1,919 research outputs found
Kadison's antilattice theorem for a synaptic algebra
We prove that if A is a synaptic algebra and the orthomodular lattice P of
projections in A is complete, then A is a factor iff A is an antilattice. We
also generalize several other results of R. Kadison pertaining to infima and
suprema in operator algebras
Modeling Quantum Mechanical Observers via Neural-Glial Networks
We investigate the theory of observers in the quantum mechanical world by
using a novel model of the human brain which incorporates the glial network
into the Hopfield model of the neural network. Our model is based on a
microscopic construction of a quantum Hamiltonian of the synaptic junctions.
Using the Eguchi-Kawai large N reduction, we show that, when the number of
neurons and astrocytes is exponentially large, the degrees of freedom of the
dynamics of the neural and glial networks can be completely removed and,
consequently, that the retention time of the superposition of the wave
functions in the brain is as long as that of the microscopic quantum system of
pre-synaptics sites. Based on this model, the classical information entropy of
the neural-glial network is introduced. Using this quantity, we propose a
criterion for the brain to be a quantum mechanical observer.Comment: 24 pages, published versio
Returnability in complex directed networks (digraphs)
The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as well as for real-world complex directed networks and are compared with the reciprocity
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