscoelastic coupling among limb segments is congruent with the idea that movement has evolved according to minimum energy criteria (1, 8). It is known that multi-segment motion of mammals locomotion is controlled by a network of coupled oscillators (CPGs, see 18, 33, 37). Flexible combination of unit oscillators gives rise to different forms of locomotion. Inter-oscillator coupling can be modified by changing the synaptic strength (or polarity) of the relative spinal connections. As a result, unit oscillators can be coupled in phase, out of phase, or with a variable phase, giving rise to different behaviors, such as speed increments or reversal of gait direction (from forward to backward). Supra-spinal centers may drive or modulate functional sets of coordinating interneurons to generate different walking modes (or gaits). Although it is often assumed that CPGs control patterns of muscle activity, an equally plausible hypothesis is that they control patterns of limb segment motion instead (22). According to this kinematic view, each unit oscillator would directly control a limb segment, alternately generating forward and backward oscillations of the segment. Inter-segmental coordination would be achieved by coupling unit oscillators with a variable phase. Inter-segmental kinematic phase plays the role of global control variable previously postulated for the network of central oscillators. In fact, inter-segmental phase shifts systematically with increasing speed both in man (4) and cat (38). Because this phase-shift is correlated with the net mechanical power output over a gait cycle (3, 4), phase control could be used for limiting the overall energy expenditure with increasing speed (22). Adaptation to different walking conditions, such as changes in body posture, body weight unloading and backward walk, also involves inter-segmental phase tuning, as does the maturation of limb kinematics in toddlers.

Forecasting ENSO events: A neural network-extended EOF approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tangang, F.T.; Tang, B.; Monahan, A.H.

The authors constructed neural network models to forecast the sea surface temperature anomalies (SSTA) for three regions: Nino 4. Nino 3.5, and Nino 3, representing the western-central, the central, and the eastern-central parts of the equatorial Pacific Ocean, respectively. The inputs were the extended empirical orthogonal functions (EEOF) of the sea level pressure (SLP) field that covered the tropical Indian and Pacific Oceans and evolved for a duration of 1 yr. The EEOFs greatly reduced the size of the neural networks from those of the authors` earlier papers using EOFs. The Nino 4 region appeared to be the best forecastedmore » region, with useful skills up to a year lead time for the 1982-93 forecast period. By network pruning analysis and spectral analysis, four important inputs were identified: modes 1, 2, and 6 of the SLP EEOFs and the SSTA persistence. Mode 1 characterized the low-frequency oscillation (LFO, with 4-5-yr period), and was seen as the typical ENSO signal, while mode 2, with a period of 2-5 yr, characterized the quasi-biennial oscillation (QBO) plus the LFO. Mode 6 was dominated by decadal and interdecadal variations. Thus, forecasting ENSO required information from the QBO, and the decadal-interdecadal oscillations. The nonlinearity of the networks tended to increase with lead time and to become stronger for the eastern regions of the equatorial Pacific Ocean. 35 refs., 14 figs., 4 tabs.« less

Pulse compression in a synchronously pumped optical parametric oscillator from group-velocity mismatch.

PubMed

Khaydarov, J D; Andrews, J H; Singer, K D

1994-06-01

We report on experimental intracavity compression of generated pulses (down to one quarter of the pumppulse duration) in a widely tunable synchronously pumped picosecond optical parametric oscillator. This pulse compression takes place when the optical parametric oscillator is well above threshold and is due to the pronounced group-velocity mismatch of the pump and oscillating waves in the nonlinear crystal.

Subthalamic stimulation, oscillatory activity and connectivity reveal functional role of STN and network mechanisms during decision making under conflict.

PubMed

Hell, Franz; Taylor, Paul C J; Mehrkens, Jan H; Bötzel, Kai

2018-05-01

Inhibitory control is an important executive function that is necessary to suppress premature actions and to block interference from irrelevant stimuli. Current experimental studies and models highlight proactive and reactive mechanisms and claim several cortical and subcortical structures to be involved in response inhibition. However, the involved structures, network mechanisms and the behavioral relevance of the underlying neural activity remain debated. We report cortical EEG and invasive subthalamic local field potential recordings from a fully implanted sensing neurostimulator in Parkinson's patients during a stimulus- and response conflict task with and without deep brain stimulation (DBS). DBS made reaction times faster overall while leaving the effects of conflict intact: this lack of any effect on conflict may have been inherent to our task encouraging a high level of proactive inhibition. Drift diffusion modelling hints that DBS influences decision thresholds and drift rates are modulated by stimulus conflict. Both cortical EEG and subthalamic (STN) LFP oscillations reflected reaction times (RT). With these results, we provide a different interpretation of previously conflict-related oscillations in the STN and suggest that the STN implements a general task-specific decision threshold. The timecourse and topography of subthalamic-cortical oscillatory connectivity suggest the involvement of motor, frontal midline and posterior regions in a larger network with complementary functionality, oscillatory mechanisms and structures. While beta oscillations are functionally associated with motor cortical-subthalamic connectivity, low frequency oscillations reveal a subthalamic-frontal-posterior network. With our results, we suggest that proactive as well as reactive mechanisms and structures are involved in implementing a task-related dynamic inhibitory signal. We propose that motor and executive control networks with complementary oscillatory mechanisms are tonically active, react to stimuli and release inhibition at the response when uncertainty is resolved and return to their default state afterwards. Copyright © 2018 Elsevier Inc. All rights reserved.

Spatial Noise in Coupling Strength and Natural Frequency within a Pacemaker Network; Consequences for Development of Intestinal Motor Patterns According to a Weakly Coupled Phase Oscillator Model

PubMed Central

Parsons, Sean P.; Huizinga, Jan D.

2016-01-01

Pacemaker activities generated by networks of interstitial cells of Cajal (ICC), in conjunction with the enteric nervous system, orchestrate most motor patterns in the gastrointestinal tract. It was our objective to understand the role of network features of ICC associated with the myenteric plexus (ICC-MP) in the shaping of motor patterns of the small intestine. To that end, a model of weakly coupled oscillators (oscillators influence each other's phase but not amplitude) was created with most parameters derived from experimental data. The ICC network is a uniform two dimensional network coupled by gap junctions. All ICC generate pacemaker (slow wave) activity with a frequency gradient in mice from 50/min at the proximal end of the intestine to 40/min at the distal end. Key features of motor patterns, directly related to the underlying pacemaker activity, are frequency steps and dislocations. These were accurately mimicked by reduction of coupling strength at a point in the chain of oscillators. When coupling strength was expressed as a product of gap junction density and conductance, and gap junction density was varied randomly along the chain (i.e., spatial noise) with a long-tailed distribution, plateau steps occurred at pointsof low density. As gap junction conductance was decreased, the number of plateaus increased, mimicking the effect of the gap junction inhibitor carbenoxolone. When spatial noise was added to the natural interval gradient, as gap junction conductance decreased, the number of plateaus increased as before but in addition the phase waves frequently changed direction of apparent propagation, again mimicking the effect of carbenoxolone. In summary, key features of the motor patterns that are governed by pacemaker activity may be a direct consequence of biological noise, specifically spatial noise in gap junction coupling and pacemaker frequency. PMID:26869875

Hints for cyclical recruitment of atelectasis during ongoing mechanical ventilation in lavage and oleic acid lung injury detected by SpO₂ oscillations and electrical impedance tomography.

PubMed

Bodenstein, Marc; Boehme, Stefan; Wang, Hemei; Duenges, Bastian; Markstaller, Klaus

2014-11-01

Detection of cyclical recruitment of atelectasis after induction of lavage (LAV) or oleic acid injury (OAI) in mechanically ventilated pigs. Primary hypothesis is that oxygen oscillations within the respiratory cycle can be detected by SpO₂ recordings (direct hint). SpO₂ oscillations reflect shunt oscillations that can only be explained by cyclical recruitment of atelectasis. Secondary hypothesis is that electrical impedance tomography (EIT) depicts specific regional changes of lung aeration and of pulmonary mechanical properties (indirect hint). Three groups (each n = 7) of mechanically ventilated pigs were investigated applying above mentioned methods before and repeatedly after induction of lung injury: (1) sham treated animals (SHAM), (2) LAV, and (3) OAI. Early oxygen oscillations occurred in the LAV group (mean calculated amplitude: 73.8 mmHg reflecting shunt oscillation of 11.2% in mean). In the OAI group oxygen oscillations occurred hours after induction of lung injury (mean calculated amplitude: 57.1 mmHg reflecting shunt oscillations of 8.4% in mean). The SHAM group had no relevant oxygen oscillations (<30 mmHg, shunt oscillations < 1.5%). Synchronously to oxygen oscillations, EIT depicted (1) a decrease of ventilation in dorsal areas, (2) an increase in ventral areas, (3) a decrease of especially dependent expiratory impedance, 3) an increase in late inspiratory flow especially in the dependant areas, (4) an increase in the speed of peak expiratory flow (PEF), and (5) a decrease of dorsal late expiratory flow. SpO2 and EIT recordings detect events that are interpreted as cyclical recruitment of atelectasis.

The role of propriospinal neuronal network in transmitting the alternating muscular activities of flexor and extensor in parkinsonian tremor.

PubMed

Hao, M; He, X; Lan, N

2012-01-01

It has been shown that normal cyclic movement of human arm and resting limb tremor in Parkinson's disease (PD) are associated with the oscillatory neuronal activities in different cerebral networks, which are transmitted to the antagonistic muscles via the same spinal pathway. There are mono-synaptic and multi-synaptic corticospinal pathways for conveying motor commands. This study investigates the plausible role of propriospinal neuronal (PN) network in the C3-C4 levels in multi-synaptic transmission of cortical commands for oscillatory movements. A PN network model is constructed based on known neurophysiological connections, and is hypothesized to achieve the conversion of cortical oscillations into alternating antagonistic muscle bursts. Simulations performed with a virtual arm (VA) model indicate that without the PN network, the alternating bursts of antagonistic muscle EMG could not be reliably generated, whereas with the PN network, the alternating pattern of bursts were naturally displayed in the three pairs of antagonist muscles. Thus, it is suggested that oscillations in the primary motor cortex (M1) of single and double tremor frequencies are processed at the PN network to compute the alternating burst pattern in the flexor and extensor muscles.

Coupled Oscillators System in the True Slime Mold

NASA Astrophysics Data System (ADS)

Takamatsu, A.; Fujii, T.; Endo, I.

The Plasmodium of true slime mold, Physarum polycephalum, which shows various oscillatory phenomena, can be regarded as a coupled nonlinear oscillators system. The partial bodies of the Plasmodium are interconnected by microscale tubes, whose dimension can be related to the coupling strength between the plasmodial oscillators. Investigation on the collective behavior of the oscillators under the condition that the configuration of the tube structure can be manipulated gives significant information on the characteristics of the Plasmodium from the viewpoint of nonlinear dynamics. In this study, we propose a living coupled oscillators system. Using a microfabricated structure, we patterned the geometry and the dimensions of the microscale tube structure of the Plasmodium. As the first step, the Plasmodium was grown in the microstructure for coupled two oscillators system that has two wells (oscillator part) and a microchannel (coupling part). We investigated the oscillation bahavior by monitoring the thickness oscillation of Plasmodium in the strucutre with various width (W) and length (L) of microchannel. We found that there are various types of oscillation bahavior, such as anti-phase and in-phase oscillations depending on the channel dimension W and L. The present method is suitable for further studies of the network of the Plasmodium as a collective nonlinear oscillators system.

Differential modulation of global and local neural oscillations in REM sleep by homeostatic sleep regulation

PubMed Central

Kim, Bowon; Kocsis, Bernat; Hwang, Eunjin; Kim, Youngsoo; Strecker, Robert E.; McCarley, Robert W.; Choi, Jee Hyun

2017-01-01

Homeostatic rebound in rapid eye movement (REM) sleep normally occurs after acute sleep deprivation, but REM sleep rebound settles on a persistently elevated level despite continued accumulation of REM sleep debt during chronic sleep restriction (CSR). Using high-density EEG in mice, we studied how this pattern of global regulation is implemented in cortical regions with different functions and network architectures. We found that across all areas, slow oscillations repeated the behavioral pattern of persistent enhancement during CSR, whereas high-frequency oscillations showed progressive increases. This pattern followed a common rule despite marked topographic differences. The findings suggest that REM sleep slow oscillations may translate top-down homeostatic control to widely separated brain regions whereas fast oscillations synchronizing local neuronal ensembles escape this global command. These patterns of EEG oscillation changes are interpreted to reconcile two prevailing theories of the function of sleep, synaptic homeostasis and sleep dependent memory consolidation. PMID:28193862

Differential modulation of global and local neural oscillations in REM sleep by homeostatic sleep regulation.

PubMed

Kim, Bowon; Kocsis, Bernat; Hwang, Eunjin; Kim, Youngsoo; Strecker, Robert E; McCarley, Robert W; Choi, Jee Hyun

2017-02-28

Homeostatic rebound in rapid eye movement (REM) sleep normally occurs after acute sleep deprivation, but REM sleep rebound settles on a persistently elevated level despite continued accumulation of REM sleep debt during chronic sleep restriction (CSR). Using high-density EEG in mice, we studied how this pattern of global regulation is implemented in cortical regions with different functions and network architectures. We found that across all areas, slow oscillations repeated the behavioral pattern of persistent enhancement during CSR, whereas high-frequency oscillations showed progressive increases. This pattern followed a common rule despite marked topographic differences. The findings suggest that REM sleep slow oscillations may translate top-down homeostatic control to widely separated brain regions whereas fast oscillations synchronizing local neuronal ensembles escape this global command. These patterns of EEG oscillation changes are interpreted to reconcile two prevailing theories of the function of sleep, synaptic homeostasis and sleep dependent memory consolidation.

Positive And Negative Feedback Loops Coupled By Common Transcription Activator And Repressor

NASA Astrophysics Data System (ADS)

Sielewiesiuk, Jan; Łopaciuk, Agata

2015-03-01

Dynamical systems consisting of two interlocked loops with negative and positive feedback have been studied using the linear analysis of stability and numerical solutions. Conditions for saddle-node bifurcation were formulated in a general form. Conditions for Hopf bifurcations were found in a few symmetrical cases. Auto-oscillations, when they exist, are generated by the negative feedback repressive loop. This loop determines the frequency and amplitude of oscillations. The positive feedback loop of activation slightly modifies the oscillations. Oscillations are possible when the difference between Hilll's coefficients of the repression and activation is sufficiently high. The highly cooperative activation loop with a fast turnover slows down or even makes the oscillations impossible. The system under consideration can constitute a component of epigenetic or enzymatic regulation network.

Triple grouping and period-three oscillations in minority-game dynamics.

PubMed

Dong, Jia-Qi; Huang, Zi-Gang; Huang, Liang; Lai, Ying-Cheng

2014-12-01

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Deep learning classification in asteroseismology

NASA Astrophysics Data System (ADS)

Hon, Marc; Stello, Dennis; Yu, Jie

2017-08-01

In the power spectra of oscillating red giants, there are visually distinct features defining stars ascending the red giant branch from those that have commenced helium core burning. We train a 1D convolutional neural network by supervised learning to automatically learn these visual features from images of folded oscillation spectra. By training and testing on Kepler red giants, we achieve an accuracy of up to 99 per cent in separating helium-burning red giants from those ascending the red giant branch. The convolutional neural network additionally shows capability in accurately predicting the evolutionary states of 5379 previously unclassified Kepler red giants, by which we now have greatly increased the number of classified stars.

Detecting spatial defects in colored patterns using self-oscillating gels

NASA Astrophysics Data System (ADS)

Fang, Yan; Yashin, Victor V.; Dickerson, Samuel J.; Balazs, Anna C.

2018-06-01

With the growing demand for wearable computers, there is a need for material systems that can perform computational tasks without relying on external electrical power. Using theory and simulation, we design a material system that "computes" by integrating the inherent behavior of self-oscillating gels undergoing the Belousov-Zhabotinsky (BZ) reaction and piezoelectric (PZ) plates. These "BZ-PZ" units are connected electrically to form a coupled oscillator network, which displays specific modes of synchronization. We exploit this attribute in employing multiple BZ-PZ networks to perform pattern matching on complex multi-dimensional data, such as colored images. By decomposing a colored image into sets of binary vectors, we use each BZ-PZ network, or "channel," to store distinct information about the color and the shape of the image and perform the pattern matching operation. Our simulation results indicate that the multi-channel BZ-PZ device can detect subtle differences between the input and stored patterns, such as the color variation of one pixel or a small change in the shape of an object. To demonstrate a practical application, we utilize our system to process a colored Quick Response code and show its potential in cryptography and steganography.

Dynamics of Propofol-Induced Loss of Consciousness Across Primate Neocortex.

PubMed

Ishizawa, Yumiko; Ahmed, Omar J; Patel, Shaun R; Gale, John T; Sierra-Mercado, Demetrio; Brown, Emery N; Eskandar, Emad N

2016-07-20

The precise neural mechanisms underlying transitions between consciousness and anesthetic-induced unconsciousness remain unclear. Here, we studied intracortical neuronal dynamics leading to propofol-induced unconsciousness by recording single-neuron activity and local field potentials directly in the functionally interconnecting somatosensory (S1) and frontal ventral premotor (PMv) network during a gradual behavioral transition from full alertness to loss of consciousness (LOC) and on through a deeper anesthetic level. Macaque monkeys were trained for a behavioral task designed to determine the trial-by-trial alertness and neuronal response to tactile and auditory stimulation. We show that disruption of coherent beta oscillations between S1 and PMv preceded, but did not coincide with, the LOC. LOC appeared to correspond to pronounced but brief gamma-/high-beta-band oscillations (lasting ∼3 min) in PMv, followed by a gamma peak in S1. We also demonstrate that the slow oscillations appeared after LOC in S1 and then in PMv after a delay, together suggesting that neuronal dynamics are very different across S1 versus PMv during LOC. Finally, neurons in both S1 and PMv transition from responding to bimodal (tactile and auditory) stimulation before LOC to only tactile modality during unconsciousness, consistent with an inhibition of multisensory integration in this network. Our results show that propofol-induced LOC is accompanied by spatiotemporally distinct oscillatory neuronal dynamics across the somatosensory and premotor network and suggest that a transitional state from wakefulness to unconsciousness is not a continuous process, but rather a series of discrete neural changes. How information is processed by the brain during awake and anesthetized states and, crucially, during the transition is not clearly understood. We demonstrate that neuronal dynamics are very different within an interconnecting cortical network (primary somatosensory and frontal premotor area) during the loss of consciousness (LOC) induced by propofol in nonhuman primates. Coherent beta oscillations between these regions are disrupted before LOC. Pronounced but brief gamma-band oscillations appear to correspond to LOC. In addition, neurons in both of these cortices transition from responding to both tactile and auditory stimulation before LOC to only tactile modality during unconsciousness. We demonstrate that propofol-induced LOC is accompanied by spatiotemporally distinctive neuronal dynamics in this network with concurrent changes in multisensory processing. Copyright © 2016 the authors 0270-6474/16/367718-09$15.00/0.

Information-geometric measures estimate neural interactions during oscillatory brain states

PubMed Central

Nie, Yimin; Fellous, Jean-Marc; Tatsuno, Masami

2014-01-01

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain. PMID:24605089

Information-geometric measures estimate neural interactions during oscillatory brain states.

PubMed

Nie, Yimin; Fellous, Jean-Marc; Tatsuno, Masami

2014-01-01

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain.

A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators

PubMed Central

2016-01-01

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology. PMID:26835539

The pedestrian watchmaker: Genetic clocks from engineered oscillators

PubMed Central

Cookson, Natalie A.; Tsimring, Lev S.; Hasty, Jeff

2010-01-01

The crucial role of time-keeping has required organisms to develop sophisticated regulatory networks to ensure the reliable propagation of periodic behavior. These biological clocks have long been a focus of research; however, a clear understanding of how they maintain oscillations in the face of unpredictable environments and the inherent noise of biological systems remains elusive. Here, we review the current understanding of circadian oscillations using Drosophila melanogaster as a typical example and discuss the utility of an alternative synthetic biology approach to studying these highly intricate systems. PMID:19903483

Thalamocortical Oscillations in the Sleeping and Aroused Brain

NASA Astrophysics Data System (ADS)

Steriade, Mircea; McCormick, David A.; Sejnowski, Terrence J.

1993-10-01

Sleep is characterized by synchronized events in billions of synaptically coupled neurons in thalamocortical systems. The activation of a series of neuromodulatory transmitter systems during awakening blocks low-frequency oscillations, induces fast rhythms, and allows the brain to recover full responsiveness. Analysis of cortical and thalamic networks at many levels, from molecules to single neurons to large neuronal assemblies, with a variety of techniques, ranging from intracellular recordings in vivo and in vitro to computer simulations, is beginning to yield insights into the mechanisms of the generation, modulation, and function of brain oscillations.

REVIEW ARTICLE: Oscillations and temporal signalling in cells

NASA Astrophysics Data System (ADS)

Tiana, G.; Krishna, S.; Pigolotti, S.; Jensen, M. H.; Sneppen, K.

2007-06-01

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-κB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

Synchronization of multi-phase oscillators: an Axelrod-inspired model

NASA Astrophysics Data System (ADS)

Kuperman, M. N.; Zanette, D. H.

2009-07-01

Inspired by Axelrod’s model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction - which occurs between homologous phases - is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where any two oscillators can be synchronized in some of their phases, while their remain unsynchronized in the others.

ERK Oscillation-Dependent Gene Expression Patterns and Deregulation by Stress-Response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waters, Katrina M.; Cummings, Brian S.; Shankaran, Harish

2014-09-15

Studies were undertaken to determine whether ERK oscillations regulate a unique subset of genes in human keratinocytes and subsequently, whether the p38 stress response inhibits ERK oscillations. A DNA microarray identified many genes that were unique to ERK oscillations, and network reconstruction predicted an important role for the mediator complex subunit 1 (MED1) node in mediating ERK oscillation-dependent gene expression. Increased ERK-dependent phosphorylation of MED1 was observed in oscillating cells compared to non-oscillating counterparts as validation. Treatment of keratinocytes with a p38 inhibitor (SB203580) increased ERK oscillation amplitudes and MED1 and phospho-MED1 protein levels. Bromate is a probable human carcinogenmore » that activates p38. Bromate inhibited ERK oscillations in human keratinocytes and JB6 cells and induced an increase in phospho-p38 and decrease in phospho-MED1 protein levels. Treatment of normal rat kidney cells and primary salivary gland epithelial cells with bromate decreased phospho-MED1 levels in a reversible fashion upon treatment with p38 inhibitors (SB202190; SB203580). Our results indicate that oscillatory behavior in the ERK pathway alters homeostatic gene regulation patterns and that the cellular response to perturbation may manifest differently in oscillating vs non-oscillating cells.« less

Diurnal influences on electrophysiological oscillations and coupling in the dorsal striatum and cerebellar cortex of the anesthetized rat

PubMed Central

Frederick, Ariana; Bourget-Murray, Jonathan; Chapman, C. Andrew; Amir, Shimon; Courtemanche, Richard

2014-01-01

Circadian rhythms modulate behavioral processes over a 24 h period through clock gene expression. What is largely unknown is how these molecular influences shape neural activity in different brain areas. The clock gene Per2 is rhythmically expressed in the striatum and the cerebellum and its expression is linked with daily fluctuations in extracellular dopamine levels and D2 receptor activity. Electrophysiologically, dopamine depletion enhances striatal local field potential (LFP) oscillations. We investigated if LFP oscillations and synchrony were influenced by time of day, potentially via dopamine mechanisms. To assess the presence of a diurnal effect, oscillatory power and coherence were examined in the striatum and cerebellum of rats under urethane anesthesia at four different times of day zeitgeber time (ZT1, 7, 13 and 19—indicating number of hours after lights turned on in a 12:12 h light-dark cycle). We also investigated the diurnal response to systemic raclopride, a D2 receptor antagonist. Time of day affected the proportion of LFP oscillations within the 0–3 Hz band and the 3–8 Hz band. In both the striatum and the cerebellum, slow oscillations were strongest at ZT1 and weakest at ZT13. A 3–8 Hz oscillation was present when the slow oscillation was lowest, with peak 3–8 Hz activity occurring at ZT13. Raclopride enhanced the slow oscillations, and had the greatest effect at ZT13. Within the striatum and with the cerebellum, 0–3 Hz coherence was greatest at ZT1, when the slow oscillations were strongest. Coherence was also affected the most by raclopride at ZT13. Our results suggest that neural oscillations in the cerebellum and striatum, and the synchrony between these areas, are modulated by time of day, and that these changes are influenced by dopamine manipulation. This may provide insight into how circadian gene transcription patterns influence network electrophysiology. Future experiments will address how these network alterations are linked with behavior. PMID:25309348

Vpliv topoloskih lastnosti kompleksnih mrez in dinamicnih lastnosti sklopljenih celicnih oscilatorjev na kolektivno dinamiko

NASA Astrophysics Data System (ADS)

Markovic, Rene

This doctor thesis is both theoretical and applicative. In the theoretical part of the thesis, we examine how the interplay of dynamical features of oscillators and structural properties of complex networks affect the collective behavior of the system. We show, that weakly dissipative and flexible oscillators synchronize best in a broad scale network topology, whereas on the other hand strongly dissipative and rigid oscillators exhibit maximal synchronization in a scale-free network topology. We provide an analytical explanation for this phenomenon and validate it by implementing various continuous as well as discrete mathematical models that exhibit different levels of dynamical complexity. In the continuation, we additionally investigate how speed of signal transmission in the network affects the collective dynamic of the system. Our results show that besides an optimal network topology, also an optimal information transmission speed exists, at which the system reaches the highest degree of global synchronization. In the second part we apply the findings and the methodology from our theoretical studies to the examination of the collective pancreatic beta cell activity in the islets of Langerhans, which represents the main mechanism for the regulation of blood glucose homeostasis by the secretion of the hormone insulin. We show that the beta cells dynamics is not synchronized on the global scale of the whole islets. Instead, the cells form local clusters of synchronized activity which tend to get less segregated under higher stimulatory glucose concentrations. Furthermore, higher glucose concentrations also lead to the presence of broad scale small world connectivity patterns in the functional beta cell network. The main findings thereby shed light on the physiology and collective behavior of the islets of Langerhans and point out the possibilities of pathological changes associated with changes in the intercellular communication pathways.

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

NASA Astrophysics Data System (ADS)

Takeda, Y.; Tamate, S.; Yamamoto, Y.; Takesue, H.; Inagaki, T.; Utsunomiya, S.

2018-01-01

We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.

Propagating wave and irregular dynamics: Spatiotemporal patterns of cholinergic theta oscillations in neocortex, in vitro

PubMed Central

Bao, Weili; Wu, Jian-young

2010-01-01

Neocortical “theta” oscillation (5- 12 Hz) has been observed in animals and human subjects but little is known about how the oscillation is organized in the cortical intrinsic networks. Here we use voltage-sensitive dye and optical imaging to study a carbachol/bicuculline induced theta (~8 Hz) oscillation in rat neocortical slices. The imaging has large signal-to-noise ratio, allowing us to map the phase distribution over the neocortical tissue during the oscillation. The oscillation was organized as spontaneous epochs and each epoch was composed of a “first spike”, a “regular” period (with relatively stable frequency and amplitude) and an “irregular” period (with variable frequency and amplitude) of oscillations. During each cycle of the regular oscillation one wave of activation propagated horizontally (parallel to the cortical lamina) across the cortical section at a velocity of ~50 mm/sec. Vertically the activity was synchronized through all cortical layers. This pattern of one propagating wave associated with one oscillation cycle was seen during all the regular cycles. The oscillation frequency varied noticeably at two neighboring horizontal locations (330 μm apart), suggesting that the oscillation is locally organized and each local oscillator is about equal or less than 300 μm wide horizontally. During irregular oscillations the spatiotemporal patterns were complex and sometimes the vertical synchronization decomposed, suggesting a de-coupling among local oscillators. Our data suggested that neocortical theta oscillation is sustained by multiple local oscillators. The coupling regime among the oscillators may determine the spatiotemporal pattern and switching between propagating waves and irregular patterns. PMID:12612003

Ketamine Protects Gamma Oscillations by Inhibiting Hippocampal LTD

PubMed Central

Huang, Lanting; Yang, Xiu-Juan; Huang, Ying; Sun, Eve Y.

2016-01-01

NMDA receptors have been widely reported to be involved in the regulation of synaptic plasticity through effects on long-term potentiation (LTP) and long-term depression (LTD). LTP and LTD have been implicated in learning and memory processes. Besides synaptic plasticity, it is known that the phenomenon of gamma oscillations is critical in cognitive functions. Synaptic plasticity has been widely studied, however it is still not clear, to what degree synaptic plasticity regulates the oscillations of neuronal networks. Two NMDA receptor antagonists, ketamine and memantine, have been shown to regulate LTP and LTD, to promote cognitive functions, and have even been reported to bring therapeutic effects in major depression and Alzheimer’s disease respectively. These compounds allow us to investigate the putative interrelationship between network oscillations and synaptic plasticity and to learn more about the mechanisms of their therapeutic effects. In the present study, we have identified that ketamine and memantine could inhibit LTD, without impairing LTP in the CA1 region of mouse hippocampus, which may underlie the mechanism of these drugs’ therapeutic effects. Our results suggest that NMDA-induced LTD caused a marked loss in the gamma power, and pretreatment with 10 μM ketamine prevented the oscillatory loss via its inhibitory effect on LTD. Our study provides a new understanding of the role of NMDA receptors on hippocampal plasticity and oscillations. PMID:27467732

Cholinergic modulation of the parafacial respiratory group

PubMed Central

Boutin, Rozlyn C. T.; Alsahafi, Zaki

2016-01-01

Key points This study investigates the effects of cholinergic transmission on the expiratory oscillator, the parafacial respiratory group (pFRG) in urethane anaesthetized adult rats.Local inhibition of the acetyl cholinesterase enzyme induced activation of expiratory abdominal muscles and active expiration.Local application of the cholinomimetic carbachol elicited recruitment of late expiratory neurons, expiratory abdominal muscle activity and active expiration. This effect was antagonized by local application of the muscarinic antagonists scopolamine, J104129 and 4DAMP.We observed distinct physiological responses between the more medial chemosensitive region of the retrotrapezoid nucleus and the more lateral region of pFRG.These results support the hypothesis that pFRG is under cholinergic neuromodulation and the region surrounding the facial nucleus contains a group of neurons with distinct physiological roles. Abstract Active inspiration and expiration are opposing respiratory phases generated by two separate oscillators in the brainstem: inspiration driven by a neuronal network located in the preBötzinger complex (preBötC) and expiration driven by a neuronal network located in the parafacial respiratory group (pFRG). While continuous activity of the preBötC is necessary for maintaining ventilation, the pFRG behaves as a conditional expiratory oscillator, being silent in resting conditions and becoming rhythmically active in the presence of increased respiratory drive (e.g. hypoxia, hypercapnia, exercise and through release of inhibition). Recent evidence from our laboratory suggests that expiratory activity in the principal expiratory pump muscles, the abdominals, is modulated in a state‐dependent fashion, frequently occurring during periods of REM sleep. We hypothesized that acetylcholine, a neurotransmitter released in wakefulness and REM sleep by mesopontine structures, contributes to the activation of pFRG neurons and thus acts to promote the recruitment of expiratory abdominal muscle activity. We investigated the stimulatory effect of cholinergic neurotransmission on pFRG activity and recruitment of active expiration in vivo under anaesthesia. We demonstrate that local application of the acetylcholinesterase inhibitor physostigmine into the pFRG potentiated expiratory activity. Furthermore, local application of the cholinomimetic carbachol into the pFRG activated late expiratory neurons and induced long lasting rhythmic active expiration. This effect was completely abolished by pre‐application of the muscarinic antagonist scopolamine, and more selective M3 antagonists 4DAMP and J104129. We conclude that cholinergic muscarinic transmission contributes to excitation of pFRG neurons and promotes both active recruitment of abdominal muscles and active expiratory flow. PMID:27808424

Neurofeedback training of gamma band oscillations improves perceptual processing.

PubMed

Salari, Neda; Büchel, Christian; Rose, Michael

2014-10-01

In this study, a noninvasive electroencephalography-based neurofeedback method is applied to train volunteers to deliberately increase gamma band oscillations (40 Hz) in the visual cortex. Gamma band oscillations in the visual cortex play a functional role in perceptual processing. In a previous study, we were able to demonstrate that gamma band oscillations prior to stimulus presentation have a significant influence on perceptual processing of visual stimuli. In the present study, we aimed to investigate longer lasting effects of gamma band neurofeedback training on perceptual processing. For this purpose, a feedback group was trained to modulate oscillations in the gamma band, while a control group participated in a task with an identical design setting but without gamma band feedback. Before and after training, both groups participated in a perceptual object detection task and a spatial attention task. Our results clearly revealed that only the feedback group but not the control group exhibited a visual processing advantage and an increase in oscillatory gamma band activity in the pre-stimulus period of the processing of the visual object stimuli after the neurofeedback training. Results of the spatial attention task showed no difference between the groups, which underlines the specific role of gamma band oscillations for perceptual processing. In summary, our results show that modulation of gamma band activity selectively affects perceptual processing and therefore supports the relevant role of gamma band activity for this specific process. Furthermore, our results demonstrate the eligibility of gamma band oscillations as a valuable tool for neurofeedback applications.

Plastic modulation of PTSD resting-state networks by EEG neurofeedback

PubMed Central

Kluetsch, Rosemarie C.; Ros, Tomas; Théberge, Jean; Frewen, Paul A.; Calhoun, Vince D.; Schmahl, Christian; Jetly, Rakesh; Lanius, Ruth A.

2015-01-01

Objective Electroencephalographic (EEG) neurofeedback training has been shown to produce plastic modulations in salience network and default mode network functional connectivity in healthy individuals. In this study, we investigated whether a single session of neurofeedback training aimed at the voluntary reduction of alpha rhythm (8–12 Hz) amplitude would be related to differences in EEG network oscillations, functional MRI (fMRI) connectivity, and subjective measures of state anxiety and arousal in a group of individuals with PTSD. Method 21 individuals with PTSD related to childhood abuse underwent 30 minutes of EEG neurofeedback training preceded and followed by a resting-state fMRI scan. Results Alpha desynchronizing neurofeedback was associated with decreased alpha amplitude during training, followed by a significant increase (‘rebound’) in resting-state alpha synchronization. This rebound was linked to increased calmness, greater salience network connectivity with the right insula, and enhanced default mode network connectivity with bilateral posterior cingulate, right middle frontal gyrus, and left medial prefrontal cortex. Conclusion Our study represents a first step in elucidating the potential neurobehavioral mechanisms mediating the effects of neurofeedback treatment on regulatory systems in PTSD. Moreover, it documents for the first time a spontaneous EEG ‘rebound’ after neurofeedback, pointing to homeostatic/compensatory mechanisms operating in the brain. PMID:24266644

Controlling self-sustained spiking activity by adding or removing one network link

NASA Astrophysics Data System (ADS)

Xu, Kesheng; Huang, Wenwen; Li, Baowen; Dhamala, Mukesh; Liu, Zonghua

2013-06-01

Being able to control the neuronal spiking activity in specific brain regions is central to a treatment scheme in several brain disorders such as epileptic seizures, mental depression, and Parkinson's diseases. Here, we present an approach for controlling self-sustained oscillations by adding or removing one directed network link in coupled neuronal oscillators, in contrast to previous approaches of adding stimuli or noise. We find that such networks can exhibit a variety of activity patterns such as on-off switch, sustained spikes, and short-term spikes. We derive the condition for a specific link to be the controller of the on-off effect. A qualitative analysis is provided to facilitate the understanding of the mechanism for spiking activity by adding one link. Our findings represent the first report on generating spike activity with the addition of only one directed link to a network and provide a deeper understanding of the microscopic roots of self-sustained spiking.

Analysis of precision in chemical oscillators: implications for circadian clocks

NASA Astrophysics Data System (ADS)

d'Eysmond, Thomas; De Simone, Alessandro; Naef, Felix

2013-10-01

Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

NASA Technical Reports Server (NTRS)

Golubitsky, Martin; Stewart, Ian

1986-01-01

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Modulation of short-term plasticity in the corticothalamic circuit by group III metabotropic glutamate receptors.

PubMed

Kyuyoung, Christine L; Huguenard, John R

2014-01-08

Recurrent connections in the corticothalamic circuit underlie oscillatory behavior in this network and range from normal sleep rhythms to the abnormal spike-wave discharges seen in absence epilepsy. The propensity of thalamic neurons to fire postinhibitory rebound bursts mediated by low-threshold calcium spikes renders the circuit vulnerable to both increased excitation and increased inhibition, such as excessive excitatory cortical drive to thalamic reticular (RT) neurons or heightened inhibition of thalamocortical relay (TC) neurons by RT. In this context, a protective role may be played by group III metabotropic receptors (mGluRs), which are uniquely located in the presynaptic active zone and typically act as autoreceptors or heteroceptors to depress synaptic release. Here, we report that these receptors regulate short-term plasticity at two loci in the corticothalamic circuit in rats: glutamatergic cortical synapses onto RT neurons and GABAergic synapses onto TC neurons in somatosensory ventrobasal thalamus. The net effect of group III mGluR activation at these synapses is to suppress thalamic oscillations as assayed in vitro. These findings suggest a functional role of these receptors to modulate corticothalamic transmission and protect against prolonged activity in the network.

Key role of coupling, delay, and noise in resting brain fluctuations

PubMed Central

Deco, Gustavo; Jirsa, Viktor; McIntosh, A. R.; Sporns, Olaf; Kötter, Rolf

2009-01-01

A growing body of neuroimaging research has documented that, in the absence of an explicit task, the brain shows temporally coherent activity. This so-called “resting state” activity or, more explicitly, the default-mode network, has been associated with daydreaming, free association, stream of consciousness, or inner rehearsal in humans, but similar patterns have also been found under anesthesia and in monkeys. Spatiotemporal activity patterns in the default-mode network are both complex and consistent, which raises the question whether they are the expression of an interesting cognitive architecture or the consequence of intrinsic network constraints. In numerical simulation, we studied the dynamics of a simplified cortical network using 38 noise-driven (Wilson–Cowan) oscillators, which in isolation remain just below their oscillatory threshold. Time delay coupling based on lengths and strengths of primate corticocortical pathways leads to the emergence of 2 sets of 40-Hz oscillators. The sets showed synchronization that was anticorrelated at <0.1 Hz across the sets in line with a wide range of recent experimental observations. Systematic variation of conduction velocity, coupling strength, and noise level indicate a high sensitivity of emerging synchrony as well as simulated blood flow blood oxygen level-dependent (BOLD) on the underlying parameter values. Optimal sensitivity was observed around conduction velocities of 1–2 m/s, with very weak coupling between oscillators. An additional finding was that the optimal noise level had a characteristic scale, indicating the presence of stochastic resonance, which allows the network dynamics to respond with high sensitivity to changes in diffuse feedback activity. PMID:19497858

Topographical differences of frontal-midline theta activity reflect functional differences in cognitive control abilities.

PubMed

Eschmann, Kathrin C J; Bader, Regine; Mecklinger, Axel

2018-06-01

Electrophysiological oscillations are assumed to be the core mechanism for large-scale network communication. The specific role of frontal-midline theta oscillations as cognitive control mechanism is under debate. According to the dual mechanisms of control framework, cognitive control processes can be divided into proactive and reactive control. The present study aimed at investigating the role of frontal-midline theta activity by assessing oscillations in two tasks varying in the type of cognitive control needed. More specifically, a delayed match to sample (DMTS) task requiring proactive control and a color Stroop task recruiting reactive control processes were conducted within the same group of participants. Moreover, both tasks contained conditions with low and high need for cognitive control. As expected larger frontal-midline theta activity was found in conditions with high need for cognitive control. However, theta activity was focally activated at frontal sites in the DMTS task whereas it had a broader topographical distribution in the Stroop task, indicating that both proactive and reactive control are reflected in frontal-midline theta activity but reactive control is additionally characterized by a broader theta activation. These findings support the conclusion that frontal-midline theta acts functionally different depending on task requirements. Copyright © 2018 Elsevier Inc. All rights reserved.