Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

Knot Floer homology detects fibred knots

Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$ is irreducible, and $\hat{HFK}(Y,K)$ is monic, then $K$ is fibred. The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, Ghiggini and the author. A corollary is that if a knot in $S^3$ admits a lens space surgery, then the knot is fibred.Comment: version 4: incorporates referee's suggestions, to appear in Inventiones Mathematica

Automorphisms of graphs of cyclic splittings of free groups

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.Comment: 22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicat

Large-scale demonstration and deployment project at Los Alamos National Laboratory

Established by the US Department of Energy (DOE) Environmental Management program through its Office of Science and Technology, the Deactivation and Decommissioning Focus Area is developing answers to the technological problems that hinder Environmental Management`s extensive cleanup efforts. The optimized application of technologies to ongoing nuclear facility decontamination and dismantlement is critical in meeting the challenge of decommissioning approximately 9,000 buildings and structures within the DOE complex. The significant technical and economic concerns in this area underscore a national imperative for the qualification and timely delivery of cost-reduction technologies and management approaches to meet federal and private needs. At Los Alamos National Laboratory (LANL), a Large-Scale Demonstration and Deployment Project (LSDDP) has been established to facilitate demonstration and deployment of technologies for the characterization, decontamination, and volume reduction of oversized metallic waste, mostly in the form of gloveboxes contaminated with transuranic radionuclides. The LANL LSDDP is being managed by an integrated contractor team (ICT) consisting of IT Corporation, ICF Incorporated, and Florida International University and includes representation from LANL`s Environmental Management Program Office. The ICT published in the Commerce Business Daily a solicitation for interest for innovative technologies capable of improving cost and performance of the baseline process. Each expression of interest response was evaluated and demonstration contract negotiations are under way for those technologies expected to be capable of meeting the project objectives. This paper discusses management organization and approach, the results of the technology search, the technology selection methodology, the results of the selection process, and future plans for the program

miR-126 Is Downregulated in Cystic Fibrosis Airway Epithelial Cells and Regulates TOM1 Expression.

Cystic fibrosis (CF) is one of the most common lethal genetic diseases in which the role of microRNAs has yet to be explored. Predicted to be regulated by miR-126, TOM1 (target of Myb1) has been shown to interact with Toll-interacting protein, forming a complex to regulate endosomal trafficking of ubiquitinated proteins. TOM1 has also been proposed as a negative regulator of IL-1beta and TNF-alpha-induced signaling pathways. MiR-126 is highly expressed in the lung, and we now show for the first time differential expression of miR-126 in CF versus non-CF airway epithelial cells both in vitro and in vivo. MiR-126 downregulation in CF bronchial epithelial cells correlated with a significant upregulation of TOM1 mRNA, both in vitro and in vivo when compared with their non-CF counterparts. Introduction of synthetic pre-miR-126 inhibited luciferase activity in a reporter system containing the full length 3\u27-untranslated region of TOM1 and resulted in decreased TOM1 protein production in CF bronchial epithelial cells. Following stimulation with LPS or IL-1beta, overexpression of TOM1 was found to downregulate NF-kappaB luciferase activity. Conversely, TOM1 knockdown resulted in a significant increase in NF-kappaB regulated IL-8 secretion. These data show that miR-126 is differentially regulated in CF versus non-CF airway epithelial cells and that TOM1 is a miR-126 target that may have an important role in regulating innate immune responses in the CF lung. To our knowledge, this study is the first to report of a role for TOM1 in the TLR2/4 signaling pathways and the first to describe microRNA involvement in CF

3-manifolds which are spacelike slices of flat spacetimes

We continue work initiated in a 1990 preprint of Mess giving a geometric parameterization of the moduli space of classical solutions to Einstein's equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has been worked out in the interim by the present author). In this paper we make a first step toward the 3+1-dimensional case by determining exactly which closed 3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).Comment: 10 page

An Economic Framework for Evaluating Personalized Medicine

Individual variation accounts for a wide range of medical and economic consequences, from inefficiencies in drug discovery and development to ineffectiveness of drug treatment to drug-induced morbidity and mortality. Addressing these consequences could benefit patients, health care providers and payers, and the pharmaceutical industry. When appropriate markers are known, diagnostic tests allow precise diagnosis and dosing, prediction of disease progression, prediction of treatment response and prediction of adverse drug reactions for individual patients. There may also be substantial savings realized by eliminating costs associated with failed treatment. We developed an analytical framework for analyzing the potential value of using a diagnostic test in clinical practice. Our framework determines the economic consequences of implementing pharmacogenomics in the clinic using a diagnostic test to predict drug response. We offer an empirical test of these ideas: we calculated the cost offset realized by predicting the likelihood of response to an alternative existing treatment using a hypothetical pharmacogenomic test in an asthma population. Because the diagnostic test is hypothetical, our framework is general and could be applied to other indications where diagnostic tests have not been developed. Our results could potentially guide future economic evaluation of new diagnostic tests. Importantly, they may also influence biomarker discovery strategies to ensure consistency between market priorities and the future stream of product introductions

Crystal and molecular structure of analgesics. II. Dezocine hydrobromide

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44834/1/10870_2005_Article_BF01200881.pd

Socioeconomic differentials in the immediate mortality effects of the national Irish smoking ban

This article has been made available through the Brunel Open Access Publishing Fund.Background: Consistent evidence has demonstrated that smoking ban policies save lives, but impacts on health inequalities are uncertain as few studies have assessed post-ban effects by socioeconomic status (SES) and findings have been inconsistent. The aim of this study was to assess the effects of the national Irish smoking ban on ischemic heart disease (IHD), stroke, and chronic obstructive pulmonary disease (COPD) mortality by discrete and composite SES indicators to determine impacts on inequalities. Methods: Census data were used to assign frequencies of structural and material SES indicators to 34 local authorities across Ireland with a 2000–2010 study period. Discrete indicators were jointly analysed through principal component analysis to generate a composite index, with sensitivity analyses conducted by varying the included indicators. Poisson regression with interrupted time-series analysis was conducted to examine monthly age and gender-standardised mortality rates in the Irish population, ages ≥35 years, stratified by tertiles of SES indicators. All models were adjusted for time trend, season, influenza, and smoking prevalence. Results: Post-ban mortality reductions by structural SES indicators were concentrated in the most deprived tertile for all causes of death, while reductions by material SES indicators were more equitable across SES tertiles. The composite indices mirrored the results of the discrete indicators, demonstrating that post-ban mortality decreases were either greater or similar in the most deprived when compared to the least deprived for all causes of death. Conclusions: Overall findings indicated that the national Irish smoking ban reduced inequalities in smoking-related mortality. Due to the higher rates of smoking-related mortality in the most deprived group, even equitable reductions across SES tertiles resulted in decreases in inequalities. The choice of SES indicator was influential in the measurement of effects, underscoring that a differentiated analytical approach aided in understanding the complexities in which structural and material factors influence mortality