TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite

The main result of this work is that an orthogonal access scheme such as TDMA achieves the all-unicast degrees of freedom (DoF) region of the topological interference management (TIM) problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem

Prediction of Stable Ground-State Lithium Polyhydrides under High Pressures

Hydrogen-rich compounds are important for understanding the dissociation of dense molecular hydrogen, as well as searching for room temperature Bardeen-Cooper-Schrieffer (BCS) superconductors. A recent high pressure experiment reported the successful synthesis of novel insulating lithium polyhydrides when above 130 GPa. However, the results are in sharp contrast to previous theoretical prediction by PBE functional that around this pressure range all lithium polyhydrides (LiHn (n = 2-8)) should be metallic. In order to address this discrepancy, we perform unbiased structure search with first principles calculation by including the van der Waals interaction that was ignored in previous prediction to predict the high pressure stable structures of LiHn (n = 2-11, 13) up to 200 GPa. We reproduce the previously predicted structures, and further find novel compositions that adopt more stable structures. The van der Waals functional (vdW-DF) significantly alters the relative stability of lithium polyhydrides, and predicts that the stable stoichiometries for the ground-state should be LiH2 and LiH9 at 130-170 GPa, and LiH2, LiH8 and LiH10 at 180-200 GPa. Accurate electronic structure calculation with GW approximation indicates that LiH, LiH2, LiH7, and LiH9 are insulative up to at least 208 GPa, and all other lithium polyhydrides are metallic. The calculated vibron frequencies of these insulating phases are also in accordance with the experimental infrared (IR) data. This reconciliation with the experimental observation suggests that LiH2, LiH7, and LiH9 are the possible candidates for lithium polyhydrides synthesized in that experiment. Our results reinstate the credibility of density functional theory in description H-rich compounds, and demonstrate the importance of considering van der Waals interaction in this class of materials.Comment: 34 pages, 15 figure