Blow-up profile of rotating 2D focusing Bose gases

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when the coupling constant approaches $a\_*$ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of $\Omega$, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141--156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for $N$ bosons, interacting with a potential rescaled in the mean-field manner $--a\_N N^{2\beta--1} w(N^{\beta} x), with$w$a positive function such that$\int\_{\mathbb{R}^2} w(x) dx = 1$. Assuming that$\beta < 1/2$and that$a\_N \to a\_*$sufficiently slowly, we prove that the many-body system is fully condensed on the Gross-Pitaevskii ground state in the limit$N \to \infty$

Impact of chemotherapy for HIV-1 related lymphoma on residual viremia and cellular HIV-1 DNA in patients on suppressive antiretroviral therapy

The first cure of HIV-1 infection was achieved through complex, multimodal therapy including myeloablative chemotherapy, total body irradiation, anti-Thymocyte globulin, and allogeneic stem cell transplantation with a CCR5 delta32 homozygous donor. The contributions of each component of this therapy to HIV-1 eradication are unclear. To assess the impact of cytotoxic chemotherapy alone on HIV-1 persistence, we longitudinally evaluated low-level plasma viremia and HIV-1 DNA in PBMC from patients in the ACTG A5001/ALLRT cohort on suppressive antiretroviral therapy (ART) who underwent chemotherapy for HIV-1 related lymphoma without interrupting ART. Plasma HIV-1 RNA, total HIV-1 DNA and 2-LTR circles (2-LTRs) in PBMC were measured using sensitive qPCR assays. In the 9 patients who received moderately intensive chemotherapy for HIV-1 related lymphoma with uninterrupted ART, low-level plasma HIV-1 RNA did not change significantly with chemotherapy: median HIV-1 RNA was 1 copy/mL (interquartile range: 1.0 to 20) pre-chemotherapy versus 4 copies/mL (interquartile range: 1.0 to 7.0) post-chemotherapy. HIV-1 DNA levels also did not change significantly, with median prechemotherapy HIV-1 DNA of 355 copies/106 CD4+ cells versus 228 copies/106 CD4+ cells post-chemotherapy. 2-LTRs were detectable in 2 of 9 patients pre-chemotherapy and in 3 of 9 patients post-chemotherapy. In summary, moderately intensive chemotherapy for HIV-1 related lymphoma in the context of continuous ART did not have a prolonged impact on HIV-1 persistence. © 2014 Cillo et al