Exact representation of crossover of transitions from first order to second order in the Potts model for rumor transmission

The L-state Potts model for rumor is the N-spin chain describing how a simple rumor transmitted by N recreant rumormongers is aggrandized. The studied rumor is represented mathematically by a simple proposition with the universal quantifier, which again is represented geometrically by a point in a proposition space. During the transmission, such a proposition is changed with the change of the rumor, which has individual number N0 at the beginning of the transmission. Correspondingly, the point expressing the proposition may start from an arbitrary site at the proposition space, and then it shifts in the space. Thus, a spin sum of the Potts model corresponds to a walk of a point in the proposition space and spin configuration's numbers is given by enumerating the corresponding walks. The concept of the lattice path in combinatorial mathematics is introduced and the exact series representation of the configuration's numbers is given. The partition function exhibits the transition of the chain and critical equivalent inverse temperature beta(c) is determined. Moreover, there is a crossover value of the individual number, N00. The model has a first-order transition when N0<N00 and a second-order one when N0>N00.

Evaluation of diagnostic criteria for atopic dermatitis: validity of the criteria of Williams et al. in a hospital-based setting

BACKGROUND

Surveys of the prevalence of atopic dermatitis (AD) have been carried out world-wide, but the results vary widely. The differences probably result from the use of different diagnostic criteria. Williams et al. proposed minimum, simplified, diagnostic criteria that require no invasive test and are easy to use. Pilot studies in European countries showed their suitability for implementation both in hospitals and in the community, and their high sensitivity and specificity.

OBJECTIVES

To evaluate the potential practical value of the criteria of Williams et al. in the Chinese population.

METHODS

The criteria of Hanifin and Rajka (gold standard), Williams et al. and Kang and Tian were applied and compared in 111 patients with AD and 121 control subjects with other skin diseases in three out-patient centres in China.

RESULTS

The criteria of Williams et al. showed a similar diagnostic efficiency to that of the gold standard, with the sensitivity, specificity and kappa value reaching 95.50%, 97.52% and 0.93, respectively. No significant difference was found between the criteria of Williams et al. and those of Kang and Tian (chi2 = 0.69, P > 0.05). 'Onset under the age of 2 years', a criterion of Williams et al. could be used in subjects of any age.

CONCLUSIONS

The diagnostic efficiency of the criteria of Williams et al. was basically similar to those of Hanifin and Rajka and of Kang and Tian in our out-patient settings. However, those of Williams et al. were easier to apply and required no invasive tests.

Ratio of canonical and microcanonical temperatures of a vibratory antiferromagnetic ising chain

The ratio of canonical and microcanonical temperatures T(c)/T(&mgr;) of a vibratory antiferromagnetic Ising chain with N spins is given by analytical calculation. The result is T(c)/T(&mgr;)=1+O(N-1), which is consistent with the natural assumption given by Rugh.