Newman Watts Research Articles

Performance of small-world feedforward neural networks for the diagnosis of diabetes

We investigate the performance of two different small-world feedforward neural networks for the diagnosis of diabetes. We use the Pima Indians Diabetic Dataset as input. We have previously shown than the Watts–Strogatz small-world feedforward neural network delivers a better classification performance than conventional feedforward neural networks. Here, we compare this performance further with the one delivered by the Newman–Watts small-world feedforward neural network, and we show that the latter is better still. Moreover, we show that Newman–Watts small-world feedforward neural networks yield the highest output correlation as well as the best output error parameters.

Effect of Spike-Timing-Dependent Plasticity on Intrinsic Coherence Resonance in Newman–Watts Stochastic Hodgkin–Huxley Neuronal Networks

In this paper, we numerically study the effect of spike-timing-dependent plasticity (STDP) on coherence resonance (CR) induced by channel noise in adaptive Newman–Watts stochastic Hodgkin–Huxley neuron networks. It is found that STDP can either enhance or suppress the intrinsic CR when the adjusting rate of STDP decreases or increases. STDP can alter the effects of network randomness and network size on the intrinsic CR. Under STDP, for electrical coupling there are optimal network randomness and network size by which the intrinsic CR becomes strongest, however, for chemical coupling the intrinsic CR is always enhanced as network randomness or network size increases, which are different from the results for fixed coupling. These results show that the intrinsic CR of the neuronal networks can be either enhanced or suppressed by STDP, and there are optimal network randomness and network size by which the intrinsic CR becomes strongest. These findings could provide a new insight into the role of STDP for the information processing and transmission in neural systems.

Spike-timing-dependent plasticity enhanced synchronization transitions induced by autapses in adaptive Newman-Watts neuronal networks

In this paper, we numerically study the effect of spike-timing-dependent plasticity (STDP) on synchronization transitions induced by autaptic activity in adaptive Newman–Watts Hodgkin–Huxley neuron networks. It is found that synchronization transitions induced by autaptic delay vary with the adjusting rate Ap of STDP and become strongest at a certain Ap value, and the Ap value increases when network randomness or network size increases. It is also found that the synchronization transitions induced by autaptic delay become strongest at a certain network randomness and network size, and the values increase and related synchronization transitions are enhanced when Ap increases. These results show that there is optimal STDP that can enhance the synchronization transitions induced by autaptic delay in the adaptive neuronal networks. These findings provide a new insight into the roles of STDP and autapses for the information transmission in neural systems.

Optimal autaptic and synaptic delays enhanced synchronization transitions induced by each other in Newman–Watts neuronal networks

In this paper, we numerically study the effect of electrical autaptic and synaptic delays on synchronization transitions induced by each other in Newman–Watts Hodgkin–Huxley neuronal networks. It is found that the synchronization transitions induced by synaptic delay vary with varying autaptic delay and become strongest when autaptic delay is optimal. Similarly, the synchronization transitions induced by autaptic delay vary with varying synaptic delay and become strongest at optimal synaptic delay. Also, there is optimal coupling strength by which the synchronization transitions induced by either synaptic or autaptic delay become strongest. These results show that electrical autaptic and synaptic delays can enhance synchronization transitions induced by each other in the neuronal networks. This implies that electrical autaptic and synaptic delays can cooperate with each other and more efficiently regulate the synchrony state of the neuronal networks. These findings could find potential implications for the information transmission in neural systems.

Effect of Autaptic Activity on Intrinsic Coherence Resonance in Newman–Watts Networks of Stochastic Hodgkin–Huxley Neurons

In this paper, we study the effect of autaptic activity on intrinsic coherence resonance (CR) induced by channel noise in Newman–Watts (NW) networks of stochastic Hodgkin–Huxley (HH) neurons. It is found that autaptic strength and autaptic delay have a big effect on the intrinsic CR. As autaptic strength increases, there is optimal autaptic strength by which the intrinsic CR is most highly enhanced. Autaptic delay can enhance, reduce, or destroy the intrinsic CR, depending on the delay length. Moreover, there are optimal coupling strength and network randomness by which autaptic activity can most highly enhance the intrinsic CR. These results show that autaptic activity has different effects on the intrinsic CR in the neuronal networks, and it can most highly enhance the intrinsic CR at optimal coupling strength and network randomness. These findings could find potential implications of channel noise and autaptic activity for the information processing and transmission in neural systems.

Quantification of degeneracy in Hodgkin–Huxley neurons on Newman–Watts small world network

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin–Huxley neuronal networks with Newman–Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus – and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity – and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.

The circadian rhythm induced by the heterogeneous network structure of the suprachiasmatic nucleus.

In mammals, the master clock is located in the suprachiasmatic nucleus (SCN), which is composed of about 20 000 nonidentical neuronal oscillators expressing different intrinsic periods. These neurons are coupled through neurotransmitters to form a network consisting of two subgroups, i.e., a ventrolateral (VL) subgroup and a dorsomedial (DM) subgroup. The VL contains about 25% SCN neurons that receive photic input from the retina, and the DM comprises the remaining 75% SCN neurons which are coupled to the VL. The synapses from the VL to the DM are evidently denser than that from the DM to the VL, in which the VL dominates the DM. Therefore, the SCN is a heterogeneous network where the neurons of the VL are linked with a large number of SCN neurons. In the present study, we mimicked the SCN network based on Goodwin model considering four types of networks including an all-to-all network, a Newman-Watts (NW) small world network, an Erdös-Rényi (ER) random network, and a Barabási-Albert (BA) scale free network. We found that the circadian rhythm was induced in the BA, ER, and NW networks, while the circadian rhythm was absent in the all-to-all network with weak cellular coupling, where the amplitude of the circadian rhythm is largest in the BA network which is most heterogeneous in the network structure. Our finding provides an alternative explanation for the induction or enhancement of circadian rhythm by the heterogeneity of the network structure.

Multiple coherence resonance and synchronization transitions induced by autaptic delay in Newman–Watts neuron networks

In this paper, we study the effect of delayed autaptic self-feedback activity on the spiking temporal coherence and spatial synchronization of Newman–Watts networks of stochastic Hodgkin–Huxley neurons. As autaptic delay is varied, the spiking behaviors of the neurons intermittently become synchronous and non-synchronous, and meanwhile they are ordered and disordered, exhibiting both synchronization transitions (ST) and multiple coherence resonance (MCR). Moreover, the autaptic delays for CR and synchronization are close. When coupling strength or network randomness increases, or when channel noise intensity decreases, MCR is enhanced, but ST becomes strongest at optimal coupling strength, network randomness, or channel noise intensity. These results show that autaptic activity can induce both MCR and ST in the neuronal networks. This implies that autaptic activity can simultaneously enhance or reduce the temporal coherence and synchronization of the neuronal network. These findings could find potential implications for the information processing and transmission in neural systems.

First Passage Percolation on the Newman–Watts Small World Model

The Newman-Watts model is given by taking a cycle graph of n vertices and then adding each possible edge $(i,j), |i-j|\neq 1 \mod n$ with probability $\rho/n$ for some $\rho>0$ constant. In this paper we add i.i.d. exponential edge weights to this graph, and investigate typical distances in the corresponding random metric space given by the least weight paths between vertices. We show that typical distances grow as $\frac1\lambda \log n$ for a $\lambda>0$ and determine the distribution of smaller order terms in terms of limits of branching process random variables. We prove that the number of edges along the shortest weight path follows a Central Limit Theorem, and show that in a corresponding epidemic spread model the fraction of infected vertices follows a deterministic curve with a random shift.

Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks

We study the effects of an autapse, which is mathematically described as a self-feedback loop, on the propagation of weak, localized pacemaker activity across a Newman–Watts small-world network consisting of stochastic Hodgkin–Huxley neurons. We consider that only the pacemaker neuron, which is stimulated by a subthreshold periodic signal, has an electrical autapse that is characterized by a coupling strength and a delay time. We focus on the impact of the coupling strength, the network structure, the properties of the weak periodic stimulus, and the properties of the autapse on the transmission of localized pacemaker activity. Obtained results indicate the existence of optimal channel noise intensity for the propagation of the localized rhythm. Under optimal conditions, the autapse can significantly improve the propagation of pacemaker activity, but only for a specific range of the autaptic coupling strength. Moreover, the autaptic delay time has to be equal to the intrinsic oscillation period of the Hodgkin–Huxley neuron or its integer multiples. We analyze the inter-spike interval histogram and show that the autapse enhances or suppresses the propagation of the localized rhythm by increasing or decreasing the phase locking between the spiking of the pacemaker neuron and the weak periodic signal. In particular, when the autaptic delay time is equal to the intrinsic period of oscillations an optimal phase locking takes place, resulting in a dominant time scale of the spiking activity. We also investigate the effects of the network structure and the coupling strength on the propagation of pacemaker activity. We find that there exist an optimal coupling strength and an optimal network structure that together warrant an optimal propagation of the localized rhythm.

Synchronization transitions induced by the fluctuation of adaptive coupling strength in delayed Newman–Watts neuronal networks

Introducing adaptive coupling in delayed neuronal networks and regulating the dissipative parameter (DP) of adaptive coupling by noise, we study the effect of fluctuations of the changing rate of adaptive coupling on the synchronization of the neuronal networks. It is found that time delay can induce synchronization transitions for intermediate DP values, and the synchronization transitions become strongest when DP is optimal. As the intensity of DP noise is varied, the neurons can also exhibit synchronization transitions, and the phenomenon is delay-dependent and is enhanced for certain time delays. Moreover, the synchronization transitions change with the change of DP and become strongest when DP is optimal. These results show that randomly changing adaptive coupling can considerably change the synchronization of the neuronal networks, and hence could play a crucial role in the information processing and transmission in neural systems.

Adaptive stochastic resonance in self-organized small-world neuronal networks with time delay

In this paper, adaptive stochastic resonance in time-delayed Newman–Watts small-world neuronal networks is studied, where the strength of synaptic connections between neurons is adaptively modulated by spike-timing-dependent plasticity (STDP). Numerical results show that, in the absence of information transmission delay, the phenomenon of stochastic resonance occurs and the efficiency of networked stochastic resonance can be slightly depressed by STDP. Due to the reduction of strong couplings induced by STDP, for a larger adjusting rate of STDP, a smaller peak value of the resonance response is obtained. In addition, the effect of stochastic resonance can be either promoted or destroyed by time delay, and multiple stochastic resonances appear intermittently at the integer multiples of periods of the subthreshold forcing. Furthermore, it is demonstrated that the networked stochastic resonance can also be dramatically affected by the small-world topology. For small and moderate adjusting rate of STDP, fine-tuning of the probability of adding links can significantly enhance the effect of stochastic resonance in adaptive neural network. Additionally, there is an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks and the location of this span depends largely on the time delay and adjusting rate.

Vibrational resonance in adaptive small-world neuronal networks with spike-timing-dependent plasticity

The phenomenon of vibrational resonance is investigated in adaptive Newman–Watts small-world neuronal networks, where the strength of synaptic connections between neurons is modulated based on spike-timing-dependent plasticity. Numerical results demonstrate that there exists appropriate amplitude of high-frequency driving which is able to optimize the neural ensemble response to the weak low-frequency periodic signal. The effect of networked vibrational resonance can be significantly affected by spike-timing-dependent plasticity. It is shown that spike-timing-dependent plasticity with dominant depression can always improve the efficiency of vibrational resonance, and a small adjusting rate can promote the transmission of weak external signal in small-world neuronal networks. In addition, the network topology plays an important role in the vibrational resonance in spike-timing-dependent plasticity-induced neural systems, where the system response to the subthreshold signal is maximized by an optimal network structure. Furthermore, it is demonstrated that the introduction of inhibitory synapses can considerably weaken the phenomenon of vibrational resonance in the hybrid small-world neuronal networks with spike-timing-dependent plasticity.

Effects of channel noise on synchronization transitions in Newman–Watts neuronal network with time delays

In this paper, we numerically study the effect of ion channel noise on the synchronization of delayed Newman–Watts network of stochastic Hodgkin–Huxley neurons. It is found that time delay can induce synchronization transitions only when channel noise intensity is intermediate, and the synchronization transitions become most obvious when channel noise intensity is optimal. As channel noise intensity is varied, the neurons can also exhibit synchronization transitions, and the phenomenon is enhanced when time delay is tuned at around time delays that can induce synchronization transitions. Moreover, this phenomenon becomes most obvious when the value of coupling strength or the value of network randomness is optimal. These results show that channel noise has a subtle regulation effect on the synchronization of the neuronal network. These findings may find potential implications for the normal and pathological functions in the brain and the information processing and transmission in neural systems.

Autaptic activity-induced synchronization transitions in Newman-Watts network of Hodgkin-Huxley neurons.

In this paper, we numerically study the effect of autapse on the synchronization of Newman-Watts small-world Hodgkin-Huxley neuron network. It is found that the neurons exhibit synchronization transitions as autaptic self-feedback delay is varied, and the phenomenon becomes strongest when autaptic self-feedback strength is optimal. This phenomenon also changes with the change of coupling strength and network randomness and become strongest when they are optimal. There are similar synchronization transitions for electrical and chemical autapse, but the synchronization transitions for chemical autapse occur more frequently and are stronger than those for electrical synapse. The underlying mechanisms are briefly discussed in quality. These results show that autaptic activity plays a subtle role in the synchronization of the neuronal network. These findings may find potential implications of autapse for the information processing and transmission in neural systems.

Effect of small-world topology on wave propagation on networks of excitable elements

We study excitation waves on a Newman–Watts small-world network model of coupled excitable elements. Depending on the global coupling strength, we find differing resilience to the added long-range links and different mechanisms of propagation failure. For high coupling strengths, we show agreement between the network and a reaction-diffusion model with additional mean-field term. Employing this approximation, we are able to estimate the critical density of long-range links for propagation failure.

Optimization of Intrinsic Stochastic Resonance in Adaptive Newman–Watts Network of Channel Blocked Hodgkin–Huxley Neurons

In this paper, we study stochastic resonance (SR) induced by channel noise in adaptive weighted Newman–Watts networks of Hodgkin–Huxley neurons with channel blocking (CB). It is found that the intrinsic SR is dependent on adaptive coupling and is strongly enhanced when the changing rate of adaptive coupling is optimal, and this phenomenon is independent of sodium and potassium CB levels. As CB increases, the channel noise for SR decreases, but the strength of intrinsic SR nearly does not change in the presence of adaptive coupling, which is different from the case for fixed coupling. These results show that intrinsic SR can be enhanced and optimized by adaptive coupling, and CB's effect on the intrinsic SR can be reduced by adaptive coupling. This implies that adaptive coupling could more efficiently improve the time precision of information processing in neural systems.

Spike coherence and synchronization on Newman–Watts small-world neuronal networks modulated by spike-timing-dependent plasticity

The effects of spike-timing-dependent plasticity (STDP) and noise intensity on the temporal and spatial dynamics of Newman–Watts small-world neuronal networks are studied. Numerical results show that, an intermediate intensity of additive noise can optimize the dynamical response of the neural system, where the noise-induced coherence resonance and spiking synchronization occur. The adaptive coupling modulated by STDP can largely depress the temporal coherence and spatial synchrony induced by external noise and random shortcuts. In particular, as the adjusting rate increases, lower noise intensity is needed to maximize the networked synchronization, and more connections are introduced to achieve coherence resonance. Moreover, the small-world topology can significantly affect the dynamics of excitable neuronal networks. It is found that the temporal coherence of neuronal activity reaches peaks for an appropriate number of random shortcuts, while the spiking synchronization is always enhanced as more shortcuts are added into the network.

A generalized volume dimension of complex networks

The fractal and self-similarity properties are investigated in many real complex networks. The volume dimension method is an effective tool to measure the fractal property of complex networks. In this paper, a new volume dimension measure is proposed based on the node degree of complex networks. We apply the proposed method to calculate the fractal dimension of some real networks and Newman–Watts (NW) small-world. The results show that the proposed method is effective when dealing with the fractal dimension problem of complex networks. In addition, we find that the fractal dimension is mainly influenced by the probability of ‘adding edges’ and the average length of the small-world network.

Modeling and adaptive pinning synchronization control for a chaotic-motion motor in complex network

We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification. • The chaotic motor complex dynamic networks are constructed. • The sufficient conditions for the adaptive pinning synchronization are derived. • The suitable adaptive feedback controllers are designed. • Nodes selective algorithm is discussed.