Quantum-like model of processing of information in the brain based on classical electromagnetic field

We propose a model of quantum-like (QL) processing of mental information. This model is based on quantum information theory. However, in contrast to models of "quantum physical brain" reducing mental activity (at least at the highest level) to quantum physical phenomena in the brain, our model matches well with the basic neuronal paradigm of the cognitive science. QL information processing is based (surprisingly) on classical electromagnetic signals induced by joint activity of neurons. This novel approach to quantum information is based on representation of quantum mechanics as a version of classical signal theory which was recently elaborated by the author. The brain uses the QL representation (QLR) for working with abstract concepts; concrete images are described by classical information theory. Two processes, classical and QL, are performed parallely. Moreover, information is actively transmitted from one representation to another. A QL concept given in our model by a density operator can generate a variety of concrete images given by temporal realizations of the corresponding (Gaussian) random signal. This signal has the covariance operator coinciding with the density operator encoding the abstract concept under consideration. The presence of various temporal scales in the brain plays the crucial role in creation of QLR in the brain. Moreover, in our model electromagnetic noise produced by neurons is a source of superstrong QL correlations between processes in different spatial domains in the brain; the binding problem is solved on the QL level, but with the aid of the classical background fluctuations.     

Phase resetting and coupling of noisy neural oscillators

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations. B. Ermentrout supported in part by NIMH and NSF. Action Editor: Wulfram Gerstner     

Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli

The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and anti-phase states even though the anti-phase state is the only stable state in the absence of noise. We study the Fokker-Planck equation of the system and perform an asymptotic reduction ρ ₀. The ρ ₀ solution is more computationally efficient than both the Monte Carlo simulations and the 2D Fokker-Planck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, ρ ₀ is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled Morris-Lecar system.

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Control of continuous fed-batch fermentation process using neural network based model predictive controller

Cell growth and metabolite production greatly depend on the feeding of the nutrients in fed-batch fermentations. A strategy for controlling the glucose feed rate in fed-batch baker’s yeast fermentation and a novel controller was studied. The difference between the specific carbon dioxide evolution rate and oxygen uptake rate (Q _c − Q _o) was used as controller variable. The controller evaluated was neural network based model predictive controller and optimizer. The performance of the controller was evaluated by the set point tracking. Results showed good performance of the controller.     

A neural circuit model of emotional learning using two pathways with different granularity and speed of information processing

We propose a neural circuit model of emotional learning using two pathways with different granularity and speed of information processing. In order to derive a precise time process, we utilized a spiking model neuron proposed by Izhikevich and spike-timing-dependent synaptic plasticity (STDP) of both excitatory and inhibitory synapses. We conducted computer simulations to evaluate the proposed model. We demonstrate some aspects of emotional learning from the perspective of the time process. The agreement of the results with the previous behavioral experiments suggests that the structure and learning process of the proposed model are appropriate.     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

A neural network model of attention-modulated neurodynamics

Visual attention appears to modulate cortical neurodynamics and synchronization through various cholinergic mechanisms. In order to study these mechanisms, we have developed a neural network model of visual cortex area V4, based on psychophysical, anatomical and physiological data. With this model, we want to link selective visual information processing to neural circuits within V4, bottom-up sensory input pathways, top-down attention input pathways, and to cholinergic modulation from the prefrontal lobe. We investigate cellular and network mechanisms underlying some recent analytical results from visual attention experimental data. Our model can reproduce the experimental findings that attention to a stimulus causes increased gamma-frequency synchronization in the superficial layers. Computer simulations and STA power analysis also demonstrate different effects of the different cholinergic attention modulation action mechanisms.     

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in two-dimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.     

UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model

A novel closed loop control framework is proposed to inhibit epileptiform wave in a neural mass model by external electric field, where the unscented Kalman filter method is used to reconstruct dynamics and estimate unmeasurable parameters of the model. Specifically speaking, the iterative learning control algorithm is introduced into the framework to optimize the control signal. In the proposed method, the control effect can be significantly improved based on the observation of the past attempts. Accordingly, the proposed method can effectively suppress the epileptiform wave as well as showing robustness to noises and uncertainties. Lastly, the simulation is carried out to illustrate the feasibility of the proposed method. Besides, this work shows potential value to design model-based feedback controllers for epilepsy treatment.     

Estimation of vertical ground reaction force during running using neural network model and uniaxial accelerometer

Wearable technology has been viewed as one of the plausible alternatives to capture human motion in an unconstrained environment, especially during running. However, existing methods require kinematic and kinetic measurements of human body segments and can be complicated. This paper investigates the use of neural network model (NN) and accelerometer to estimate vertical ground reaction force (VGRF). An experimental study was conducted to collect sufficient samples for training, validation and testing. The estimated results were compared with VGRF measured using an instrumented treadmill. The estimates yielded an average root mean square error of less than 0.017 of the body weight (BW) and a cross-correlation coefficient greater than 0.99. The results also demonstrated that NN could estimate impact force and active force with average errors ranging between 0.10 and 0.18 of BW at different running speeds. Using NN and uniaxial accelerometer can (1) simplify the estimation of VGRF, (2) reduce the computational requirement and (3) reduce the necessity of multiple wearable sensors to obtain relevant parameters.     

Phase response and entrainment: Model computations on their relation using Wever's oscillator model

Abstract

Enright's theory, which explains entrainment as periodically repeated phase response, is applied to Wever's self‐sustained oscillation model of are circadian rhythm and tested by computer simulation. Ranges of phase response and entrainment are compared and the oscillatory behaviour is shown in the phase diagram for the cases of phase response and entrainment. It is shown that Enright's theory is not valid for self‐sustained oscillations in general, but it need not necessarily fail in case of the biological circadian rhythm.     

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.     

A neural circuit model for changing the amount of information maintained in short-term memory depending on stimuli relationships

We propose a neural circuit model of changes in amount of information maintained in short-term memory depending on stimuli relationships. The relationships between stimuli are represented by the synchronous firings of overlapping neuronal groups for semantically related stimuli and the excitatory mutual connections for semantically unrelated but simultaneously presented stimuli. We conduct computer simulations to confirm our proposed neural circuit model. The resultant numbers of stored informational input patterns are almost consistent with the maximum numbers in the psychological experiments for both semantically related and unrelated stimuli. This agreement with the psychological experiments suggests that the structure and informational representation of the proposed model are appropriate.     

Active muscle response using feedback control of a finite element human arm model

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.     

利用随机效应模型模拟东北三省胡桃楸地位指数

通过精确模拟东北三省胡桃楸多形地位指数混合效应模型,为胡桃楸立地质量评价提供科学依据,本研究在辽宁、吉林和黑龙江三省23个典型区域内,采用样圆法布设样地197块,测定样地内胡桃楸树高-年龄数据,共得到数据1537组,同时将立地因子进行划分和赋值,应用方差分析和模型拟合进行计算。结果表明: 坡位是影响胡桃楸优势木生长最显著的因素,其次为土壤深度、坡度和坡向等;对8种常见基础模型进行拟合与分析,发现逻辑斯蒂模型H=a/[1+exp(b+cA)]为最优基础模型(R²=0.70),平均绝对误差(MAE)为2.52;对4种主要影响因素进行随机组合,得到随机组合因素最优地位指数模型M_8.15,其R²=0.90,提高了基础模型的拟合精度;采用K均值聚类分组法进一步将初始的立地类型划分为6个立地类型组,按6个立地类型组建立的非线性混合效应模型M_final,即H=(20.1837+u_i)/[1+exp (1.7352-0.0961A)]+ε_ij,其R²=0.92,AIC=912.65,模型的拟合度和精确度显著提高,可以用于东北三省复杂立地类型下胡桃楸立地质量的准确评价。