Equidistribution of primitive rational points on expanding horospheres

We confirm a conjecture of Jens Marklof regarding the equidistribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This equidistribution result is then used along the lines suggested by Marklof to give an analogue of a result of W. Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.Comment: Revised version. To appear in Compositi

Effects of dissipation on quantum phase transitions

We discuss the effect of dissipation on quantum phase transitions. In particular we concentrate on the Superconductor to Insulator and Quantum-Hall to Insulator transitions. By invoking a phenomenological parameter $\alpha$ to describe the coupling of the system to a continuum of degrees of freedom representing the dissipative bath, we obtain new phase diagrams for the quantum Hall and superconductor-insulator problems. Our main result is that, in two-dimensions, the metallic phases observed in finite magnetic fields (possibly also strictly zero field) are adiabatically deformable from one to the other. This is plausible, as there is no broken symmetry which differentiates them.Comment: 13 pages, 4 figure

A clinical evaluation of an ex vivo organ culture system to predict patient response to cancer therapy

IntroductionEx vivo organ cultures (EVOC) were recently optimized to sustain cancer tissue for 5 days with its complete microenvironment. We examined the ability of an EVOC platform to predict patient response to cancer therapy.MethodsA multicenter, prospective, single-arm observational trial. Samples were obtained from patients with newly diagnosed bladder cancer who underwent transurethral resection of bladder tumor and from core needle biopsies of patients with metastatic cancer. The tumors were cut into 250 μM slices and cultured within 24 h, then incubated for 96 h with vehicle or intended to treat drug. The cultures were then fixed and stained to analyze their morphology and cell viability. Each EVOC was given a score based on cell viability, level of damage, and Ki67 proliferation, and the scores were correlated with the patients’ clinical response assessed by pathology or Response Evaluation Criteria in Solid Tumors (RECIST).ResultsThe cancer tissue and microenvironment, including endothelial and immune cells, were preserved at high viability with continued cell division for 5 days, demonstrating active cell signaling dynamics. A total of 34 cancer samples were tested by the platform and were correlated with clinical results. A higher EVOC score was correlated with better clinical response. The EVOC system showed a predictive specificity of 77.7% (7/9, 95% CI 0.4–0.97) and a sensitivity of 96% (24/25, 95% CI 0.80–0.99).ConclusionEVOC cultured for 5 days showed high sensitivity and specificity for predicting clinical response to therapy among patients with muscle-invasive bladder cancer and other solid tumors