Metastable States in Two-Lane Traffic Flow Models With Slow-To-Start Rule

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers (\textit{which do not look back before changing lanes}) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability $p_{ch}$ and the number of aggressive drivers present in the circuit. It is found also that the relaxation time $\tau$ diverges as the form of a power-law : $\tau\propto p_{ch}^{-\beta}, \beta=1$.Comment: 7 pages, 6 figure

Comment on "Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning"

A Comment on the Letter by M. Rupp et al., Phys. Rev. Lett. 108 058301 (2012).Comment: 1 page, 2 figures, see [arXiv:1109.2618v1

An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1 edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd graceful if and only if m even, she proved the cycle graph is not graceful if m odd. In this paper, firstly, we studied the graph C_m $\cup$ P_m when m = 4, 6,8,10 and then we proved that the graph C_ $\cup$ P_n is odd graceful if m is even. Finally, we described an algorithm to label the vertices and the edges of the vertex set V(C_m $\cup$ P_n) and the edge set E(C_m $\cup$ P_n).Comment: 9 Pages, JGraph-Hoc Journa