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A Pellionisz

Publications and source records attributed to A Pellionisz.

11 recordsLinked to original sources
PubMed1985

Tensor network theory of the metaorganization of functional geometries in the central nervous system.

Here we present an elaboration and a quantitative example for a hypothetical neuronal process, implementing what we refer to as the metaorganization principle. This process allows the internalization of external (body) geometries into the central nervous system (CNS) and a reciprocal and equally important action of the CNS geometry on the external (body) geometry. The hypothesis is based on the distinction, within the CNS, between covariant sensory and contravariant motor vectorial expressions of the extrinsic geometry. These sensory and motor expressions, given in natural co-ordinate systems, are transformed from one to the other by a neuronal network which acts as a metric tensor. The metric tensor determines the relationship of these two expressions and thus comprises the functional geometry of the system. The emergence through metaorganization of networks that implement such metric function is viewed as the result of interactions between the covariant motor execution which generates a physical action on the external world (via the musculoskeletal system) and the covariant sensory proprioception which measures the effect of such motor output. In this transformation of contravariants to covariants by the physical geometry of the motor system, a covariant metric tensor is expressed implicitly. However, co-ordinated motor action requires its dual tensor (the contravariant metric) which is assembled in the CNS based on the metaorganization principle, i.e. the ability of CNS and external geometries to mold one another. The two metric transformations acting on each other detect error signals whenever the match of the physical and functional geometries is imperfect. Such error signals are utilized by the metaorganization process to improve the match between the two metrics, so that with use the internal representation becomes increasingly homeometric with the geometry of the external world. The proposed physical process by which the metaorganization principle is implemented is based on oscillatory reverberation. If covariant proprioception is used as a recurrent signal to the motor apparatus, as if it were a contravariant motor expression, then reverberations at their steady-state yield the eigenvectors and eigenvalues of the system. The stored eigenvectors and eigenvalues can serve, respectively, as a means for the genesis of a metric (in the form of its spectral representation) with the given eigenvectors and as a means of comparing the eigenvalues that are implicit in the external body geometry and those of the internal metric.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1985

Tensorial computer model of gaze--I. Oculomotor activity is expressed in non-orthogonal natural coordinates.

The central nervous system expresses its function in natural frames of reference. A most conspicuous feature of such frames is their non-orthogonality. Gaze stabilization and, in particular, the sensorimotor transformations performed by the vestibulo-ocular reflex, are prime examples of such general coordinate transformations between and within multidimensional non-orthogonal frames. Since such operations can be described by tensor formalisms in an abstract manner, this methodology is applied here to develop a tensorial computer model of gaze stabilization. The representation of sensorimotor transformations by a reference-frame independent method obviates the necessity to simplify the intrinsic coordinate systems either by a reduction of the dimensionality or by a presumption of orthogonality. The frames of reference intrinsic to vestibulo-ocular reflex transformation (the vestibular semicircular canals and extraocular muscles) as well as the covariant character of the sensory input and the contravariant character of the motor output are physically obvious. A model built on these intrinsic systems of coordinates first serves to quantitate the degree of non-orthogonality in the extraocular muscle system, and thus to demonstrate both the necessity and the applicability of representing them by a formalism suitable for non-orthogonal systems, such as tensor network theory. The actual non-orthogonality of the gaze-stabilization system can be quantitated on the basis of the difference of covariant and contravariant expressions as follows. Tensor network theory describes sensorimotor transformations by employing a covariant embedding procedure. This, however, yields a covariant intention-type motor vector. If the central nervous system were to transmit these sensory-type components directly to the extraocular muscle motor mechanism, an error-angle would occur since covariants do not physically compose the intended movement. The error in every direction of gaze would be zero only if the extraocular muscle system would constitute an orthogonal set of rotation axes. Otherwise, the error, called refraction angle, is a measure of non-orthogonality. The complexity of the quantitation of non-orthogonality is compounded by the fact that these rotation axes change with the moving eye. Calculation of eye movements, executed both by covariant and contravariant vectors from primary and secondary eye positions, is based on the simplest assumption that the central nervous system establishes the covariant-contravariant transformation in the retinal tangent plane.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1974

Dynamic single unit simulation of a realistic cerebellar network model. II. Purkinje cell activity within the basic circuit and modified by inhibitory systems.

In continuation of earlier computer simulation studies 15 of the feedback inhibition exercised by the Golgi cells of the cerebellum, an attempt is made at modeling the behavior of Purkinje and basket cells under somewhat more complex functional circumstances. The simulation study is based on a realistic network model (with respect to numerical and metrical parameters, and consisting of more than 3 X 10(4) units) of the cat cerebellar cortex, derived from a recent quantitative histological and stereological analysis 9-12. As an input two identical pairs of foci of incoming mossy fiber activity are applied, separated from one another both spatially and temporally. The stimulation results showed that the assumption of a rigidly preaddressed wiring in the parallel fiber--Purkinje cell synaptic system (i.e. that parallel fibers would systematically select for contact Purkinje cells standing in register) would hardly be realistic because such a solution would offer no advantage whatever over a randomly connected synaptic system. The results would favor the contention that dendritic geometry of the Purkinje cells has a crucial significance in the sense of the concepts developed by W. Rall. The stimulation gives some important hints for the ways in which the specific inhibitory interneuron systems (Golgi and basket cells) add refinement to the operations of the network, particularly in securing integration of the influences of parallel fibers thrown into action by mossy input to spatially and temporally separated foci, especially at the level of Purkinje cells positioned in interfocal areas. Reducing the length of the parallel fibers to one-half of what was suggested by the stereological studies causes a serious breakdown of interfocal neighborhood interactions.

Action Potentials↗