Automatic structures, rational growth and geometrically finite hyperbolic groups

We show that the set $SA(G)$ of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic group $G$ is dense in the product of the sets $SA(P)$ over all maximal parabolic subgroups $P$. The set $BSA(G)$ of equivalence classes of biautomatic structures on $G$ is isomorphic to the product of the sets $BSA(P)$ over the cusps (conjugacy classes of maximal parabolic subgroups) of $G$. Each maximal parabolic $P$ is a virtually abelian group, so $SA(P)$ and $BSA(P)$ were computed in ``Equivalent automatic structures and their boundaries'' by M.Shapiro and W.Neumann, Intern. J. of Alg. Comp. 2 (1992) We show that any geometrically finite hyperbolic group has a generating set for which the full language of geodesics for $G$ is regular. Moreover, the growth function of $G$ with respect to this generating set is rational. We also determine which automatic structures on such a group are equivalent to geodesic ones. Not all are, though all biautomatic structures are.Comment: Plain Tex, 26 pages, no figure

Dimension of the Torelli group for Out(F_n)

Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure

Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

Discriminating Groups

A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups

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

Der Einfluss der Kapazitätsgröße und -auslastung auf den Kostenverlauf ausgewählter Hilfskostenstellen von Molkereien - Abteilung Dampfversorgung

Die Kostenanalyse zur Bestimmung des Einflusses der Kapazitätsgröße und -auslastung auf den Kostenverlauf von Hilfskostenstellen (Hilfsabteilungen) erfolgt mit Hilfe von Modellkalkulationen. Eine spezielle Form der Teilkostenrechnung ermöglicht die Zurechnung der Kosten nach Kostenkategorien (jahresfix, tagesfix, ggf. chargenfix und mengenproportional) auf die entsprechenden Kostenträger (z. B. Kälte, Dampf) der jeweiligen Hilfskostenstelle. Durch computergestützte Simulationen können die Auswirkungen der verschiedenen Kosteneinflußfaktoren im einzelnen quantifiziert werden

Preconceptional Folate Supplementation and the Risk of Spontaneous Preterm Birth: A Cohort Study

In an analysis of a cohort of pregnant women, Radek Bukowski and colleagues describe an association between taking folic acid supplements and a reduction in the risk of preterm birth

Constraints to exclusive breastfeeding practice among breastfeeding mothers in Southwest Nigeria: implications for scaling up

<p>Abstract</p> <p>Background</p> <p>The practice of exclusive breastfeeding is still low despite the associated benefits. Improving the uptake and appropriating the benefits will require an understanding of breastfeeding as an embodied experience within a social context. This study investigates breastfeeding practices and experiences of nursing mothers and the roles of grandmothers, as well as the work-related constraints affecting nurses in providing quality support for breastfeeding mothers in Southwest Nigeria.</p> <p>Methods</p> <p>Using a concurrent mixed method approach, a structured questionnaire was administered to 200 breastfeeding mothers. In-depth interviews were also held with breastfeeding mothers (11), nurses (10) and a focus group discussion session with grandmothers.</p> <p>Results</p> <p>Breastfeeding was perceived as essential to baby's health. It strengthens the physical and spiritual bond between mothers and their children. Exclusive breastfeeding was considered essential but demanding. Only a small proportion (19%) of the nursing mothers practiced exclusive breastfeeding. The survey showed the major constraints to exclusive breastfeeding to be: the perception that babies continued to be hungry after breastfeeding (29%); maternal health problems (26%); fear of babies becoming addicted to breast milk (26%); pressure from mother-in-law (25%); pains in the breast (25%); and the need to return to work (24%). In addition, the qualitative findings showed that significant others played dual roles with consequences on breastfeeding practices. The desire to practice exclusive breastfeeding was often compromised shortly after child delivery. Poor feeding, inadequate support from husband and conflicting positions from the significant others were dominant constraints. The nurses decried the effects of their workload on providing quality supports for nursing mothers.</p> <p>Conclusion</p> <p>Breastfeeding mothers are faced with multiple challenges as they strive to practice exclusive breastfeeding. Thus, scaling up of exclusive breastfeeding among mothers requires concerted efforts at the macro, meso and micro levels of the Nigerian society.</p

Traditional use of the Andean flicker (Colaptes rupicola) as a galactagogue in the Peruvian Andes

This paper explores the use of the dried meat and feathers of the Andean Flicker (Colaptes rupicola) to increase the milk supply of nursing women and domestic animals in the Andes. The treatment is of preColumbian origin, but continues to be used in some areas, including the village in the southern Peruvian highlands where I do ethnographic research. I explore the factors giving rise to and sustaining the practice, relate it to other galactagogues used in the Andes and to the use of birds in ethnomedical and ethnoveterinary treatments in general, and situate it within the general tendency in the Andes and elsewhere to replicate human relations in the treatment of valuable livestock. The bird's use as a galactagogue appears to be motivated by both metaphorical associations and its perceived efficacy, and conceptually blends human and animal healthcare domains