Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

Critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulations and a finite-size scaling analysis. By using a field programmable gate array, we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but also with different scenarios: transient effects due to a value of the lower critical dimension slightly below 3 could be very important.

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Splitting of a prevalent Mycobacterium bovis spoligotype by variable-number tandem-repeat typing reveals high heterogeneity in an evolving clonal group

Mycobacterium bovis populations in countries with persistent bovine tuberculosis usually show a prevalent spoligotype with a wide geographical distribution. This study applied mycobacterial interspersed repetitive-unit-variable-number tandem-repeat (MIRU-VNTR) typing to a random panel of 115 M. bovis isolates that are representative of the most frequent spoligotype in the Iberian Peninsula, SB0121. VNTR typing targeted nine loci: ETR-A (alias VNTR2165), ETR-B (VNTR2461), ETR-D (MIRU4, VNTR580), ETR-E (MIRU31, VNTR3192), MIRU26 (VNTR2996), QUB11a (VNTR2163a), QUB11b (VNTR2163b), QUB26 (VNTR4052), and QUB3232 (VNTR3232). We found a high degree of diversity among the studied isolates (discriminatory index [D] = 0.9856), which were split into 65 different MIRU-VNTR types. An alternative short-format MIRU-VNTR typing targeting only the four loci with the highest variability values was found to offer an equivalent discriminatory index. Minimum spanning trees using the MIRU-VNTR data showed the hypothetical evolution of an apparent clonal group. MIRU-VNTR analysis was also applied to the isolates of 176 animals from 15 farms infected by M. bovis SB0121; in 10 farms, the analysis revealed the coexistence of two to five different MIRU types differing in one to six loci, which highlights the frequency of undetected heterogeneity.