Theoretical models and computer simulations of neural learning systems

It has been generally assumed for a long time that learning is accomplished in the central nervous system (CNS) by modifying strengths of ties between neurons. Various mechanisms may contribute to this process, but it is not known which are the specific mechanisms, and what are the rules by which they operate. Theoretical models, which are based on that general assumption are introduced. The purpose of the models is to suggest plausible ways by which learned information may be stored in the neural network, and be retrieved when it is needed. The networks in the models consist of four basic subunits, in accordance with identified units in the CNS: sensing, response, feeling, and control, plus association areas. The suggested operation rules are based on established operation rules of individual neurons, and assumed rules when neurons in groups are considered. Computer simulations are done, to check the consistency of the models, and to illustrate how they work. They simulate how an hypothetical kitten learns part of its environment, and show how relevant information may be stored and retrieved in its neuronal network. The suggested mechanisms could be examined in experiments, albeit not easy ones to conduct.     

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.     

Eye tracking using artificial neural networks for human computer interaction

This paper describes an ongoing project that has the aim to develop a low cost application to replace a computer mouse for people with physical impairment. The application is based on an eye tracking algorithm and assumes that the camera and the head position are fixed. Color tracking and template matching methods are used for pupil detection. Calibration is provided by neural networks as well as by parametric interpolation methods. Neural networks use back-propagation for learning and bipolar sigmoid function is chosen as the activation function. The user's eye is scanned with a simple web camera with backlight compensation which is attached to a head fixation device. Neural networks significantly outperform parametric interpolation techniques: 1) the calibration procedure is faster as they require less calibration marks and 2) cursor control is more precise. The system in its current stage of development is able to distinguish regions at least on the level of desktop icons. The main limitation of the proposed method is the lack of head-pose invariance and its relative sensitivity to illumination (especially to incidental pupil reflections).     

Mathematical model for the self-organization of neural networks

Mutual inhibition between neurons combined with a learning principle similar to that proposed by Hebb is shown to secure a powerful selforganizing property for neural networks. Numerical analysis reveals that the system investigated always organizes itself into the same final state from any arbitrarily chosen initial state.     

Functional model of biological neural networks

A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.     

An efficient model development strategy for bioprocesses based on neural networks in macroscopic balances

In the serial gray box modeling strategy, generally available knowledge, represented in the macroscopic balance, is combined naturally with neural networks, which are powerful and convenient tools to model the inaccurately known terms in the macroscopic balance. This article shows, for a typical biochemical conversion, that in the serial gray box modeling strategy the identification data only have to cover the input-output space of the inaccurately known term in the macroscopic balances and that the accurately known terms can be used to achieve reliable extrapolation. The strategy is demonstrated successfully on the modeling of the enzymatic (repeated) batch conversion of penicillin G, for which real-time results are presented. Compared with a more data-driven black box strategy, the serial gray box strategy leads to models with reliable extrapolation properties, so that with the same number of identification experiments the model can be applied to a much wider range of different conditions. Compared to a more knowledge-driven white box strategy, the serial gray box model structure is only based on readily available or easily obtainable knowledge, so that the development time of serial gray box models still may be short in a situation where there is no detailed knowledge of the system available. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 549-566, 1997.     

Multicellular model for intercellular synchronization in circadian neural networks

We developed a multicellular model characterized by a high degree of heterogeneity to investigate possible mechanisms that underlie circadian network synchronization and rhythmicity in the suprachiasmatic nucleus (SCN). We populated a two-dimensional grid with 400 model neurons coupled via γ-aminobutyric acid (GABA) and vasoactive intestinal polypeptide (VIP) neurotransmitters through a putative Ca²⁺ mediated signaling cascade to investigate their roles in gene expression and electrical firing activity of cell populations. As observed experimentally, our model predicted that GABA would affect the amplitude of circadian oscillations but not synchrony among individual oscillators. Our model recapitulated experimental findings of decreased synchrony and average periods, loss of rhythmicity, and reduced circadian amplitudes as VIP signaling was eliminated. In addition, simulated increases of VIP reduced periodicity and synchrony. We therefore postulated a physiological range of VIP within which the system is able to produce sustained and synchronized oscillations. Our model recapitulated experimental findings of diminished amplitudes and periodicity with decreasing intracellular Ca²⁺ concentrations, suggesting that such behavior could be due to simultaneous decrease of individual oscillation amplitudes and population synchrony. Simulated increases in Cl⁻ levels resulted in increased Cl⁻ influx into the cytosol, a decrease of inhibitory postsynaptic currents, and ultimately a shift of GABA-elicited responses from inhibitory to excitatory. The simultaneous reduction of IPSCs and increase in membrane resting potential produced GABA dose-dependent increases in firing rates across the population, as has been observed experimentally. By integrating circadian gene regulation and electrophysiology with intracellular and intercellular signaling, we were able to develop the first (to our knowledge) multicellular model that allows the effects of clock genes, electrical firing, Ca²⁺, GABA, and VIP on circadian system behavior to be predicted.     

Bioprocess model building using artificial neural networks

Artificial neural networks are made upon of highly interconnected layers of simple neuron-like nodes. The neurons act as non-linear processing elements within the network. An attractive property of artificial neural networks is that given the appropriate network topology, they are capable of learning and characterising non-linear functional relationships. Furthermore, the structure of the resulting neural network based process model may be considered generic, in the sense that little prior process knowledge is required in its determination. The methodology therefore provides a cost efficient and reliable process modelling technique. One area where such a technique could be useful is biotechnological systems. Here, for example, the use of a process model within an estimation scheme has long been considered an effective means of overcoming inherent on-line measurement problems. However, the development of an accurate process model is extremely time consuming and often results in a model of limited applicability. Artificial neural networks could therefore prove to be a useful model building tool when striving to improve bioprocess operability. Two large scale industrial fermentation systems have been considered as test cases; a fed-batch penicillin fermentation and a continuous mycelial fermentation. Both systems serve to demonstrate the utility, flexibility and potential of the artificial neural network approach to process modelling.     

Sequential configuration model for firing patterns in local neural networks

This paper presents a sequential configuration model to represent the coordinated firing patterns of memory traces in groups of neurons in local networks. Computer simulations are used to study the dynamic properties of memory traces selectively retrieved from networks in which multiple memory traces have been embedded according to the sequential configuration model. Distinct memory traces which utilize the same neurons, but differ only in temporal sequencing are selectively retrievable. Firing patterns of constituent neurons of retrieved memory traces exhibit the main properties of neurons observed in multi microelectrode recordings. The paper shows how to adjust relative synaptic weightings so as to control the disruptive influences of cross-talk in multipy-embedded networks. The theoretical distinction between (primarily anatomical) beds and (primarily physiological) realizations underlines the fundamentally stochastic nature of network firing patterns, and allows the definition of 4 degrees of clarity of retrieved memory traces.     

Testable predictions from realistic neural network simulations of vestibular compensation: integrating the behavioural and physiological data

Neural network simulations have been used previously in the investigation of the horizontal vestibulo-ocular reflex (HVOR) and vestibular compensation. The simulations involved in the present research were based on known anatomy and physiology of the vestibular pathway. This enabled the straightforward comparison of the network response, both in terms of behavioural (eye movement) and physiological (neural activity) data to empirical data obtained from guinea pig. The network simulations matched the empirical data closely both in terms of the static symptoms (spontaneous nystagmus) of unilateral vestibular deafferentation (UVD) as well as in terms of the dynamic symptoms (decrease in VOR gain). The use of multiple versions of the basic network, trained to simulate individual guinea pigs, highlighted the importance of the particular connections: the vestibular ganglion to the type I medial vestibular nucleus (MVN) cells on the contralesional side. It also indicated the significance of the relative firing rate in type I MVN cells which make excitatory connections with abducens cells as contributors to the variability seen in the level of compensated response following UVD. There was an absence of any difference (both in terms of behavioural and neural response) between labyrinthectomised and neurectomised simulations. The fact that a dynamic VOR gain asymmetry remained following the elimination of the spontaneous nystagmus in the network suggested that the amelioration of both the static and dynamic symptoms of UVD may be mediated by a single network. The networks were trained on high acceleration impulse stimuli but displayed the ability to generalise to low frequency, low acceleration sinusoids and closely approximated the behavioural responses to those stimuli. Received: 12 October 1998 / Accepted in revised form: 11 February 1999     

An efficient model development strategy for bioprocesses based on neural networks in macroscopic balances: Part II

There is a need for efficient modeling strategies which quickly lead to reliable mathematical models that can be applied for design and optimization of (bio)-chemical processes. The serial gray box modeling strategy is potentially very efficient because no detailed knowledge is needed to construct the white box part of the model and because covenient black box modeling techniques like neural networks can be used for the black box part of the model. This paper shows for a typical biochemical conversion how the serial gray box modeling strategy can be applied efficiently to obtain a model with good frequency extrapolation properties. Models with good frequency extrapolation properties can be applied under dynamic conditions that were not present during the identification experiments. For a given application domain of a model, this property can be used to considerably reduce the number of identification experiments. The serial gray box modeling strategy is demonstrated to be successful for the modeling of the enzymatic conversion of penicillin G In the concentration range of 10-100 mM and temperature range of 298-335 K. Frequency extrapolation is shown by using only constant temperatures in the (batch) identification experiments, while the model can be used reliable with varying temperatures during the (batch) validation experiments. No reliable frequency extrapolation properties could be obtained for a black box model, and for a more knowledge-driven white box model reliable frequency extrapolation properties could only be obtained by incorporating more knowledge in the model. Copyright 1999 John Wiley & Sons, Inc.     

Correction for missed events based on a realistic model of a detector.

Quantitative patch-clamp analysis based on dwell-time histograms has to deal with the problem of missed events. The correction of the evaluated time constants has to take into account the characteristics of the detector used for the reconstruction of the time series. In previous approaches a simple model of the detector has been used, which is based on the assumption that all events shorter than the temporal resolution tres were missed, irrespective of the preceding events. Rather than the standard assumption of a fixed dead time, we introduce a more realistic model of a detector by a continuous-time version of the Hinkley detector. The combined state of the channel and the detector obeys a Markov model, which is governed by a Fokker-Planck-Kolmogorov partial differential equation. The steady-state solution leads to the determination of the apparent time constants tau o and tau c depending on the true rate constants koc and kco and the temporal resolution tres of the detector. Simulations with different kinds of detectors, including the Bessel filter with half-amplitude threshold detection, are performed. They show that our new equation predicts the dependence of tau c and tau o on koc, kco, and tres better than the standard equation used until now.     

A local training-pruning approach for recurrent neural networks

The global extended Kalman filtering (EKF) algorithm for recurrent neural networks (RNNs) is plagued by the drawback of high computational cost and storage requirement. In this paper, we present a local EKF training-pruning approach that can solve this problem. In particular, the by-products, obtained along with the local EKF training, can be utilized to measure the importance of the network weights. Comparing with the original global approach, the proposed local approach results in much lower computational cost and storage requirement. Hence, it is more practical in solving real world problems. Simulation showed that our approach is an effective joint-training-pruning method for RNNs under online operation.     

A method for characterizing transition concertedness from polymer dynamics computer simulations

A statistical method based on classifying the transitions among a set of dihedral angles within an “energy transfer window” is developed, and used to analyze Brownian (BD) and molecular dynamics (MD) simulations of the acyl chains in a lipid bilayer, and MD of neat hexadecane. It is shown for the BD simulation that when a transition of the dihedral angle in the center of the chain occurs, a transition of a particular next nearest neighbor (or angle 2-apart) will follow concertedly with a probability of approximately 0.10 within a lime window of approximately 3 ps. The MD bilayer simulations, which are based on a more flexible model of the hydrocarbon chains, yield corresponding concerted transition probabilities of approximately 0.083 and window sizes of 1–2 ps. An analysis of angles 4-apart yields concerted transition probabilities of 0.03 and 0.04 for the BD and MD bilayer simulations, respectively, and window sizes close to those of the corresponding 2-apart cases. Statistical hypothesis testing very strongly rejects the assertion that these follower transitions are occurring at random. Similar analysis reveals marginal or no evidence of concertedness between 1-apart (nearest neighbor) and between 3-apart dihedral angle transitions. The pattern of concertedness for hexadecane is qualitatively similar to that of the lipid chains, although concertedness is somewhat stronger for the 3-apart transitions and somewhat weaker for those 4-apart. Finally, it is suggested that the diffusion of small solute molecules in membranes is better facilitated by non concerted transitions, which are associated with relatively large displacements of the chains, than by concerted transitions, which do little to change the chain shape. © 1995 John Wiley & Sons, Inc.     

A recurrent neural model for proto-object based contour integration and figure-ground segregation

Visual processing of objects makes use of both feedforward and feedback streams of information. However, the nature of feedback signals is largely unknown, as is the identity of the neuronal populations in lower visual areas that receive them. Here, we develop a recurrent neural model to address these questions in the context of contour integration and figure-ground segregation. A key feature of our model is the use of grouping neurons whose activity represents tentative objects (“proto-objects”) based on the integration of local feature information. Grouping neurons receive input from an organized set of local feature neurons, and project modulatory feedback to those same neurons. Additionally, inhibition at both the local feature level and the object representation level biases the interpretation of the visual scene in agreement with principles from Gestalt psychology. Our model explains several sets of neurophysiological results (Zhou et al. Journal of Neuroscience, 20(17), 6594–6611 2000; Qiu et al. Nature Neuroscience, 10(11), 1492–1499 2007; Chen et al. Neuron, 82(3), 682–694 2014), and makes testable predictions about the influence of neuronal feedback and attentional selection on neural responses across different visual areas. Our model also provides a framework for understanding how object-based attention is able to select both objects and the features associated with them.     

A late-stopping method for optimal aggregation of neural networks

Ensembles of artificial neural networks have been used in the last years as classification/regression machines, showing improved generalization capabilities that outperform those of single networks. However, it has been recognized that for aggregation to be effective the individual networks must be as accurate and diverse as possible. An important problem is, then, how to tune the aggregate members in order to have an optimal compromise between these two conflicting conditions. We propose here a simple method for constructing regression/classification ensembles of neural networks that leads to overtrained aggregate members with an adequate balance between accuracy and diversity. The algorithm is favorably tested against other methods recently proposed in the literature, producing an improvement in performance on the standard statistical databases used as benchmarks. In addition, and as a concrete application, we apply our method to the sunspot time series and predict the remainder of the current cycle 23 of solar activity.