Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Dynamic and structural stability of cubic vanadium nitride

Structural phase transitions in epitaxial stoichiometric VN/MgO(011) thin films are investigated using temperature-dependent synchrotron x-ray diffraction (XRD), selected-area electron diffraction (SAED), resistivity measurements, high-resolution cross-sectional transmission electron microscopy, and ab initio molecular dynamics (AIMD). At room temperature, VN has the B1 NaCl structure. However, below T_c=250K, XRD and SAED results reveal forbidden (001) reflections of mixed parity associated with a noncentrosymmetric tetragonal structure. The intensities of the forbidden reflections increase with decreasing temperature following the scaling behavior I∝(T_c−T)^(1/2). Resistivity measurements between 300 and 4 K consist of two linear regimes resulting from different electron/phonon coupling strengths in the cubic and tetragonal-VN phases. The VN transport Eliashberg spectral function α^(2)_(tr)F(ℏω), the product of the phonon density of states F(ℏω) and the transport electron/phonon coupling strengthα^(2)_(tr)(ℏω), is determined and used in combination with AIMD renormalized phonon dispersion relations to show that anharmonic vibrations stabilize the NaCl structure at T>T_c. Free-energy contributions due to vibrational entropy, often neglected in theoretical modeling, are essential for understanding the room-temperature stability of NaCl-structure VN, and of strongly anharmonic systems in general

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Geons with spin and charge

We construct new geon-type black holes in D>3 dimensions for Einstein's theory coupled to gauge fields. A static nondegenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D-2 with a pure F^2 action can be included by an appropriate (and in most cases nontrivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers-Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuously deformed to zero angular momentum. With a negative cosmological constant, we construct geons with angular momenta on a torus at the infinity. As an example of a nonabelian gauge field, we show that the D=4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalisations, including both black-brane geons and Yang-Mills theories with Chern-Simons terms, are briefly discussed.Comment: 26 pages, 1 figure. LaTeX with amssymb, amsmath. (v2: References and a figure added.

Development of a core set of outcome measures for OAB treatment

© 2017, The Author(s). Introduction and hypothesis: Standardized measures enable the comparison of outcomes across providers and treatments giving valuable information for improving care quality and efficacy. The aim of this project was to define a minimum standard set of outcome measures and case-mix factors for evaluating the care of patients with overactive bladder (OAB). Methods: The International Consortium for Health Outcomes Measurement (ICHOM) convened an international working group (WG) of leading clinicians and patients to engage in a structured method for developing a core outcome set. Consensus was determined by a modified Delphi process, and discussions were supported by both literature review and patient input. Results: The standard set measures outcomes of care for adults seeking treatment for OAB, excluding residents of long-term care facilities. The WG focused on treatment outcomes identified as most important key outcome domains to patients: symptom burden and bother, physical functioning, emotional health, impact of symptoms and treatment on quality of life, and success of treatment. Demographic information and case-mix factors that may affect these outcomes were also included. Conclusions: The standardized outcome set for evaluating clinical care is appropriate for use by all health providers caring for patients with OAB, regardless of specialty or geographic location, and provides key data for quality improvement activities and research