Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional $\pi$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

Estimation of biochemical variables using quantumbehaved particle swarm optimization (QPSO)-trained radius basis function neural network: A case study of fermentation process of L-glutamic acid

Due to the difficulties in the measurement of biochemical variables in fermentation process, softsensing model based on radius basis function neural network had been established for estimating the variables. To generate a more efficient neural network estimator, we employed the previously proposed quantum-behaved particle swarm optimization (QPSO) algorithm for neural network training. The experiment results of L-glutamic acid fermentation process showed that our established estimator could predict variables such as the concentrations of glucose, biomass and glutamic acid with higher accuracy than the estimator trained by the most widely used orthogonal least squares (OLS). According to its global convergence, QPSO generated a group of more proper network parameters than the most popular OLS. Thus, QPSO-RBF estimator was more favorable to the control and fault diagnosis of the fermentation process, and consequently, it increased the yield of fermentation.Key words: Soft-sensing model, quantum-behaved particle swarm optimization algorithm, neural network

Validity and reliability of a phone App and stopwatch for the measurement of 505 change of direction performance: a test-retest study design

Purpose: The aim of this study was to explore the validity and reliability of a phone app (named: COD timer) and stopwatches for the measurement of change of direction (COD) performance. Methods: Sixty-two youth basketball players (age: 15.9 ± 1.4 yrs, height: 178.8 ± 11.0 cm, body mass: 70.0 ± 14.1 kg) performed six trials of 505 COD test (with the left side being the plant leg first, then the right side). The completion time was measured simultaneously via timing gates (with error correction processing algorithms), the phone app and stopwatches. Results: There was an almost perfect correlation and agreement between timing gates and COD timer (r = 0.978; SEE = 0.035 s; LoA =-0.08~0.06 s), but a lower correlation and agreement between timing gates and stopwatch (r = 0.954; SEE = 0.050 s; LoA =-0.17~0.04 s) with statistical significance in completion time (ES = 1.29, 95%CI: 1.15-1.43, p < 0.01). The coefficient of variation revealed similar level of dispersion between the three timing devices (timing gates: 6.58%; COD timer: 6.32%; stopwatch: 6.71%). Inter-observer reliability (ICC = 0.991) and test-retest reliability (ICC = 0.998) were excellent in COD timer, while the inter-observer reliability was lower (ICC = 0.890) in the stopwatches. Conclusion: In the 505 COD test, the COD timer was able to provide a valid and reliable measurement. On the contrary, stopwatch was not recommended because of large error. Thus, if timing gates are unavailable, practitioners can adopt the COD timer app to assess 505 COD speed times

A CrC^{r} Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense

L-Monomethyl-arginine decreases apoptosis of chondrocytes by altering Bax and Bcl-2 expression in osteoarthritis of rabbit knee

Previous studies found that NG-monomethyl-L-arginine (L-NMMA) treatment inhibits progression of osteoarthritis. Here, we aimed to explore the effects of L-NMMA on chondrocyte apoptosis and Bax and Bcl-2 mRNA expression in rabbits with knee osteoarthritis. Knee osteoarthritis was induced in 24 healthy rabbits by Hulth method, and rabbits were randomly divided into control (n = 12) and experimental (n = 12) groups. Once weekly, knee joints of control rabbits were injected with saline solution, while knees of experimental rabbits were injected with L-NMMA. Knee joint samples were collected after 6 weeks of treatment. Apoptosis of chondrocytes was detected by terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL), and Bax and Bcl-2 mRNA expression by in situ hybridization. The results show that the mean rate of chondrocyte apoptosis in knees of the experimental rabbits was significantly lower than that of the control rabbits (P&lt;0.05). Additionally, Bax expression decreased and Bcl-2 expression increased in the experimental group (P&lt;0.05). In brief, LNMMA can inhibit apoptosis of joint chondrocytes through changes in the expression of apoptosisrelated genes. Thus, this molecule offers the potential for treating osteoarthritis.Key words: NG-Monomethyl-L-arginine, knee osteoarthritis, chondrocyte, apoptosis-related regulatory gene