Fourier Series Formalization in ACL2(r)

We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r). Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

The Phonology of the Canadian Shift Revisited: Thunder Bay & Cape Breton

Previous accounts of the Canadian Shift, which have interpreted this diachronic process as a purely phonetic consequence of the low back LOT-THOUGHT vowel merger, have not clearly explained the strong connection between phonetic TRAP vowel retraction and the phonological process of the low back merger. This paper addresses this issue in several ways. Relying on the Modified Contrastive Specification theory (Dresher et al. 1994) and the Contrastive Hierarchy approach (Dresher 2009), two phonological frameworks, as well as phonetic insights from Vowel Dispersion theory (Liljencrants and Lindblom 1972) and Dispersion-Focalization theory (Schwartz et al. 1997, Schwartz et al. 2007), we propose that the catalyst of the Canadian Shift is a three-way merger of the PALM, LOT and THOUGHT lexical sets, in combination with a simultaneous change in the underlying feature specifications of the TRAP vowel. This results in a phonology that allows for the TRAP and DRESS vowels, in particular, to undergo the influence of the phonetic principles of dispersion and focalization, which lead to lowering and retraction in the acoustic vowel space. Comparison of data from speakers in Thunder Bay, Ontario, and Cape Breton, Nova Scotia, lends support to this hypothesis because the Cape Breton data reveals evidence of two concurrent phonological systems, despite no evidence of change over apparent time. Some Cape Breton speakers display the Ontario (i.e., inland Canada) Canadian Shifted vowel system, while others display a system that bears much greater resemblance to the Eastern New England non-shift dialect, where PALM merges with TRAP instead of LOT-THOUGHT. The current analysis thus predicts that the Canadian Shift or a similar change to the TRAP, DRESS, and KIT vowels will occur in any North American dialect where the PALM-LOT-THOUGHT merger occurs, unless an intervening phonological change alters the contrasts within the phonological system

Does distrust in providers affect health-care utilization in China?

How trust affects health-care utilization is not well-understood, especially in low- and middle-income countries. This article focuses on China, a middle-income country where low trust in health-care settings has become a prominent issue, but actual levels of distrust and their implications for utilization are unknown. We conducted a nationally representative survey of the Chinese population (November 2012 to January 2013), which resulted in a sample of 3680 adult men and women. Respondents rated their trust in different types of health-care providers. Using multivariate logistic and negative binomial regression models, we estimated the association between distrust in clinics and respondents' hospital visits in the last year; whether they had sought hospital treatment first for two common symptoms (headache, cold) in the last 2 months; and whether they said they would go first to a hospital if they had a minor or major illness. We analysed these associations before and after adjusting for performance evaluations of clinics and hospitals, controlling for sex, age, education, income, insurance status, household registration and self-assessed health. We found that distrust in hospitals is low, but distrust in clinics is high and strongly associated with increased hospital utilization, especially for minor symptoms and illnesses. Further research is needed to understand the reasons for distrust in clinics because its effects are not fully accounted for by poor evaluations of their competence. © 2016 The Author 2016. Published by Oxford University Press. All rights reserved

Comparing the effectiveness of using generic and specific search terms in electronic databases to identify health outcomes for a systematic review: a prospective comparative study of literature search methods

<p>Objective: To compare the effectiveness of systematic review literature searches that use either generic or specific terms for health outcomes.</p> <p>Design Prospective comparative study of two electronic literature search strategies. The 'generic' search included general terms for health such as 'adolescent health', 'health status', 'morbidity', etc. The 'specific' search focused on terms for a range of specific illnesses, such as 'headache', 'epilepsy’, 'diabetes mellitus', etc.</p> <p>Data: sources The authors searched Medline, Embase, the Cumulative Index to Nursing and Allied Health Literature, PsycINFO and the Education Resources Information Center for studies published in English between 1992 and April 2010.</p> <p>Main: outcome measures Number and proportion of studies included in the systematic review that were identified from each search.</p> <p>Results: The two searches tended to identify different studies. Of 41 studies included in the final review, only three (7%) were identified by both search strategies, 21 (51%) were identified by the generic search only and 17 (41%) were identified by the specific search only. 5 of the 41 studies were also identified through manual searching methods. Studies identified by the two ELS differed in terms of reported health outcomes, while each ELS uniquely identified some of the review's higher quality studies.</p> <p>Conclusions: Electronic literature searches (ELS) are a vital stage in conducting systematic reviews and therefore have an important role in attempts to inform and improve policy and practice with the best available evidence. While the use of both generic and specific health terms is conventional for many reviewers and information scientists, there are also reviews that rely solely on either generic or specific terms. Based on the findings, reliance on only the generic or specific approach could increase the risk of systematic reviews missing important evidence and, consequently, misinforming decision makers. However, future research should test the generalisability of these findings.</p&gt

Soft Palate Modification Using a Collagen Crosslinking Reagent for Equine Dorsal Displacement of the Soft Palate and Other Upper Airway Breathing Disorders

The mechanical properties of the soft palate can be associated with breathing abnormalities. Dorsal displacement of the soft palate (DDSP) is a naturally occurring equine soft palate disorder caused by displacement of the caudal edge of the soft palate. Snoring and a more serious, sometimes life-threatening, condition called obstructive sleep apnea (OSA) are forms of sleep-related breathing disorders in humans which may involve the soft palate. The goal of this study was to investigate the effect of injecting the protein crosslinker genipin into the soft palate to modify its mechanical properties for the treatment of equine DDSP with potential implications for the treatment of snoring and OSA in humans. Ex vivo experiments consisted of mechanical testing and a wind tunnel study to examine the effect of genipin on the mechanical properties, displacement, and vibration of equine soft palates. A pilot in vivo study was completed using DDSP and control horses to test the safety and effectiveness of injecting a genipin reagent into the soft palate. The wind tunnel testing demonstrated a greater than 50% decrease in transient deformation and a greater than 33% decrease in steady-state vibrations for all doses of genipin tested. Ultimate tensile stress, yield stress, and Young’s modulus were higher in the genipin-treated distal soft palate specimens by 52%, 53%, and 63%, respectively. The pilot in vivo study showed a reduction of snoring loudness in all DDSP horses and elimination of DDSP in at least one of three horses. The difficulty of using a 1-meter-long endoscopic injection needle contributed to a consistent overinjection of the equine soft palates, causing excessive stretching (pillowing) and related degradation of the tissue. These ex vivo and in vivo results demonstrated reduced vibration amplitude and flaccidity and increased strength of genipin-treated soft palates, suggesting that genipin crosslinking could become an effective and safe treatment for soft palate related breathing abnormalities

The Jelly Team: citizen science at a small community aquarium

The efforts and successes of a community volunteer group, ‘The Jelly Team’, exemplify citizen science achievement at the Marine Science and Technology Center, the marine biology and aquarium facility of Highline College in Des Moines, Washington. With little professional direction or funding, these volunteers have succeeded in culturing Moon Jellies to provide an ongoing display in the public aquarium, and are now expanding their activities to culturing other species and looking to provide specimens to local schools. A popular display at the MaST public aquarium is a kreisel tank featuring Aurelia labiata, the Pacific coast species of the Moon Jelly. Due to the short lifespan of wild-caught specimens in captivity, the aquarium faced an ongoing problem of keeping this display stocked with jellies. A team of community volunteers, who have been largely self-educated in jelly biology and husbandry, have developed a protocol for culturing Aurelia labiata in the small wet lab at the center. After seven years, the MaST now has a self-sustaining ‘Jelly Team’ and MaST staff felt it essential to maintain volunteer interest by providing the citizen scientists with an ongoing sense of direction in the project. Current projects include culturing the Egg Yolk jellyfish (Phacellophora camtschatica) and a middle school education program where Aurelia labiata tanks can be placed in schools such that students can observe the entire life cycle of the species over the school year. In addition, training of new and prospective volunteers has been facilitated by provision of an online ‘jelly curriculum.’ This poster presentation details how the technical challenges of culturing jellies inexpensively in a small facility have been addressed. We also discuss the dynamics of recruiting, training, and maintaining an active and skilled body of volunteers with minimal direction from professional staff

Low-level and high-level modulations of fixational saccades and high frequency oscillatory brain activity in a visual object classification task

Until recently induced gamma-band activity (GBA) was considered a neural marker of cortical object representation. However, induced GBA in the electroencephalogram (EEG) is susceptible to artifacts caused by miniature fixational saccades. Recent studies have demonstrated that fixational saccades also reflect high-level representational processes. Do high-level as opposed to low-level factors influence fixational saccades? What is the effect of these factors on artifact-free GBA? To investigate this, we conducted separate eye tracking and EEG experiments using identical designs. Participants classified line drawings as objects or non-objects. To introduce low-level differences, contours were defined along different directions in cardinal color space: S-cone-isolating, intermediate isoluminant, or a full-color stimulus, the latter containing an additional achromatic component. Prior to the classification task, object discrimination thresholds were measured and stimuli were scaled to matching suprathreshold levels for each participant. In both experiments, behavioral performance was best for full-color stimuli and worst for S-cone isolating stimuli. Saccade rates 200–700 ms after stimulus onset were modulated independently by low and high-level factors, being higher for full-color stimuli than for S-cone isolating stimuli and higher for objects. Low-amplitude evoked GBA and total GBA were observed in very few conditions, showing that paradigms with isoluminant stimuli may not be ideal for eliciting such responses. We conclude that cortical loops involved in the processing of objects are preferentially excited by stimuli that contain achromatic information. Their activation can lead to relatively early exploratory eye movements even for foveally-presented stimuli

The potential of Heat as a service as a route to decarbonisation for Scotland

To reach its target of net-zero carbon emissions by 2045, Scotland needs to decarbonise heat and improve the energy efficiency of its buildings. This evidence review examines the potential of Heat as a Service (HaaS) to support this aim by providing a route to the decarbonisation of heat in domestic properties in Scotland. Heat as a Service is a term which covers a range of services that enable people to achieve a warm home in a variety of ways. These include services which provide or enable finance to purchase and install heating equipment; maintenance of heating equipment; energy efficiency upgrades of building fabric; paying for the amount of heat delivered to the home; paying for the temperature the home is heated to; paying flat-rate tariffs for the home to be heated; or combinations of these. Although, to date, there is not much evidence as to what has been tried or how effective it has been in delivering substantial emissions reductions, the limited evidence we found suggests that some HaaS offers potential to: help get Scotland to net zero by accelerating the uptake of low-carbon heating systems and improving energy efficiency across the domestic energy market; improve outcomes for consumers, especially the more vulnerable, by helping target financial support and providing better cost certainty; and support businesses in developing new, sustainable, business models and creating new jobs. The report outlines HaaS business models that have been tried across Europe, and categorises them in terms of the outcomes they offer consumers. It looks into the potential benefits of HaaS for Scotland, and some of the current barriers. Through case studies, it explores in more detail how different business models might work and be adapted to Scotland, and makes six recommendations as to how the Scottish Government could take HaaS forward

Lifting options for stratospheric aerosol geoengineering: advantages of tethered balloon systems

The Royal Society report 'Geoengineering the Climate' identified solar radiation management using albedo-enhancing aerosols injected into the stratosphere as the most affordable and effective option for geoengineering, but did not consider in any detail the options for delivery. This paper provides outline engineering analyses of the options, both for batch-delivery processes, following up on previous work for artillery shells, missiles, aircraft and free-flying balloons, as well as a more lengthy analysis of continuousdelivery systems that require a pipe connected to the ground and supported at a height of 20 km, either by a tower or by a tethered balloon. Towers are shown not to be practical, but a tethered balloon delivery system, with high-pressure pumping, appears to have much lower operating and capital costs than all other delivery options. Instead of transporting sulphuric acid mist precursors, such a system could also be used to transport slurries of high refractive index particles such as coated titanium dioxide. The use of such particles would allow useful experiments on opacity, coagulation and atmospheric chemistry at modest rates so as not to perturb regional or global climatic conditions, thus reducing scale-up risks. Criteria for particle choice are discussed, including the need to minimize or prevent ozone destruction. The paper estimates the time scales and relatively modest costs required if a tethered balloon system were to be introduced in a measured way with testing and development work proceeding over three decades, rather than in an emergency. The manufacture of a tether capable of sustaining the high tensions and internal pressures needed, as well as strong winds, is a significant challenge, as is the development of the necessary pumping and dispersion technologies. The greatest challenge may be the manufacture and launch of very large balloons, but means have been identified to significantly reduce the size of such balloons or aerostats