Conjugacy in singular Artin monoids

We define a notion of conjugacy in singular Artin moniods, and solve the corresponding conjugacy problem for finite types. We sgiw that this definition is appropriate to describe type (1) singular Markov moves on singular braids. Parabolic submonoids of singular Artin monoids are defined and, in finite type, are shown to be singular Artin monoids. Solutions to conjugacy-type problems of parabolic submonoids are described. Geometric objects defined by Fenn, Rolfsen and Zhu, called (j, k)-bands, are algebraically characterised, and a procedure is given which determines when a word represents a (j, k)-ban

Braid groups of imprimitive complex reflection groups

We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group $B(de,e,r)$ is a semidirect product of the braid group of affine type $\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $B(de,e,r)$ are visualized as geometric braids on $r+1$ strings whose first string is pure and whose winding number is a multiple of $e$. We classify periodic elements, and show that the roots are unique up to conjugacy and that the braid group $B(de,e,r)$ is strongly translation discrete.Comment: published versio

Clinical Trial of Oral Nelfinavir before and during Radiation Therapy for Advanced Rectal Cancer

Purpose Nelfinavir, a PI3-kinase pathway inhibitor, is a radiosensitizer which increases tumor blood flow in preclinical models. We conducted an early-phase study to demonstrate the safety of nelfinavir combined with hypofractionated radiotherapy (RT) and to develop biomarkers of tumor perfusion and radiosensitization for this combinatorial approach. Patients and Methods Ten patients with T3-4 N0-2 M1 rectal cancer received 7 days of oral nelfinavir (1250 mg bd) and a further 7 days of nelfinavir during pelvic RT (25 Gy/5 fractions/7 days). Perfusion CT (p-CT) and DCE-MRI scans were performed pre-treatment, after 7 days of nelfinavir and prior to last fraction of RT. Biopsies taken pre-treatment and 7 days after the last fraction of RT were analysed for tumor cell density (TCD). Results There were 3 drug-related grade 3 adverse events: diarrhea, rash, lymphopenia. On DCE-MRI, there was a mean 42% increase in median Ktrans, and a corresponding median 30% increase in mean blood flow on p-CT during RT in combination with nelfinavir. Median TCD decreased from 24.3% at baseline to 9.2% in biopsies taken 7 days after RT (P=0.01). Overall, 5/9 evaluable patients exhibited good tumor regression on MRI assessed by Tumor Regression Grade (mrTRG). Conclusions This is the first study to evaluate nelfinavir in combination with RT without concurrent chemotherapy. It has shown that nelfinavir-RT is well tolerated and is associated with increased blood flow to rectal tumors. The efficacy of nelfinavir-RT versus RT alone merits clinical evaluation, including measurement of tumor blood flow

School-based surveys of malaria in Oromia Regional State, Ethiopia: a rapid survey method for malaria in low transmission settings

BACKGROUND: In Ethiopia, malaria transmission is seasonal and unstable, with both Plasmodium falciparum and Plasmodium vivax endemic. Such spatial and temporal clustering of malaria only serves to underscore the importance of regularly collecting up-to-date malaria surveillance data to inform decision-making in malaria control. Cross-sectional school-based malaria surveys were conducted across Oromia Regional State to generate up-to-date data for planning malaria control interventions, as well as monitoring and evaluation of operational programme implementation. METHODS: Two hundred primary schools were randomly selected using a stratified and weighted sampling frame; 100 children aged five to 18 years were then randomly chosen within each school. Surveys were carried out in May 2009 and from October to December 2009, to coincide with the peak of malaria transmission in different parts of Oromia. Each child was tested for malaria by expert microscopy, their haemoglobin measured and a simple questionnaire completed. Satellite-derived environmental data were used to assess ecological correlates of Plasmodium infection; Bayesian geostatistical methods and Kulldorff's spatial scan statistic were employed to investigate spatial heterogeneity. RESULTS: A total 20,899 children from 197 schools provided blood samples, two selected schools were inaccessible and one school refused to participate. The overall prevalence of Plasmodium infection was found to be 0.56% (95% CI: 0.46-0.67%), with 53% of infections due to P. falciparum and 47% due to P. vivax. Of children surveyed, 17.6% (95% CI: 17.0-18.1%) were anaemic, while 46% reported sleeping under a mosquito net the previous night. Malaria was found at 30 (15%) schools to a maximum elevation of 2,187 metres, with school-level Plasmodium prevalence ranging between 0% and 14.5%. Although environmental variables were only weakly associated with P. falciparum and P. vivax infection, clusters of infection were identified within Oromia. CONCLUSION: These findings demonstrate the marked spatial heterogeneity of malaria in Oromia and, in general, Ethiopia, and provide a strong epidemiological basis for planning as well as monitoring and evaluating malaria control in a setting with seasonal and unstable malaria transmission