An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of $\eta$ type associated to $K^1$ representatives on even dimensional manifolds, which should be of independent interests. For example, it gives an intrinsic interpretation of the so called Wess-Zumino term in the WZW theory in physics.Comment: Completely revised. A gap in the proof fixed. To appear in JF

Rateless-Coding-Assisted Multi-Packet Spreading over Mobile Networks

A novel Rateless-coding-assisted Multi-Packet Relaying (RMPR) protocol is proposed for large-size data spreading in mobile wireless networks. With this lightweight and robust protocol, the packet redundancy is reduced by a factor of $\sqrt n$, while the spreading time is reduced at least by a factor of $\ln (n)$. Closed-form bounds and explicit non-asymptotic results are presented, which are further validated through simulations. Besides, the packet duplication phenomenon in the network setting is analyzed for the first time

Light Induced Hall effect in semiconductors with spin-orbit coupling

We show that optically excited electrons by a circularly polarized light in a semiconductor with spin-orbit coupling subject to a weak electric field will carry a Hall current transverse to the electric field. This light induced Hall effect is a result of quantum interference of the light and the electric field, and can be viewed as a physical consequence of the spin current induced by the electric field. The light induced Hall conductance is calculated for the p-type GaAs bulk material, and the n-type and p-type quantum well structures.Comment: 5 pages, 3 figure

Mobile Conductance in Sparse Networks and Mobility-Connectivity Tradeoff

In this paper, our recently proposed mobile-conductance based analytical framework is extended to the sparse settings, thus offering a unified tool for analyzing information spreading in mobile networks. A penalty factor is identified for information spreading in sparse networks as compared to the connected scenario, which is then intuitively interpreted and verified by simulations. With the analytical results obtained, the mobility-connectivity tradeoff is quantitatively analyzed to determine how much mobility may be exploited to make up for network connectivity deficiency.Comment: Accepted to ISIT 201