Reconstruction of the time-dependent wave function exclusively from position data.

A method is presented that reconstructs the amplitude and phase of an unknown time-dependent pure-state wave function entirely from experimental position data. No assumptions about the wave function are needed. At a series of times, a large collection of position data is taken, but no measurements of momentum or energy are necessary.

Entrainment control in a noisy neural system.

The open-plus-closed-loop (OPCL) entrainment control put forth by Jackson and Grosu [Physica D 85, 1 (1995)] is applied to an effective-neuron system as a way to extract stable limit cycles from a chaotic attractor, analogous to the retrieval of memories from a memory searching state. Additive Gaussian white noise, representing the natural noise inherent in any real dynamical system, is added to the entrainment control mechanism. Moderate levels of additive noise have little effect on successful entrainment, as reflected in phase-space plots and Lyapunov exponents.

Tsallis maximum entropy principle and the law of large numbers.

Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this Brief Report, we show that the generalized canonical distribution so obtained may differ from that predicted by the law of large numbers when empirical samples are held to the same constraint. This conclusion is based on a result regarding the large deviation property of conditional measures and is confirmed by numerical evidence.