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

On Vertex- and Empty-Ply Proximity Drawings

We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is to relate the concept of ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-ply number 1 can be seen as a weak proximity drawing, which we call empty-ply drawing. We show non-trivial relationships between the ply number and the vertex-ply number. Then, we focus on empty-ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the ply and the vertex-ply of planar drawings.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Water, Sanitation, and Hygiene Interventions to Reduce Diarrhoea in Less Developed Countries: A Systematic Review and Meta-analysis

The authors developed a comprehensive research strategy designed to identify all peer-reviewed articles, in any language, that presented water, sanitation, or hygiene interventions. Out of 2,120 publications, ultimately 40 studies were judged to contain relevant evidence. Most of the studies confined their study groups to children aged under 5 or 6 years. The identified studies were done in a wide range of settings, in many countries, and over many years. All of the interventions studied were found to reduce significantly the risks of diarrheal illness. The results generally agree with those from previous reviews, but water quality interventions (point-of-use water treatment) were found to be more effective than previously thought, and multiple interventions (consisting of combined water, sanitation, and hygiene measures) were not more effective than interventions with a single focus

Autistic behavior in boys with fragile X syndrome: social approach and HPA-axis dysfunction

The primary goal of this study was to examine environmental and neuroendocrine factors that convey increased risk for elevated autistic behavior in boys with Fragile X syndrome (FXS). This study involves three related analyses: (1) examination of multiple dimensions of social approach behaviors and how they vary over time, (2) investigation of mean levels and modulation of salivary cortisol levels in response to social interaction, and (3) examination of the relationship of social approach and autistic behaviors to salivary cortisol. Poor social approach and elevated baseline and regulation cortisol are discernible traits that distinguish boys with FXS and ASD from boys with FXS only and from typically developing boys. In addition, blunted cortisol change is associated with increased severity of autistic behaviors only within the FXS and ASD group. Boys with FXS and ASD have distinct behavioral and neuroendocrine profiles that differentiate them from those with FXS alone and typically developing boys

Lymphocyte subsets and the role of Th1/Th2 balance in stressed chronic pain patients

Background: The complex regional pain syndrome (CRPS) and fibromyalgia (FM) are chronic pain syndromes occurring in highly stressed individuals. Despite the known connection between the nervous system and immune cells, information on distribution of lymphocyte subsets under stress and pain conditions is limited. Methods: We performed a comparative study in 15 patients with CRPS type I, 22 patients with FM and 37 age- and sex-matched healthy controls and investigated the influence of pain and stress on lymphocyte number, subpopulations and the Th1/Th2 cytokine ratio in T lymphocytes. Results: Lymphocyte numbers did not differ between groups. Quantitative analyses of lymphocyte subpopulations showed a significant reduction of cytotoxic CD8+ lymphocytes in both CRPS (p < 0.01) and FM (p < 0.05) patients as compared with healthy controls. Additionally, CRPS patients were characterized by a lower percentage of IL-2-producing T cell subpopulations reflecting a diminished Th1 response in contrast to no changes in the Th2 cytokine profile. Conclusions: Future studies are warranted to answer whether such immunological changes play a pathogenetic role in CRPS and FM or merely reflect the consequences of a pain-induced neurohumoral stress response, and whether they contribute to immunosuppression in stressed chronic pain patients. Copyright (c) 2008 S. Karger AG, Basel

Islands of ice: Influence of free-drifting Antarctic icebergs on pelagic marine ecosystems

Regional warming around West Antarctica, including the Antarctic Peninsula, is related to the retreat of glaciers that has resulted in significant ice mass loss in recent decades. We examined freedrifting icebergs in the Atlantic sector of the Southern Ocean in December 2005, aboard ARSV Laurence M. Gould, and in June 2008 and March/April 2009, aboard RVIB Nathaniel B. Palmer. Prior to these studies, little information was available about the effects of icebergs on the pelagic realm.Facultad de Ciencias Naturales y Muse

Worm Grunting, Fiddling, and Charming—Humans Unknowingly Mimic a Predator to Harvest Bait

Background: For generations many families in and around Florida’s Apalachicola National Forest have supported themselves by collecting the large endemic earthworms (Diplocardia mississippiensis). This is accomplished by vibrating a wooden stake driven into the soil, a practice called ‘‘worm grunting’’. In response to the vibrations, worms emerge to the surface where thousands can be gathered in a few hours. Why do these earthworms suddenly exit their burrows in response to vibrations, exposing themselves to predation? Principal Findings: Here it is shown that a population of eastern American moles (Scalopus aquaticus) inhabits the area where worms are collected and that earthworms have a pronounced escape response from moles consisting of rapidly exiting their burrows to flee across the soil surface. Recordings of vibrations generated by bait collectors and moles suggest that ‘‘worm grunters’ ’ unknowingly mimic digging moles. An alternative possibility, that worms interpret vibrations as rain and surface to avoid drowning is not supported. Conclusions: Previous investigations have revealed that both wood turtles and herring gulls vibrate the ground to elicit earthworm escapes, indicating that a range of predators may exploit the predator-prey relationship between earthworms and moles. In addition to revealing a novel escape response that may be widespread among soil fauna, the results sho