Expanders and right-angled Artin groups

The purpose of this article is to give a characterization of families of expander graphs via right-angled Artin groups. We prove that a sequence of simplicial graphs $\{\Gamma_i\}_{i\in\mathbb{N}}$ forms a family of expander graphs if and only if a certain natural mini-max invariant arising from the cup product in the cohomology rings of the groups $\{A(\Gamma_i)\}_{i\in\mathbb{N}}$ agrees with the Cheeger constant of the sequence of graphs, thus allowing us to characterize expander graphs via cohomology. This result is proved in the more general framework of \emph{vector space expanders}, a novel structure consisting of sequences of vector spaces equipped with vector-space-valued bilinear pairings which satisfy a certain mini-max condition. These objects can be considered to be analogues of expander graphs in the realm of linear algebra, with a dictionary being given by the cup product in cohomology, and in this context represent a different approach to expanders that those developed by Lubotzky-Zelmanov and Bourgain-Yehudayoff.Comment: 21 pages. Accepted version. To appear in J. Topol. Ana

Pena, Pinahua, and Prestige: Shame and Linguistic Insecurity in Upper Balsas Classrooms

This ethnography is a topical analysis of the Indigenous Education system in rural Guerrero, Mexico. The purpose of this research is to draw out the correlations between coercive monolingual ‘Spanish only’ language policies implemented during the mid 20th century and the systematic disintegration of the Nahuatl language within what were once monolingual Nahua communities in the Upper Balsas valley. The data presented in this paper is framed and analyzed through language ideologies discourse. The conceptualizations of language held within the cultural ideology allow for the complexities surrounding language loss and revitalization to be taken into consideration within their dynamic and fluid states. As an ethnography of the particular, this work compiles and analyzes data gathered from rural, historically Indigenous, and linguistically diverse populations in southwest Mexico. The foremost goal in this research is to determine if trans-generational shame is a plausible explanation and subsequently a contributing factor to Nahuatl language loss. The coercive nature of the language practices outlined in this ethnography, which caused, in my summation, psychological trauma due to the use of humiliation, shaming, which corresponded with a loss of agency, further stigmatized the Nahua communities. The secondary focus of the research is to look at the lasting effects or intergenerational manifestations of shame and stigmatization as it pertains to the cessation of language transmission leading to language dormancy. This ethnography is structured through interviews from three generations within the target population to capture the generational effects of Spanish only and monolingual bridging policies, which undermined Nahua agency regarding language transmission from the 1950s to the present. Through interviews, surveys and participant observation, the work presented in this ethnography comes together to create a snapshot of language shift within the region focusing primarily on the bilingual classroom. The implications drawn from the research illustrate the varying levels of shame, stigma, value, and prestige placed on language usage and includes Nahuatl, Spanish, and English. The research presented takes note of the speech communities and contexts in which ideologies are maintained, making this study significant to ongoing research in the fields of Indigenous Language Education policy, anthropology, and sociolinguistic research

Orden y distancia de fracciones y decimales en la recta numérica: el caso de Abigaíl

Este es un estudio de un caso acerca de las representaciones de números racionales en la recta numérica hechas a mano y utilizando un programa interactivo de una alumna de nivel medio superior. En un principio las representaciones de la alumna mostraron una clara comprensión de cómo representar el orden entre diferentes números en la recta numérica, pero no cómo representar correctamente las distancias entre ellos. La forma de representación utilizada (decimales o fracciones) también fue importante para que ella pudiera o no mostrar su comprensión de las distancias entre diversos números racionales. El estudio muestra el pensamiento de la alumna, sus dificultades y avances, a través de las interacciones con el entrevistador y el programa de computadora

Case study supermarkets and quality and safety standards for produce in Latin America

"Food safety standards that developed countries impose on developing-country exports have sometimes created a barrier to market access. But in Latin America today, the standards set by supermarkets in the region affect local producers far more than do those imposed by developed countries. Latin American farmers sell 2.5 times more to supermarkets within their own countries than they export to the rest of the world. Drawing on case studies from several Latin American countries, this brief focuses on how supermarkets in the region have gone about imposing quality and safety standards on producers of fresh fruits and vegetables for the domestic market." from TextFood safety ,food security ,Public health ,

Process to Remove Cholesterol from Dairy Products

The present invention relates to a process for the removal of cholesterol from a processed or unprocessed dairy product, which process comprises: (a) obtaining a processed or unprocessed dairy product containing cholesterol (b) contacting the dairy product at a temperature of between about 35° and 80° C. with an amount of saponin effective to bind up to about 90% of the cholesterol present in the dairy product; (c) contacting a temperature of between about 35° and 80° C the cholesterol: saponin with an effective amount of diatomaceous earth; (d) separating the insoluble cholesterol: saponin/diatomaceous earth by filtration or centrifugation; and (e) recovering the dairy product having a reduced content of cholesterol. The process particularly useful wherein the dairy product is selected from raw milk, pasteurized milk, raw cream, pasteurized cream, butteroil or anhydrous fat. The dairy product having a lowered cholesterol level is useful as a food to restrict cholesterol intake in a human being

Caryophyllales 2015 in Berlin and the Global Caryophyllales Initiative

Fil: Arias, Salvador. Universidad Nacional Autónoma de México; MéxicoFil: Berendsohn, Walter G.. Freie Universität Berlin; AlemaniaFil: Borsch, Thomas. Freie Universität Berlin; AlemaniaFil: Flores Olvera, Hilda. Universidad Nacional Autónoma de México; MéxicoFil: Ochoterena, Helga. Universidad Nacional Autónoma de México; MéxicoFil: von Mering, Sabine. Freie Universität Berlin; AlemaniaFil: Zuloaga, Fernando Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; Argentin