Synapses reduction in autoassociative Hopfield network

In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing.

Networks of coupled periodic oscillators (similar to the Kuramoto model) have been proposed as models of associative memory. However, error-free retrieval states of such oscillatory networks are typically unstable, resulting in a near zero capacity. This puts the networks at disadvantage as compared with the classical Hopfield network. Here we propose a simple remedy for this undesirable property and show rigorously that the error-free capacity of our oscillatory, associative-memory networks can be made as high as that of the Hopfield network. They can thus not only provide insights into the origin of biological memory, but can also be potentially useful for applications in information science and engineering.

We present here a dynamic formalism which allow to compute analitically the stationary properties of networks of neural oscillators. This technique, derived originally to study situations away from equilibrium, is an alternative to standard methods developed to analyze the behaviour of attractor neural networks.

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 networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most networks display damped oscillations, even when their units - and linear chains of these units - behave in a non-oscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a new 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. In particular, we show how to treat production and networks as transport problems governed by balance equations and equations for the adaptation of production speeds. The stability and dynamic behavior of networks is investigated for different topologies, including sequential chains, supply circles, supply ladders, and supply hierarchies. Moreover, analytical conditions for absolute and convective instabilities are derived. The empirically observed bullwhip effect in chains is explained as a form of convective instability based on resonance effects. An application of this theory to the optimization of production networks has large optimization potentials.

Using the linear noise approximation, we approach to the problem of evaluation and prediction of behavior of autonomous oscillatory genetic networks fluctuated by intrinsic noise. In this approach, the state covariance of the networks represents all the information concerning the fluctuation by intrinsic noise, and further, when the genetic network is an autonomous oscillatory system, the state covariance obeys a periodic Lyapunov differential equation that has generally unbounded solutions. Based on the analysis of stability and periodicity properties of the solution to the periodic Lyapunov differential equation, we propose two measures for evaluating intrinsic noise. Circadian clock is a typical example of autonoumous oscillatory genetic networks. Focusing on the simple core model (Gonze and Goldbeter, 2006) for circadian clocks and using the proposed measures, we evaluate robust performances concerning periodicity and amplitude of oscillations in the model fluctuated by intrinsic noise by changing system parameters.

Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering. Author Summary The prefrontal cortex (PFC) flexibly encodes task-relevant representations and outputs biases to mediate higher cognitive functions. The relevant neural ensembles undergo task-related changes in oscillatory dynamics at beta- and gamma frequencies. Using a computational model of the PFC network, we show that strong feedback inhibition causes the PFC to generate internal oscillations and to prefer external oscillations at similar frequencies. The precise frequencies that are generated and preferred can be flexibly tuned by varying the synchrony and strength of input network activity, the level of background excitation, and neuromodulation of intrinsic ion currents. We also show that the peak output frequency in response to external oscillations, which depends on the synchrony and strength of the input as well as the strong inhibitory feedback, is faster than the internally generated frequency, and that this difference enables exclusive response to oscillatory inputs. These properties enable changes in oscillatory dynamics to govern the selective processing and gating of task-relevant signals in service of cognitive control.

Motivated by the recent interests in implementing both grid-forming (GFM) and grid-following (GFL) inverters in the grid, this work studies the stability of such inverter-dominated systems by analyzing the equivalent model using networked oscillators. The equivalent oscillator models for both GFM and GFL inverters are developed, respectively, which characterize the behavior of the electric network of inverters and loads. The synchronization of the networked oscillators is studied. It is proved that such a system has a set of unique and locally stable operating states when it is synchronized. Moreover, a necessary condition for the system to reach synchronization is derived, which provides a large-signal stability assessment for the system. At last, the proposed work is validated using simulation results.

ABSTRACTThe clock in embedded systems usually is driven by a crystal oscillator and implemented via a counter register, such a crystal clock is non-identical and drifting due to the manufacturing tolerance and variation of working conditions. Thus, a common time among distributed wireless sensor nodes, also referred to as Time Synchronization, is required for many time-sensitive wireless applications, such as collaborative condition monitoring, coordinated control and localization. Inspired by fireflies’ behaviour, the Pulse-Coupled Oscillators (PCO) has been proposed for synchronization in complex networks. Since the concurrent transmission of PCO’s Pulses is impossible in Wireless Sensor Networks (WSNs), the desynchronization mechanism is adopted to ensure the implementation of PCO in WSNs. Moreover, due to the uncertainties in radio channels and the complexities of communication protocols and packet-exchange behaviours in wireless networks, it is challenging to have a closed-form solution to the performance of PCO synchronization in WSNs. The realistic software simulation, in particular, the discrete event simulator has been a powerful tool to exam the performance of communication protocols in various scenarios, since an order sequence of well-defined event in time is to represent the behaviour of a complex system. This paper presents the development of a pulse-coupled oscillators time synchronization simulator on the OMNeT++ platform for simulating and studying its behaviour and performance in sensor networks. A clock module with configurable phase and frequency noises, and adjustable and higher resolution is developed to mimic various crystal oscillators in embedded systems, for example, the real-time clock. The developed simulator also supports the full functions devices defined by ZigBee protocol, which allows realistic simulation of multi-hop IEEE 802.15.4 wireless networks. Finally, the intensive simulations of classical PCO with the refractory period in IEEE 802.15.4-based WSNs have been carried out to demonstrate the features and benefits of the developed simulator. It is shown that for the non-identical and time-varying PCO clocks in the WSNs, the achieved synchronization will lose gradually, and the time that maintained synchronization depends on the length of refractory period.

We investigate the limit sets of a network of coupled Kuramoto oscillators with a coupling matrix determined by a Hebb rule. These limit sets are the output of the network if used for the recognition of a defective binary pattern out of several given patterns, with the output pattern encoded in the oscillators' phases. We show that if all pairs of given patterns have maximum Hamming distance, there exists a degenerate attractive limit set that contains the steady states corresponding to each of the given patterns. As a result, switching between output patterns occurs for arbitrarily small modifications of the dynamics (for example, due to frequency inaccuracies). Even if the maximum Hamming distance constraint is dropped, numerical results suggest that the structural instability of the vector field persists. We conclude that the unique interchangeability of output patterns in Hebbian networks of Kuramoto oscillators, while sacrificing robustness, makes these networks more flexible than similar neural networks with separated, attractive output states.

In this work, we investigate the onset of synchronization in a network of Piecewise-Linear (PWL) oscillators. Instead of using a commutation function for each system, as usually assumed in the literature, here, we consider a common mean-field commutation function, which governs the oscillatory behavior of the whole network, where the oscillators are synchronized via diffusive coupling. Some of the advantages of the proposed approach are: a more tractable mathematical analysis of the stability of the synchronous solution and a reduction in the computational burden. We illustrate this by three examples: a network of planar systems driven by hysteresis, a network of multiscroll oscillators, and a network of PWL Rössler systems. In all cases, we provide analytic conditions that guarantee the asymptotic stability of the synchronous solution for different input–output combinations and also, we illustrate our findings by numerical simulations. Additionally, the effect of initial conditions on the boundedness of solutions in the network is numerically investigated. An interesting characteristic of the proposed mean-field commutation function approach is that the nodes in the network act as oscillators only if the whole network is synchronized; otherwise, the nodes behave as unstable systems. Thus, the proposed scheme rewards the cooperative motion but penalizes the divergent individual behavior.

Hyperchaotic multiscroll dynamics, complex behavior in a simple homogeneous dynamical network of jerk oscillators: bidirectional coupling scheme method, dynamical study, analog circuit and microcontroller-based implementation

The transcription factor p53 is the core of the cellular stress network, which controls cell fate decisions on genotoxic stress in a dynamics response manner. Mdm2 is an E3 ubiquitin ligase, which play a dual role in p53 regulation, that is, on the one hand, Mdm2 destroys the stability of p53 via ubiquitin labeling, and on the other hand, Mdm2 increase the efficiency of p53 production through binding p53 messenger RNA. A number of models indicate that Mdm2's inhibitory function on p53 plays a constructive role in the p53-Mdm2 vibrator, the research of how Mdm2's promotion function on p53 regulates the dynamics of this gene network, however, is still lacking. To this end, this paper uses a mathematical model to comprehensively explore the influence of the Mdm2 up-regulation p53 pathway on p53 dynamics. We adopt the ordinary differential equations (ODE) model and the bifurcation analysis method to investigate the multiple role of Mdm2 on p53 gene networks dynamics control. The results show that the phosphorylation of Mdm2 at Ser395, which forming a positive feedback loop (PFL) with p53, is essential for the oscillation of this gene network and may be the reason why there is a bimodal switch of p53 kinetics under etoposide stimulation; the previously reported phosphatase Wip1 is required for the oscillation of p53, which may only occur in situations where the intensity of the PFL mediated by phosphorylated Mdm2 is high, and we predict that Wip1 will inhibit the p53 oscillation in some weak PFL cases; Finally, our model also proves that Mdm2 promotes the deactivation and ubiquitination degradation of p53 is a key factor in the occurrence of repeated vibration dynamics of p53. The main conclusions of this paper are exhibited in some two-dimensional bifurcation diagrams. In order to confirm these bifurcation phenomena, we discuss the case where the Hill coefficient describing the degree of nonlinearity is small. As a result, there is no obvious shape change of the bifurcation curves surrounding the oscillation region. The robustness of these conclusions is verified again. We believe that our results can play a guiding role in the future related experiments of p53 kinetics.

This paper studies the application of neural networks in frequency bin detection. The structure of the neural network, the initial condition of weights, and the creation of the training patterns for this specific application determine the dimension and the convergence behavior of the neural network. After being trained, the neural network can detect the presence of multiple tones from time sampled data, which may contain amplitude errors, phase errors, and additive noise. Remedies for errors are proposed via modifying weights or increasing the dimension of the neural network. Simulation results are given to support the analysis.

Spin torque nanodevices are promising candidates to provide a computational platform beyond Moore's law. The network of spin oscillators can have only local, cellular interconnections because of the underlying physics: the interaction between the oscillators is implemented by spin waves through the magnetic field and the computation is done by the synchronization of the oscillators in an array. In this paper we summarize the dynamics of weakly coupled spin-torque oscillator networks and we also show how functionality can be designed for one dimensional cellular spin-torque oscillator networks and how the connection strength will determine the output. spin torque oscillators, synchronization, weakly coupled oscillators, cellular array, cellular nanoscale network.

A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism and economic networks. It consists in a directed graph G, each node (or cell) representing an agent of the network and each directed arrow representing which agent acts on which. It yields a system of differential equations , where the component i of f depends only on the cells xj(t) for which the arrow j → i exists in G. In this paper, we investigate the observation problems in coupled cell networks: can one deduce the behaviour of the whole network (oscillations, stabilization, etc) by observing only one of the cells? We show that the natural observation properties hold for almost all the interactions f.