Bounding the inefficiency of logit-based stochastic user equilibrium

Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time. We establish upper bounds on the inefficiency of SUE in both situations

Deep learning method in testing the cosmic distance duality relation

The cosmic distance duality relation (DDR) is constrained from the combination of type-Ia supernovae (SNe Ia) and strong gravitational lensing (SGL) systems using deep learning method. To make use of the full SGL data, we reconstruct the luminosity distance from SNe Ia up to the highest redshift of SGL using deep learning, then it is compared with the angular diameter distance obtained from SGL. Considering the influence of lens mass profile, we constrain the possible violation of DDR in three lens mass models. Results show that in the SIS model and EPL model, DDR is violated at high confidence level, with the violation parameter $\eta_0=-0.193^{+0.021}_{-0.019}$ and $\eta_0=-0.247^{+0.014}_{-0.013}$, respectively. In the PL model, however, DDR is verified within 1$\sigma$ confidence level, with the violation parameter $\eta_0=-0.014^{+0.053}_{-0.045}$. Our results demonstrate that the constraints on DDR strongly depend on the lens mass models. Given a specific lens mass model, DDR can be constrained at a precision of $\textit{O}(10^{-2})$ using deep learning.Comment: 11 pages,4 figure

Orbital density wave induced by electron-lattice coupling in orthorhombic iron pnictides

In this paper we explore the magnetic and orbital properties closely related to a tetragonal-orthorhombic structural phase transition in iron pnictides based on both two- and five-orbital Hubbard models. The electron-lattice coupling, which interplays with electronic interaction, is self-consistently treated. Our results reveal that the orbital polarization stabilizes the spin density wave (SDW) order in both tetragonal and orthorhombic phases. However, the ferro-orbital density wave (F-ODW) only occurs in the orthorhombic phase rather than in the tetragonal one. Magnetic moments of Fe are small in the intermediate Coulomb interaction region for the striped antiferromangnetic phase in the realistic five orbital model. The anisotropic Fermi surface in the SDW/ODW orthorhombic phase is well in agreement with the recent angle-resolved photoemission spectroscopy experiments. These results suggest a scenario that the magnetic phase transition is driven by the ODW order mainly arising from the electron-lattice coupling.Comment: 21 pages, 10 figure

The Pantheon+ supernovae are consistent with a large-scale isotropic universe

We investigate the possible anisotropy of the universe using the most up-to-date type Ia supernovae, i.e. the Pantheon+ compilation. We fit the full Pantheon+ data with the dipole-modulated $\Lambda$CDM model, and find that it is well consistent with a null dipole. We further divide the full sample into several subsamples with different high-redshift cutoff $z_c$. It is shown that the dipole appears at $2\sigma$ confidence level only if $z_c\leq 0.1$, and in this redshift region the dipole is very stable, almost independent of the specific value of $z_c$. For $z_c=0.1$, the dipole amplitude is $D=1.0_{-0.4}^{+0.4}\times 10^{-3}$, pointing towards $(l,b)=(334.5_{\ -21.6^{\circ}}^{\circ +25.7^{\circ}},16.0_{\ -16.8^{\circ}}^{\circ +27.1^{\circ}})$, which is about$65^{\circ}$ away from the CMB dipole. This implies that the full Pantheon+ is consistent with a large-scale isotropic universe, but the low-redshift anisotropy couldn't be purely explained by the peculiar motion of the local universe.Comment: 11 pages, 6 figure