Assessing the effect of lens mass model in cosmological application with updated galaxy-scale strong gravitational lensing sample

By comparing the dynamical and lensing masses of early-type lens galaxies, one can constrain both the cosmological parameters and the density profiles of galaxies. We explore the constraining power on cosmological parameters and the effect of the lens mass model in this method with 161 galaxy-scale strong lensing systems, which is currently the largest sample with both high resolution imaging and stellar dynamical data. We assume a power-law mass model for the lenses, and consider three different parameterizations for $\gamma$ (i.e., the slope of the total mass density profile) to include the effect of the dependence of $\gamma$ on redshift and surface mass density. When treating $\delta$ (i.e., the slope of the luminosity density profile) as a universal parameter for all lens galaxies, we find the limits on the cosmological parameter $\Omega_m$ are quite weak and biased, and also heavily dependent on the lens mass model in the scenarios of parameterizing $\gamma$ with three different forms. When treating $\delta$ as an observable for each lens, the unbiased estimate of $\Omega_m$ can be obtained only in the scenario of including the dependence of $\gamma$ on both the redshift and the surface mass density, that is $\Omega_m = 0.381^{+0.185}_{-0.154}$ at 68\% confidence level in the framework of a flat $\Lambda$CDM model. We conclude that the significant dependencies of $\gamma$ on both the redshift and the surface mass density, as well as the intrinsic scatter of $\delta$ among the lenses, need to be properly taken into account in this method.Comment: Accepted for publication in MNRAS; 17 pages, 5 figures, 2 table

Methotrexate nanoparticle delivery system for treatment of inflammatory bowel disease in pediatric patients

Purpose: To evaluate the efficacy and safety of methotrexate (MTX) nanoparticles in pediatric patients with inflammatory bowel disease (IBD).Methods: In this randomized, open-label clinical study, 28 pediatric patients with moderate to severe IBD were randomly assigned to treatment (MTX  nanoparticles,15 mg/week) or control (azathioprine, AZA, 2 mg/kg/day) group.  Nanoparticles were synthesized by adding calcium chloride to sodium alginate solution containing MTX, and was further treated with poly-L-lysine aqueous  solution. The nanoparticles were evaluated for particle size, zeta potential and drug encapsulation efficacy. Erythrocyte sedimentation rate, C-reactive protein, aspartate aminotransferase, alanine transaminase, and disease activity scores were used to assess IBD remission.Results: Nanoparticle size, zeta potential and encapsulation efficacy were 164.4 ± 6.9 nm, -32.6 ± 3.7 mV, and 97.8 ± 4.2 %, respectively. After 12 weeks of therapy, the mean Pediatric Crohn's Disease Activity Index (PCDAI) scores for control and treatment groups were 22.3 ± 2.14 and 16.8 ± 1.87, respectively, while mean Pediatric Ulcerative Colitis Activity (PUCAI) Index scores were 24.3 ± 1.47 and18.7 ± 1.92, respectively. Eight patients in the treatment and five patients in the control group achieved remission. Biochemical parameters varied significantly between the groups.Conclusion: MTX nanoparticles are safe and more effective than standard first-line IBD therapy. However, further studies are required to determine the suitability of the formulation for therapeutic use.Keywords: Pediatric patient, Methotrexate nanoparticle, Inflammatory bowel disease, Azathioprin

Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagom\'{e} lattice

The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as ferromagnetic, ferrimagnetic and paramagnetic phases, along with the second-order phase transitions, have been identified. The TRG results are quite accurate and reliable in comparison to the exact solutions. In a magnetic field, the magnetization ($m$), susceptibility and specific heat are studied by the TRG algorithm, where the $m=1/3$ plateaux are observed in the magnetization curves for some couplings. The experimental data of susceptibility for the complex Co(N$_3$)$_2$(bpg)$\cdot$ DMF$_{4/3}$ are fitted with the TRG results, giving the couplings of the complex $J=22K$ and $J'=33K$

Mass Reconstruction of Galaxy-scale Strong Gravitational Lenses Using a Broken Power-law Model

With mock strong gravitational lensing images, we investigate the performance of the broken power-law (BPL) model proposed by \citet{2020ApJ...892...62D} on the mass reconstruction of galaxy-scale lenses. An end-to-end test is carried out, including the creation of mock strong lensing images, the subtraction of lens light, and the reconstruction of lensed images, where the lenses are selected from the galaxies in the Illustris-1 simulation. We notice that, regardless of the adopted mass models (the BPL model or its special cases), the Einstein radius can be robustly determined from imaging data alone, and the median bias is typically less than $1\%$. Away from the Einstein radius, the lens mass distribution tends to be harder to measure, especially at radii where there are no lensed images detected. We find that, with rigid priors, the BPL model can clearly outperform the single power-law models by achieving $<5\%$ median bias on the radial convergence profile within the Einstein radius. As for the source light reconstructions, they are found to be sensitive to both lens light contamination and lens mass models, where the BPL model with rigid priors still performs best when there is no lens light contamination. We show that, by correcting for the projection effect, the BPL model can estimate the aperture and luminosity weighted line-of-sight velocity dispersions to an accuracy of $\sim6\%$ scatter. These results highlight the great potential of the BPL model in strong lensing related studies.Comment: Accepted for publication in ApJ, 24 pages, 13 figures, 2 table

Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice

We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$, the system scales exponentially, either with or without a magnetic field $h$: the order parameter, the five critical fields that separate the $J_e$-$h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on $J_e$. We calculate the temperature dependence of the specific heat, which can be directly compared with future experiments.Comment: 7 pages, 6 figure

Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models

A linearized tensor renormalization group (LTRG) algorithm is proposed to calculate the thermodynamic properties of one-dimensional quantum lattice models, that is incorporated with the infinite time-evolving block decimation technique, and allows for treating directly the two-dimensional transfer-matrix tensor network. To illustrate its feasibility, the thermodynamic quantities of the quantum XY spin chain are calculated accurately by the LTRG, and the precision is shown to be comparable with (even better than) the transfer matrix renormalization group (TMRG) method. Unlike the TMRG scheme that can only deal with the infinite chains, the present LTRG algorithm could treat both finite and infinite systems, and may be readily extended to boson and fermion quantum lattice models.Comment: published versio