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Analytical methods to differentiate similar electroencephalographic spectra: neural network and discriminant analysis.

Differences in electroencephalographic (EEG) power spectra obtained under similar, but not identical, conditions may be difficult to discern using standard techniques. Statistical analysis may not be useful because of the large number of comparisons necessary. Visual recognition of differences also may be difficult. A new technique, neural network analysis, has been used successfully in other problems of pattern recognition and classification. We examined a number of methods of classifying similar EEG data: standard statistical analysis (analysis of variance), visual recognition, discriminant analysis, and neural network analysis. Twenty-nine volunteers received either thiopental (n = 9), midazolam (n = 10), or propofol (n = 10) in sedative doses in 3 different studies. These drugs produced very similar changes in the EEG power spectra. Except for beta 2 power during thiopental infusion, differences between drugs could not be detected using analysis of variance. Visual categorization was correct in 72% of the baseline EEGs, 70% of thiopental EEGs, 27% of propofol EEGs, and 46% of midazolam EEGs. A classification neural network (Learning Vector Quantization network) containing a Kohonen hidden layer was able to successfully classify 57 of 58 EEG samples (of 4 minutes' duration). Discriminant analysis had a similar rate of success. This level of performance was achieved by dividing the EEG power spectrum from 1 to 30 Hz into 15 2-Hz bandwidths. When the EEG power spectrum was divided into the "classical" frequency bandwidths (alpha, beta 1, beta 2, theta, delta), both neural network and discriminant analysis performance deteriorated. By training the network using only certain inputs we were able to identify drug-specific bandwidths that seemed to be important in correct classification. We conclude that propofol, thiopental, and midazolam produce different effects on the EEG and that both neural network and discriminant analysis are useful in identifying these differences. We also conclude that EEG spectra should be analyzed without using classical EEG bands (alpha, beta, etc.). Additionally, neural networks can be used to identify frequency bands that are "important" in specific drug effects on the EEG. Once a classification algorithm is obtained using either a neural network or discriminant analysis, it could be used as an on-line monitor to recognize drug-specific EEG patterns.

Adult↗

German research network on schizophrenia-bridging the gap between research and care.

The German Research Network on Schizophrenia (GRNS) is a nationwide network of presently 16 psychiatric university departments, 14 state and district hospitals, as well as six local networks of psychiatric practices and general practitioners, which are collaborating in about 25 interrelated, multicentre projects on schizophrenia research. The GRNS aims to intensify collaboration and knowledge exchange between leading research institutions and qualified routine care facilities, both within (horizontal network) and between (vertical network) the two levels of research and care, in order to create the scientific preconditions for optimization of care in patients with schizophrenia. With respect to illness development, the network is organized into two main "Project Networks" (PN). Whereas PN I targets the implementation of early detection and early intervention strategies, PN II aims at optimization of acute and long-term treatment, especially in first-episode patients. PN II also includes projects aiming at improvement of rehabilitation, particularly in patients with residual symptoms. Furthermore, there is a "Special Network" on molecular and pharmaco-genetics. Several more general projects address fighting stigma and discrimination, health care economy, continuing medical education, quality assurance, and methodology. The network is mainly funded by the German Ministry for Research spanning a period of 5 years.

Community Networks↗

From swimming to walking: a single basic network for two different behaviors.

In this paper we consider the hypothesis that the spinal locomotor network controlling trunk movements has remained essentially unchanged during the evolutionary transition from aquatic to terrestrial locomotion. The wider repertoire of axial motor patterns expressed by amphibians would then be explained by the influence from separate limb pattern generators, added during this evolution. This study is based on EMG data recorded in vivo from epaxial musculature in the newt Pleurodeles waltl during unrestrained swimming and walking, and on a simplified model of the lamprey spinal pattern generator for swimming. Using computer simulations, we have examined the output generated by the lamprey model network for different input drives. Two distinct inputs were identified which reproduced the main features of the swimming and walking motor patterns in the newt. The swimming pattern is generated when the network receives tonic excitation with local intensity gradients near the neck and girdle regions. To produce the walking pattern, the network must receive (in addition to a tonic excitation at the girdles) a phasic drive which is out of phase in the neck and tail regions in relation to the middle part of the body. To fit the symmetry of the walking pattern, however, the intersegmental connectivity of the network had to be modified by reversing the direction of the crossed inhibitory pathways in the rostral part of the spinal cord. This study suggests that the input drive required for the generation of the distinct walking pattern could, at least partly, be attributed to mechanosensory feedback received by the network directly from the intraspinal stretch-receptor system. Indeed, the input drive required resembles the pattern of activity of stretch receptors sensing the lateral bending of the trunk, as expressed during walking in urodeles. Moreover, our results indicate that a nonuniform distribution of these stretch receptors along the trunk can explain the discontinuities exhibited in the swimming pattern of the newt. Thus, separate limb pattern generators can influence the original network controlling axial movements not only through a direct coupling at the central level but also via a mechanical coupling between trunk and limbs, which in turn influences the sensory signals sent back to the network. Taken together, our findings support the hypothesis of a phylogenetic conservatism of the spinal locomotor networks generating axial motor patterns from agnathans to amphibians.

Animals↗

Changing excitation and inhibition in simulated neural networks: effects on induced bursting behavior.

The development of synchronous bursting in neuronal ensembles represents an important change in network behavior. To determine the influences on development of such synchronous bursting behavior we study the dynamics of small networks of sparsely connected excitatory and inhibitory neurons using numerical simulations. The synchronized bursting activities in networks evoked by background spikes are investigated. Specifically, patterns of bursting activity are examined when the balance between excitation and inhibition on neuronal inputs is varied and the fraction of inhibitory neurons in the network is changed. For quantitative comparison of bursting activities in networks, measures of the degree of synchrony are used. We demonstrate how changes in the strength of excitation on inputs of neurons can be compensated by changes in the strength of inhibition without changing the degree of synchrony in the network. The effects of changing several network parameters on the network activity are analyzed and discussed. These changes may underlie the transition of network activity from normal to potentially pathologic (e.g., epileptic) states.

Action Potentials↗

Activity dynamics and propagation of synchronous spiking in locally connected random networks.

Random network models have been a popular tool for investigating cortical network dynamics. On the scale of roughly a cubic millimeter of cortex, containing about 100,000 neurons, cortical anatomy suggests a more realistic architecture. In this locally connected random network, the connection probability decreases in a Gaussian fashion with the distance between neurons. Here we present three main results from a simulation study of the activity dynamics in such networks. First, for a broad range of parameters these dynamics exhibit a stationary state of asynchronous network activity with irregular single-neuron spiking. This state can be used as a realistic model of ongoing network activity. Parametric dependence of this state and the nature of the network dynamics in other regimes are described. Second, a synchronous excitatory stimulus to a fraction of the neurons results in a strong activity response that easily dominates the network dynamics. And third, due to that activity response an embedding of a divergent-convergent feed-forward subnetwork (as in synfire chains) does not naturally lead to a stable propagation of synchronous activity in the subnetwork; this is in contrast to our earlier findings in isolated subnetworks of that type. Possible mechanisms for stabilizing the interplay of volleys of synchronous spikes and network dynamics by specific learning rules or generalizations of the subnetworks are discussed.

Action Potentials↗

Emergence of clusters in the hidden layer of a dynamic recurrent neural network.

The neural integrator of the oculomotor system is a privileged field for artificial neural network simulation. In this paper, we were interested in an improvement of the biologically plausible features of the Arnold-Robinson network. This improvement was done by fixing the sign of the connection weights in the network (in order to respect the biological Dale's Law). We also introduced a notion of distance in the network in the form of transmission delays between its units. These modifications necessitated the introduction of a general supervisor in order to train the network to act as a leaky integrator. When examining the lateral connection weights of the hidden layer, the distribution of the weights values was found to exhibit a conspicuous structure: the high-value weights were grouped in what we call clusters. Other zones are quite flat and characterized by low-value weights. Clusters are defined as particular groups of adjoining neurons which have strong and privileged connections with another neighborhood of neurons. The clusters of the trained network are reminiscent of the small clusters or patches that have been found experimentally in the nucleus prepositus hypoglossi, where the neural integrator is located. A study was conducted to determine the conditions of emergence of these clusters in our network: they include the fixation of the weight sign, the introduction of a distance, and a convergence of the information from the hidden layer to the motoneurons. We conclude that this spontaneous emergence of clusters in artificial neural networks; performing a temporal integration, is due to computational constraints, with a restricted space of solutions. Thus, information processing could induce the emergence of iterated patterns in biological neural networks.

Animals↗

Analytical description of the evolution of neural networks: learning rules and complexity.

We present the foundation of a physical formalism that allows us to characterize the dynamics of the evolution of neural networks both in regard to the network configuration and to network performance. Model runs were performed on a simple network consisting of six neurons, allowing complete analytical description of the network's behaviour. Order parameters are characterized that allow an analytical description of critical periods in network evolution. Thus, correlations of the local dynamics and the system's global behaviour could be computed. It is shown that local learning rules are sufficient to model complex dynamical aspects of the evolution of networks. It is demonstrated in how far novel statistical formalisms, e.g. neural complexity, can be employed to evaluate the system's dynamics. The introduction of order parameters allows an analytical characterization of transient phases in the network's behaviour, correlating network connectivity with neuronal firing patterns. The relevance of this approach for the interpretation of physiological data is discussed.

Animals↗

Artificial neural networks for the electrocardiographic diagnosis of healed myocardial infarction.

Artificial neural networks are computer-based expert systems that learn by example, in contrast to the currently used rule-based electrocardiographic interpretation programs. For the purpose of this study, 1,107 electrocardiograms (ECGs) from patients who had undergone cardiac catheterization were used to train and test neural networks for the diagnosis of myocardial infarction. Different combinations of QRS and ST-T measurements were used as input to the neural networks. In a learning process, the networks automatically adjusted their characteristics to correctly diagnose anterior or inferior wall myocardial infarction from the ECG. Two thirds of the ECGs were used in this process. Thereafter, the performance of the networks was studied in a separate test set, using the remaining third of the ECGs. The results from the networks were also compared with that of conventional electrocardiographic criteria. The sensitivity for the diagnosis of anterior myocardial infarction was 81% for the best network and 68% for the conventional criteria (p < 0.01), both having a specificity of 97.5%. The corresponding sensitivities of the network and the criteria for the diagnosis of inferior myocardial infarction were 78% and 65.5% (p < 0.01), respectively, compared at a specificity of 95%. The results indicate that artificial neural networks may be of interest in the attempt to improve computer-based electrocardiographic interpretation programs.

Case-Control Studies↗

Predicting protein secondary structure content. A tandem neural network approach.

A priori knowledge of secondary structure content can be of great use in theoretical and experimental determination of protein structure. We present a method that uses two computer-simulated neural networks placed in "tandem" to predict the secondary structure content of water-soluble, globular proteins. The first of the two networks, NET1, predicts a protein's helix and strand content given information about the protein's amino acid composition, molecular weight and heme presence. Because NET1 contained more adjustable parameters (network weights) than learning examples, this network experienced problems with memorization, which is the inability to generalize onto new, never-seen-before examples. To overcome this problem, we designed a second network, NET2, which learned to determine when NET1 was in a state of generalization. Together, these two networks produce prediction errors as low as 5.0% and 5.6% for helix and strand content, respectively, on a set of protein crystal structures bearing little homology to those used in network training. A comparison between three other methods including a multiple linear regression analysis, a non-hidden-node network analysis and a secondary structure assignment analysis reveals that our tandem neural network scheme is, indeed, the best method for predicting secondary structure content. The results of our analysis suggest that the knowledge of sequence information is not necessary for highly accurate predictions of protein secondary structure content.

Databases, Bibliographic↗

Charting epilepsy by searching for intelligence in network space with the help of evolving autonomous agents.

The problem of demarcating neural network space is formidable. A simple fully connected recurrent network of five units (binary activations, synaptic weight resolution of 10) has 3.2 *10(26) possible initial states. The problem increases drastically with scaling. Here we consider three complementary approaches to help direct the exploration to distinguish epileptic from healthy networks. [1] First, we perform a gross mapping of the space of five-unit continuous recurrent networks using randomized weights and initial activations. The majority of weight patterns (>70%) were found to result in neural assemblies exhibiting periodic limit-cycle oscillatory behavior. [2] Next we examine the activation space of non-periodic networks demonstrating that the emergence of paroxysmal activity does not require changes in connectivity. [3] The next challenge is to focus the search of network space to identify networks with more complex dynamics. Here we rely on a major available indicator critical to clinical assessment but largely ignored by epilepsy modelers, namely: behavioral states. To this end, we connected the above network layout to an external robot in which interactive states were evolved. The first random generation showed a distribution in line with approach [1]. That is, the predominate phenotypes were fixed-point or oscillatory with seizure-like motor output. As evolution progressed the profile changed markedly. Within 20 generations the entire population was able to navigate a simple environment with all individuals exhibiting multiply-stable behaviors with no cases of default locked limit-cycle oscillatory motor behavior. The resultant population may thus afford us a view of the architectural principles demarcating healthy biological networks from the pathological. The approach has an advantage over other epilepsy modeling techniques in providing a way to clarify whether observed dynamics or suggested therapies are pointing to computational viability or dead space.

Action Potentials↗

Identification of large-scale networks in the brain using fMRI.

Cognition is thought to result from interactions within large-scale networks of brain regions. Here, we propose a method to identify these large-scale networks using functional magnetic resonance imaging (fMRI). Regions belonging to such networks are defined as sets of strongly interacting regions, each of which showing a homogeneous temporal activity. Our method of large-scale network identification (LSNI) proceeds by first detecting functionally homogeneous regions. The networks of functional interconnections are then found by comparing the correlations among these regions against a model of the correlations in the noise. To test the LSNI method, we first evaluated its specificity and sensitivity on synthetic data sets. Then, the method was applied to four real data sets with a block-designed motor task. The LSNI method correctly recovered the regions whose temporal activity was locked to the stimulus. In addition, it detected two other main networks highly reproducible across subjects, whose activity was dominated by slow fluctuations (0-0.1 Hz). One was located in medial and dorsal regions, and mostly overlapped the "default" network of the brain at rest [Greicius, M.D., Krasnow, B., Reiss, A.L., Menon, V., 2003. Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proceedings of the National Academy of Sciences of the U.S.A. 100, 253-258]; the other was composed of lateral frontal and posterior parietal regions. The LSNI method we propose allows to detect in an exploratory and systematic way all the regions and large-scale networks activated in the working brain.

Adult↗

A novel method for generation of signature networks as biomarkers from complex high throughput data.

Traditionally, gene signatures are statistically deduced from large gene expression and proteomics datasets and have been applied as an experimental molecular diagnostic technique that is sensitive to experimental design and statistical treatment. We have developed and applied the approach of "signature networks" which overcomes some of the drawbacks of clustering methods. We have demonstrated signature network assembly, functional analysis and logical operations on the networks that can be generated. In addition, we have used this technique in a proof of concept study to compare the effect of differential drug treatment using 4-hydroxytamoxifen and estrogen on the MCF-7 breast cancer cell line from a previously published study. We have shown that the two compounds can be differentiated by the networks of interacting genes. Both networks consist of a core module of genes including c-Fos as part of c-Fos/c-Jun heterodimer and c-Myc which is clearly visible. Using algorithms in our MetaCore software we are able to subtract the 4-hydroxytamoxifen and estrogen networks to further understand differences between these two treatments and show that the estrogen network is assembled around the core with other modules essential for all phases of the cell cycle. For example, Cyclin D1 is present in networks for the estrogen treated cells from two separate studies. These signature networks represent an approach to identify biomarkers and a general approach for discovering new relationships in complex high throughput toxicology data.

Algorithms↗

Respiratory rhythm generation in neonatal and adult mammals: the hybrid pacemaker-network model.

We review a new unified model of respiratory rhythm generation - the hybrid pacemaker-network model. This model represents a comprehensive synthesis of cellular and network mechanisms that can theoretically account for rhythm generation in different functional states, from the most reduced states in the neonatal nervous system in vitro to the intact adult system in vivo. The model incorporates a critical neuronal kernel consisting of a network of excitatory neurons with state-dependent, oscillatory bursting or pacemaker properties. This kernel, located in the pre-Bötzinger complex of the ventrolateral medulla, provides a rudimentary pacemaker network mechanism for generating an inspiratory rhythm, revealed predominately in functionally reduced states in vitro. In vivo the kernel is embedded in a larger network that interacts with the kernel via inhibitory synaptic connections that provide the dynamic control required for the evolution of the complete pattern of inspiratory and expiratory network activity. The resulting hybrid of cellular pacemaker and network properties functionally endows the system with multiple mechanisms of rhythm generation. New biophysically realistic mathematical models of the hybrid pacemaker-network have been developed that illustrate these concepts and provide a computational framework for investigating interactions of cellular and network processes that must be analyzed to understand rhythm generation.

Animals↗

Comparison of intraocular lens computations using a neural network versus the Holladay formula.

PURPOSE: To compare the accuracy of intraocular lens (IOL) calculations using Holladay personalized calculations and a new method of trained neural networks. SETTING: A private ophthalmic practice. METHODS: We developed and trained a neural network to predict IOL powers using a personalized Holladay program and clinical data from 200 consecutive cases of one surgeon's results with one IOL. Clinical data included preoperative axial length, both keratometry values, anterior chamber depth, and human lens thickness. The neural network was trained to produce the actual postoperative refractive error, and the Holladay surgeon factor was continuously refined using the same results. After the network was successfully trained against the clinical data, it was used to compute IOL power in a double-masked study. Ninety-five patients were randomized between the Holladay personalized calculation and the neural network computation. There were no significant differences in age or preoperative refractive errors between the two groups. Manifest refractions were obtained during the masked period at least 6 weeks after surgery. RESULTS: Mean postoperative error from predicted refraction was +0.271 diopters (D) for the neural network group and -0.217 D for the Holladay personal group. Mean absolute error from predicted refraction was +0.63 D for the neural network group and +0.93 D for the Holladay personal group. There was a significant difference in postoperative refractive errors and mean absolute error between the two groups (P < .022; nonparametric Mann-Whitney test). An error of less than +/- 0.75 D was obtained by 72.5% of the neural network group and 50.0% of the Holladay group. CONCLUSIONS: The neural network prediction formula can improve IOL implantation calculations by tightening the variance of errors.

Cataract Extraction↗

Three learning phases for radial-basis-function networks.

In this paper, learning algorithms for radial basis function (RBF) networks are discussed. Whereas multilayer perceptrons (MLP) are typically trained with backpropagation algorithms, starting the training procedure with a random initialization of the MLP's parameters, an RBF network may be trained in many different ways. We categorize these RBF training methods into one-, two-, and three-phase learning schemes. Two-phase RBF learning is a very common learning scheme. The two layers of an RBF network are learnt separately; first the RBF layer is trained, including the adaptation of centers and scaling parameters, and then the weights of the output layer are adapted. RBF centers may be trained by clustering, vector quantization and classification tree algorithms, and the output layer by supervised learning (through gradient descent or pseudo inverse solution). Results from numerical experiments of RBF classifiers trained by two-phase learning are presented in three completely different pattern recognition applications: (a) the classification of 3D visual objects; (b) the recognition hand-written digits (2D objects); and (c) the categorization of high-resolution electrocardiograms given as a time series (ID objects) and as a set of features extracted from these time series. In these applications, it can be observed that the performance of RBF classifiers trained with two-phase learning can be improved through a third backpropagation-like training phase of the RBF network, adapting the whole set of parameters (RBF centers, scaling parameters, and output layer weights) simultaneously. This, we call three-phase learning in RBF networks. A practical advantage of two- and three-phase learning in RBF networks is the possibility to use unlabeled training data for the first training phase. Support vector (SV) learning in RBF networks is a different learning approach. SV learning can be considered, in this context of learning, as a special type of one-phase learning, where only the output layer weights of the RBF network are calculated, and the RBF centers are restricted to be a subset of the training data. Numerical experiments with several classifier schemes including k-nearest-neighbor, learning vector quantization and RBF classifiers trained through two-phase, three-phase and support vector learning are given. The performance of the RBF classifiers trained through SV learning and three-phase learning are superior to the results of two-phase learning, but SV learning often leads to complex network structures, since the number of support vectors is not a small fraction of the total number of data points.

Algorithms↗

The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks.

In a previous paper we introduced the notion of frustrated chaos occurring in Hopfield networks [Neural Networks 11 (1998) 1017]. It is a dynamical regime which appears in a network when the global structure is such that local connectivity patterns responsible for stable oscillatory behaviors are intertwined, leading to mutually competing attractors and unpredictable itinerancy among brief appearance of these attractors. Frustration destabilizes the network and provokes an erratic 'wavering' among the orbits that characterize the same network when it is connected in a non-frustrated way. In this paper, through a detailed study of the bifurcation diagram given for some connection weights, we will show that this frustrated chaos belongs to the family of intermittency type of chaos, first described by Berge et al. [Order within chaos (1984)] and Pomeau and Manneville [Commun. Math. Phys. 74 (1980) 189]. Indeed, the transition to chaos is a critical one, and all along the bifurcation diagram, in any chaotic window, the duration of the intermittent cycles, between two chaotic bursts, grows as an invert ratio of the connection weight. Specific to this regime are the intermittent cycles easily identifiable as the non-frustrated regimes obtained by altering the values of these same connection weights. We will more specifically show that anywhere in the bifurcation diagram, a chaotic window always lies between two oscillatory regimes, and that the resulting chaos is a merging of, among others, the cycles at both ends. The strength (i.e. the duration of its oscillatory phase before the chaotic burst) of the first cycle decreases while the regime tends to stabilize into the second cycle (with the strength of this second cycle increasing) that will finally get the control. Since in our study, the bifurcation diagram concerns the same connection weights responsible for the learning mechanism of the Hopfield network, we will discuss the relations existing between bifurcation, learning and control of chaos. We will show that, in some cases, the addition of a slower Hebbian learning mechanism onto the Hopfield networks makes the resulting global dynamics to drive the network into a stable oscillatory regime, through a succession of intermittent and quasiperiodic regimes. Finally, we will present a series of possible logical steps to manually construct a frustrated network.

Computer Simulation↗

A functions localized neural network with branch gates.

In this paper, a functions localized network with branch gates (FLN-bg) is studied, which consists of a basic network and a branch gate network. The branch gate network is used to determine which intermediate nodes of the basic network should be connected to the output node with a gate coefficient ranging from 0 to 1. This determination will adjust the outputs of the intermediate nodes of the basic network depending on the values of the inputs of the network in order to realize a functions localized network. FLN-bg is applied to function approximation problems and a two-spiral problem. The simulation results show that FLN-bg exhibits better performance than conventional neural networks with comparable complexity.

Animals↗

Neural network modeling for estimation of the aqueous solubility of structurally related drugs.

The ability of neural network models to predict aqueous solubility within series of structurally related drugs was evaluated. Three sets of compounds representing different drug classes (28 steroids, 31 barbituric acid derivatives, and 24 heterocyclic reverse transcriptase inhibitors) were studied. Topological descriptors (connectivity indices, kappa indices, and electrotopological state indices) were used to link the structures of compounds with their aqueous solubility. Separate models were built for each class of drugs using back-propagation neural networks with one hidden layer and five topological indices as input parameters. The effect of network size and training time on the prediction ability of the network was studied by the leave-one-out (LOO) procedure. In all three compound groups a neural network structure of 5-3-1 was optimal. To avoid chance effects, artificial neural network (ANN) ensembles (i.e.; averaging neural network predictions over several independent networks) were used. The cross-validated squared correlation coefficient (Q2) for 10 averaged predictions was 0.796 in the case of the steroid set. The corresponding standard error of prediction (SDEP) was 0.288 log units. For the barbiturates, Q2 and SDEP were 0.856 and 0.383, respectively, and for the RT inhibitors, these parameters were 0.721 and 0.401, respectively. The results indicate that neural networks can produce useful models of the aqueous solubility of a congeneric set of compounds, even with simple structural parameters.

Drug Design↗