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

@article{Pellionisz1985TensorNT, title={Tensor network theory of the metaorganization of functional geometries in the central nervous system}, author={A. J. Pellionisz and Rodolfo R. Llin{\'a}s}, journal={Neuroscience}, year={1985}, volume={16}, pages={245-273} }

## 308 Citations

Consciousness, Functional Geometry and Internal Representation

- Biology
- 2014

The approach henceforth named tensor network theory is sufficiently rich to allow specific computational modelling and addressed the issue of prediction, based on Taylor series expansion properties of the system, at the neuronal level, as a basic property of brain function.

Dynamic geometry, brain function modeling, and consciousness.

- Computer ScienceProgress in brain research
- 2008

Geometrical approach to neural net control of movements and posture.

- Computer ScienceProgress in brain research
- 1993

METRIC TENSOR AS DEGREE OF COHERENCE IN THE DYNAMICAL ORGANIZATION OF THE CENTRAL NERVOUS SYSTEM

- Biology
- 2012

The degree of coherence in the oscillatory activities of neuron can be interpreted as embodying a metric tensor of non-Euclidean space that produce topological order associated to CNS development.

Tensor geometry: a language of brains & neurocomputers. Generalized coordinates in neuroscience & robotics

- Computer Science
- 1988

Utilizations of the tensor approach center on natural and artificial sensorimotor operations, promoting a co-evolution of coordinated (and intelligent) robots with Nature’s systems such as adaptive cerebellar compensatory reflexes.

Tensorial aspects of the multidimensional massively parallel sensorimotor function of neuronal networks.

- Biology, PsychologyProgress in brain research
- 1988

Predictability of Brain and Decision Making

- Computer Science
- 2016

The central issue in brain function is to understand how the internalization of the properties of the external world is realized within an internal functional space, which is closely related to dynamic geometry where Bayesian probability has been shown to be necessary for understanding this predictability.

Recursive Genome Function of the Cerebellum: Geometric Unification of Neuroscience and Genomics

- BiologyHandbook of the Cerebellum and Cerebellar Disorders
- 2021

Recursive Fractal Genome Function in the geometric mind frame of Tensor Network Theory (TNT) leads through FractoGene to a mathematical unification of physiological and pathological development of…

Does the Cerebellum Implement or Select Geometries? A Speculative Note

- Biology, PsychologyThe Cerebellum
- 2020

It is speculated that the cerebellum should be involved in implementing and/or selecting task-specific geometries for motor and cognitive skills, and its geometrical role deserves a renewal of interest, which may provide a better understanding of its specific contributions to motor and associative (cognitive) functions.

Towards a Theory of Brain Structure and Function

- Psychology
- 2014

The eminent mathematician Henri Poincare wrote “The aim of science is not things in themselves, as the dogmatists in their simplicity imagine, but the relations between things; outside those…

## References

SHOWING 1-10 OF 117 REFERENCES

Tensorial approach to the geometry of brain function: Cerebellar coordination via a metric tensor

- Computer ScienceNeuroscience
- 1980

Coordination: a vector-matrix description of transformations of overcomplete CNS coordinates and a tensorial solution using the Moore-Penrose generalized inverse.

- Computer ScienceJournal of theoretical biology
- 1984

Brain modeling by tensor network theory and computer simulation. The cerebellum: Distributed processor for predictive coordination

- BiologyNeuroscience
- 1979

Tensor Theory of Brain Function. The Cerebellum as a Space-Time Metric

- Biology
- 1982

The Tensor Network Theory of Central Nervous System (a geometrical abstraction and generalization of the known vector-matrix approaches) is capable of yielding a usable understanding and a tensorial network model capable of generating motor coordination via cerebellar-type neuronal circuits is offered.

Space-time representation in the brain. The cerebellum as a predictive space-time metric tensor

- Computer ScienceNeuroscience
- 1982

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

- BiologyNeuroscience
- 1985

Tensorial Brain Theory in Cerebellar Modelling

- Biology
- 1984

The cerebellum has been studied by now in more detail than virtually any other part of the brain and attempts have been made to erect a structure in order to show how knowledge of the functioning may be built into an understanding of neural function.

VESTIBULO-OCULAR REFLEX ARC

- Biology
- 1933

When Cajal and van Gehuchten developed the concept of axonal polarization, the elementary reflex arc acquired a more general significance and became the expression of the fundamental plan of structure and function of the nervous system.

The Cerebellum—New Vistas

- Biology
- 1982

The present volume consists of papers prepared for a conference on the cerebellum which was held at the National Institutes of Health in Bethesda on 15 -17 May 1980, and offers the best model the authors have for analyzing the vertebrate central nervous system.