LR property of non-well-formed scales

This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be naturally inserted in the Christoffel tree of well-formed words. Our primary focus in this study is on the left- and right-Lyndon factorization of these words. We will characterize the non-well-formed words for which both factorizations coincide. We say that these words satisfy the LR property and show that the LR property is satisfied exactly for half of the non-well-formed words. These are symmetrically distributed in the extended Christoffel tree. Moreover, we find a surprising connection between the LR property and the Christoffel duality. Finally, we prove that there are infinitely many Christoffel–Lyndon words among the set of non-well-formed words and thus there are infinitely many generated scales having as step-pattern a Christoffel–Lyndon word.

Automorphism groups of non-orientable elliptic-hyperelliptic Klein surfaces with boundary

A classical study about Klein and Riemann surfaces consists in determining their groups of automorphisms. This problem is very difficult in general,and it has been solved for particular families of surfaces or for fixed topological types. In this paper, we calculate the automorphism groups of non-orientable bordered elliptic-hyperelliptic Klein surfaces of algebraic genus p> 5.

Risk factors associated with negative in-vivo diagnostic results in bovine tuberculosis-infected cattle in Spain

BACKGROUND Despite great effort and investment incurred over decades to control bovine tuberculosis (bTB), it is still one of the most important zoonotic diseases in many areas of the world. Test-and-slaughter strategies, the basis of most bTB eradication programs carried out worldwide, have demonstrated its usefulness in the control of the disease. However, in certain countries, eradication has not been achieved due in part to limitations of currently available diagnostic tests. In this study, results of in-vivo and post-mortem diagnostic tests performed on 3,614 animals from 152 bTB-infected cattle herds (beef, dairy, and bullfighting) detected in 2007-2010 in the region of Castilla y León, Spain, were analyzed to identify factors associated with positive bacteriological results in cattle that were non-reactors to the single intradermal tuberculin test, to the interferon-gamma (IFN-γ) assay, or to both tests applied in parallel (Test negative/Culture + animals, T-/C+). The association of individual factors (age, productive type, and number of herd-tests performed since the disclosure of the outbreak) with the bacteriology outcome (positive/negative) was analyzed using a mixed multivariate logistic regression model. RESULTS The proportion of non-reactors with a positive post-mortem result ranged from 24.3% in the case of the SIT test to 12.9% (IFN-γ with 0.05 threshold) and 11.9% (95% CI 9.9-11.4%) using both tests in parallel. Older (>4.5 years) and bullfighting cattle were associated with increased odds of confirmed bTB infection by bacteriology, whereas dairy cattle showed a significantly lower risk. Ancillary use of IFN-γ assay reduced the proportion of T-/C + animals in high risk groups. CONCLUSIONS These results demonstrate the likelihood of positive bacteriological results in non-reactor cattle is influenced by individual epidemiological factors of tested animals. Increased surveillance on non-reactors with an increased probability of being false negative could be helpful to avoid bTB persistence, particularly in chronically infected herds. These findings may aid in the development of effective strategies for eradication of bTB in Spain.