Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Adeno-tonsillectomy and rapid maxillary distraction in pre-pubertal children: a pilot study

Introduction When both narrow maxilla and moderately enlarged tonsils are present in children with obstructive sleep apnea, the decision of which treatment to do first is unclear. A preliminary randomized study was done to perform a power analysis and determine the number of subjects necessary to have an appropriate response. Thirtyone children, 14 boys, diagnosed with OSA based on clinical symptoms and polysomnography (PSG) findings had presence of both narrow maxillary complex and enlarged tonsils. They were scheduled to have both adeno-tonsillectomy and RME for which the order of treatment was randomized: group 1 received surgery followed by orthodontics, while group 2 received orthodontics followed by surgery. Each child was seen by an ENT, an orthodontist, and a sleep medicine specialist. The validated pediatric sleep questionnaire and PSG were done at entry and after each treatment phase at time of PSG. Statistical analyses were ANOVA repeated measures and t tests. Results The mean age of the children at entry was 6.5± 0.2 years (mean ± SEM). Overall, even if children presented improvement of both clinical symptoms and PSG findings, none of the children presented normal results after treatment 1, at the exception of one case. There was no significant difference in the amount of improvement noted independently of the first treatment approach. Thirty children underwent treatment 2, with an overall significant improvement shown for PSG findings compared to baseline and compared to treatment 1, without any group differences. Conclusion This preliminary study emphasizes the need to have more than subjective clinical scales for determination of sequence of treatments

Radio Galaxy Zoo: Knowledge Transfer Using Rotationally Invariant Self-Organising Maps

With the advent of large scale surveys the manual analysis and classification of individual radio source morphologies is rendered impossible as existing approaches do not scale. The analysis of complex morphological features in the spatial domain is a particularly important task. Here we discuss the challenges of transferring crowdsourced labels obtained from the Radio Galaxy Zoo project and introduce a proper transfer mechanism via quantile random forest regression. By using parallelized rotation and flipping invariant Kohonen-maps, image cubes of Radio Galaxy Zoo selected galaxies formed from the FIRST radio continuum and WISE infrared all sky surveys are first projected down to a two-dimensional embedding in an unsupervised way. This embedding can be seen as a discretised space of shapes with the coordinates reflecting morphological features as expressed by the automatically derived prototypes. We find that these prototypes have reconstructed physically meaningful processes across two channel images at radio and infrared wavelengths in an unsupervised manner. In the second step, images are compared with those prototypes to create a heat-map, which is the morphological fingerprint of each object and the basis for transferring the user generated labels. These heat-maps have reduced the feature space by a factor of 248 and are able to be used as the basis for subsequent ML methods. Using an ensemble of decision trees we achieve upwards of 85.7% and 80.7% accuracy when predicting the number of components and peaks in an image, respectively, using these heat-maps. We also question the currently used discrete classification schema and introduce a continuous scale that better reflects the uncertainty in transition between two classes, caused by sensitivity and resolution limits

A weighted reduced basis method for parabolic PDEs with random data

This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate according to a probability measure in the set-up of the reduced space. The error of stochastic finite element solutions is usually measured in a root mean square sense regarding their dependence on the stochastic input parameters. An orthogonal projection of a snapshot set onto a corresponding POD basis defines an optimum reduced approximation in terms of a Monte Carlo discretization of the root mean square error. The errors of a weighted POD-greedy Galerkin solution are compared against an orthogonal projection of the underlying snapshots onto a POD basis for a numerical example involving thermal conduction. In particular, it is assessed whether a weighted POD-greedy solutions is able to come significantly closer to the optimum than a non-weighted equivalent. Additionally, the performance of a weighted POD-greedy Galerkin solution is considered with respect to the mean absolute error of an adjoint-corrected functional of the reduced solution.Comment: 15 pages, 4 figure

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of mathematician

The lowest eigenvalue of Jacobi random matrix ensembles and Painlev\'e VI

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painleve VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painleve VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.Comment: 30 pages, 2 figure

Lunar and Meteorite Sample Education Disk Program - Space Rocks for Classrooms, Museums, Science Centers, and Libraries

NASA is eager for students and the public to experience lunar Apollo samples and meteorites first hand. Lunar rocks and soil, embedded in Lucite disks, are available for educators to use in their classrooms, museums, science centers, and public libraries for education activities and display. The sample education disks are valuable tools for engaging students in the exploration of the Solar System. Scientific research conducted on the Apollo rocks reveals the early history of our Earth-Moon system and meteorites reveal much of the history of the early solar system. The rocks help educators make the connections to this ancient history of our planet and solar system and the basic processes accretion, differentiation, impact and volcanism. With these samples, educators in museums, science centers, libraries, and classrooms can help students and the public understand the key questions pursued by many NASA planetary missions. The Office of the Curator at Johnson Space Center is in the process of reorganizing and renewing the Lunar and Meteorite Sample Education Disk Program to increase reach, security and accountability. The new program expands the reach of these exciting extraterrestrial rocks through increased access to training and educator borrowing. One of the expanded opportunities is that trained certified educators from science centers, museums, and libraries may now borrow the extraterrestrial rock samples. Previously the loan program was only open to classroom educators so the expansion will increase the public access to the samples and allow educators to make the critical connections to the exciting exploration missions taking place in our solar system. Each Lunar Disk contains three lunar rocks and three regolith soils embedded in Lucite. The anorthosite sample is a part of the magma ocean formed on the surface of Moon in the early melting period, the basalt is part of the extensive lunar mare lava flows, and the breccias sample is an important example of the violent impact history of the Moon. The disks also include two regolith soils and orange glass from a pyroclastic deposit. Each Meteorite Disk contains two ordinary chondrites, one carbonaceous chondrite, one iron, one stony iron, and one achondrite. These samples will help educators share the early history of the solar system with students and the public. Educators may borrow either lunar or meteorite disks and the accompanying education materials through the Johnson Space Center Curatorial Office. In trainings provided by the NASA Aerospace Education Services Program specialists, educators certified to borrow the disk learn about education resources, the proper use of the samples, and the special security for care and shipping of the disks. The Lunar and Meteorite Sample Education Disk Program will take NASA exploration to more people. Getting Space Rocks out to the public and inspiring the public about new space exploration is the focus of the NASA disk loan program

Damage assessment of concrete gravity dams using vibration characteristics

Vibration-based Structural Health Monitoring (VBSHM) has emerged as a feasible technique in long-term monitoring, structural performance evaluation and damage assessment of civil structures. As an important as-pect of the complete VBSHM system, over the last three decades, many vibration-based damage detection methods have been developed for buildings and bridges. However, the application of these techniques to con-crete gravity (CG) dams has been limited. In the present study, damage indices based on changes in modal flexibility and modal strain energy are suitably enhanced to be applicable for plane-strain structures. They are then used to investigate the feasibility of detecting and locating damage in a finite element CG dam model without noise effects. Results show that the enhanced damage indices can be promising for locating damage in the upstream part of CG dams by using only the first lateral mode of vibration. In addition, it is necessary to monitor both horizontal and vertical mode shape components and use these for structural damage diagnoses in CG dams

The ATLAS 5.5 GHz survey of the Extended Chandra Deep Field South: Catalogue, Source Counts and Spectral Indices

Star forming galaxies are thought to dominate the sub-mJy radio population, but recent work has shown that low luminosity AGN can still make a significant contribution to the faint radio source population. Spectral indices are an important tool for understanding the emission mechanism of the faint radio sources. We have observed the extended Chandra Deep Field South at 5.5 GHz using a mosaic of 42 pointings with the Australia Telescope Compact Array (ATCA). Our image reaches an almost uniform sensitivity of ~12 microJy rms over 0.25 deg^2 with a restoring beam of 4.9 x 2.0 arcsec, making it one of the deepest 6cm surveys to date. We present the 5.5 GHz catalogue and source counts from this field. We take advantage of the large amounts of ancillary data in this field to study the 1.4 to 5.5 GHz spectral indices of the sub-mJy population. For the full 5.5 GHz selected sample we find a flat median spectral index, alpha_med = -0.40, which is consistent with previous results. However, the spectral index appears to steepen at the faintest flux density levels (S_{5.5 GHz} < 0.1 mJy), where alpha_med = -0.68. We performed stacking analysis of the faint 1.4 GHz selected sample (40 < S_{1.4 GHz} < 200 microJy) and also find a steep average spectral index, alpha = -0.8, consistent with synchrotron emission. We find a weak trend of steepening spectral index with redshift. Several young AGN candidates are identified using spectral indices, suggesting Gigahertz Peaked Spectrum (GPS) sources are as common in the mJy population as they are at Jy levels.Comment: 18 pages, 16 figures, accepted for publication in MNRA