Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Networks”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,549 records · Page 86Linked to original sources
PubMed1991

Age-dependent alterations in the operations of hippocampal neural networks.

Results from numerous studies suggest that the functioning of rat hippocampal neural networks during the second postnatal week of life differs distinctly from that in the mature brain. During this critical period, network behavior might be considered hyperexcitable. Spontaneous network-driven bursts of synaptic potentials, which have not been reported in mature hippocampus, are commonly observed. While these events could be attributable to a late onset of GABAergic synaptic transmission, results suggest that this is not the case. In the immature hippocampus orthodromic stimulation leads to prolonged depolarizations and often repetitive synchronized discharging of the entire CA3 population. These events are in many ways reproduced by application of drugs that suppress GABAergic synaptic transmission. The synchronized discharging of the CA3 population is blocked by excitatory amino acid antagonists. This finding, coupled with our growing understanding of the role that recurrent excitation plays in CA3 network functioning, has led to the hypothesis that the differences in network behavior early in life may be largely attributable to an overabundance of local-circuit recurrent excitatory synapses. With maturation, axon collaterals and attendant synapses would regress to achieve an adult complement. Results from dual intracellular recordings as well as anatomical studies of individual CA3 pyramidal cells support this hypothesis. Unique properties of the NMDA receptor at these recurrent excitatory synapses early in life may also promote network excitability. The participation of extracellular Ca2+ in the voltage dependency of the NMDA receptor-linked iontophore could also contribute to synapse consolidation during maturation and thus in the establishment of network connectivity.

Aging↗
PubMed1986

Correspondence of two nuclear networks observed in situ with the nuclear matrix.

In resting lymphocytes, three well defined networks are observed and attempts were made to superimpose them upon the networks described in isolated nuclear matrices. These three nuclear structures are seen after DNase and RNase treatment. They are digested by pepsin but their sensitivity to this enzyme is different. The more resistant network corresponds to the outer lamina of the isolated nuclear matrix. The second network is located in the inter-chromatin area. It is more sensitive to pepsin than the lamina and this sensitivity is increased ten-fold when digestion with pepsin is preceded by RNase digestion. This network corresponds to the internal network of isolated nuclear matrices. The third network is located in the intrachromatin area and is the most sensitive to pepsin action.

3,3'-Diaminobenzidine↗
PubMed1966

Rhythmic activity in a simulated neuronal network.

1. A digital computer has been programmed to simulate a neuronal network consisting of eighty cells with the following characteristics:(a) All cells in the network had a set random probability of discharge when not affected by other cells. The probability of discharge was chosen as one system parameter (PD).(b) Subsequent to the firing of any neurone in the network, a certain number of other neurones underwent a change in their probability of discharge, consisting of an inhibitory period followed by a period of increased excitability. The changes of excitability mimic the changes of the membrane potential recorded for spontaneously rhythmically active cells in the animal thalamus.2. Starting the network, a typical transient response appeared, consisting of a burst-like activity. The initial activity was followed, first by random fluctuations of the number of active cells, later by periods of spontaneous rhythmic activity that had several characteristics in common with the type of spontaneous activity seen in the animal thalamus.3. The parameters which affected the rhythmic activity of the network most strongly were the degree of the post-inhibitory increase of the probability of discharge and the degree of distribution of the inhibition to neighbouring cells.4. The results are compatible with the inhibitory phasing theory advanced by Andersen & Sears (1964) to explain the occurrence of spontaneous rhythmic activity in the animal thalamus. However, before sufficient experimental knowledge is available, it is difficult to establish whether the rhythmic activity in the network is of the same type as that of the animal thalamus.5. A closer study of the parameters governing the behaviour of the simulated network has given indications of some parameters to be more closely investigated in future animal experiments.

Journal Article↗
PubMed1980

Behaviour of the rod network in the tiger salamander retina mediated by membrane properties of individual rods.

1. The spread of electrical signals between rods in the salamander retina was examined by passing current into one rod and recording the voltage responses in nearby rods. Rod network behaviour, measured in this way, was simulated from data on rod membrane properties gathered in voltage-clamp experiments on single isolated rods.2. The network voltage responses to square current pulses became smaller, more transient, and had a longer time-to-peak, for rods further away from the site of current injection. Depolarizing currents produced smaller responses than hyperpolarizing currents of the same magnitude.3. Neighbouring rods and cones were coupled less strongly than neighbouring rods.4. The response of the rod network to current injection was unaffected by 2 mm-aspartate(-), which eliminates transmission from receptors to horizontal cells.5. The input resistance of single isolated rods, measured at the resting potential, varied between 100 and 680 MOmega. The lower values were probably due to damage by the micro-electrodes. Electrical coupling was found to be very strong between the rod inner and outer segments.6. A strong ;instantaneous' outward rectification seen in isolated rods at potentials positive to -35 mV was reduced, but not abolished, by 15 mm-TEA.7. In normal solution, isolated rods exhibited a voltage- and time-dependent current, I(A), whose kinetics were approximated by a single first-order gating variable, and whose activation curve spanned the range between -40 and -80 mV. The time constant for the current varied with voltage and was 60-200 msec between -140 and -40 mV.8. A reversal potential for I(A) could not be found between -140 and -40 mV in normal solution, and the fully activated current, I(A), was approximately voltage-independent, with a magnitude of approximately 0.1 nA over this potential range.9. By several criteria, I(A) behaved as a single inward current activated by hyperpolarization. Pharmacological studies suggest, however, that it is the sum of at least two currents with very similar kinetics.10. Most isolated rods exhibited a very slow (tau approximately 3 sec) increase in net outward current on depolarizing beyond -35 mV. The magnitude of this current varied considerably between cells.11. Assuming that the rod network can be approximated by a square lattice of individual rods, resistively coupled together, the voltage-clamp data on isolated rods were used to predict the response of the network to current injection at one cell. The theoretical and observed network behaviour were in good agreement. The resistance coupling neighbouring rods was estimated to be approximately 300 MOmega. The current I(A) plays a major role in determining the behaviour of the rod network.12. The time-dependent current, I(A), is responsible for the peak-plateau wave form of the response to a bright flash. A current similar to I(A) could also account for the negative propagation velocity of the peak of the dim flash response, through the rod network of the turtle, observed by Detwiler, Hodgkin & McNaughton (1978).

Animals↗
PubMed2002

Specificity and stability in topology of protein networks.

Molecular networks guide the biochemistry of a living cell on multiple levels: Its metabolic and signaling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network. To address topological properties of these two networks, we quantified correlations between connectivities of interacting nodes and compared them to a null model of a network, in which all links were randomly rewired. We found that for both interaction and regulatory networks, links between highly connected proteins are systematically suppressed, whereas those between a highly connected and low-connected pairs of proteins are favored. This effect decreases the likelihood of cross talk between different functional modules of the cell and increases the overall robustness of a network by localizing effects of deleterious perturbations.

Cell Nucleus↗
PubMed2006

Empirical analysis of an evolving social network.

Social networks evolve over time, driven by the shared activities and affiliations of their members, by similarity of individuals' attributes, and by the closure of short network cycles. We analyzed a dynamic social network comprising 43,553 students, faculty, and staff at a large university, in which interactions between individuals are inferred from time-stamped e-mail headers recorded over one academic year and are matched with affiliations and attributes. We found that network evolution is dominated by a combination of effects arising from network topology itself and the organizational structure in which the network is embedded. In the absence of global perturbations, average network properties appear to approach an equilibrium state, whereas individual properties are unstable.

Electronic Mail↗
PubMed2004

Soft networks for bridging the gap between research and practice: illuminative evaluation of CHAIN.

OBJECTIVES: To explore the process of knowledge exchange in an informal email network for evidence based health care, to illuminate the value of the service and its critical success factors, and to identify areas for improvement. DESIGN: Illuminative evaluation. SETTING: Targeted email and networking service for UK healthcare practitioners and researchers. PARTICIPANTS: 2800 members of a networking service. MAIN OUTCOME MEASURES: Tracking of email messages, interviews with core staff, and a qualitative analysis of messages, postings from focus groups, and invited and unsolicited feedback to the service. RESULTS: The informal email network helped to bridge the gap between research and practice by serving as a rich source of information, providing access to members' experiences, suggestions, and ideas, facilitating cross boundary collaboration, and enabling participation in networking at a variety of levels. Ad hoc groupings and communities of practice emerged spontaneously as members discovered common areas of interest. CONCLUSION: This study illuminated how knowledge for evidence based health care can be targeted, personalised, and made meaningful through informal social processes. Critical success factors include a broad based membership from both the research and service communities; a loose and fluid network structure; tight targeting of messages based on members' interests; the presence of a strong network identity and culture of reciprocity; and the opportunity for new members to learn through passive participation.

Attitude to Computers↗
PubMed1996

A prospective study of social networks in relation to total mortality and cardiovascular disease in men in the USA.

STUDY OBJECTIVE: Previous studies have established a relationship between low levels of social networks and total mortality, but few have examined cause specific mortality or disease incidence. This study aimed to examine prospectively the relationships between social networks and total and cause specific mortality, as well as cardiovascular disease incidence. DESIGN: This was a four year follow up study in an ongoing cohort of men, for whom information on social networks was collected at baseline. The main outcome measures were total mortality, further categorised into deaths from cardiovascular disease (stroke and coronary heart disease), total cancer, accidents/suicides, and all other causes; as well as stroke and coronary heart disease incidence. PARTICIPANTS: Altogether 32,624 US male health professionals aged 42 to 77 years in 1988, who were free of coronary heart disease, stroke, and cancer at baseline. RESULTS: A total of 511 deaths occurred during 122,911 person years of follow up. Compared with men with the highest level of social networks, socially isolated men (not married, fewer than six friends or relatives, no membership in church or community groups) were at increased risk for cardiovascular disease mortality (age adjusted relative risk, 1.90; 95% CI 1.07, 3.37) and deaths from accidents and suicides (age adjusted relative risk 2.22; 95% CI 0.76, 6.47). No excess risks were found for other causes of death. Socially isolated men were also at increased risk of stroke incidence (relative risk, 2.21; 95% CI, 1.12, 4.35), but not incidence of non-fatal myocardial infarction. CONCLUSIONS: Social networks were associated with lower total mortality by reducing deaths from cardiovascular disease and accidents/suicides. Strong social networks were associated with reduced incidence of stroke, though not of coronary heart disease. However, social networks may assist in prolonging the survival of men with established coronary heart disease.

Accidents↗
PubMed2003

Translating clinical research into practice: practice-based research networks--a promising solution.

Greater effort is needed to translate research discoveries into clinical practice and to ensure that proven treatments are routinely implemented by physicians. Practice-based research networks are an undervalued resource in the endeavor to bring research results to bear in patient care. These networks are groups of practicing health care providers who have organized to address research questions of primary importance to their patients. Existing practice-based research networks have addressed a wide range of issues, including improvement of preventive service delivery, reliability of diagnostic measures, practice variation, disease prevention, and systems of care coordination. Several deficiencies in the current system prevent practice-based research networks from reaching their full potential as mechanisms of translating clinic research into practice. For practice-based research networks to flourish, they need increased funding for practice-based research networks; information systems to facilitate research by practicing physicians; training programs for health care providers; and communication networks between providers, clinical researchers, professional societies, and academic health centers.

Academic Medical Centers↗
PubMed2002

Sexual network structure as an indicator of epidemic phase.

Ascertaining epidemic phase for a sexually transmitted disease (STD) has depended on secular trend data which often contain significant artefacts. The usefulness of sexual network structure as an indicator of STD epidemic phase is explored in an analysis of community wide genital chlamydia reports, with network analysis of interviewed cases and linked sexual partners, in Colorado Springs, USA, 1996 to 1999. In this period, the chlamydia case rate per 100,000 increased by 46%. Three quarters of cases (n=4953) were interviewed, nominating 7365 partners; these, combined with index cases, made up the 9114 persons in the network. Epidemiologic analysis of cases suggests that secular trend increases are artefactual. Network analysis supports this view: overall network structure is fragmented and dendritic, notably lacking the cyclic (closed loops) structures associated with network cohesion and thus with efficient STD transmission. Comparison of network structure with that of an intense STD outbreak (characterised by numerous cyclic structures) suggests low level or declining endemic rather than epidemic chlamydia transmission during the study interval. These observations accord with intuitive and stochastic predictions.

Adolescent↗
PubMed2004

Effect of shear stress on microvessel network formation of endothelial cells with in vitro three-dimensional model.

Shear stress stimulus is expected to enhance angiogenesis, the formation of microvessels. We determined the effect of shear stress stimulus on three-dimensional microvessel formation in vitro. Bovine pulmonary microvascular endothelial cells were seeded onto collagen gels with basic fibroblast growth factor to make a microvessel formation model. We observed this model in detail using phase-contrast microscopy, confocal laser scanning microscopy, and electron microscopy. The results show that cells invaded the collagen gel and reconstructed the tubular structures, containing a clearly defined lumen consisting of multiple cells. The model was placed in a parallel-plate flow chamber. A laminar shear stress of 0.3 Pa was applied to the surfaces of the cells for 48 h. Promotion of microvessel network formation was detectable after approximately 10 h in the flow chamber. After 48 h, the length of networks exposed to shear stress was 6.17 (+/-0.59) times longer than at the initial state, whereas the length of networks not exposed to shear stress was only 3.30 (+/-0.41) times longer. The number of bifurcations and endpoints increased for networks exposed to shear stress, whereas the number of bifurcations alone increased for networks not exposed to shear stress. These results demonstrate that shear stress applied to the surfaces of endothelial cells on collagen gel promotes the growth of microvessel network formation in the gel and expands the network because of repeated bifurcation and elongation.

Animals↗
PubMed1980

A dorsal spinal neural network in cat. I. Responses to single impulses in single type I cutaneous input fibers.

1. We have studied some properties of a sacral dorsal spinal gray matter network. the lamina 4:type 1 afferent fiber network (L4:T1 network) in 24 adult cats that were anesthetized with urethan and the spinal cord transected at the thoracolumbar junction. 2. The network in the first sacral segment is composed of a subgroup of lamina 4 cells as principal neurons that are connected to type 1 afferent fibers emerging from the skin, the manipulable input channels. Other primary afferent fibers and axons of central cells of other segments may also be input elements. Cells of the substantia gelatinosa (SG) and of the marginal layer constitute the intrinsic neurons. We monitored the output of the network by unit recording of the lamina 4 cell's impulse activity. 3. We activated the network by single impulses delivered via single type 1 afferent fibers. We stimulated fibers individually by focused electrical stimulation and monitored the selectivity of the stimulus by a computer-averaging procedure. The basic stimulus paradigm (each stimulus trial) consisted of 100 single impulses delivered 1 impulse/3 s. For nine networks, each of the accessible type 1 fibers was used as an input channel. 4. The typical pattern of response to the 100 impulses was composed of: a) an early discharge lasting for 5 ms after the input impulse invades the central arbor of the type 1 fiber, b) a late discharge of variable duration terminated by c) a postresponse reduction in ongoing discharge rate. Early-only and late-only discharges were occasionally observed. We conclude that the response pattern reflects the specific neuronal and synaptic configuration that is engaged by each input channel. 5. Across input channels, the early discharge was characterized by: a) a bimodal distribution of low- and high-probability responses, reflecting two predominating groups of type 1 input channels, one believed to be weakly coupled and the other strongly coupled to the principal neuron; b) relatively little multiple discharge; c) modal response during the first 2 ms of the discharge; d) response produced via a monosynaptic connection of the type 1 fiber with the lamina 4 neuron and average synaptic delay of 0.53 +/- 0.01 ms (mean +/- SE, n = 100); e) in general, a stable response throughout the 5-min stimulus trial, although an occasional habituating response was noted. 6. The late discharge was characterized by: a) a multiple discharge and a wide response jitter; b) mean duration approximately 29 ms; c) in general, high-probability response; d) a tendency for the response to wane during the course of the stimulus trial. 7. We observed no relationship between the magnitude of the early or late response and the level of ongoing discharge when considered across input channels. However, for a given input channel over time, the output response was often highly correlated with the level of ongoing discharge. The effect was best described by a log-log relationship...

Animals↗
PubMed1998

Long-term expression of two interacting motor pattern-generating networks in the stomatogastric system of freely behaving lobster.

Rhythmic movements of the gastric mill and pyloric regions of the crustacean foregut are controlled by two stomatogastric neuronal networks that have been intensively studied in vitro. By using electromyographic recordings from the European lobster, Homarus gammarus, we have monitored simultaneously the motor activity of pyloric and gastric mill muscles for </=3 mo in intact and freely behaving animals. Both pyloric and gastric mill networks are almost continuously active in vivo regardless of the presence of food. In unfed resting animals kept under "natural-like" conditions, the pyloric network expresses the typical triphasic pattern seen in vitro but at considerably slower cycle periods (2. 5-3.5 s instead of 1-1.5 s). Gastric mill activity occurs at mean cycle periods of 20-50 s compared with 5-10 s in vitro but may suddenly stop for up to tens of minutes, then restart without any apparent behavioral reason. When conjointly active, the two networks express a strict coupling that involves certain but not all motor neurons of the pyloric network. The posterior pyloric constrictor muscles, innervated by a total of 8 pyloric (PY) motor neurons, are influenced by the onset of each gastric mill medial gastric/lateral gastric(MG/LG) neuron powerstroke burst, and for one cycle, PY neuron bursts may attain >300% of their mean duration. However, the duration of activity in the lateral pyloric constrictor muscle, innervated by the unique lateral pyloric (LP) motor neuron, remains unaffected by this perturbation. During this period after gastric perturbation, LP neuron and PY neurons thus express opposite burst-to-period relationships in that LP neuron burst duration is independent of the ongoing cycle period, whereas PY neuron burst duration changes with period length. In vitro the same type of gastro-pyloric interaction is observed, indicating that it is not dependent on sensory inputs. Moreover, this interaction is intrinsic to the stomatogastric ganglion itself because the relationship between the two networks persists after suppression of descending inputs to the ganglion. Intracellular recordings reveal that this gastro-pyloric interaction originates from the gastric MG and LG neurons of the gastric network, which inhibit the pyloric pacemaker ensemble. As a consequence, the pyloric PY neurons, which are inhibited by the pyloric dilator (PD) neurons of the pyloric pacemaker group, extend their activity during the time that PD neuron is held silent. Moreover, there is evidence for a pyloro-gastric interaction, apparently rectifying, from the pyloric pacemakers back to the gastric MG/LG neuron group.

Animals↗
PubMed2000

Segregation of nociceptive and non-nociceptive networks in the squirrel monkey somatosensory thalamus.

The somatosensory thalamus (here we examine neurons in the caudal cutaneous portion of ventral posterior lateral nucleus, VPL) is composed of a somatotopic arrangement of anteroposteriorly oriented rods. Each rod is a collection of neurons with homogeneous properties that relay sensory information to specific cortical columns. We developed a multi-electrode recording technique, using fixed-geometry four-tip electrodes that allow simultaneous recordings from small populations of neurons (4-11), in a approximately 150 x 150 x 150 micrometer(3) volume of brain tissue (i.e., the approximate diameter of rods) and study of their spatiotemporal interactions. Due to the fixed geometry of the four-tip electrodes, the relative locations of these neurons can be determined, and due to the simultaneity of the recordings, their spike-timing coordination can be calculated. With this method, we demonstrate the existence of two distinct functional networks: nociceptive and non-nociceptive networks. The population dynamics of these two types of networks are different: cross-correlations in each type of network were different in direction and strength, were a function of the distance between neurons, had an opponent organization for nociceptive networks and a non-opponent organization for non-nociceptive networks, and rapidly changed under different stimulus conditions independent of changes in firing rates. A simple neural network model mimicked these physiological findings, demonstrating the necessity of inhibitory interneurons and different amounts of afferent input synchronization. Based on these results, we conclude that the somatosensory thalamus is composed of two modules, nociceptive and non-nociceptive rods, and that the response dynamics differences between these modules are due to spatiotemporal differences of their afferent inputs.

Action Potentials↗
PubMed2001

Identification of two types of inspiratory pacemaker neurons in the isolated respiratory neural network of mice.

In the respiratory network of mice, we characterized with the whole cell patch-clamp technique pacemaker properties in neurons discharging in phase with inspiration. The respiratory network was isolated in a transverse brain stem slice containing the pre-Bötzinger complex (PBC), the presumed site for respiratory rhythm generation. After blockade of respiratory network activity with 6-cyano-7-nitroquinoxalene-2,3-dione (CNQX), 18 of 52 inspiratory neurons exhibited endogenous pacemaker activity, which was voltage dependent, could be reset by brief current injections and could be entrained by repetitive stimuli. In the pacemaker group (n = 18), eight neurons generated brief bursts (0.43 +/- 0.03 s) at a relatively high frequency (1.05 +/- 0.12 Hz) in CNQX. These bursts resembled the bursts that these neurons generated in the intact network during the interval between two inspiratory bursts. Cadmium (200 microM) altered but did not eliminate this bursting activity, while 0.5 microM tetrodotoxin suppressed bursting activity. Another set of pacemaker neurons (10 of 18) generated in CNQX longer bursts (1.57 +/- 0.07 s) at a lower frequency (0.35 +/- 0.01 Hz). These bursts resembled the inspiratory bursts generated in the intact network in phase with the population activity. This bursting activity was blocked by 50-100 microM cadmium or 0.5 microM tetrodotoxin. We conclude that the respiratory neural network contains pacemaker neurons with two types of bursting properties. The two types of pacemaker activities might have different functions within the respiratory network.

6-Cyano-7-nitroquinoxaline-2,3-dione↗
PubMed2002

Long-term modulation of respiratory network activity following anoxia in vitro.

Neural networks that produce rhythmic behaviors require flexibility to respond to changes in the internal and external state of the animal. It is important to not only understand how a network responds during such perturbations but also how the network recovers. For example, the respiratory network needs to respond to and recover from temporary changes in oxygen level that can occur during sleep, exercise, and respiratory disorders. During a temporary decrease in oxygen level, there is an increase in respiratory frequency followed by a depression that can lead to complete apnea. Here we used a mouse brain stem slice preparation as a model system to examine the recovery of respiratory network activity after brief episodes of anoxia. We found the respiratory network recovers from a single anoxic episode with a transient increase in fictive respiratory frequency. Although repetitive anoxia does not elicit a greater frequency increase, it does elicit a longer lasting frequency increase persisting < or =90 min. Thus there is a centrally mediated long-lasting influence on the respiratory network elicited by decreased oxygen levels. This modulation occurs as a prolonged facilitation of fictive respiratory frequency after brief repetitive but not single anoxic exposure. These data are important to consider in the context of disorders such as sleep apnea in which brief periodic anoxic episodes are experienced.

Animals↗
PubMed1990

Blood flow in microvascular networks. Experiments and simulation.

A theoretical model has been developed to simulate blood flow through large microcirculatory networks. The model takes into account the dependence of apparent viscosity of blood on vessel diameter and hematocrit (the Fahraeus-Lindqvist effect), the reduction of intravascular hematocrit relative to the inflow hematocrit of a vessel (the Fahraeus effect), and the disproportionate distribution of red blood cells and plasma at arteriolar bifurcations (phase separation). The model was used to simulate flow in three microvascular networks in the rat mesentery with 436,583, and 913 vessel segments, respectively, using experimental data (length, diameter, and topological organization) obtained from the same networks. Measurements of hematocrit and flow direction in all vessel segments of these networks tested the validity of model results. These tests demonstrate that the prediction of parameters for individual vessel segments in large networks exhibits a high degree of uncertainty; for example, the squared coefficient of correlation between predicted and measured hematocrit of single vessel segments ranges only between 0.15 and 0.33. In contrast, the simulation of integrated characteristics of the network hemodynamics, such as the mean segment hematocrit or the distribution of blood flow velocities, is very precise. In addition, the following conclusions were derived from the comparison of predicted and measured values: 1) The low capillary hematocrits found in mesenteric microcirculatory networks as well as their heterogeneity can be explained on the basis of the Fahraeus effect and phase-separation phenomena. 2) The apparent viscosity of blood in vessels of the investigated tissue with diameters less than 15 microns is substantially higher than expected compared with measurements in glass tubes with the same diameter.

Animals↗
PubMed2002

Descartes' rule of signs for radial basis function neural networks.

We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the Vapnik-Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two or more input nodes have superlinear VC dimension. The rules also give rise to lower bounds for network sizes, thus demonstrating the relevance of network parameters for the complexity of computing with RBF neural networks.

Journal Article↗