Global existence of the harmonic map heat flow into Lorentzian manifolds

We investigate a parabolic-elliptic system for maps $(u,v)$ from a compact Riemann surface $M$ into a Lorentzian manifold $N\times{\mathbb{R}}$ with a warped product metric. That system turns the harmonic map type equations into a parabolic system, but keeps the $v$-equation as a nonlinear second order constraint along the flow. We prove a global existence result of the parabolic-elliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a Lorentzian harmonic map in a given homotopy class with fixed boundary data.Comment: to appear in J. Math. Pures App

Reliable Broadcast to A User Group with Limited Source Transmissions

In order to reduce the number of retransmissions and save power for the source node, we propose a two-phase coded scheme to achieve reliable broadcast from the source to a group of users with minimal source transmissions. In the first phase, the information packets are encoded with batched sparse (BATS) code, which are then broadcasted by the source node until the file can be cooperatively decoded by the user group. In the second phase, each user broadcasts the re-encoded packets to its peers based on their respective received packets from the first phase, so that the file can be decoded by each individual user. The performance of the proposed scheme is analyzed and the rank distribution at the moment of decoding is derived, which is used as input for designing the optimal BATS code. Simulation results show that the proposed scheme can reduce the total number of retransmissions compared with the traditional single-phase broadcast with optimal erasure codes. Furthermore, since a large number of transmissions are shifted from the source node to the users, power consumptions at the source node is significantly reduced.Comment: ICC 2015. arXiv admin note: substantial text overlap with arXiv:1504.0446

V2X Content Distribution Based on Batched Network Coding with Distributed Scheduling

Content distribution is an application in intelligent transportation system to assist vehicles in acquiring information such as digital maps and entertainment materials. In this paper, we consider content distribution from a single roadside infrastructure unit to a group of vehicles passing by it. To combat the short connection time and the lossy channel quality, the downloaded contents need to be further shared among vehicles after the initial broadcasting phase. To this end, we propose a joint infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) communication scheme based on batched sparse (BATS) coding to minimize the traffic overhead and reduce the total transmission delay. In the I2V phase, the roadside unit (RSU) encodes the original large-size file into a number of batches in a rateless manner, each containing a fixed number of coded packets, and sequentially broadcasts them during the I2V connection time. In the V2V phase, vehicles perform the network coded cooperative sharing by re-encoding the received packets. We propose a utility-based distributed algorithm to efficiently schedule the V2V cooperative transmissions, hence reducing the transmission delay. A closed-form expression for the expected rank distribution of the proposed content distribution scheme is derived, which is used to design the optimal BATS code. The performance of the proposed content distribution scheme is evaluated by extensive simulations that consider multi-lane road and realistic vehicular traffic settings, and shown to significantly outperform the existing content distribution protocols.Comment: 12 pages and 9 figure

Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the $3$-user $M_T\times M_R$ multiple-input multiple-output (MIMO) interference channel (IC) with \emph{rank-deficient} channel matrices, where each transmitter is equipped with $M_T$ antennas and each receiver with $M_R$ antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks $D_1$ and $D_2$, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., $D_1+D_2\leq \min(M_T, M_R)$, zero forcing is sufficient to achieve the optimal DoF. On the other hand, when $D_1+D_2> \min(M_T, M_R)$, a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.Comment: 28 pages, 7 figures. To appear in IEEE transactions on wireless communication

Transesterification of Poly(ethyl glyoxylate): A Route to Structurally Diverse Polyglyoxylates

Polyglyoxylates are a class of self-immolative polymers that depolymerize in solution and the solid state. The glyoxylic acid degradation product is a metabolite in the glyoxylate cycle and can also be processed in the liver in humans, making polyglyoxylates attractive for applications in the environment and in medicine. Although expanding the scope of available polyglyoxylates would enable new properties and applications, highly pure glyoxylate monomers are required for polymerization, and this level of purity is difficult to achieve for many potential monomers. To address this challenge, we report here the 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD)-catalyzed post-polymerization transesterification of poly(ethyl glyoxylate) (PEtG) as a general method for the synthesis of directly inaccessible polyglyoxylates. Using a new end-capping strategy, PEtG compatible with the transesterification reaction was developed. n-Propanol, i-propanol, n-butanol, t-butanol, n-pentanol, n-hexanol, n-octanol, and benzyl alcohol were employed and the reactivities of these different alcohols were investigated. The resulting polyglyoxylates were characterized chemically and their thermal properties were compared. In all cases, the transesterified polyglyoxylates retained the stimuli-responsive depolymerization properties of the parent PEtG. In addition, functional polyglyoxylates based on allyl, propargyl, and furfuryl esters, which are suitable for subsequent click reactions, were prepared. The propargyl-functionalized polyglyoxylate was used to conjugate pyrene, and the resulting molecules underwent a change in fluorescence properties upon depolymerization