Everything should be as simple as possible, but no simpler : towards a protocol for accumulating evidence regarding the active content of health behaviour change interventions

Supplemental data for this article can be accessed here: 10.1080/17437199.2013.848409Peer reviewedPublisher PD

Chabauty-Coleman experiments for genus 3 hyperelliptic curves

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in $C(\mathbb{Q})$.Comment: 18 page

Emission of reactive oxygen species during degradation of iron gall ink

Iron gall inks are characterised by high contents of acids and transition metals, promoting degradation of cellulose due to hydrolysis and oxidation, respectively. Their chemical interaction with the environment is not well understood, especially in view of emissions of degradation products which could lead to spread of degradation processes. In order to study the emissions, we employed gas chromatography/mass spectrometry following headspace micro-extraction, and liquid chromatography following hydroxyl radical scavenging with appropriate probes. We also studied chemiluminescence of cellulose affected by ink degradation. We show that while the emissions of organic volatile degradation compounds by inks are less intense than those of surrounding paper, ink does promote the degradation of cellulose across big distances (from object to object). We were able to link this to emission of reactive oxygen species, probably hydrogen peroxide. Its emission from ink is considerably more intensive than from paper

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Effects of NO2 and acetic acid on the stability of historic paper

This research investigates degradation of historic paper in polluted environments during long-term dark storage. In an innovative experiment, degradation rates at realistic pollution levels are compared with degradation rates in the absence of pollution, using a set of real historic papers. The most abundant pollutants in repositories in post-industrial environments are taken into account: acetic acid and nitrogen dioxide. Their action was assessed in terms of reduction of ‘handling’ (as defined by decrease in degree of polymerisation) and ‘display’ (as defined by discolouration) lifetimes. Extrapolations to room conditions enabled lifetime predictions in conditions that are comparable to a real archival or library repository environments while prediction uncertainties were analytically evaluated to assess the significance of conclusions. While 10 ppb of NO2 does reduce the handling lifetime of almost all types of paper, their predicted lifetimes were still assessed to be several millennia, with the exception of acidic paper. Acetic acid at concentrations that are typical for archival and library repositories (<100 ppb) has significantly less effect than NO2 while it does not affect display lifetimes. From a conservation management perspective, it needs to be addressed whether the predicted reductions in otherwise significant handling lifetimes are of real concern and whether air filtration in archival and library repositories is justified

Dose-response functions for historic paper

Paper degradation has been studied extensively over the past few decades from both the conservation and the material science perspectives. This review focuses on the quantifiable impacts of the environment and material composition, from the viewpoint of long-term storage of historic paper-based collections. Therefore, temperature, relative humidity and their variation, and pollution are of major interest while photoinitiated processes are covered only briefly. New experiments comparing the effects of the most abundant indoor pollutants (NO2, acetic acid and formaldehyde) and the effects of fluctuating temperature and relative humidity are also presented as part of the discussion. This work highlights the need for revision of the existing dose–response (damage) functions for paper and their further development