Role of peripheral afference during acquisition of a complex coordination task

It has long been supposed that the interference observed in certain patterns of coordination is mediated, at least in part, by peripheral afference from the moving limbs. We manipulated the level of afferent input, arising from movement of the opposite limb, during the acquisition of a complex coordination task. Participants learned to generate flexion and extension movements of the right wrist, of 75degrees amplitude, that were a quarter cycle out of phase with a 1-Hz sinusoidal visual reference signal. On separate trials, the left wrist either was at rest, or was moved passively by a torque motor through 50degrees, 75degrees or 100degrees, in synchrony with the reference signal. Five acquisition sessions were conducted on successive days. A retention session was conducted I week later. Performance was initially superior when the opposite limb was moved passively than when it was static. The amplitude and frequency of active movement were lower in the static condition than in the driven conditions and the variation in the relative phase relation across trials was greater than in the driven conditions. In addition, the variability of amplitude, frequency and the relative phase relation during each trial was greater when the opposite limb was static than when driven. Similar effects were expressed in electromyograms. The most marked and consistent differences in the accuracy and consistency of performance (defined in terms of relative phase) were between the static condition and the condition in which the left wrist was moved through 50degrees. These outcomes were exhibited most prominently during initial exposure to the task. Increases in task performance during the acquisition period, as assessed by a number of kinematic variables, were generally well described by power functions. In addition, the recruitment of extensor carpi radialis (ECR), and the degree of co-contraction of flexor carpi radialis and ECR, decreased during acquisition. Our results indicate that, in an appropriate task context, afferent feedback from the opposite limb, even when out of phase with the focal movement, may have a positive influence upon the stability of coordination.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Approach to designing rotating drum bioreactors for solid-state fermentation on the basis of dimensionless design factors

The development of large-scale solid-stale fermentation (SSF) processes is hampered by the lack of simple tools for the design of SSF bioreactors. The use of semifundamental mathematical models to design and operate SSF bioreactors can be complex. In this work, dimensionless design factors are used to predict the effects of scale and of operational variables on the performance of rotating drum bioreactors. The dimensionless design factor (DDF) is a ratio of the rate of heat generation to the rate of heat removal at the time of peak heat production. It can be used to predict maximum temperatures reached within the substrate bed for given operational variables. Alternatively, given the maximum temperature that can be tolerated during the fermentation, it can be used to explore the combinations of operating variables that prevent that temperature from being exceeded. Comparison of the predictions of the DDF approach with literature data for operation of rotating drums suggests that the DDF is a useful tool. The DDF approach was used to explore the consequences of three scale-up strategies on the required air flow rates and maximum temperatures achieved in the substrate bed as the bioreactor size was increased on the basis of geometric similarity. The first of these strategies was to maintain the superficial flow rate of the process air through the drum constant. The second was to maintain the ratio of volumes of air per volume of bioreactor constant. The third strategy was to adjust the air flow rate with increase in scale in such a manner as to maintain constant the maximum temperature attained in the substrate bed during the fermentation. (C) 2000 John Wiley & Sons, Inc.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.