A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200

Observer weighting of interaural cues in positive and negative envelope slopes of amplitude-modulated waveforms

The auditory system can encode interaural delays in highpass-filtered complex sounds by phase locking to their slowly modulating envelopes. Spectrotemporal analysis of interaurally time-delayed highpass waveforms reveals the presence of a concomitant interaural level cue. The current study systematically investigated the contribution of time and concomitant level cues carried by positive and negative envelope slopes of a modified sinusoidally amplitude-modulated (SAM) high-frequency carrier. The waveforms were generated from concatenation of individual modulation cycles whose envelope peaks were extended by the desired interaural delay, allowing independent control of delays in the positive and negative modulation slopes. In experiment 1, thresholds were measured using a 2-interval forced-choice adaptive task for interaural delays in either the positive or negative modulation slopes. In a control condition, thresholds were measured for a standard SAM tone. In experiment 2, decision weights were estimated using a multiple-observation correlational method in a single-interval forced-choice task for interaural delays carried simultaneously by the positive, and independently, negative slopes of the modulation envelope. In experiment 3, decision weights were measured for groups of 3 modulation cycles at the start, middle, and end of the waveform to determine the influence of onset dominance or recency effects. Results were consistent across experiments: thresholds were equal for the positive and negative modulation slopes. Decision weights were positive and equal for the time cue in the positive and negative envelope slopes. Weights were also larger for modulations cycles near the waveform onset. Weights estimated for the concomitant interaural level cue were positive for the positive envelope slope and negative for the negative slope, consistent with exclusive use of time cues.We thank Virginia M. Richards and Bruce G. Berg for helpful discussions. We also thank Brian C. J. Moore and an anonymous reviewer for their insightful comments on an earlier draft of the manuscript. Work supported by grants from the National Science Council, Taiwan NSC 98-2410-H-008-081-MY3 and NIH R01DC009659

Interactive Music with Active Audio CDs

International audienc