Present and permanent address: Physik-Department der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1

Abstract. Networks of compartmental model neurons were used to investigate the biophysical basis of the synchronization observed between sparsely-connected neurons in neocortex. A model of a single column in layer 5 consisted of 100 model neurons: 80 pyramidal and 20 inhibitory. The pyramidal cells had conductances that caused intrinsic repetitive bursting at different frequencies when driven with the same input. When connected randomly with a connection density of lo%, a single model column displayed synchronous oscillatory action potentials in response to stationary, uncorrelated Poisson spike-train inputs. Synchrony required a high ratio of inhibitory to excitatory synaptic strength; the optimal ratio was 4: 1, within the range observed in cortex. The synchrony was insensitive to variation in amplitudes of postsynaptic potentials and synaptic delay times, even when the mean synaptic delay times were varied over the range 1 to 7 ms. Synchrony was found to be sensitive to the strength of reciprocal inhibition between the inhibitory neurons in one column: Too weak or too strong reciprocal inhibition degraded intra-columnar synchrony. The only parameter that affected the oscillation frequency of the network was the strength of the external driving input which could shift the frequency between 35 to 60 Hz. The same results were obtained using a model column of 1000 neurons with a connection density of 5%, except that the oscillation became more regular. Synchronization between cortical columns was studied in a model consisting of two columns with 100 model

Although perseveration---the inappropriate repetition of previous responses---is quite common among patients with neurological damage, relatively few detailed computational accounts of its various forms have been put forth. A particularly well-documented variety involves the pattern of errors made by "optic aphasic" patients, who have a selective deficit in naming visually-presented objects. Based on our previous work in modeling impaired reading for meaning in deep dyslexia, we develop a connectionist simulation of visual object naming. The major extension in the present work is the incorporation of short-term correlational weights that bias the network towards reproducing patterns of activity that have occurred on recently preceding trials. Under damage, the network replicates the complex semantic and perseverative effects found in the optic aphasic error pattern. Further analysis reveals that the perseverative effects are strongest when the lesions are near or within semanti...

. We present the requirements for a neurocomputer for spike-processing neural networks. In a simulation study we investigated the performance of available hardware and showed, that there is still a need for a specific neurocomputer dedicated to the simulation of spike-processing networks. On the basis of our simulation study and an investigation of the features of spike-processing networks we analyses the requirements for the design of dedicated hardware. An efficient hardware architecture should contain an event-list module, a sender-oriented connection module and a number of fixed-point processing units. 1 Introduction Experimental results [1] [2] together with theoretical studies [3] [4] suggest that the time structure of neuronal spike trains is relevant in neuronal signal processing. The synchronized firing of neuronal assemblies could serve as a versatile and general mechanism for feature binding, pattern segmentation and figure/ground separation. This mechanism could also be u...

To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas using spiking neurons. Area P corresponds to the orientation selective subsystem of the primary visual cortex, while the central visual area C is modeled as associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, a single stimulus results in relatively slow and irregular activity, synchronized only for neighboring patches (slow state), while in the complete model activity is faster with enlarged synchronization range (fast state). Presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast state, where neurons representing the same object are simultaneously in the fast state. Correlation analysis reveals synchronization on different time scales as found in experiments (T,C,H peaks). On the fast time scale (T peaks, gamma frequency range), recordings from two sites coding either different or the same object lead to correlograms that are either at or exhibit oscillatory modulations with a central peak. This is in agreement with experimental findings while standard phase coding models would predict shifted peaks in the case of different objects.

Introduction In the eighties interest in artificial neural networks was revived by the incorporation of statistical methods and analogies in physical systems, e.g. the back-propagation algorithm and the Hopfield model. This led to the well-known growth of this field. For a few years there has been a strong tendency towards a return to biology and towards including more details of neuronal signal processing. The background of this shift of interest is the experimental proof of stimulus-induced synchronized brain activity [Eckh88] [Gray89]. Together with the Correlation Theory by von der Malsburg [Mals86] this results in the assumption, that temporal correlation of activity might be used by the brain as a code to bind features to one object and to segregate one object from others. The synchronised firing of neuronal assemblies could serve as a versatile and general mechanism for feature binding, pattern segmentation and figure /ground separation. How the brain accomplishes these

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We investigate a model in which excitatory neurons have dynamical thresholds which display both fatigue and potentiation. The fatigue property leads to oscillatory behavior. It is responsible for the ability of the model to perform segmentation, i.e., decompose a mixed input into staggered oscillations of the activities of the cell-assemblies (memories) affected by it. Potentiation is responsible for sustaining these staggered oscillations after the input is turned off, i.e. the system serves as a model for short term memory. It has a limited STM capacity, reminiscent of the magical number 7 6 2. 1 Introduction The limited capacity (7 6 2) of the short term memory (STM) has been a subject of major interest in the psychological and physiological literature. It seems quite natural to assume that the limited capacity is due to the special dynamical nature of STM. Recently, Crick and Koch (1990) suggested that the working memory is functionally related to the binding process, and...

This paper investigates the constraints placed on some synchronized oscillator models by their underlying dynamics. Phase response graphs are used to determine the phase locking behaviours of three oscillator models. These results are compared with idealized phase response graphs for single phase and multiple phase systems. We find that all three oscillators studied are best suited to operate in a single phase system and that the requirements placed on oscillatory models for operation in a multiple phase system are not compatible with the underlying dynamics of oscillatory behaviour for these types of oscillator models. 1 Introduction Following observations of oscillations and synchronization behaviour in cat visual cortex (Eckhorn et al., 1989; Gray et al., 1989a) a number of interpretations have been put forward to explain these results (Gray et al., 1989b; Eckhorn et al., 1988; Grossberg & Somers, 1991; Shastri, 1989; Sompolinsky et al., 1990). It has been suggested that a possibl...

Zero--lag synchrony arises between two points on the cerebral cortex when these receive concurrent independent inputs and has generally been ascribed to nonlinear mechanisms. We report results obtained by Principal Component Analysis (PCA) applied to simulations of cerebral cortex which exhibit zero--lag synchrony and realistic spectral content, and show that synchrony can arise by distinct and separable linear and nonlinear mechanisms. For lower levels of cortical activation synchrony between the sites of input can be accounted for by the eigenmodes associated with the wave activity generated by the inputs. The first spatial eigenmode arises from even 2 Clare L. Chapman et al. components in the independent input signals and the second spatial eigenmode arises from odd components in the inputs. Together these account for most of the signal variance, while the predominance of the first mode over the second within the near--field of the inputs accounts for zero--lag synchrony in the ne...