Quantum Brain: A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets

A theoretical quantum brain model is proposed using a nonlinear Schroedinger wave equation. The model proposes that there exists a quantum process that mediates the collective response of a neural lattice (classical brain). The model is used to explain eye movements when tracking moving targets. Using a Recurrent Quantum Neural Network(RQNN) while simulating the quantum brain model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical brain, a wave packet is triggered in the quantum brain. This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of 'jumps' and 'rests'. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter.Comment: 7 pages, 7 figures submitted to Physical Review Letter

Heat treatment enhances the plant phenolic (+)-catechin, a weak antimicrobial agent when combined with copper sulphate

The aim of the study was to compare the antimicrobial activities of freshly-made, heat-treated (HT), and 14 d stored (+)-Catechin solutions with (+)-catechin flavanol isomers in the presence of copper sulphate. (+)-Catechin activity was investigated when combined with different ratios of Cu(2+) ; 100°C heat treatment; autoclaving; and 14 d storage against Staphylococcus aureus. Cu(2+) -(+)-Catechin complexation, isomer structure-activity relationships, and H2 O2 generation were also investigated. Freshly-made, HT, and 14d stored flavanols showed no activity. Whilst combined Cu(2+) -autoclaved (+)-Catechin and -HT(+)-Catechin activities were similar, HT(+)-Catechin was more active than either freshly-made (+)-catechin (generating more H2 O2 ) or (-)-Epicatechin (though it generated less H2 O2 ) or 14d-(+)-Catechin (which had similar activity to Cu(2+) controls - though it generated more H2 O2 ). When combined with Cu(2+) , in terms of rates of activity, HT(+)-Catechin was lower than (-)-Epigallocatechin gallate and greater than freshly-made (+)-Catechin. Freshly-made and HT(+)-Catechin formed acidic complexes with Cu(2+) as indicated by pH and UV-vis measurements although pH changes did not account for antimicrobial activity. Freshly-made and HT(+)-Catechin both formed Cu(2+) complexes. The HT(+)-Catechin complex generated more H2 O2 which could explain its higher antimicrobial activity. This article is protected by copyright. All rights reserved

Quantum Mechanical Interaction-Free Measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91

A C-squared Polygonal Surface Patch

A polygonal patch is defined to fill an n-sided hole within a C2 parametric continuous rectangular patch complex

Projective spaces of a C*-algebra

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group of A. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean - in Schwarz-Zaks terminology) are considered, allowing a comparison among P(p), the Grassmann manifold of A and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection e = 2p-1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics.Comment: 26 pages, Late

Seeing a c-theorem with holography

There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms. The latter allows us to distinguish the flow of the central charges $a$ and $c$ in the dual field theories in four dimensions. One finds that the flow of $a$ is naturally monotonic but that of $c$ is not. Extending the analysis of holographic RG flows to higher dimensions, we are led to formulate a novel c-theorem in arbitrary dimensions for a universal coefficient appearing in the entanglement entropy of the fixed point CFT's.Comment: 5 pages, 1 figure, v2: minor change