Showing papers by "J. Leo van Hemmen published in 1994"

Coding and information processing in neural networks

Abstract: This paper reviews some central notions of the theoretical biophysics of neural networks, viz., information coding through coherent firing of the neurons and spatio-temporal spike patterns. After an introduction to the neural coding problem we first turn to oscillator models and analyze their dynamics in terms of a Lyapunov function. The rest of the paper is devoted to spiking neurons, a pulse code. We review the current neuron models, introduce a new and more flexible one, the spike response model (SRM), and verify that it offers a realistic description of neuronal behavior. The corresponding spike statistics is considered as well. For a network of SRM neurons we present an analytic solution of its dynamics, analyze the possible asymptotic states, and check their stability. Special attention is given to coherent oscillations. Finally we show that Hebbian learning also works for low activity spatio-temporal spike patterns. The models which we study always describe globally connected networks and, thus, have a high degree of feedback. We only touch upon functional feedback, that is, feedback between areas that have different tasks. Information processing in conjunction with functional feedback is treated explicitly in a companion paper [94].

Emergence of spatiotemporal receptive fields and its application to motion detection

Abstract: A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.

Associative binding and segregation in a network of spiking neurons

Abstract: A model of an associative network of spiking neurons (the Spike Response Model) with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neuron spikes and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. The patterns have been learned by an asymmetric Hebbian rule that can handle a low activity which may vary from pattern to pattern. During retrieval of a pattern all active neurons exhibit periodic spike bursts which may or may not be synchronized ( “locked” ) into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. It is argued that in a biological network an intermediate scenario of “weak locking” is most likely. In this regime, we discuss applications to feature linking and pattern segmentation as well as the problem of context sensitive binding that can be solved in a layered structure including feedback. In addition, we address the question of synchronization between the two hemispheres of the brain.