On a power-type coupled system of Monge-Ampère equations

We study an elliptic system coupled by Monge--Amp\`{e}re equations:$$\begin{cases}      \det D^{2}u_{1}={(-u_{2})}^\alpha & \hbox{in  $\Omega,$} \\      \det D^{2}u_{2}={(-u_{1})}^\beta & \hbox{in $\Omega,$} \\      u_{1}<0,\ u_{2}<0& \hbox{in  $\Omega,$}\\     u_{1}=u_{2}=0 & \hbox{on $ \partial \Omega,$}   \end{cases}$$%here $\Omega$~is a smooth, bounded and strictly convex domainin~$\mathbb{R}^{N}$, $N\geq2$, \alpha >0, \beta >0. When $\Omega$ isthe unit ball in $\mathbb{R}^{N}$, we use index theory of fixedpoints for completely continuous operators to get existence, uniqueness results and nonexistence of radial convex solutions undersome corresponding assumptions on $\alpha$, $\beta$. When \alpha>0,\beta>0 and $\alpha\beta=N^2$  we also study a~corresponding eigenvalue problem in more general domains

Observation of the Disorder-Induced Crystal-to-Glass Transition

The role of frustration and quenched disorder in driving the transformation of a crystal into a glass is investigated in quasi-two-dimensional binary colloidal suspensions. Frustration is induced by added smaller particles. The crystal-glass transition is measured to differ from the liquid-glass transition in quantitative and qualitative ways. The crystal-glass transition bears structural signatures similar to those of the crystal-fluid transition: at the transition point, the persistence of orientational order decreases sharply from quasilong range to short range, and the orientational order susceptibility exhibits a maximum. The crystal-glass transition also features a sharp variation in particle dynamics: at the transition point, dynamic heterogeneity grows rapidly, and a dynamic correlation length scale increases abruptly

Helical Packings and Phase Transformations of Soft Spheres in Cylinders

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as particle volume fraction is reduced, consistent with recent hard sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter psi_6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase transition-like behavior in quasi-1D systems.Comment: 5 pages, with additional 4 pages of supplemental material, accepted to Physical Review E: Rapid Communication

SIG-VC: A Speaker Information Guided Zero-shot Voice Conversion System for Both Human Beings and Machines

Nowadays, as more and more systems achieve good performance in traditional voice conversion (VC) tasks, people's attention gradually turns to VC tasks under extreme conditions. In this paper, we propose a novel method for zero-shot voice conversion. We aim to obtain intermediate representations for speaker-content disentanglement of speech to better remove speaker information and get pure content information. Accordingly, our proposed framework contains a module that removes the speaker information from the acoustic feature of the source speaker. Moreover, speaker information control is added to our system to maintain the voice cloning performance. The proposed system is evaluated by subjective and objective metrics. Results show that our proposed system significantly reduces the trade-off problem in zero-shot voice conversion, while it also manages to have high spoofing power to the speaker verification system