A one line factoring algorithm

We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package

Class invariants from a new kind of Weber-like modular equation

A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method. They are obtained by means of specialising certain modular equations related to Weber's modular equations of `irrational type'. The technique works for certain eta quotients evaluated at points in an imaginary quadratic field with discriminant d1 (mod 8)

The locality of the square-root method for improved staggered quarks

We study the effects of improvement on the locality of square-rooted staggered Dirac operators in lattice QCD simulations. We find the localisation lengths of the improved operators (FAT7TAD and ASQTAD) to be very similar to that of the one-link operator studied by Bunk et al., being at least the Compton wavelength of the lightest particle in the theory, even in the continuum limit. We conclude that improvement has no effect. We discuss the implications of this result for the locality of the nth-rooted fermion determinant used to reduce the number of sea quark flavours, and for possible staggered valence quark formulations

Qualitative analysis of psychosocial impact of diagnosis of Chlamydia trachomatis: implications for screening

OBJECTIVES: To investigate the psychosocial impact for women of a diagnosis of Chlamydia trachomatis and discuss the implications for the proposed UK chlamydia screening programme. DESIGN: Qualitative study with semistructured interviews. Interview transcripts analysed to identify recurrent themes. PARTICIPANTS: Seventeen women with a current or recent diagnosis of chlamydia. SETTING: A family planning clinic and a genitourinary medicine clinic in Glasgow. RESULTS: Three themes were identified: perceptions of stigma associated with sexually transmitted infection, uncertainty about reproductive health after diagnosis, and anxieties regarding partner's reaction to diagnosis. Most women had not previously perceived sexually transmitted infections as personally relevant; this was a function of stereotypical beliefs about who was "at risk" of sexually transmitted infection. These beliefs were pervasive and negatively affected reactions to diagnosis and produced anxiety about disclosure of the condition to others (particularly sexual partners) and future reproductive morbidity. This anxiety, given the uncertain natural history of chlamydia, may prove difficult to dispel. CONCLUSIONS: There are three primary areas of concern for women after a diagnosis of chlamydia which need to be examined in the proposed screening programme. Information provided should normalise and destigmatise chlamydial infection and positively promote genitourinary medicine services. Support services should be available because notification of partner can cause anxiety. Uncertainty about future reproductive morbidity may be inevitable; staff providing screening will require guidance in providing advice under such conditions