Length functions on currents and applications to dynamics and counting

The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of projective geodesic currents with uniform north-south dynamics.Comment: 35pp, 2 figures, comments welcome! Second version: minor corrections. To appear as a chapter in the forthcoming book "In the tradition of Thurston" edited by V. Alberge, K. Ohshika and A. Papadopoulo

The VLA Frontier Field Survey: A Comparison of the Radio and UV/Optical Size of 0.3 ≲ z ≲ 3 Star-forming Galaxies

o investigate the growth history of galaxies, we measure the rest-frame radio, ultraviolet (UV), and optical sizes of 98 radio-selected, star-forming galaxies (SFGs) distributed over 0.3 ≲ z ≲ 3 with a median stellar mass of $\mathrm{log}({M}_{\star }/{M}_{\odot })\approx 10.4$. We compare the size of galaxy stellar disks, traced by rest-frame optical emission, relative to the overall extent of star formation activity that is traced by radio continuum emission. Galaxies in our sample are identified in three Hubble Frontier Fields: MACS J0416.1−2403, MACS J0717.5+3745, and MACS J1149.5+2223. Radio continuum sizes are derived from 3 and 6 GHz radio images (≲0farcs6 resolution, ≈0.9 μJy beam−1 noise level) from the Karl G. Jansky Very Large Array. Rest-frame UV and optical sizes are derived using observations from the Hubble Space Telescope and the Advanced Camera for Surveys and Wide Field Camera 3 instruments. We find no clear dependence between the 3 GHz radio size and stellar mass of SFGs, which contrasts with the positive correlation between the UV/optical size and stellar mass of galaxies. Focusing on SFGs with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 10$, we find that the radio/UV/optical emission tends to be more compact in galaxies with high star formation rates (≳100 M⊙ yr−1), suggesting that a central, compact starburst (and/or an active galactic nucleus) resides in the most luminous galaxies of our sample. We also find that the physical radio/UV/optical size of radio-selected SFGs with log(M⋆/M⊙) > 10 increases by a factor of 1.5–2 from z ≈ 3 to z ≈ 0.3, yet the radio emission remains two to three times more compact than that from the UV/optical. These findings indicate that these massive, radio-selected SFGs at 0.3 ≲ z ≲ 3 tend to harbor centrally enhanced star formation activity relative to their outer disks

Patient, companion, and oncologist agreement regarding information discussed during triadic oncology clinical interactions

Background Although people with cancer want and need information from their oncologists, patients and oncologists often disagree about what information was discussed during clinical interactions. Most patients have companions present during oncology visits; we investigated whether companions process information more accurately than patients. Specifically, we examined whether patients and companions differed in agreement with oncologists about what was discussed. We also investigated the effect of topic on agreement and patient/companion self‐reported understanding of discussions. Methods Patients with companions were invited to participate on first visits to a cancer center in Detroit, MI. Patients, companions, and oncologists independently completed questionnaires immediately following visits. Participants were asked whether five topics were discussed (diagnosis, prognosis, metastasis, treatment/treatment goals, and side effects) and, if discussed, what oncologists said. Participants were also asked to estimate their own and each other's understanding of discussions. Results A total of 66 patient–companion–oncologist triads participated. Agreement was higher regarding whether topics were discussed than what oncologists said. Agreement did not differ by dyad type. Patients, companions, and oncologists were equally likely to be the source of triadic disagreements. Agreement was high about diagnosis (>90%) but much lower about other topics, particularly side effects. Patients and companions reported greater understanding of discussions than oncologists estimated and more accurately estimated each other's understanding than did oncologists. Conclusions Companions and patients showed similar levels of agreement with oncologists about what they discussed during visits. Interventions are needed to improve communication of information to both patients and companions, especially about particular topics. Copyright © 2012 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96703/1/pon3045.pd

Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the B\"{a}cklund transformations (BT) which are not the ordinary ones. We call them ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.Comment: 13 pages, LaTe

The modular geometry of Random Regge Triangulations

We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial quantum gravity. In particular, we discuss in detail an explicit bijection between the space of possible random Regge triangulations (of given genus g and with N vertices) and a suitable decorated version of the (compactified) moduli space of genus g Riemann surfaces with N punctures. Such an analysis allows us to associate a Weil-Petersson metric with the set of random Regge triangulations and prove that the corresponding volume provides the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio

Exact beta function from the holographic loop equation of large-N QCD_4

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the quantum effective action has been changed, because it has been employed a holomorphic rather than a hermitean resolution of identity in the functional integral. Beta function unchanged. New explanations and references added, typos correcte

Size-selective nanoparticle growth on few-layer graphene films

We observe that gold atoms deposited by physical vapor deposition onto few layer graphenes condense upon annealing to form nanoparticles with an average diameter that is determined by the graphene film thickness. The data are well described by a theoretical model in which the electrostatic interactions arising from charge transfer between the graphene and the gold particle limit the size of the growing nanoparticles. The model predicts a nanoparticle size distribution characterized by a mean diameter D that follows a scaling law D proportional to m^(1/3), where m is the number of carbon layers in the few layer graphene film.Comment: 15 pages, 4 figure

From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR