On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

The Public Repository of Xenografts enables discovery and randomized phase II-like trials in mice

More than 90% of drugs with preclinical activity fail in human trials, largely due to insufficient efficacy. We hypothesized that adequately powered trials of patient-derived xenografts (PDX) in mice could efficiently define therapeutic activity across heterogeneous tumors. To address this hypothesis, we established a large, publicly available repository of well-characterized leukemia and lymphoma PDXs that undergo orthotopic engraftment, called the Public Repository of Xenografts (PRoXe). PRoXe includes all de-identified information relevant to the primary specimens and the PDXs derived from them. Using this repository, we demonstrate that large studies of acute leukemia PDXs that mimic human randomized clinical trials can characterize drug efficacy and generate transcriptional, functional, and proteomic biomarkers in both treatment-naive and relapsed/refractory disease

The Polygenic and Monogenic Basis of Blood Traits and Diseases

Blood cells play essential roles in human health, underpinning physiological processes such as immunity, oxygen transport, and clotting, which when perturbed cause a significant global health burden. Here we integrate data from UK Biobank and a large-scale international collaborative effort, including data for 563,085 European ancestry participants, and discover 5,106 new genetic variants independently associated with 29 blood cell phenotypes covering a range of variation impacting hematopoiesis. We holistically characterize the genetic architecture of hematopoiesis, assess the relevance of the omnigenic model to blood cell phenotypes, delineate relevant hematopoietic cell states influenced by regulatory genetic variants and gene networks, identify novel splice-altering variants mediating the associations, and assess the polygenic prediction potential for blood traits and clinical disorders at the interface of complex and Mendelian genetics. These results show the power of large-scale blood cell trait GWAS to interrogate clinically meaningful variants across a wide allelic spectrum of human variation. Analysis of blood cell traits in the UK Biobank and other cohorts illuminates the full genetic architecture of hematopoietic phenotypes, with evidence supporting the omnigenic model for complex traits and linking polygenic burden with monogenic blood diseases