Star 5-edge-colorings of subcubic multigraphs

The star chromatic index of a multigraph $G$, denoted $\chi'_{s}(G)$, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored. A multigraph $G$ is star $k$-edge-colorable if $\chi'_{s}(G)\le k$. Dvo\v{r}\'ak, Mohar and \v{S}\'amal [Star chromatic index, J Graph Theory 72 (2013), 313--326] proved that every subcubic multigraph is star $7$-edge-colorable, and conjectured that every subcubic multigraph should be star $6$-edge-colorable. Kerdjoudj, Kostochka and Raspaud considered the list version of this problem for simple graphs and proved that every subcubic graph with maximum average degree less than $7/3$ is star list-$5$-edge-colorable. It is known that a graph with maximum average degree $14/5$ is not necessarily star $5$-edge-colorable. In this paper, we prove that every subcubic multigraph with maximum average degree less than $12/5$ is star $5$-edge-colorable.Comment: to appear in Discrete Mathematics. arXiv admin note: text overlap with arXiv:1701.0410

Time variation of Newton's gravitational constant in superstring theories

Journal ArticleThe present time variation of coupling constants in superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of the internal space. If the potential is almost flat, as in perturbation theory to all orders, the value of G/G for Newton's gravitational constant is calculable and estimated to be - 1x10- 11 ± yr-1 . If the potential has a minimum with finite curvature due to unknown nonperturbative effects, G/G will become unobservably small. Improvement of the measurement of G/ G would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed

Absence of (1,0) supersymmetry anomaly in world-sheet gauge theories: a purely cohomological proof

Journal ArticleA purely cohomological proof is given for the absence of the (1,0) supersymmetry anomaly in gauge theories on a world sheet. In particular, it is shown that generalized cohomological approaches to anomalies in supersymmetric gauge theory, either formulated in whole superconnection space or only in the Wess-Zumino-gauge surface, yield results which agree with those obtained by noncohomological field-theoretical methods. We argue that the success of the cohomological arguments implies that there should be a generalization of (family) index theorem in the supersymmetric cases

General bubble expansion at strong coupling

The strongly-coupled system like the quark-hadron transition (if it is of first order) is becoming an active play-yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly-coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the non-relativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We have also found in our previous study a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the non-relativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly-coupled first-order phase transitionsComment: 22 pages, 10 figure

Dynamic Layer Aggregation for Neural Machine Translation with Routing-by-Agreement

With the promising progress of deep neural networks, layer aggregation has been used to fuse information across layers in various fields, such as computer vision and machine translation. However, most of the previous methods combine layers in a static fashion in that their aggregation strategy is independent of specific hidden states. Inspired by recent progress on capsule networks, in this paper we propose to use routing-by-agreement strategies to aggregate layers dynamically. Specifically, the algorithm learns the probability of a part (individual layer representations) assigned to a whole (aggregated representations) in an iterative way and combines parts accordingly. We implement our algorithm on top of the state-of-the-art neural machine translation model TRANSFORMER and conduct experiments on the widely-used WMT14 English-German and WMT17 Chinese-English translation datasets. Experimental results across language pairs show that the proposed approach consistently outperforms the strong baseline model and a representative static aggregation model.Comment: AAAI 201

(2E,6E)-2,6-Difurfurylidenecyclo­hexa­none

The complete mol­ecule of the title compound, C16H14O3, is generated by crystallographic mirror symmetry, with two C atoms and one O atom lying on the mirror plane. The mol­ecule adopts an E configuration about the C=C bond and the dihedral angle between the furan rings is 16.1 (2)°