Vortex twins and anti-twins supported by multi-ring gain landscapes

We address the properties of multi-vortex soliton complexes supported by multi-ring gain landscapes in focusing Kerr nonlinear media with strong two-photon absorption. Stable complexes incorporating two, three, or four vortices featuring opposite or identical topological charges are shown to exist. In the simplest geometries with two amplifying rings vortex twins with equal topological charges exhibit asymmetric intensity distributions, while vortex anti-twins may be symmetric or asymmetric, depending on the gain level and separation between rings. Different arrangements of amplifying rings allow generation of stable multi-vortex soliton complexes with various topologies, with twins and anti-twins as building blocks.Comment: 3 pages, 3 figures, to appear in Optics Letter

Treatment responses in multidrug-resistant tuberculosis in Germany.

BACKGROUND: Excellent treatment outcomes have recently been reported for patients with multi/extensively drug-resistant tuberculosis (M/XDR-TB) in settings where optimal resources for individualised therapy are available. OBJECTIVE: To ascertain whether differences remain in treatment responses between patients with M/XDR-TB and those with non-M/XDR-TB. METHOD: Patients with TB were prospectively enrolled between March 2013 and March 2016 at five hospitals in Germany. Treatment was conducted following current guidelines and individualised on the basis of drug susceptibility testing. Two-month and 6-month sputum smear and sputum culture conversion rates were assessed. A clinical and radiological score were used to assess response to anti-tuberculosis treatment. RESULTS: Non-M/XDR-TB (n = 29) and M/XDR-TB (n = 46) patients showed similar rates of microbiological conversion: 2-month smear conversion rate, 90% vs. 78%; culture conversion rate, 67% vs. 61%; time to smear conversion, 19 days (IQR 10-32) vs. 31 days (IQR 14-56) (P = 0.066); time to culture conversion, 39 days (IQR 17-67) vs. 39 days (IQR 6-85) (P = 0.191). Both clinical and radiological scores decreased after the introduction of anti-tuberculosis treatment. CONCLUSION: There were no significant differences in scores between the two groups until 6 months of treatment. Under optimal clinical conditions, with the availability of novel diagnostics and a wide range of therapeutic options for individualised treatment, patients with M/XDR-TB achieved 6-month culture conversion rates that were compatible with those in patients with non-M/XDR-TB

On the groups SL2(ℤ[x]) and SL2(k[x, y])

Grunewald F, Mennicke J, Vaserstein L. On the groups SL2(ℤ[x]) and SL2(k[x, y]). Israel Journal of Mathematics. 1994;86(1-3):157-193.This paper studies free quotients of the groups SL(2)(Z[x]) and SL(2)(k[x, y]), k a finite field. These quotients give information about the relation of the above groups to their subgroups generated by elementary or unipotent elements