Statistical wave field theory.

In this paper, we introduce the foundations of the Statistical Wave Field Theory. This theory establishes the statistical laws of waves propagating in a closed bounded volume, that are mathematically implied by the boundary-value problem of the wave equation. These laws are derived from the Sturm-Liouville theory and the mathematical theory of dynamical billiards.

Absorptive nature of scattering coefficients in stress-energy tensor formalism for room acoustics.

In the stress-energy tensor formalism, the symmetry between absorption and scattering coefficients, as proven by measurements combined with simulations, is counterintuitive. By introducing the wall admittance, we show that the scattering coefficient is partly created by the real part of the wall admittance combined with the active intensity, that is, is partly due to absorption. However, for curved surfaces or finite source distances, it also depends on the imaginary part of the wall admittance in combination with the reactive intensity, which confers its genuine scattering properties inversely proportional to the distances to the sources.

Common mathematical framework for stochastic reverberation models.

In the field of room acoustics, it is well known that reverberation can be characterized statistically in a particular region of the time-frequency domain (after the transition time and above Schroeder's frequency). Since the 1950s, various formulas have been established, focusing on particular aspects of reverberation: exponential decay over time, correlations between frequencies, correlations between sensors at each frequency, and time-frequency distribution. In this paper, the author introduces a stochastic reverberation model, which permits us to retrieve all these well-known results within a common mathematical framework.

Stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization.

Multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints, such as the famous nonnegative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov's stability theory provides a very enlightening viewpoint on the problem.