O(N) and O(N) and O(N)

Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an $\epsilon$ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large $N$ methods to establish formulas for anomalous dimensions which are valid equally for field theories over the $p$-adic numbers and field theories on $\mathbb{R}^n$. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the $O(N)$ model on $\mathbb{R}^n$, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theories in four real Euclidean dimensions.Comment: 44 pages, 8 figure

Higher melonic theories

We classify a large set of melonic theories with arbitrary $q$-fold interactions, demonstrating that the interaction vertices exhibit a range of symmetries, always of the form $\mathbb{Z}_2^n$ for some $n$, which may be $0$. The number of different theories proliferates quickly as $q$ increases above $8$ and is related to the problem of counting one-factorizations of complete graphs. The symmetries of the interaction vertex lead to an effective interaction strength that enters into the Schwinger-Dyson equation for the two-point function as well as the kernel used for constructing higher-point functions.Comment: 43 pages, 12 figure

Superconductivity in Boron under pressure - why are the measured Tc_c's so low?

Using the full potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure-dependence of superconductivity in the two metallic phases of Boron: bct and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to stiffening of phonons with an accompanying decrease in electron-phonon coupling. This is in contrast to a recent report, where T$_c$ is found to increase with pressure. Even more drastic is the difference between the measured T$_c$, in the range 4-11 K, and the calculated values for both bct and fcc phases, in the range 60-100 K. The calculation reveals that the transition from the fcc to bct phase, as a result of increasing volume or decreasing pressure, is caused by the softening of the X-point transverse phonons. This phonon softening also causes large electron-phonon coupling for high volumes in the fcc phase, resulting in coupling constants in excess of 2.5 and T$_c$ nearing 100 K. We discuss possible causes as to why the experiment might have revealed T$_c$'s much lower than what is suggested by the present study. The main assertion of this paper is that the possibility of high T$_c$, in excess of 50 K, in high pressure pure metallic phases of boron cannot be ruled out, thus substantiating the need for further experimental investigations of the superconducting properties of high pressure pure phases of boron.Comment: 16 pages, 8 figures, 1 Tabl

Opportunities to Develop Programs and Engage Amish Youth in Safety Education

Understanding and designing appropriate educational youth safety programs for the Amish requires an appreciation of their history, their distinctiveness in an American society built on economic, social and cultural change, and how the Amish themselves have changed over the years. The qualitative research study highlighted in this paper sought to determine culturally and age-appropriate curricula useful to community educators interested in youth safety programs for Amish and other conservative Anabaptist groups. Researchers identified rural safety topics of interest to Amish families to include lawn mowers, string trimmers, chemicals, water, livestock, confined spaces, tractors and skid loaders. Parents regularly involved children in daily farm chores, where they made assignments based on the child’s physical development, maturity, interest in the task, and birth-order. Findings suggest opportunities for cooperative extension professionals to develop and engage Amish children in safety education programs

Efforts to Improve Roadway Safety: A Collaborative Approach between Amish Communities and a Professional Engineering Society

Lighting and marking recommendations for animal-drawn buggies and wagons were first established in 2001 through an American Society of Agricultural and Biological Engineers (ASABE) Engineering Practice, EP576.1. Many Anabaptist communities who primarily rely on animal-drawn vehicles utilize this practice for marking their buggies and wagons; however they do not utilize the practice for their low-profile vehicles, such as pony carts. Visibility for pony carts on public roads is important to protect the operators, typically women and children. Following a series of tragic deaths in their community, the Holmes and Wayne Counties, Ohio, Amish safety committee raised the concern of having a consistent lighting and marking scheme for these low-profile vehicles. They also called for an additional aerial device to boost the cart\u27s visibility to the motoring public. This project took approximately two years to develop consensus among Anabaptist stakeholders and members of the professional engineering society. The result of this effort was a revised Engineering Practice, EP576.2, which enhanced the previous recommendations to include consistent lighting and marking of low-profile animal-drawn vehicles

The association of periodontal diseases with metabolic syndrome and obesity

Periodontitis is a multifactorial chronic inflammatory disease associated with dysbiotic plaque biofilms and characterized by progressive destruction of the tooth‐supporting apparatus. Globally, it is estimated that 740 million people are affected by its severe form. Periodontitis has been suggested to be linked to obesity and metabolic syndrome. Obesity, defined as excessive fat accumulation, is a complex multifactorial chronic inflammatory disease, with a high and increasing prevalence. Metabolic syndrome is defined as a cluster of obesity, dyslipidemia, hypertension, and dysglycemia. Obesity, metabolic syndrome and periodontitis are among the most common non‐communicable diseases and a large body of evidence from epidemiologic studies supports the association between these conditions. Extensive research has established plausible mechanisms to explain how these conditions can negatively impact each other, pointing to a bidirectional adverse relationship. At present there is only limited evidence available from a few intervention studies. Nevertheless, the global burden of periodontitis combined with the obesity epidemic has important clinical and public health implications for the dental team. In accordance with the common risk factor approach for tackling non‐communicable diseases, it has been proposed that oral healthcare professionals have an important role in the promotion of periodontal health and general well‐being through facilitation of healthy lifestyle behaviours

Edge length dynamics on graphs with applications to pp-adic AdS/CFT

We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with $p$-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. We compute simple correlators of the operator holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor.Comment: 42 pages, 6 figure