Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

Nitrate and the origin of saliva influence composition and short chain fatty acid production of oral microcosms

Nitrate is emerging as a possible health benefactor. Especially the microbial conversion of nitrate to nitrite in the oral cavity and the subsequent conversion to nitric oxide in the stomach are of interest in this regard. Yet, how nitrate influences the composition and biochemistry of the oral ecosystem is not fully understood. To investigate the effect of nitrate on oral ecology, we performed a 4-week experiment using the multiplaque artificial mouth (MAM) biofilm model. This model was inoculated with stimulated saliva of two healthy donors. Half of the microcosms (n = 4) received a constant supply of nitrate, while the other half functioned as control (n = 4). Additionally, all microcosms received a nitrate and sucrose pulse, each week, on separate days to measure nitrate reduction and acid formation. The bacterial composition of the microcosms was determined by 16S rDNA sequencing. The origin of the saliva (i.e., donor) showed to be the strongest determinant for the development of the microcosms. The supplementation of nitrate was related to a relatively high abundance of Neisseria in the microcosms of both donors, while Veillonella was highly abundant in the nitrate-supplemented microcosms of only one of the donors. The lactate concentration after sucrose addition was similarly high in all microcosms, irrespective of treatment or donor, while the concentration of butyrate was lower after nitrate addition in the nitrate-receiving microcosms. In conclusion, nitrate influences the composition and biochemistry of oral microcosms, although the result is strongly dependent on the inoculum

INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at [email protected] (internet)

The Dipole Moments and Molar Refractions of Several Trans-Beta-Nitrostyrenes

The dipole moments and molar refractions are reported for p-nitrostyrene (4.24 D, 44.3 ml.), trans-betanitrostyrene (4.50 D, 45.7 ml.), the p-methoxy (5.45 D, 56.3 ml.), p-methyl (4.97 D, 52.0 ml.), p-fluoro (3-12 D, 45.5ml), p-chloro (2.90 D, 51.8 ml.), p-bromo (3.02 D, 54.4 ml.), p-iodo (3.26 D, 58.0 ml.), p-nitro (0.83 D, 52.0 ml.), and p-cyano 0.96 D, 47.9 ml.) derivatives of trans-beta-nitrostyrene. It is suggested that the large dipole moments obtained for the p-nitro and p-cyano-beta-nitrostyrenes may be due to unusually large atomic polarizations which would not be taken into consideration by the present method of measurement and calculation