Coherent quantum effects have been confirmed for several
biological processes. These processes exist in the environment of a warm wet cell
where decoherence can be a serious concern. Here we propose a mechanism whereby
quantum coherence may extend through the water matrix of a cell. The model is based on coherent waves of established ultrafast energy
transfers in water. Computations based on the model are found to agree
with several experimental results and numerical and descriptive predictions are
presented. We compute wave speed, ~156 km/s,
and wavelength, ~9.3 nm, and determine that these waves retain local coherence. Close agreements are found for the
dipole moment of water dimers, results of microwave radiation on yeast, and the
Kleiber law of metabolic rates. The theory requires that a spherical cell must have
a minimum diameter of ~20 nm to accommodate a standing energy wave.
The quantum properties of the modelsuggest that cellular chemistry favors reactions that support perpetuation of the
energy waves.

Abstract:
Quantum processes have been confirmed for various biological phenomena. Here we model a quantum process in cells based on coherent waves of established ultrafast energy transfers in water. We compute wave speed, ~156 km/s, and wavelength, ~9.3 nm, and determine that the waves retain local coherence. The model is compared with observations and diverse numerical applications lend support to the hypothesis that rapid energy transfers in water are characteristic of living cells. Close agreements are found for the dipole moment of water dimers, microwave radiation on yeast, and the Kleiber law of metabolic rates. We find a sphere with diameter ~20 nm is a lower bound for life in this theory. The quantum properties of the model suggest that cellular chemistry favors reactions that support perpetuation of the energy waves

Abstract:
Since molecular energy transformations are responsible for chemical reaction rates at the most fundamental level, chemical kinetics should provide some information about molecular energies. This is the premise and objective of this note. We describe a Hamiltonian formulation for kinetic rate equations where the concentrations are the generalized coordinates and the conjugate momenta are simply related to individual average molecular energies. Simple examples are presented and the resulting energy relations naturally include non-equilibrium reactions. An analysis predicts the reasonable outcome that thermal agitation of a composite molecule increases its rate of dissociation.

Abstract:
All living cells transport molecules and ions across membranes, often against concentration gradients. This active transport requires continual energy expenditure and is clearly a nonequilibrium process for which standard equilibrium thermodynamics is not rigorously applicable. Here we derive a nonequilibrium effective potential that evaluates the per particle transport energy invested by the membrane. A novel method is used whereby a Hamiltonian function is constructed using particle concentrations as generalized coordinates. The associated generalized momenta are simply related to the individual particle energy from which we identify the effective potential. Examples are given and the formalism is compared with the equilibrium Gibb's free energy.

Abstract:
Adult humans’ recognition of self and others in diverse media (e.g., mirrors, videos) provides evidence for their skills at kinesthetic-visual and visual-visual matching, respectively. In this study, we examine self- and other-recognition in point-light displays (PLDs). Participants (7 men, 4 women) were filmed while walking in the dark with lighted joints to create two PLDs each, one showing a frontal view and one showing a half-profile view. Ten of the participants then observed 22 PLDs, two of themselves and two each of 10 familiar persons, and named whom they perceived in each PLD. Participants achieved greater than chance levels of accuracy in identifying themselves (55% of the time) and others (29.5%). Comparisons using three measures showed that participants were better at detecting themselves than others; however, variability in self- and other-detection within and across studies suggests caution prior to generalizing. Participants were equally successful in detecting walkers in frontal and half-profile PLDs, on average detecting about 3 walkers out of 11 in each perspective. Thus, participants showed some skill in using kinesthetic-visual and visual-visual matching in recognizing self and other, respectively, from the limited information present in PLDs.

Abstract:
We propose a technique for gait recognition from motion capture data based on two successive stages of principal component analysis (PCA) on kinematic data. The first stage of PCA provides a low dimensional representation of gait. Components of this representation closely correspond to particular spatiotemporal features of gait that we have shown to be important for visual recognition of gait in a separate psychophysical study. A second stage of PCA captures the shape of the trajectory within the low dimensional space during a given gait cycle across different individuals or gaits. The projection space of the second stage of PCA has distinguishable clusters corresponding to the individual identity and type of gait. Despite the simple eigen-analysis based approach, promising recognition performance is obtained.

Abstract:
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time step. Although redundant in the dx->0 limit, what if spatial derivatives were also stored? This paper presents an iterated, multipoint differential transform method (IMDTM) for numerically evolving PDE IVPs. Using this scheme, it is demonstrated that stored spatial derivatives can be propagated in an efficient and self-consistent manner; and can effectively contribute to the evolution procedure in a way which can confer several advantages, including aiding solution verification. Lastly, in order to efficiently implement the IMDTM scheme, a generalized finite-difference stencil formula is derived which can take advantage of multiple higher-order spatial derivatives when computing even-higher-order derivatives. As is demonstrated, the performance of these techniques compares favorably to other explicit evolution schemes in terms of speed, memory footprint and accuracy.

Abstract:
We show that, from a topological point of view, 2-tape B\"uchi automata have the same accepting power than Turing machines equipped with a B\"uchi acceptance condition. In particular, we show that for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete infinitary rational relations accepted by 2-tape B\"uchi automata. This very surprising result gives answers to questions of W. Thomas [Automata and Quantifier Hierarchies, in: Formal Properties of Finite automata and Applications, Ramatuelle, 1988, LNCS 386, Springer, 1989, p.104-119], of P. Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March 1992], and of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In: "A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].

Abstract:
We prove in this paper that the length of the Wadge hierarchy of omega context free languages is greater than the Cantor ordinal epsilon_omega, which is the omega-th fixed point of the ordinal exponentiation of base omega. The same result holds for the conciliating Wadge hierarchy, defined by J. Duparc, of infinitary context free languages, studied by D. Beauquier. We show also that there exist some omega context free languages which are Sigma^0_omega-complete Borel sets, improving previous results on omega context free languages and the Borel hierarchy.

Abstract:
We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power than Turing machines equipped with a B\"uchi acceptance condition. In particular, for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free languages accepted by 1-counter B\"uchi automata, and the supremum of the set of Borel ranks of context free omega languages is the ordinal gamma^1_2 which is strictly greater than the first non recursive ordinal. This very surprising result gives answers to questions of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].