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Results for “Graph neural network”

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PubMed1997

Classification of rhythmic patterns in the stomatogastric ganglion.

A large class of neural pattern generators change their rhythmic output under the influence of neuromodulators. We present a method for identifying the variety of rhythmic patterns generated by small neural networks. The technique provides a tool for investigating the biological mechanisms responsible for pattern generation and pattern switching. Discrete methods based on transition graphs are applied to dynamic biological networks to generate sets of possible rhythmic behaviours. A measure is introduced onto the set of rhythms to quantify their differences and organize the set according to clusters of similar rhythms. Each cluster represents a different operational mode of the network. Examples are drawn from the stomatogastric ganglion, a well studied network that controls the muscles in the foregut of crustaceans. Classes of rhythms are found that correspond to experimentally observed patterns, and other classes of rhythms are found that have not yet been observed. Predictions are made for the rhythmic output of the stomatogastric ganglion under specific manipulations of parameters in the biological network.

Animals↗
PubMed1995

A system of IAC neural networks as the basis for self-organization in a sociological dynamical system simulation.

This sociological simulation uses the ideas of semiotics and symbolic interactionism to demonstrate how an appropriately developed associative memory in the minds of individuals on the microlevel can self-organize into macrolevel dissipative structures of societies such as racial cultural/economic classes, status symbols and fads. The associative memory used is based on an extension of the IAC neural network (the Interactive Activation and Competition network). Several IAC networks act together to form a society by virtue of their human-like properties of intuition and creativity. These properties give them the ability to create and understand signs, which lead to the macrolevel structures of society. This system is implemented in hierarchical object oriented container classes which facilitate change in deep structure. Graphs of general trends and an historical account of a simulation run of this dynamical system are presented.

Black or African American↗
PubMed2026

Knowledge-driven interpretable neural networks provide mechanistic insight.

Analyzing omics data in the context of pathway knowledge is critical for understanding the molecular mechanisms underlying pathological changes. However, current pathway analysis methods do not model the detailed mechanistic nature of biological interactions, limiting the understanding of pathway behavior to a relatively shallow level. To address this issue, we present a knowledge-driven machine learning framework that embeds features into pathway graphs and models reactions analytically, producing interpretable feature hierarchies and subnetworks in which functional associations are estimated to model biological interactions. The approach is agnostic to feature selection, enabling the use of full omics data sets without discarding weak signals. Applications to breast cancer microRNA-gene regulation data and COVID-19 metabolomic data highlight immune and metabolic pathways relevant to disease progression. This framework bridges predictive modeling with mechanistic interpretation and offers a foundation for integrative pathway analysis.

Humans↗
PubMed2003

Network participation indices: characterizing component roles for information processing in neural networks.

We propose a set of indices that characterize-on the basis of connectivity data-how a network node participates in a larger network and what roles it may take given the specific sub-network of interest. These Network Participation Indices are derived from simple graph theoretic measures and have the interesting property of linking local features of individual network components to distributed properties that arise within the network as a whole. We use connectivity data on large-scale cortical networks to demonstrate the virtues of this approach and highlight some interesting features that had not been brought up in previously published material. Some implications of our approach for defining network characteristics relevant to functional segregation and functional integration, for example, from functional imaging studies are discussed.

Mental Processes↗
PubMed1997

Discrete State Neural Networks and Energies.

In this paper we give under an appropriate theoretical framework a characterization about neural networks (evolving in a binary set of states) which admit an energy. We prove that a neural network, iterated sequentially, admits an energy if and only if the weight matrix verifies two conditions: the diagonal elements are non-negative and the associated incidence graph does not admit non-quasi-symmetric circuits. In this situation the dynamics are robust with respect to a class of small changes of the weight matrix. Further, for the parallel update we prove that a necessary and sufficient condition to admit an energy is that the incidence graph does not contain non-quasi-symmetric circuits. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

Journal Article↗
PubMed2006

Percolation in living neural networks.

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with an exponent beta approximately or = 0.65. Beta is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is Gaussian rather than scale free.

Animals↗
PubMed1996

The hippocampus as a cognitive graph.

A theory of cognitive mapping is developed that depends only on accepted properties of hippocampal function, namely, long-term potentiation, the place cell phenomenon, and the associative or recurrent connections made among CA3 pyramidal cells. It is proposed that the distance between the firing fields of connected pairs of CA3 place cells is encoded as synaptic resistance (reciprocal synaptic strength). The encoding occurs because pairs of cells with coincident or overlapping fields will tend to fire together in time, thereby causing a decrease in synaptic resistance via long-term potentiation; in contrast, cells with widely separated fields will tend never to fire together, causing no change or perhaps (via long-term depression) an increase in synaptic resistance. A network whose connection pattern mimics that of CA3 and whose connection weights are proportional to synaptic resistance can be formally treated as a weighted, directed graph. In such a graph, a "node" is assigned to each CA3 cell and two nodes are connected by a "directed edge" if and only if the two corresponding cells are connected by a synapse. Weighted, directed graphs can be searched for an optimal path between any pair of nodes with standard algorithms. Here, we are interested in finding the path along which the sum of the synaptic resistances from one cell to another is minimal. Since each cell is a place cell, such a path also corresponds to a path in two-dimensional space. Our basic finding is that minimizing the sum of the synaptic resistances along a path in neural space yields the shortest (optimal) path in unobstructed two-dimensional space, so long as the connectivity of the network is great enough. In addition to being able to find geodesics in unobstructed space, the same network enables solutions to the "detour" and "shortcut" problems, in which it is necessary to find an optimal path around a newly introduced barrier and to take a shorter path through a hole opened up in a preexisting barrier, respectively. We argue that the ability to solve such problems qualifies the proposed hippocampal object as a cognitive map. Graph theory thus provides a sort of existence proof demonstrating that the hippocampus contains the necessary information to function as a map, in the sense postulated by others (O'Keefe, J., and L. Nadel. 1978. The Hippocampus as a Cognitive Map. Clarendon Press, Oxford, UK). It is also possible that the cognitive mapping functions of the hippocampus are carried out by parallel graph searching algorithms implemented as neural processes. This possibility has the great attraction that the hippocampus could then operate in much the same way to find paths in general problem space; it would only be necessary for pyramidal cells to exhibit a strong nonpositional firing correlate.

Animals↗
PubMed2001

Physicochemical and graph theoretical descriptors in developmental toxicity SAR: a comparative study.

Chemical insults to the developing fetus can lead to growth retardation, malformation, death, and functional deficits. The present study seeks to determine if physicochemical and/or graph theoretical parameters can be used to determine a structure-activity relationship (SAR) for developmental toxicity, and if consistency is observed among the selected features. The biological data utilized consists of a diverse series of compounds evaluated within the Chernoff-Kavlock in vivo mouse assay. Physicochemical parameters calculated correspond to electronic, steric, and transport properties. Graph theoretical parameters calculated include the simple, valence, and kappa indices. Both sets of parameters were independently applied to derive SARs in order to compare the quality of the respective models. Multiple random sampling, without replacement, was utilized to obtain ten training/test partitions. Models were built by linear discriminant analysis, decision trees, and neural networks respectively. Comparisons on identical sets of data were carried out to determine if any of the model building procedures had a significant advantage in terms of predictive performance. Furthermore, comparison of the features selected within and across the model building processes led to the determination of model consistency. Our results indicate that consistent features related to developmental toxicity are observed and that both physicochemical and graph theoretical parameters have equal utility.

Animals↗
PubMed1997

Ant colonies for the travelling salesman problem.

We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to both symmetric and asymmetric instances of the TSP. The method is an example, like simulated annealing, neural networks and evolutionary computation, of the successful use of a natural metaphor to design an optimization algorithm.

Algorithms↗
PubMed1999

Scaling and percolation in the small-world network model.

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

Disease Outbreaks↗
PubMed2002

Theoretical neuroanatomy and the connectivity of the cerebral cortex.

Over recent years, a wealth of neuroanatomical information on the pattern of interconnections between segregated areas of the cerebral cortex has become available. Here, we describe a set of structural measures, based on graph theory, which can be used to analyze these anatomical patterns. We describe relationships between these structural measures and measures based on patterns of functional connectivity, i.e. patterns of correlations in neural activity. We find that networks capable of producing highly complex functional dynamics share common structural motifs. These motifs are also found in cortical connection matrices, which are characterized by the existence of densely linked groups of areas, low potential wiring length, and a high abundance of reciprocal connections and short cycles. An analysis of cortical functional connectivity demonstrates the existence of functional clusters of highly interactive areas, producing highly complex dynamics. The combined structural and functional analysis outlined in this chapter provides insight into the large-scale functional organization of distributed cortical systems.

Animals↗
PubMed2002

Synchronization in small-world systems.

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.

Models, Theoretical↗
PubMed2004

Counter-propagation artificial neural network as a tool for the independent variable selection: structure-mutagenicity study on aromatic amines.

The counter-propagation artificial neural network (CP ANN) technique was applied for the independent variable selection and for structure-mutagenic potency modeling on a set of 95 aromatic and heteroaromatic amines with biological activity investigated experimentally by an in vitro assay. The molecular structures were represented by 275 independent variables classified as topostructural, topochemical, geometrical and quantum-chemical descriptors. As a result of the neural network modeling, the following descriptors were found to be the most important for structure-activity relationship: 5 chi -path connectivity index of order h = 5, 3chibC-bond cluster connectivity index of order h = 3, J(B)-Balaban's J index based on bond types, SHSNH2-electrotopological state index values for atoms, phia-flexibility index (kappa p1 x kappa p2/nvx), IC0-mean information content or complexity of a graph based on the 0 order neighborhood of vertices in a hydrogen-filled graph and ELUMO. The leave one out (LOO) method was used in order to test and select the models for mutagenicity prediction. The statistical parameters for the 7-descriptors model are R(Model) = 0.96 and Rcv = 0.85, respectively. In the next step, the number of variables was reduced and the 4-descriptors model was found (R(Model) = 0.95 and Rcv = 0.85) and classified as the best one.

Algorithms↗
PubMed2001

Small worlds: how and why.

We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network architecture. In situations such as neural or transportation networks, where a physical distance between the nodes of the network exists, we study whether the small-world topology arises as a consequence of a tradeoff between maximal connectivity and minimal wiring. Using simulated annealing, we study the properties of a randomly rewired network as the relative tradeoff between wiring and connectivity is varied. When the network seeks to minimize wiring, a regular graph results. At the other extreme, when connectivity is maximized, a "random" network is obtained. In the intermediate regime, a small-world network is formed. However, unlike the model of Watts and Strogatz [Nature 393, 440 (1998)], we find an alternate route to small-world behavior through the formation of hubs, small clusters where one vertex is connected to a large number of neighbors.

Algorithms↗
PubMed1997

Image analysis based grading of bladder carcinoma. Comparison of object, texture and graph based methods and their reproducibility.

The possibility that computerized image analysis could increase the reproducibility of grading of bladder carcinoma as compared to conventional subjective grading made by pathologists was investigated. Object, texture and graph based analysis were carried out from Feulgen stained histological tissue sections. The object based features were extracted from gray scale images, binary images obtained by thresholding the nuclei and several other images derived through image processing operations. The textural features were based on the spatial gray-tone co-occurrence probability matrices and the graph based features were extracted from the minimum spanning trees connecting all nuclei. The large numbers of extracted features were evaluated in relation to subjective grading and to factors related to prognosis using multivariate statistical methods and multilayer backpropagation neural networks. All the methods were originally developed and tested on material from one patient and then tested for reproducibility on entirely different patient material. The results indicate reasonably good reproducibility for the best sets of features. In addition, image analysis based grading showed almost identical correlation to mitotic density and expression of p53 protein as subjective grading. It should thus be possible to use this kind of image analysis as a prognostic tool for bladder carcinoma.

Humans↗
PubMed2006

Adaptive reconfiguration of fractal small-world human brain functional networks.

Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical delta (low and high), , alpha, beta, and gamma frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency gamma network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both beta and gamma networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters.

Brain↗
PubMed2006

Language models based on Hebbian cell assemblies.

This paper demonstrates how associative neural networks as standard models for Hebbian cell assemblies can be extended to implement language processes in large-scale brain simulations. To this end the classical auto- and hetero-associative paradigms of attractor nets and synfire chains (SFCs) are combined and complemented by conditioned associations as a third principle which allows for the implementation of complex graph-like transition structures between assemblies. We show example simulations of a multiple area network for object-naming, which categorises objects in a visual hierarchy and generates different specific syntactic motor sequences ("words") in response. The formation of cell assemblies due to ongoing plasticity in a multiple area network for word learning is studied afterwards. Simulations show how assemblies can form by means of percolating activity across auditory and motor-related language areas, a process supported by rhythmic, synchronized propagating waves through the network. Simulations further reproduce differences in own EEG&MEG experiments between responses to word- versus non-word stimuli in human subjects.

Animals↗
PubMed2001

Using three-dimensional microfluidic networks for solving computationally hard problems.

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control.

Algorithms↗