Neutral triplet Collective Mode as a new decay channel in Graphite

In an earlier work we predicted the existence of a neutral triplet collective mode in undoped graphene and graphite [Phys. Rev. Lett. {\bf 89} (2002) 16402]. In this work we study a phenomenological Hamiltonian describing the interaction of tight-binding electrons on honeycomb lattice with such a dispersive neutral triplet boson. Our Hamiltonian is a generalization of the Holstein polaron problem to the case of triplet bosons with non-trivial dispersion all over the Brillouin zone. This collective mode constitutes an important excitation branch which can contribute to the decay rate of the electronic excitations. The presence of such collective mode, modifies the spectral properties of electrons in graphite and undoped graphene. In particular such collective mode, as will be shown in this paper, can account for some part of the missing decay rate in a time-domain measurement done on graphite

Heterogeneities in ventricular conduction following treatment with heptanol: A multi-electrode array study in Langendorff-Perfused mouse hearts

Background: Previous studies have associated slowed ventricular conduction with the arrhythmogenesis mediated by the gap junction and sodium channel inhibitor heptanol in mouse hearts. However, they did not study the propagation patterns that might contribute to the arrhythmic substrate. This study used a multi-electrode array mapping technique to further investigate different conduction abnormalities in Langendorff-perfused mouse hearts exposed to 0.1 or 2 mM heptanol. Methods: Recordings were made from the left ventricular epicardium using multi-electrode arrays in spontaneously beating hearts during right ventricular 8 Hz pacing or S1S2 pacing. Results: In spontaneously beating hearts, heptanol at 0.1 and 2 mM significantly reduced the heart rate from 314 ± 25 to 189 ± 24 and 157 ± 7 bpm, respectively (ANOVA, p < 0.05 and p < 0.001). During regular 8 Hz pacing, the mean LATs were increased by 0.1 and 2 mM heptanol from 7.1 ± 2.2 ms to 19.9 ± 5.0 ms (p < 0.05) and 18.4 ± 5.7 ms (p < 0.05). The standard deviation of the mean LATs was increased from 2.5 ± 0.8 ms to 10.3 ± 4.0 ms and 8.0 ± 2.5 ms (p < 0.05), and the median of phase differences was increased from 1.7 ± 1.1 ms to 13.9 ± 7.8 ms and 12.1 ± 5.0 ms by 0.1 and 2 mM heptanol (p < 0.05). P5 took a value of 0.2 ± 0.1 ms and was not significantly altered by heptanol at 0.1 or 2 mM (1.1 ± 0.9 ms and 0.9 ± 0.5 ms, p > 0.05). P50 was increased from 7.3 ± 2.7 ms to 24.0 ± 12.0 ms by 0.1 mM heptanol and then to 22.5 ± 7.5 ms by 2 mM heptanol (p < 0.05). P95 was increased from 1.7 ± 1.1 ms to 13.9 ± 7.8 ms by 0.1 mM heptanol and to 12.1 ± 5.0 ms by 2 mM heptanol (p < 0.05). These changes led to increases in the absolute inhomogeneity in conduction (P5–95) from 7.1 ± 2.6 ms to 31.4 ± 11.3 ms, 2 mM: 21.6 ± 7.2 ms, respectively (p < 0.05). The inhomogeneity index (P5–95/P50) was significantly reduced from 3.7 ± 1.2 to 3.1 ± 0.8 by 0.1 mM and then to 3.3 ± 0.9 by 2 mM heptanol (p < 0.05). Conclusion: Increased activation latencies, reduced CVs, and the increased inhomogeneity index of conduction were associated with both spontaneous and induced ventricular arrhythmias

On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure