JSJ decompositions of Quadratic Baumslag-Solitar groups

Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in "On uniqueness of JSJ decompositions of finitely generated groups", Comment. Math. Helv. 78 (2003) pp 740-751) that in most cases the defining graphs are cyclic JSJ decompositions, in the sense of Rips and Sela. Here we extend Forester's results to graphs of groups with vertex groups that can be either infinite cyclic or quadratically hanging surface groups.Comment: 20 pages, 2 figures. Several corrections and improvements from referee's report. Imprtant changes in Definition 5.1, and the proof of Theorem 5.5 (previously 5.4). Lemma 5.4 was adde

Stabilization, amalgamation, and curves of intersection of Heegaard splittings

We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3-manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer $n$ there are 3-manifolds containing an essential torus and a Heegaard splitting such that the torus and splitting surface must intersect in at least $n$ simple closed curves. These give the first examples of lower bounds on the minimum number of curves of intersection between an essential surface and a Heegaard surface that are greater than one.Comment: Version for publication. To appear in Algebraic and Geometric Topolog

How obesity impacts the muscle fiber cross-sectional area and fiber type composition in an untrained, sedentary population

Introduction: Obese individuals possess excess adipose tissue interacting with the skeletal muscle, resulting in an alteration in the contractile properties of the muscle tissue resulting in reduced muscle quality and function. Purpose of study: The aim of the study was to investigate how the degree of obesity impacted the muscle fiber type CSA and composition in an overweight sedentary population after a 10-week resistance training intervention. Method: 29 men and women between 30-60 years of age were recruited and completed 10 weeks of 2 weekly supervised resistance training sessions. Biopsies and ultrasound of m. vastus lateralis, DXA scans and isokinetic knee extensor strength tests were conducted prior to supplementation period, prior to intervention period and after intervention period. Results were analysed in RStudio. Results: The results indicated no significant increase in muscle fiber type CSA for type I nor II between the timepoints, but there was a significant increase in the intervention period in comparison with the control period of CSA for both fiber types. There was a significant increase in isokinetic strength and muscular growth measured as muscle thickness amongst the participants. Conclusion: Based on these findings there's reason to believe that in relation to individuals with a BMI within recommended values, the increased chronic inflammation due to obesity, in correlation with inactivity, leads to an increased muscle fiber type CSA, shift in fiber type composition with increased ratio of fiber type II as well as a reduction in relative muscle strength

Corrigendum to "Knot Floer homology detects fibred knots"

We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some arguments in \cite{Ni} are also slightly modified accordingly.Comment: 3 page

Barley silage effects on poultry behaviour

A series of trials were conducted to determine the effect of feeding barley silage to laying hens and broiler breeder pullets on performance, stress and behaviour. In the first study, two trials were conducted each with 20 hens and 2 roosters (n=176) randomly assigned to one of 8 community cages. The birds in 4 cages were provided with a nutritionally balanced soy/wheat–based laying hen diet ad libitum, whereas the birds in another 4 cages were given free access to barley silage in addition to the regular laying hen diet. In both trials, the control birds consumed more feed (P 0.05) were found in regards to egg quality, egg production and bird weights at various ages; however yolk colour was darker by silage treatment in each trial. At the end of each trial, the feather score was improved in silage-fed birds compared to the control birds. It was concluded that feeding barley silage as a supplement to laying hens can improve their welfare without negatively affecting the egg production and egg quality. A second study was conducted to determine the effect of feeding barley silage on body weight, stereotypic behaviour, stress and fear on broiler breeder pullets during the brooding and rearing periods. The 3 week old broiler breeder pullets (n=180) were randomly allocated into 12 straw litter floor pens having 15 birds per pen. The birds in 6 pens were provided with a nutritionally balanced corn/oat-soybean/canola meal-based broiler breeder diet at recommended restricted levels, whereas the birds in another 6 pens were given free access to barley silage in addition to a regular broiler breeder diet. Total DM intake was significantly higher (P < 0.05) for silage-fed birds compared to their control counterparts without affecting mean body weights. Dietary treatment had no significant effect on bird behaviour with the exception of object pecking behaviour which was reduced with silage feeding. Aggressive and gentle feather pecking behaviour was consistently numerically higher in the control birds than the silage-fed birds, although not significantly. Age affected many of the behaviours recorded in this study. Silage feeding had no significant effect on heterophil to lymphocyte ratios and tonic immobility values indicating that birds in both treatments were not very stressed or fearful. It was concluded that feeding barley silage to broiler breeder pullets has potential to aid in improving their welfare

Genus two 3-manifolds are built from handle number one pieces

Let M be a closed, irreducible, genus two 3-manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M. Then each component manifold M_i of M-F has handle number at most one, i.e. admits a Heegaard splitting obtained by attaching a single 1-handle to one or two components of boundary M_i. This result also holds for a decomposition of M along a maximal collection of incompressible tori.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-38.abs.htm

Probabilistic Problems in Graph Theory

In this thesis, I examine two different problems in graph theory using probabilistic techniques. The first is a question on graph colourings. A proper total k-colouring of a graph G = (V, E) is a map φ : V υ E → {1, 2,…, k} such that φ|V is a proper vertex colouring, φ|E is a proper edge colouring, and if v V and vw E then φ(v) ≠ φ(vw). Such a colouring is called adjacent vertex distinguishing if for every pair of adjacent vertices, u and v, the set {φ(u)} υ {φ(uw) : uw E}, the `colour set of u\u27, is distinct from the colour set of v. It is shown that there is an absolute constant C such that the minimal number of colours needed for such a colouring is at most Δ(G) + C. The second problem is related to a modification of bootstrap percolation on a finite square grid. In an n × n grid, the 1 × 1 squares, called sites, can be in one of two states: `uninfected\u27 or `infected\u27. Sites are initially infected independently at random and the state of each vertex is updated simultaneously by the following rule: every uninfected site that shares an edge with at least two infected sites becomes itself infected while each infected site with no infected neighbours becomes uninfected. This process is repeated and the central question is, when is it either likely or unlikely that all sites eventually become infected? Here, both upper and lower bounds are given for the probability that all sites eventually become infected and these bounds are used to determine a critical probability for the event that all sites eventually become infected

Residually free 3-manifolds

We classify those compact 3-manifolds with incompressible toral boundary whose fundamental groups are residually free. For example, if such a manifold $M$ is prime and orientable and the fundamental group of $M$ is non-trivial then $M \cong \Sigma\times S^1$, where $\Sigma$ is a surface.Comment: 19 pages, referee's comments incorporated, to appear in Algebraic & Geometric Topolog

How Not to Incorporate Voluntary Standards into Smart Regulation: ISO 14001 and Ontario\u27s Environmental Penalties Regulations

In June, 2007 the province of Ontario, Canada, released environmental penalties (EPs) regulations. EPs (or administrative penalties, as they are called in the US) are the environmental equivalent of speeding tickets for facilities that violate pollution laws. They are found in numerous jurisdictions and are widely understood as part of a move toward smart regulation. The Ontario regulations offer reduced EPs to facilities with an environmental management system (EMS) that meets the requirements of ISO 14001 or the chemical industry\u27s Responsible Care initiative. We argue that non-governmental, consensus-based standards such as ISO 14001 can and should play a constructive role in smart regulation and the pursuit of sustainability, but that the Ontario government\u27s attempt to incorporate them into its EPs regulations was anything but smart. We present six tips for how to incorporate voluntary standards into official regulation. First, don\u27t reinvent the wheel. If a standard exists that fulfills the objectives of a proposed regulation, and the standard was developed by a recognized standards body through a multi-stakeholder consensus process, regulators should incorporate the standard into the regulatory scheme as far as possible and appropriate, rather than drafting a new standard from scratch. Second, avoid unexplained discrepancies between the regulation and the standard. Third, if an existing widely accepted standard does not, on its own, meet all the public policy goals of the proposed regulation, indicate clearly how the standard is deficient and what more is required to meet public policy objectives. Fourth, should consult relevant standards development committees when developing regulations. Fifth, take advantage of ongoing opportunities to participate in the work of relevant standards development committees, to keep abreast of developments and influence the content of standards. Finally, and this is the biggest challenge, both regulators and standards development bodies should address the special characteristics and challenges of small businesses