No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

A nonlocally weighted soft-constrained natural gradient iterative method is introduced for robust blind separation in reverberant environment. The nonlocal weighting of the iterations promotes stability and convergence of the algorithm for long demixing filters. The scaling degree of freedom is controlled by soft-constraints built into the auxiliary difference equations. The small divisor problem of iterations in silence durations of speech is resolved. Computations on synthetic speech mixtures based on measured binaural room impulse responses show that the algorithm achieves higher signal-to-inteference ratio improvement than existing method (natural gradient time domain algorithm) in an office size room with reverberation time over 0.5 second.

We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each volume spectrum is realized by the min-max value of certain relative homotopy class of sweepouts of boundaries of Caccioppoli sets. The main result follows by approximating such min-max value using the min-max theory for hypersurfaces with prescribed mean curvature established by the author with Zhu.