Spatiotemporal inseparability in early visual processing

We examine the implications of significant inseparable behaviour in centre-surround retinal cell types. From the form of a spatiotemporal centre-surround (CS) model which agrees qualitatively with physiological observations, we find that the sustained/transient dichotomy is a poor distinction for X-type/Y-type retinal ganglion cells since both exhibit inseparability. Static centre-surround models and spatiotemporal separable models are not valid for time-varying stimuli. Our results contradict the models for X- and Y-type ganglion cells proposed by Marr and Hildreth (1980) and Marr and Ullman (1981), and raise doubts about the physiological validity of Marr's zerocrossing theory. The CS filter is an attractive precursor to the extraction of 2-d motion information.     

Identification of plant volatiles activating single receptor neurons in the pine weevil (Hylobius abietis)

Naturally produced plant volatiles, eliciting responses of single olfactory receptor neurons in the pine weevil, have been identified by gas chromatography linked with mass spectrometry. The receptor neurons (n = 72) were classified in 30 types, according to the compound which elicited the strongest response in each neuron, 20 of which compounds were identified. Most potent for 14 types of neurons (n = 50) were monoterpenes, including bicyclic (e.g. α-pinene, camphor and myrtenal) for 8 types (n = 32), monocyclic (limonene, carvone, α-terpinene) for 3 types (n = 12) and acyclic (e.g. β-myrcene and linalool) for 3 types (n = 6). Other compounds eliciting strongest responses of a neuron were five sesquiterpenes, including α-copaene and a farnesene-isomer, and an anethole type which has no biosynthetic relationship with terpenes. Within one type, receptor neurons with quite selective responses to the most potent compound as well as neurons with additional responses to several, structurally similar compounds were found, indicating that the neurons may have the same functional types of membrane receptors, but different sensitivities. Response spectra of neurons within the bicyclic-, mono-cyclic and acyclic types showed more overlapping than across the neuron types. Minimal overlapping response spectra was found between monoterpene and sesquiterpene neurons. The results suggest that this structure-activity relationship is significant for encoding plant odour information in the pipe weevil. Accepted: 6 January 1997     

Bayesian inference in populations of cortical neurons: a model of motion integration and segmentation in area MT

A major issue in cortical physiology and computational neuroscience is understanding the interaction between extrinsic signals from feedforward connections and intracortical signals from lateral connections. We propose here a computational model for motion perception based on the assumption that the local cortical circuits in the medio-temporal area (area MT) implement a Bayesian inference principle. This approach establishes a functional balance between feedforward and lateral, excitatory and inhibitory, inputs. The model reproduces most of the known properties of the neurons in area MT in response to moving stimuli. It accounts for important motion perception phenomena including motion transparency, spatial and temporal integration/segmentation. While integrating several properties of previously proposed models, it makes specific testable predictions concerning, in particular, temporal properties of neurons and the architecture of lateral connections in area MT. In addition, the proposed mechanism is consistent with the known properties of local cortical circuits in area V1. This suggests that Bayesian inference may be a general feature of information processing in cortical neuron populations. Received: 3 December 1997 / Accepted in revised form: 21 July 1998     

Schema design and implementation of the grasp-related mirror neuron system

 Mirror neurons within a monkey's premotor area F5 fire not only when the monkey performs a certain class of actions but also when the monkey observes another monkey (or the experimenter) perform a similar action. It has thus been argued that these neurons are crucial for understanding of actions by others. We offer the hand-state hypothesis as a new explanation of the evolution of this capability: the basic functionality of the F5 mirror system is to elaborate the appropriate feedback – what we call the hand state– for opposition-space based control of manual grasping of an object. Given this functionality, the social role of the F5 mirror system in understanding the actions of others may be seen as an exaptation gained by generalizing from one's own hand to an other's hand. In other words, mirror neurons first evolved to augment the “canonical” F5 neurons (active during self-movement based on observation of an object) by providing visual feedback on “hand state,” relating the shape of the hand to the shape of the object. We then introduce the MNS1 (mirror neuron system 1) model of F5 and related brain regions. The existing Fagg–Arbib–Rizzolatti–Sakata model represents circuitry for visually guided grasping of objects, linking the anterior intraparietal area (AIP) with F5 canonical neurons. The MNS1 model extends the AIP visual pathway by also modeling pathways, directed toward F5 mirror neurons, which match arm–hand trajectories to the affordances and location of a potential target object. We present the basic schemas for the MNS1 model, then aggregate them into three “grand schemas”– visual analysis of hand state, reach and grasp, and the core mirror circuit – for each of which we present a useful implementation (a non-neural visual processing system, a multijoint 3-D kinematics simulator, and a learning neural network, respectively). With this implementation we show how the mirror system may learnto recognize actions already in the repertoire of the F5 canonical neurons. We show that the connectivity pattern of mirror neuron circuitry can be established through training, and that the resultant network can exhibit a range of novel, physiologically interesting behaviors during the process of action recognition. We train the system on the basis of final grasp but then observe the whole time course of mirror neuron activity, yielding predictions for neurophysiological experiments under conditions of spatial perturbation, altered kinematics, and ambiguous grasp execution which highlight the importance of the timingof mirror neuron activity. Received: 6 August 2001 / Accepted in revised form: 5 February 2002     

Antennal response of codling moth males, Cydia pomonella L. (Lepidoptera: Tortricidae), to the geometric isomers of codlemone and codlemone acetate

Single sensillum recordings from Cydia pomonella male antennae showed three different types of receptor neurons. The most abundant type was most sensitive to the main pheromone compound (E,E)-8,10-dodecadienol, while its response to the geometric isomers E,Z, Z,E and Z,Z was comparable to a tenfold lower dose of (E,E)-8,10-dodecadienol. This neuron type also responded to the four behaviorally antagonistic isomers of (Δ,Δ)-8,10-dodecadienyl acetate, among which it was most sensitive to the E,E isomer. Cross-adaptation studies showed that these compounds were all detected by the same receptor neuron type. Receptor neurons specifically tuned to (E,Z) or (Z,Z)-8,10-dodecadienol were not found, although these two compounds are behaviorally active. A second type of receptor neuron responded to all isomers of (Δ,Δ)-8,10-dodecadienyl acetate and was most sensitive to the E,E isomer. This neuron type did not respond to any of the isomers of (Δ,Δ)-8,10-dodecadienol. A third receptor neuron type was highly sensitive to the plant compound α-farnesene. The finding that the receptor neuron type tuned to the main pheromone compound responded even to strong behavioral antagonists aids the interpretation of ongoing behavioral studies for the development of the mating disruption technique in codling moth. Accepted: 3 March 2000     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Visual channels, Hebbian assemblies and the effect of Hebb's rule

 A model of sensory learning is proposed that is based upon Hebb's rule, where Hebb's rule has been generalised by introducing a stabilising function representing some feedback process within or at the adapting (cortical) neuron, preventing synaptic weights from increasing without limit. It will be shown that neurons adapting according to this stabilised Hebb rule will turn into a matched filter for that part of the stimulus pattern that covers the receptive field of a neuron. It follows that the presentation of a stimulus pattern may imply the formation of a set of neurons with overlapping receptive fields, where each neuron has adapted to a certain part of the stimulus. Making simplifying assumptions about the detection process, the model will be illustrated, fitting it to data from Meinhardt and Mortensen [Meinhardt G, Mortensen U (1998) Biol Cybern 79:413–425] which are not compatible with the classical matched filter model introduced by Hauske et al. [Hauske G, Wolf W, Lupp U (1976) Biol Cybern 22:181–188]. Received: 10 May 1999 / Accepted in revised form: 22 October 1999     

Morphological characterization of single fan-shaped body neurons in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

The fan-shaped body is the largest substructure of the central complex in Drosophila melanogaster. Two groups of large-field neurons that innervate the fan-shaped body, viz., F1 and F5 neurons, have recently been found to be involved in visual pattern memory for “contour orientation” and “elevation” in a rut-dependent manner. The F5 neurons have been found to be responsible for the parameter “elevation” in a for-dependent manner. We have shown here that the F1 neuron also affects visual memory for “contour orientation” in a for-dependent way. With the help of Gal4/UAS and FLP-out techniques, we have characterized the morphological features of these two groups of neurons at single neuron resolution. We have observed that F1 or F5 neurons are groups of isomorphic individual neurons. Single F1 neurons have three main arborization regions: one in the first layer of the fan-shaped body, one in the ventral body, and another in the inferior medial protocerebrum. Single F5 neurons have two arborization regions: one in the fifth layer of the fan-shaped body and the other in the superior medial protocerebrum. The polarity of the F1 and F5 neurons has been studied with the Syt-GFP marker. Our results indicate the existence of presynaptic sites of both F1 and F5 neurons located in the fan-shaped body and postsynaptic sites outside of the fan-shaped body. This work was supported by the “973 Program” (2005CB522804 and 2009CB918702), the National Natural Sciences Foundation of China (30621004, 30625022, and 30770682), and the Knowledge Innovation Program of the Chinese Academy of Sciences (KSCX2-YW-R-28).     

A stochastic model and a functional central limit theorem for information processing in large systems of neurons

The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1≤i≤N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.     

<Emphasis Type="Italic">Brn-3a</Emphasis> Deficiency Transiently Increases Expression of Calbindin D-28 k and Calretinin in the Trigeminal Ganglion During Embryonic Development

Immunohistochemistry for neuron-specific nuclear protein (NeuN), caspase-3, calcitonin gene-related peptide (CGRP), and calcium-binding proteins was performed on the trigeminal ganglion (TG) in wild type and Brn-3a knockout mice at embryonic days 12.5–16.5 (E12.5–E16.5). In Brn-3a knockout mice, the number of NeuN-immunoreactive (ir) neuron profiles increased at E14.5 (40.0% increase) and decreased at E16.5 (28.3% reduction) compared to wild type mice. Caspase-3-ir neuron profiles were abundant in the TG of wild type mice at E12.5–E16.5. However, the loss of Brn-3a decreased the number of caspase-3-ir neuron profiles at E12.5 (69.7% reduction) and E14.5 (51.7% reduction). At E16.5, the distribution of caspase-3-ir neuron profiles was barely affected by the deficiency. CGRP-ir neuron profiles were observed in the TG of wild type mice but not knockout mice at E12.5. At E14.5 and E16.5, CGRP-ir neuron profiles were abundant in both wild type and knockout mice. Calbindin D-28 k (CB)-ir neuron profiles decreased in the TG of mutant mice at E12.5 compared to wild type mice (56.4% reduction). At E14.5, however, Brn-3a deficiency transiently increased CB-ir neuron profiles (169.4% increase as compared to wild type mice). Calretinin (CR)-ir neuron profiles could not be detected in the TG of wild type mice at E12.5–16.5. However, numerous CR-ir neuron profiles transiently appeared in the knockout mouse at E14.5. Parvalbumin (PV)-ir neurons appeared in wild type and knockout mice at E14.5. At this stage, the number of large (>50 μm²) PV-ir neuron profiles in knockout mice was fewer than that in wild type mice. The number and cell size of PV-ir neuron profiles were barely affected by the deficiency at E16.5. The present study indicates that the loss of Brn-3a causes increase of TG neurons at E14.5 and decrease of TG neurons at E16.5. It is also suggested that Brn-3a deficiency affects the number and cell size of CGRP- and calcium-binding protein-containing neurons at E12.5 and E14.5. Caspase-3-dependent cell death of CB- and CR-ir neurons may be suppressed by the deficiency at E14.5.     

A novel key–lock mechanism for inactivating amino acid neurotransmitters during transit across extracellular space

There are two kinds of neurotransmissions that occur in brain. One is neuron to neuron at synapses, and the other is neuron to glia via extracellular fluid (ECF), both of which are important for maintenance of proper neuronal functioning. For neuron to neuron communications, several potent amino acid neurotransmitters are used within the confines of synaptic space. However, their presence at elevated concentrations in extra-synaptic space could be detrimental to well organized neuronal functioning. The significance of the synthesis and release of N-acetylaspartylglutamate (NAAG) by neurons has long been a puzzle since glutamate (Glu) itself is the “key” that can interact with all Glu receptors on membranes of all cells. Nonetheless, neurons synthesize this acetylated dipeptide, which cannot be catabolized by neurons, and release it to ECF where its specific physiological target is the Glu metabotropic receptor 3 on the surface of astrocytes. Since Glu is excitotoxic at elevated concentrations, it is proposed that formation and release of NAAG by neurons allows large quantities of Glu to be transported in ECF without the risk of injurious excitotoxic effects. The metabolic mechanism used by neurons is a key–lock system to detoxify Glu during its intercellular transit. This is accomplished by first synthesizing N-acetylaspartate (NAA), and then joining this molecule via a peptide bond to Glu. In this paper, a hypothesis is presented that neurons synthesize a variety of relatively nontoxic peptides and peptide derivatives, including NAA, NAAG, homocarnosine (γ-aminobutyrylhistidine) and carnosine (β-alanylhistidine) from potent excitatory and inhibitory amino acids for the purpose of releasing them to ECF to function as cell-specific neuron-to-glia neurotransmitters.     

Parameters for a model of an oscillating neuronal network in the cochlear nucleus defined by genetic algorithms

Chopper neurons in the cochlear nucleus are characterized by intrinsic oscillations with short average interspike intervals (ISIs) and relative level independence of their response (Pfeiffer, Exp Brain Res 1:220–235, 1966; Blackburn and Sachs, J Neurophysiol 62:1303–1329, 1989), properties which are unattained by models of single chopper neurons (e.g., Rothman and Manis, J Neurophysiol 89:3070–3082, 2003a). In order to achieve short ISIs, we optimized the time constants of Rothman and Manis single neuron model with genetic algorithms. Some parameters in the optimization, such as the temperature and the capacity of the cell, turned out to be crucial for the required acceleration of their response. In order to achieve the relative level independence, we have simulated an interconnected network consisting of Rothman and Manis neurons. The results indicate that by stabilization of intrinsic oscillations, it is possible to simulate the physiologically observed level independence of ISIs. As previously reviewed and demonstrated (Bahmer and Langner, Biol Cybern 95:371–379, 2006a), chopper neurons show a preference for ISIs which are multiples of 0.4 ms. It was also demonstrated that the network consisting of two optimized Rothman and Manis neurons which activate each other with synaptic delays of 0.4 ms shows a preference for ISIs of 0.8 ms. Oscillations with various multiples of 0.4 ms as ISIs may be derived from neurons in a more complex network that is activated by simultaneous input of an onset neuron and several auditory nerve fibers.     

Primary culture and characteristic morphologies of neurons from the cerebral ganglion of the mud crab, <Emphasis Type="Italic">Scylla paramamosain</Emphasis>

Crustacean neurons, obtained from the cerebral ganglion of the mud crab Scylla paramamosain, were successfully cultured in vitro. They maintained typical morphological characteristics and showed better outgrowth in modified Medium 199 (M199) medium than that in Liebowitz’s L-15 medium. Fetal bovine serum (FBS), muscle extracts, and hemolymph of the mud crab S. paramamosain were added as supplements. Only 20% FBS could promote neuron outgrowth, while muscle extracts and hemolymph of S. paramamosain did not improve neuron outgrowth. For cell dissociation, both collagenase type I and trypsin worked well as determined by initial cell viability and following cell outgrowth potential. More than six kinds of cells with different morphological characteristics were identified in the neuron outgrowth. They were “small cells”, “veilers”, “branchers”, “multipolar cells”, “super-large cell”, and “bipolar cells”. Among all of the cells, bipolar cells were identified for the first time in crustacean neurons culture and they could live longer than other cells. The neurons could grow for more than a week before retraction and eventual degradation.     

Sensorin-A immunocytochemistry reveals putative mechanosensory neurons inLymnaea CNS

The pond snailLymnaea stagnalis is a useful model system for studying the neural basis of behaviour but the mechanosensory inputs that impact on behaviours such as respiration, locomotion, reproduction and feeding are not known. InAplysia, the peptide sensorin-A appears to be specific to a class of central mechanosensory neurons. We show that in theLymnaea central nervous system sensorin-A immunocytochemistry reveals a discrete pattern of staining involving well over 100 neurons. Identifiable sensorin positive clusters of neurons are located in the buccal and cerebral ganglia, and a single large neuron is immunopositive in each pedal ganglion. These putative mechanosensory neurons are not in the same locations as previously identified motoneurons, interneurons or neurosecretory cells. As would be expected for a mechanoafferent, sensorin positive fibres were found in nerve tracts innervating the body wall. This study lays the foundation for future electrophysiological and behavioural analysis of these putative mechanosensory neurons.     

Contribution to the probabilistic theory of neural nets: IV. Various models for inhibition

Input-output formulas are derived for a neuron upon which converge single axones of two other neurons, which are subjected to a Poisson shower, where a number of different assumptions are made concerning the mechanism of inhibition. In one assumption so-called “bilateral pre-inhibition” is considered. That is to say, both neuronsN ₁ andN ₂ may exciteN ₃, but if the stimulus of one of them follows within a certain interval σ of the other, the second stimulus is not effective. This model is essentially no different from that involving two excitatory neurons acting upon a neuron having a refractory period. Another mechanism considered involves so-called “pre-and-post” inhibition, in which if two stimuli fromN ₁ andN ₂ fall within σ,both are ineffective. This case being mathematically much more involved than the preceding, an approximation method is used for deriving the input-output formula. Previous papers of this series are denoted by I, II, and III in this paper.     

A retinal circuit model accounting for wide-field amacrine cells

In previous experimental studies on the visual processing in vertebrates, higher-order visual functions such as the object segregation from background were found even in the retinal stage. Previously, the “linear–nonlinear” (LN) cascade models have been applied to the retinal circuit, and succeeded to describe the input-output dynamics for certain parts of the circuit, e.g., the receptive field of the outer retinal neurons. And recently, some abstract models composed of LN cascades as the circuit elements could explain the higher-order retinal functions. However, in such a model, each class of retinal neurons is mostly omitted and thus, how those neurons play roles in the visual computations cannot be explored. Here, we present a spatio-temporal computational model of the vertebrate retina, based on the response function for each class of retinal neurons and on the anatomical inter-cellular connections. This model was capable of not only reproducing the spatio-temporal filtering properties of the outer retinal neurons, but also realizing the object segregation mechanism in the inner retinal circuit involving the “wide-field” amacrine cells. Moreover, the first-order Wiener kernels calculated for the neurons in our model showed a reasonable fit to the kernels previously measured in the real retinal neuron in situ.     

Octopamine modulates the sensitivity of silkmoth pheromone receptor neurons

Effects of octopamine and its antagonist epinastine on electrophysiological responses of receptor neurons of Antheraea polyphemus specialised to the pheromone components (E,Z)-6,11-hexadecadienyl acetate and (E,Z)-6,11-hexadecadienal were investigated. Injections of octopamine and epinastine into the moths had no effect on the transepithelial potential of the antennal-branch preparation nor on the spontaneous nerve impulse frequency in either type of receptor neuron. However, in the presence of continuous low-intensity pheromone stimulation, octopamine significantly increased the nerve impulse frequency in the acetate receptor neuron, but not in the aldehyde receptor neuron. Octopamine and epinastine had no significant effect on the receptor potential amplitudes elicited in both receptor neuron types by pheromone stimulation. However, the peak nerve impulse frequency in the response of both receptor neuron types to pheromone was significantly affected: decreased by epinastine and increased by octopamine over a broad range of pheromone concentrations. In control experiments, injection of physiological saline did not significantly alter the peak nerve impulse frequency. The effect of octopamine was established within 1 h after injection and persisted for about 4 h. The possibility of a direct action of octopamine on the nerve impulse generation by the receptor neurons is discussed. Accepted: 8 January 2000     

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics. Received: 8 August 1997 / Accepted in revised form: 18 June 1998     

Analysis of the exponential decay model of the neuron showing frequency threshold effects

The exponential decay model of a neuron has been analyzed using the “random walk” approach of stochastic processes and an “absorbing barrier” solution is obtained forg ^T (s)—the Laplace transform of the output pulse interval density function. An expression for the mean output frequency is derived from this and a variety of input-output curves plotted which show frequency threshold effects in single neurons. Our results are compared with those of other authors obtained by computer simulation techniques, and the significance of these results discussed with reference to the possible behavior of networks constructed of such neuron units.     

Fault tolerance in the cardiac ganglion of the lobster

Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results. Received: 2 April 1998 / Accepted in revised form: 2 July 1998