Ghost circles in lattice Aubry-Mather theory

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics as models for fe?rromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multidimensional counterpart of monotone twist maps. They often admit a variational structure, so that the solutions are the stationary points of a formal action function. Classical Aubry-Mather theory establishes the existence of a large collection of solutions of any rotation vector. For irrational rotation vectors this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the gradient flow of the formal action function and we prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called "ghost circle". The existence of ghost circles is first proved for rational rotation vectors and Morse action functions. The main technical result is a compactness theorem for ghost circles, based on a parabolic Harnack inequality for the gradient flow, which implies the existence of ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be parametrized by minimizers, or contain a non-minimizing solution.Comment: 39 pages, 1 figur

Portfolio Vol. IV N 3

Benson, Virginia. Rejected. Prose. 3. Phillips, Alison. Lure in April. Poetry. 6. Shields, Margaret. Wedding Morning. Prose. 7. Willett, Thelma. Ex Libris: G.K.W. Poetry. 8. Benson, Virginia. High Note. Poetry. 8. Maxwell, Bob. Discovery. Poetry. 8. Eschman, Karl. The Case for Modern Music. Prose. 8-9. Wyman, John. Dissonance. Prose. 10-11. Hart, Dorothy. The Origin of Memorial Day. Prose. 12. Reed, Roger. Notes on the Drama. Prose. 13. Parker, Mab. Black Girl. Picture. 14. Mather, William. The Pasquin. Prose. 15. Hammer, John. Over the Green Grass. Prose. 16. Maxwell, Bob. Genesis... Poetry. 19. Maxwell, Bob. We Three. Poetry. 19. Stransky, Ed. Concerning The Well-Known \u27Butch.\u27 Prose. 20. Seagrave, Leslie. Memory. Prose. 21

Advanced Technology Large-Aperture Space Telescope (ATLAST): A Technology Roadmap for the Next Decade

The Advanced Technology Large-Aperture Space Telescope (ATLAST) is a set of mission concepts for the next generation of UVOIR space observatory with a primary aperture diameter in the 8-m to 16-m range that will allow us to perform some of the most challenging observations to answer some of our most compelling questions, including "Is there life elsewhere in the Galaxy?" We have identified two different telescope architectures, but with similar optical designs, that span the range in viable technologies. The architectures are a telescope with a monolithic primary mirror and two variations of a telescope with a large segmented primary mirror. This approach provides us with several pathways to realizing the mission, which will be narrowed to one as our technology development progresses. The concepts invoke heritage from HST and JWST design, but also take significant departures from these designs to minimize complexity, mass, or both. Our report provides details on the mission concepts, shows the extraordinary scientific progress they would enable, and describes the most important technology development items. These are the mirrors, the detectors, and the high-contrast imaging technologies, whether internal to the observatory, or using an external occulter. Experience with JWST has shown that determined competitors, motivated by the development contracts and flight opportunities of the new observatory, are capable of achieving huge advances in technical and operational performance while keeping construction costs on the same scale as prior great observatories.Comment: 22 pages, RFI submitted to Astro2010 Decadal Committe

Sometimes it is better to know less: How known words influence referent selection and retention in 18 to 24-month-old children

Young children are surprisingly good word learners. Despite their relative lack of world knowledge and limited vocabularies, they consistently map novel words to novel referents and, at later ages, show retention of these new word–referent pairs. Prior work has implicated the use of mutual exclusivity constraints and novelty biases, which require that children use knowledge of well-known words to disambiguate uncertain naming situations. The current study, however, presents evidence that weaker vocabulary knowledge during the initial exposure to a new word may be better for retention of new mappings. Children aged 18–24 months selected referents for novel words in the context of foil stimuli that varied in their lexical strength and novelty: well-known items (e.g., shoe), just-learned weakly known items (e.g., wif), and completely novel items. Referent selection performance was significantly reduced on trials with weakly known foil items. Surprisingly, however, children subsequently showed above-chance retention for novel words mapped in the context of weakly known competitors compared with those mapped with strongly known competitors or with completely novel competitors. We discuss implications for our understanding of word learning constraints and how children use known words and novelty during word learning

The James Webb Space Telescope Mission: Optical Telescope Element Design, Development, and Performance

The James Webb Space Telescope (JWST) is a large, infrared space telescope that has recently started its science program which will enable breakthroughs in astrophysics and planetary science. Notably, JWST will provide the very first observations of the earliest luminous objects in the Universe and start a new era of exoplanet atmospheric characterization. This transformative science is enabled by a 6.6 m telescope that is passively cooled with a 5-layer sunshield. The primary mirror is comprised of 18 controllable, low areal density hexagonal segments, that were aligned and phased relative to each other in orbit using innovative image-based wavefront sensing and control algorithms. This revolutionary telescope took more than two decades to develop with a widely distributed team across engineering disciplines. We present an overview of the telescope requirements, architecture, development, superb on-orbit performance, and lessons learned. JWST successfully demonstrates a segmented aperture space telescope and establishes a path to building even larger space telescopes.Comment: accepted by PASP for JWST Overview Special Issue; 34 pages, 25 figure

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

The Science Performance of JWST as Characterized in Commissioning

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.Comment: 5th version as accepted to PASP; 31 pages, 18 figures; https://iopscience.iop.org/article/10.1088/1538-3873/acb29

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Origins Space Telescope: baseline mission concept

The Origins Space Telescope will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did galaxies evolve from the earliest galactic systems to those found in the Universe today? How do habitable planets form? How common are life-bearing worlds? To answer these alluring questions, Origins will operate at mid- and far-infrared (IR) wavelengths and offer powerful spectroscopic instruments and sensitivity three orders of magnitude better than that of the Herschel Space Observatory, the largest telescope flown in space to date. We describe the baseline concept for Origins recommended to the 2020 US Decadal Survey in Astronomy and Astrophysics. The baseline design includes a 5.9-m diameter telescope cryocooled to 4.5 K and equipped with three scientific instruments. A mid-infrared instrument (Mid-Infrared Spectrometer and Camera Transit spectrometer) will measure the spectra of transiting exoplanets in the 2.8 to 20  μm wavelength range and offer unprecedented spectrophotometric precision, enabling definitive exoplanet biosignature detections. The far-IR imager polarimeter will be able to survey thousands of square degrees with broadband imaging at 50 and 250  μm. The Origins Survey Spectrometer will cover wavelengths from 25 to 588  μm, making wide-area and deep spectroscopic surveys with spectral resolving power R  ∼  300, and pointed observations at R  ∼  40,000 and 300,000 with selectable instrument modes. Origins was designed to minimize complexity. The architecture is similar to that of the Spitzer Space Telescope and requires very few deployments after launch, while the cryothermal system design leverages James Webb Space Telescope technology and experience. A combination of current-state-of-the-art cryocoolers and next-generation detector technology will enable Origins’ natural background-limited sensitivity