Tree automata and pigeonhole classes of matroids -- II

Let $\psi$ be a sentence in the counting monadic second-order logic of matroids. Let F be a finite field. Hlineny's Theorem says there is a fixed-parameter tractable algorithm for testing whether F-representable matroids satisfy $\psi$, with respect to the parameter of branch-width. In a previous paper we proved there is a similar fixed-parameter tractable algorithm for any efficiently pigeonhole class. In this sequel we apply results from the first paper and thereby extend Hlineny's Theorem to the classes of fundamental transversal matroids, lattice path matroids, bicircular matroids, and H-gain-graphic matroids, when H is a finite group. As a consequence, we can obtain a new proof of Courcelle's Theorem.Comment: Extending the main theorem slightly to cover a more expressive logi

Defining bicircular matroids in monadic logic

We conjecture that the class of frame matroids can be characterised by a sentence in the monadic second-order logic of matroids, and we prove that there is such a characterisation for the class of bicircular matroids. The proof does not depend on an excluded-minor characterisation

Tree automata and pigeonhole classes of matroids -- I

Hlineny's Theorem shows that any sentence in the monadic second-order logic of matroids can be tested in polynomial time, when the input is limited to a class of F-representable matroids with bounded branch-width (where F is a finite field). If each matroid in a class can be decomposed by a subcubic tree in such a way that only a bounded amount of information flows across displayed separations, then the class has bounded decomposition-width. We introduce the pigeonhole property for classes of matroids: if every subclass with bounded branch-width also has bounded decomposition-width, then the class is pigeonhole. An efficiently pigeonhole class has a stronger property, involving an efficiently-computable equivalence relation on subsets of the ground set. We show that Hlineny's Theorem extends to any efficiently pigeonhole class. In a sequel paper, we use these ideas to extend Hlineny's Theorem to the classes of fundamental transversal matroids, lattice path matroids, bicircular matroids, and H-gain-graphic matroids, where H is any finite group. We also give a characterisation of the families of hypergraphs that can be described via tree automata: a family is defined by a tree automaton if and only if it has bounded decomposition-width. Furthermore, we show that if a class of matroids has the pigeonhole property, and can be defined in monadic second-order logic, then any subclass with bounded branch-width has a decidable monadic second-order theory.Comment: Slightly extending the main theorem to cover a more expressive logi

On excluded minors for real-representability

AbstractWe show that for any infinite field K and any K-representable matroid N there is an excluded minor for K-representability that has N as a minor

Commissioning ShARCS: the Shane Adaptive optics infraRed Camera-Spectrograph for the Lick Observatory 3-m telescope

We describe the design and first-light early science performance of the Shane Adaptive optics infraRed Camera-Spectrograph (ShARCS) on Lick Observatory's 3-m Shane telescope. Designed to work with the new ShaneAO adaptive optics system, ShARCS is capable of high-efficiency, diffraction-limited imaging and low-dispersion grism spectroscopy in J, H, and K-bands. ShARCS uses a HAWAII-2RG infrared detector, giving high quantum efficiency (>80%) and Nyquist sampling the diffraction limit in all three wavelength bands. The ShARCS instrument is also equipped for linear polarimetry and is sensitive down to 650 nm to support future visible-light adaptive optics capability. We report on the early science data taken during commissioning.Comment: 9 pages, 7 figures. Presented at SPIE Astronomical Telescopes + Instrumentation conference, paper 9148-11

Opto-Mechanical Design of ShaneAO: the Adaptive Optics System for the 3-meter Shane Telescope

A Cassegrain mounted adaptive optics instrument presents unique challenges for opto-mechanical design. The flexure and temperature tolerances for stability are tighter than those of seeing limited instruments. This criteria requires particular attention to material properties and mounting techniques. This paper addresses the mechanical designs developed to meet the optical functional requirements. One of the key considerations was to have gravitational deformations, which vary with telescope orientation, stay within the optical error budget, or ensure that we can compensate with a steering mirror by maintaining predictable elastic behavior. Here we look at several cases where deformation is predicted with finite element analysis and Hertzian deformation analysis and also tested. Techniques used to address thermal deformation compensation without the use of low CTE materials will also be discussed.Comment: 14 pages, 14 figures, 4 tables. Presented at SPIE Astronomical Telescopes + Instrumentation conference, paper 9148-11

Understanding packet loss for sound monitoring in a smart stadium IoT testbed

The Smart Stadium for Smarter Living project provides an end-to-end testbed for IoT innovation through a collaboration between Croke Park Stadium in Dublin, Ireland and Dublin City University, Intel and Microsoft. This enables practical evaluations of IoT solutions in a controlled environment that is small enough to conduct trials but large enough to prove and challenge the technologies. An evaluation of sound monitoring capabilities during the 2016 sporting finals was used to test the capture, transfer, storage and analysis of decibel level sound monitoring. The purpose of the evaluation was to use existing sound level microphones to measure crowd response to pre-determined events for display on big screens at half-time and to test the end-to-end performance of the testbed. While this is not the specific original purpose of the sound level microphones, it provided a useful test case and produced engaging content for the project. Analysis of the data streams showed significant packet loss during the events and further investigations were conducted to understand where and how this loss occurred. This paper describes the smart stadium testbed configuration using Intel gateways linking with the Azure cloud platform and analyses the performance of the system during the sound monitoring evaluation