Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

Compactifications and algebraic completions of Limit groups

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are proved in the context of compact groups and algebraic groups over local fields. In addition we prove a generalization of the classical Baumslag lemma which is a useful tool for generating eventually faithful sequences of homomorphisms. The last section is dedicated to correct a mistake from [BGSS] and to get rid of the even genus assumption.Comment: v2: Substantial changes to sections 7 and 8.2. Typos corrected. References added. v3: Acknowledgement correcte

Prevalence and risk factors of helminths and intestinal protozoa infections among children from primary schools in western Tajikistan

BACKGROUND: Intestinal parasitic infections represent a public health problem in Tajikistan, but epidemiological evidence is scarce. The present study aimed at assessing the extent of helminths and intestinal protozoa infections among children of 10 schools in four districts of Tajikistan, and to make recommendations for control. METHODS: A cross-sectional survey was carried out in early 2009. All children attending grades 2 and 3 (aged 7-11 years) from 10 randomly selected schools were invited to provide a stool sample and interviewed about sanitary situation and hygiene behaviour. A questionnaire pertaining to demographic and socioeconomic characteristics was addressed to the heads of households. On the spot, stool samples were subjected to duplicate Kato-Katz thick smear examination for helminth diagnosis. Additionally, 1-2 g of stool was fixed in sodium acetate-acetic acid formalin, transferred to a specialized laboratory in Europe and examined for helminths and intestinal protozoa. The results from both methods combined served as diagnostic 'gold' standard. RESULTS: Out of 623 registered children, 602 participated in our survey. The overall prevalence of infection with helminths and pathogenic intestinal protozoa was 32.0% and 47.1%, respectively. There was pronounced spatial heterogeneity. The most common helminth species was Hymenolepis nana (25.8%), whereas the prevalences of Ascaris lumbricoides, hookworm and Enterobius vermicularis were below 5%. The prevalence of pathogenic intestinal protozoa, namely Giardia intestinalis and Entamoeba histolytica/E. dispar was 26.4% and 25.9%, respectively. Almost half of the households draw drinking water from unimproved sources, such as irrigation canals, rivers and unprotected wells. Sanitary facilities were pit latrines, mostly private, and a few shared with neighbours. The use of public tap/standpipe as a source of drinking water emerged as a protective factor for G. intestinalis infection. Protecte spring water reduced the risk of infection with E. histolytica/E. dispar and H. nana. CONCLUSIONS: Our data obtained from the ecological 'lowland' areas in western Tajikistan call for school-based deworming (recommended drugs: albendazole and metronidazole), combined with hygiene promotion and improved sanitation. Further investigations are needed to determine whether H. nana represents a public health problem

Insect Pollinated Crops, Insect Pollinators and US Agriculture: Trend Analysis of Aggregate Data for the Period 1992–2009

In the US, the cultivated area (hectares) and production (tonnes) of crops that require or benefit from insect pollination (directly dependent crops: apples, almonds, blueberries, cucurbits, etc.) increased from 1992, the first year in this study, through 1999 and continued near those levels through 2009; aggregate yield (tonnes/hectare) remained unchanged. The value of directly dependent crops attributed to all insect pollination (2009 USD) decreased from $14.29 billion in 1996, the first year for value data in this study, to$10.69 billion in 2001, but increased thereafter, reaching $15.12 billion by 2009. The values attributed to honey bees and non-Apis pollinators followed similar patterns, reaching$11.68 billion and $3.44 billion, respectively, by 2009. The cultivated area of crops grown from seeds resulting from insect pollination (indirectly dependent crops: legume hays, carrots, onions, etc.) was stable from 1992 through 1999, but has since declined. Production of those crops also declined, albeit not as rapidly as the decline in cultivated area; this asymmetry was due to increases in aggregate yield. The value of indirectly dependent crops attributed to insect pollination declined from$15.45 billion in 1996 to $12.00 billion in 2004, but has since trended upward. The value of indirectly dependent crops attributed to honey bees and non-Apis pollinators, exclusive of alfalfa leafcutter bees, has declined since 1996 to$5.39 billion and $1.15 billion, respectively in 2009. The value of alfalfa hay attributed to alfalfa leafcutter bees ranged between$4.99 and $7.04 billion. Trend analysis demonstrates that US producers have a continued and significant need for insect pollinators and that a diminution in managed or wild pollinator populations could seriously threaten the continued production of insect pollinated crops and crops grown from seeds resulting from insect pollination