Graphical Representations and Worm Algorithms for the O(NN) Spin Model

We present a family of graphical representations for the O($N$) spin model, where $N \ge 1$ represents the spin dimension, and $N=1,2,3$ corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter $0 \le \ell \le N/2$, each configuration is the coupling of $\ell$ copies of subgraphs consisting of directed flows and $N -2\ell$ copies of subgraphs constructed by undirected loops, which we call the XY and Ising subgraphs, respectively. On each lattice site, the XY subgraphs satisfy the Kirchhoff flow-conservation law and the Ising subgraphs obey the Eulerian bond condition. Then, we formulate worm-type algorithms and simulate the O($N$) model on the simple-cubic lattice for $N$ from 2 to 6 at all possible $\ell$. It is observed that the worm algorithm has much higher efficiency than the Metropolis method, and, for a given $N$, the efficiency is an increasing function of $\ell$. Beside Monte Carlo simulations, we expect that these graphical representations would provide a convenient basis for the study of the O($N$) spin model by other state-of-the-art methods like the tensor network renormalization.Comment: 10 pages, 6 figure

A theoretical study of the mechanism of the addition reaction between carbene and azacyclopropane

The mechanism of the addition reaction between carbene and azacyclopropane was investigated using the second-order Moller–Plesset perturbation theory (MP2). By using the 6-311+G* basis set, geometry optimization, vibrational analysis and the energy properties of the involved stationary points on the potential energy surface were calculated. From the surface energy profile, it can be predicted that there are two reaction mechanisms. The first one (1) is carbene attack at the N atom of azacyclopropane to form an intermediate, 1a (IM1a), which is a barrier-free exothermic reaction. Then, IM1a can isomerize to IM1b via a transition state 1a (TS1a), in which the potential barrier is 30.0 kJ/mol. Subsequently, IM1b isomerizes to a product (Pro1) via TS1b with a potential barrier of 39.3 kJ/mol. The other one (2) is carbene attack at the C atom of azacyclopropane, firstly to form IM2 via TS2a, the potential barrier is 35.4 kJ/mol. Then IM2 isomerizes to a product (Pro2) via TS2b with a potential barrier of 35.1 kJ/mol. Correspondingly, the reaction energy for the reactions (1) and (2) is –478.3 and –509.9 kJ/mol, respectively. Additionally, the orbital interactions are also discussed for the leading intermediate

Major Schools of Marxist Economics in Japan: History and Contemporary Development

Marxist economics was introduced into Japan in the 1920s and diverged into several schools. These Marxist schools developed and evolved along with the socio-economic conditions of Japanese society. Japanese Marxism made significant achievements, even though it is facing various difficulties at present. This article offers an account of the formation, development and current quandary of Japanese Marxist economics, so that a comprehensive understanding and overview of Japanese Marxist economics can be obtained

Frequency Conversion of Entangled State

The quantum characteristics of sum-frequency process in an optical cavity with an input signal optical beam, which is a half of entangled optical beams, are analyzed. The calculated results show that the quantum properties of the signal beam can be maintained after its frequency is conversed during the intracavity nonlinear optical interaction. The frequency-conversed output signal beam is still in an entangled state with the retained other half of initial entangled beams. The resultant quantum correlation spectra and the parametric dependences of the correlations on the initial squeezing factor, the optical losses and the pump power of the sum-frequency cavity are calculated. The proposed system for the frequency conversion of entangled state can be used in quantum communication network and the calculated results can provide direct references for the design of experimental systems.Comment: Accepted by Phys. Rev.

A theoretical study on the mechanism of the addition reaction between cyclopropenylidene and ethylene

The reaction mechanism between cyclopropenylidene and ethylene has been systematically investigated employing the MP2/6-311+G* level of theory to better understand the cyclopropenylidene reactivity with unsaturated hydrocarbons. Geometry optimization, vibrational analysis, and energy property for the involved stationary points on the potential energy surface have been calculated. Energies of all the species are also further refined by the CCSD(T)/6-311+G* single-point calculations. Firstly, one important reaction intermediate (INTa) has been located via a transition state (TSa). After that, the common intermediate (INTb) for the two pathways (1) and (2) has been formed via TSb. At last, two different products possessing three- and four-membered ring characters have been obtained through two reaction pathways. In the reaction pathway (1), a three-membered ring alkyne compound has been obtained. As for the reaction pathway (2), a four-membered ring conjugated diene compound has been formed, which is the most favorable reaction to occur from the kinetic and thermodynamic viewpoints

LMBAO: A Landmark Map for Bundle Adjustment Odometry in LiDAR SLAM

LiDAR odometry is one of the essential parts of LiDAR simultaneous localization and mapping (SLAM). However, existing LiDAR odometry tends to match a new scan simply iteratively with previous fixed-pose scans, gradually accumulating errors. Furthermore, as an effective joint optimization mechanism, bundle adjustment (BA) cannot be directly introduced into real-time odometry due to the intensive computation of large-scale global landmarks. Therefore, this letter designs a new strategy named a landmark map for bundle adjustment odometry (LMBAO) in LiDAR SLAM to solve these problems. First, BA-based odometry is further developed with an active landmark maintenance strategy for a more accurate local registration and avoiding cumulative errors. Specifically, this paper keeps entire stable landmarks on the map instead of just their feature points in the sliding window and deletes the landmarks according to their active grade. Next, the sliding window length is reduced, and marginalization is performed to retain the scans outside the window but corresponding to active landmarks on the map, greatly simplifying the computation and improving the real-time properties. In addition, experiments on three challenging datasets show that our algorithm achieves real-time performance in outdoor driving and outperforms state-of-the-art LiDAR SLAM algorithms, including Lego-LOAM and VLOM.Comment: 9 pages, 3 tables, 6 figure

Correlation of Circulating Glucocorticoid-Induced TNFR-Related Protein Ligand Levels with Disease Activity in Patients with Systemic Lupus Erythematosus

The aim of this paper is to investigate the correlation of glucocorticoid-induced tumor necrosis factor receptor- (TNFR-) related protein ligand (GITRL) with disease activity and organ involvement in patients with systemic lupus erythematosus (SLE). Serum GITRL levels were measured in 58 patients with SLE and 30 healthy controls matched for age and sex. Patients were assessed for clinical and laboratory variables. Correlations of serum GITRL levels with SLEDAI, laboratory values, and clinical manifestations were assessed. Serum GITRL levels were determined by ELISA. Serum GITRL levels were markedly increased in patients with SLE compared with healthy controls (mean 401.3 ng/mL and 36.59 ng/mL, resp.; P<0.0001). SLE patients with active disease showed higher serum GITRL levels compared to those with inactive disease (mean 403.3 ng/mL and 136.3 ng/mL, resp; P=0.0043) as well as normal controls (36.59 ng/mL; P<0.0001). Serum GITRL levels were positively correlated with SLEDAI, titers of anti-dsDNA antibody, erythrocyte sedimentation rate (ESR), and IgM and negatively correlated with complement3 (C3). Serum GITRL levels were higher in SLE patients with renal involvement and vasculitis compared with patients without the above-mentioned manifestations