Controlling Chaotic Resonance using External Feedback Signals in Neural Systems

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

An adaptive approach to machine learning for compact particle accelerators

Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

An Approach for Stabilizing Abnormal Neural Activity in ADHD Using Chaotic Resonance

Reduced integrity of neural pathways from frontal to sensory cortices has been suggested as a potential neurobiological basis of attention-deficit hyperactivity disorder. Neurofeedback has been widely applied to enhance reduced neural pathways in attention-deficit hyperactivity disorder by repeated training on a daily temporal scale. Clinical and model-based studies have demonstrated that fluctuations in neural activity underpin sustained attention deficits in attention-deficit hyperactivity disorder. These aberrant neural fluctuations may be caused by the chaos–chaos intermittency state in frontal-sensory neural systems. Therefore, shifting the neural state from an aberrant chaos–chaos intermittency state to a normal stable state with an optimal external sensory stimulus, termed chaotic resonance, may be applied in neurofeedback for attention-deficit hyperactivity disorder. In this study, we applied a neurofeedback method based on chaotic resonance induced by “reduced region of orbit” feedback signals in the Baghdadi model for attention-deficit hyperactivity disorder. We evaluated the stabilizing effect of reduced region of orbit feedback and its robustness against noise from errors in estimation of neural activity. The effect of chaotic resonance successfully shifted the abnormal chaos-chaos intermittency of neural activity to the intended stable activity. Additionally, evaluation of the influence of noise due to measurement errors revealed that the efficiency of chaotic resonance induced by reduced region of orbit feedback signals was maintained over a range of certain noise strengths. In conclusion, applying chaotic resonance induced by reduced region of orbit feedback signals to neurofeedback methods may provide a promising treatment option for attention-deficit hyperactivity disorder.

Transition of Neural Activity From the Chaotic Bipolar-Disorder State to the Periodic Healthy State Using External Feedback Signals

Chronotherapy is a treatment for mood disorders, including major depressive disorder, mania, and bipolar disorder (BD). Neurotransmitters associated with the pathology of mood disorders exhibit circadian rhythms. A functional deficit in the neural circuits related to mood disorders disturbs the circadian rhythm; chronotherapy is an intervention that helps resynchronize the patient's biological clock with the periodic daily cycle, leading to amelioration of symptoms. In previous reports, Hadaeghi et al. proposed a non-linear dynamic model composed of the frontal and sensory cortical neural networks and the hypothalamus to explain the relationship between deficits in neural function in the frontal cortex and the disturbed circadian rhythm/mood transitions in BD (hereinafter referred to as the Hadaeghi model). In this model, neural activity in the frontal and sensory lobes exhibits periodic behavior in the healthy state; while in BD, this neural activity is in a state of chaos-chaos intermittency; this temporal departure from the healthy periodic state disturbs the circadian pacemaker in the hypothalamus. In this study, we propose an intervention based on a feedback method called the “reduced region of orbit” (RRO) method to facilitate the transition of the disturbed frontal cortical neural activity underlying BD to healthy periodic activity. Our simulation was based on the Hadaeghi model. We used an RRO feedback signal based on the return-map structure of the simulated frontal and sensory lobes to induce synchronization with a relatively weak periodic signal corresponding to the healthy condition by applying feedback of appropriate strength. The RRO feedback signal induces chaotic resonance, which facilitates the transition to healthy, periodic frontal neural activity, although this synchronization is restricted to a relatively low frequency of the periodic input signal. Additionally, applying an appropriate strength of the RRO feedback signal lowered the amplitude of the periodic input signal required to induce a synchronous state compared with the periodic signal applied alone. In conclusion, through a chaotic-resonance effect induced by the RRO feedback method, the state of the disturbed frontal neural activity characteristic of BD was transformed into a state close to healthy periodic activity by relatively weak periodic perturbations. Thus, RRO feedback-modulated chronotherapy might be an innovative new type of minimally invasive chronotherapy.

Resonance phenomena controlled by external feedback signals and additive noise in neural systems

Chaotic resonance is a phenomenon that can replace the fluctuation source in stochastic resonance from additive noise to chaos. We previously developed a method to control the chaotic state for suitably generating chaotic resonance by external feedback even when the external adjustment of chaos is difficult, establishing a method named reduced region of orbit (RRO) feedback. However, a feedback signal was utilized only for dividing the merged attractor. In addition, the signal sensitivity in chaotic resonance induced by feedback signals and that of stochastic resonance by additive noise have not been compared. To merge the separated attractor, we propose a negative strength of the RRO feedback signal in a discrete neural system which is composed of excitatory and inhibitory neurons. We evaluate the features of chaotic resonance and compare it to stochastic resonance. The RRO feedback signal with negative strength can merge the separated attractor and induce chaotic resonance. We also confirm that additive noise induces stochastic resonance through attractor merging. The comparison of these resonance modalities verifies that chaotic resonance provides more applicability than stochastic resonance given its capability to handle attractor separation and merging.