2,522 research outputs found
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 and
, respectively. In the PL model, however, DDR
is verified within 1 confidence level, with the violation parameter
. 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 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 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
. It is shown that the dipole appears at confidence level only
if , and in this redshift region the dipole is very stable, almost
independent of the specific value of . For , the dipole amplitude
is , pointing towards $(l,b)=(334.5_{\
-21.6^{\circ}}^{\circ +25.7^{\circ}},16.0_{\ -16.8^{\circ}}^{\circ
+27.1^{\circ}})65^{\circ}$ 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
On sumsets involving th power residues
In this paper, we study some topics concerning the additive decompostions of
the set of all th power residues modulo a prime . For example, we
prove that
where is the number of primes and denotes the
cardinality of the set
\{p\le x: p\equiv1\pmod k; D_k\ \text{has a non-trivial 2-additive
decomposition}\}.$
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