Triangle-free subgraphs of random graphs

Recently there has been much interest in studying random graph analogues of well known classical results in extremal graph theory. Here we follow this trend and investigate the structure of triangle-free subgraphs of $G(n,p)$ with high minimum degree. We prove that asymptotically almost surely each triangle-free spanning subgraph of $G(n,p)$ with minimum degree at least $\big(\frac{2}{5} + o(1)\big)pn$ is $\mathcal O(p^{-1}n)$-close to bipartite, and each spanning triangle-free subgraph of $G(n,p)$ with minimum degree at least $(\frac{1}{3}+\varepsilon)pn$ is $\mathcal O(p^{-1}n)$-close to $r$-partite for some $r=r(\varepsilon)$. These are random graph analogues of a result by Andr\'asfai, Erd\H{o}s, and S\'os [Discrete Math. 8 (1974), 205-218], and a result by Thomassen [Combinatorica 22 (2002), 591--596]. We also show that our results are best possible up to a constant factor.Comment: 18 page

UA35/7 Proposal for the Establishment of the Kentucky Academy of Mathematics & Science at WKU

Initial proposal for the creation of the Gatton Academy at WKU. The proposal was written by Julia Roberts of the WKU\u27s Gifted & Talented Center and submitted to Charles McGruder of WKU\u27s Physics & Astronomy Department

Developing a Podcast: Decoding Creativity

Details the process of a student creating a podcast about creativity. The show’s goal is to entertain as well as inform, a tone that can be hard to achieve. As well as entertain and inform, the podcast is intended to attract clients to the creativity coaching business found at www.decodingcreativity.com . Discusses the three phases of the production – content, production, and promotion – and gives resources, timeline and process as to how each phase was achieved. For content guidance, influences included: Wilfred, and How I Met Your Mother and Homestarrunner, and existing radio series like Welcome to Nightvale. For educational tone, the Torrance Incubation Model and Beyonder traits were consulted. Many formats were considered and discussed, and a newscast parody format was ultimately chosen and produced. For production, Adobe’s Audition software and freeconferencecallHD.com were used. Both were effective platforms for quality audio product. For promotion, a webpage was dedicated to two episodes per month. Audience development got a boost by engaging 20+ voices in the first two shows and by using Facebook to keep people aware of the show’s progress. Postcards were developed as the graphic on the webpage, as well as an inexpensive print marketing tactic

Women, Men, and Taverns in Tavern-Keeper Ely Playter's Journal

Ely Playter kept a tavern in York, Upper Canada, in 1801 and 1802. His journal depicts his public house and those he frequented as places in which women were seen as often as men. Yet gender was a powerful determinant of who enjoyed free access to the public life that taverns housed. Only within the context of close male companionship did women find room there. Taverns were also sites in which public life mixed with household life, and many women were thus literally at home in taverns. By constructing taverns as male spaces, we hide the complex experiences of these women. Without contradicting the power of male privilege, Playter’s journal places taverns within the rest of the pre-industrial social landscape, as spaces in which women and men both belonged.Ely Playter a tenu une taverne à York, dans le Haut-Canada, en 1801 et en 1802. Son journal décrit son établissement public et ceux qu’il fréquentait comme des endroits où l’on voyait aussi souvent des femmes que des hommes. Pourtant, le genre était un puissant déterminant de qui avait accès gratuitement à la vie publique des tavernes. Les femmes n’avaient droit d’y entrer qu’en compagnie de proches compagnons masculins. Les tavernes étaient également des endroits où s’entremêlaient vie publique et vie familiale, si bien que de nombreuses femmes étaient pratiquement à la maison dans les tavernes. En construisant les tavernes comme des espaces masculins, nous occultons l’expérience complexe de ces femmes. Sans contredire la puissance du privilège des hommes, le journal de Playter situe les tavernes sur le reste de la toile sociale préindustrielle comme des lieux d’appartenance tant des femmes que des hommes

Work of the NHS England Youth Forum and its effect on health services.

©2018 RCN Publishing Company Ltd. All rights reserved. Not to be copied, transmitted or recorded in any way, in whole or part, without prior permission of the publishers.AIM: To examine the role of members of the NHS England Youth Forum (NHSEYF) and the strategies used to influence health service provision for children and young people. METHOD: An evaluative mixed-methods study was commissioned by NHS England and undertaken by the University of Hertfordshire between July 2015 and September 2016. Data collection comprised activity logs, a form of questionnaire, and semi-structured interviews. FINDINGS: The analysis of the activity logs revealed that the young people were undertaking a wide range of activities across England. Seven themes emerged from the interviews: the young people; motivation; commitment; community (the local area as well as a community spirit); knowledge experts; youth workers; and funding. In summary, the members of the NHSEYF were committed to their role and their work was having a positive effect on health service provision. CONCLUSION: The NHSEYF has developed rapidly and successfully. It is enabling the voice of young people to be heard.Peer reviewedFinal Published versio

Direct in-situ evaluation of liquefaction susceptibility

textEarthquake-induced soil liquefaction that occurs within the built environment is responsible for billions of dollars of damage to infrastructure and loss of economic productivity. There is an acute need to accurately predict the risk of soil liquefaction as well as to quantify the effectiveness of soil improvement techniques that are meant to decrease the risk of soil liquefaction. Current methods indirectly measure the risk of soil liquefaction by empirically correlating certain soil characteristics to known instances of surficial evidence of soil liquefaction, but these methods tend to overpredict the risk in sands with silts, to poorly predict instances of soil liquefaction without surface manifestations, and fail to adequately quantify the effectiveness of soil improvement techniques. Direct in-situ evaluation of liquefaction susceptibility was performed at a single site at the Wildlife Liquefaction Array (WLA) in Imperial Valley, California, in March 2012. The project included a CPT sounding, crosshole testing, and liquefaction testing. The liquefaction testing involved the measurement of water pressure and ground particle motion under earthquake-simulating cyclic loading conditions. The objective of this testing technique is to observe the relationship between shear strain in the soil and the resulting generation of excess pore water pressure. This fundamental relationship dictates whether or not a soil will liquefy during an earthquake event. The direct in-situ evaluation of liquefaction susceptibility approach provides a more accurate and comprehensive analysis of the risks of soil liquefaction. It also has the ability to test large-scale soil improvements in-situ, providing researchers an accurate representation of how the improved soil will perform during a real earthquake event. The most important results in this thesis include the identification of the cyclic threshold strain around 0.02% for the WLA sand, which is very similar to results achieved by other researchers (Vucetic and Dobry, 1986, and Cox, 2006) and is a characteristic of liquefiable soils. Another key characteristic is the 440 to 480 ft/sec (134 to 146 m/s) shear wave velocity of the soil, which are well below the upper limit 656 ft/sec (200 m/s) and an indication that the soil is loose enough for soil liquefaction to occur. The third significant point is that the compression wave velocity of the sand is greater than 4,500 ft/sec (1,370 m/s), indicating that it is at least 99.9% saturated and capable of generating large pore water pressure due to cyclic loading. These three conditions (cyclic threshold strain, shear wave velocity, and compression wave velocity) are among the most important parameters for characterizing a soil liquefaction risk and must all be met in order for soil liquefaction to occur.Civil, Architectural, and Environmental Engineerin

Acquisition of Variable Rules: (-t,d) Deletion and (ing) Production in Preschool Children

There have been many studies over the past few decades documenting the existence of variable rules in adult language. It is only recently, however, that the acquisition of these rules has been the focus of research, and that event has opened the door for questions about the interaction of the learning of categorical rules and that of variable rules. Specifically, questions have arisen as to whether these rules might not be construed as either a performance factor and/or a reflection of universal constraints on language. The present study examines the acquisition of (-t,d) deletion and (ing) production in 3- and 4-year-old children in order to ascertain their degree of mastery of phonological, grammatical, and social constraints. Seventeen children were tape recorded during play interview sessions in their South Philadelphia day care center. Six to thirteen sessions per child over a three month period were required to obtain sufficient data for analysis. In addition, eight of their parents were interviewed in their homes for purposes of comparison. Results of the study revealed that children as young as three had, for the most part, mastered the process of variation of (ing) and the phonological constraints on (-t,d) deletion, and they were well into the process of acquiring the grammatical constraints on (-t,d) deletion. Their learning of a dialect specific phonological constraint demonstrated that their mastery of this variable rule was not a reflection of universal constraints. Further, their independent analysis of semi-weak verbs made it clear that they were not simply copying frequencies of their parents\u27 forms but learning an abstract rule. The children\u27s acquisition of the extralinguistic constraints on these rules lagged behind that of the linguistic factors. Of particular interest to the issue of gender differences in language was the girls\u27 surprising tendency to delete (-t,d) more often than the boys, demonstrating that they had not yet learned linguistic conservatism in instances of stable variation and arguing against a biological basis for sex-based sociolinguistic differences