On the least common multiple of qq-binomial coefficients

In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page

Scaling in the vicinity of the four-state Potts fixed point

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure

Recent Trends in Hospitalization for Acute Myocardial Infarction in Beijing: Increasing Overall Burden and a Transition From ST-Segment Elevation to Non-ST-Segment Elevation Myocardial Infarction in a Population-Based Study

Comparable data on trends of hospitalization rates for ST-segment elevation myocardial infarction (STEMI) and non-STEMI (NSTEMI) remain unavailable in representative Asian populations.To examine the temporal trends of hospitalization for acute myocardial infarction (AMI) and its subtypes in Beijing.Patients hospitalized for AMI in Beijing from January 1, 2007 to December 31, 2012 were identified from the validated Hospital Discharge Information System. Trends in hospitalization rates, in-hospital mortality, length of stay (LOS), and hospitalization costs were analyzed by regression models for total AMI and for STEMI and NSTEMI separately. In total, 77,943 patients were admitted for AMI in Beijing during the 6 years, among whom 67.5% were males and 62.4% had STEMI. During the period, the rate of AMI hospitalization per 100,000 population increased by 31.2% (from 55.8 to 73.3 per 100,000 population) after age standardization, with a slight decrease in STEMI but a 3-fold increase in NSTEMI. The ratio of STEMI to NSTEMI decreased dramatically from 6.5:1.0 to 1.3:1.0. The age-standardized in-hospital mortality decreased from 11.2% to 8.6%, with a significant decreasing trend evident for STEMI in males and females (P < 0.001) and for NSTEMI in males (P = 0.02). The rate of percutaneous coronary intervention increased from 28.7% to 55.6% among STEMI patients. The total cost for AMI hospitalization increased by 56.8% after adjusting for inflation, although the LOS decreased by 1 day.The hospitalization burden for AMI has been increasing in Beijing with a transition from STEMI to NSTEMI. Diverse temporal trends in AMI subtypes from the unselected "real-world" data in Beijing may help to guide the management of AMI in China and other developing countries

Theoretic Limits on the Equation of State Parameter of Quintessence

The value of scalar field coupled to gravity should be less than the Planck scale in the consistent theory of quantum gravity. It provides a theoretic constraint on the equation of state parameter for the quintessence. In some cases our theoretic constraints are more stringent than the constraints from the present experiments.Comment: 4 pages, 2 figures; minor corrections and refs adde

Quantum Non-Demolition Bell State Measurement and N-party GHZ State Preparation in Quantum Dot

By exploiting the fermionic qubit parity measurement, we present a scheme to realize quantum non-demolition (QND) measurement of Bell-states and generate n-party GHZ state in quantum dot. Compared with the original protocol, the required electron transfer before and after parity measurement can be nonadiabatic, which may speed up the operation speed and make the omitting of spin-orbit interaction more reasonable. This may help us to construct CNOT gate without highly precise control of coupling as the way of D. Gottesman and I. L. Chuang.Comment: some modification to introduction and some details are adde

Geometric properties of two-dimensional O(n) loop configurations

We study the fractal geometry of O($n$) loop configurations in two dimensions by means of scaling and a Monte Carlo method, and compare the results with predictions based on the Coulomb gas technique. The Monte Carlo algorithm is applicable to models with noninteger $n$ and uses local updates. Although these updates typically lead to nonlocal modifications of loop connectivities, the number of operations required per update is only of order one. The Monte Carlo algorithm is applied to the O($n$) model for several values of $n$, including noninteger ones. We thus determine scaling exponents that describe the fractal nature of O($n$) loops at criticality. The results of the numerical analysis agree with the theoretical predictions.Comment: 18 pages, 6 figure

A large-scale one-way quantum computer in an array of coupled cavities

We propose an efficient method to realize a large-scale one-way quantum computer in a two-dimensional (2D) array of coupled cavities, based on coherent displacements of an arbitrary state of cavity fields in a closed phase space. Due to the nontrivial geometric phase shifts accumulating only between the qubits in nearest-neighbor cavities, a large-scale 2D cluster state can be created within a short time. We discuss the feasibility of our method for scale solid-state quantum computationComment: 5 pages, 3 figure