Neighbourhoods and oral health:Agent-based modelling of tooth decay

This research used proof of concept agent-based models to test various theoretical mechanisms by which neighbourhoods may influence tooth decay in adults. Theoretical pathways were constructed using existing literature and tested in two study areas in Sheffield, UK. The models found a pathway between shops and sugar consumption had the most influence on adult tooth decay scores, revealing that similar mechanisms influence this outcome in different populations. This highlighted the importance of the interactions between neighbourhood features and individual level variables in influencing outcomes in tooth decay. Further work is required to improve the accuracy and reliability of the models

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Spacings and pair correlations for finite Bernoulli convolutions

We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure $\nu_r$, as $N$ tends to infinity. Numerical evidence suggests that for a generic $r$, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic $r$ the behavior is totally different.Comment: 17 pages, 6 figure

Effect of phytase on phytate P utilization by turkeys

An in vitro method was developed for poultry to predict inorganic phosphorus release from maize-soya bean feeds containing supplemental phytase (E.C. 3.1.3.8), and to quantify the effect of acid phosphatase (E.C. 3.1,3.2.), fungal protease (E.C. 3.4.23.6) and Aspergillus niger cellulase (E.C. 3.2.1.4.) on phytate dephosphorylation. Pepsin and pancreatin digestion periods were preceded by a 30 min preincubation at pH 5.25 to simulate digestion in the crop of poultry. Pancreatin digestion was carried out in dialysis tubings, with a ratio of about 1:25 (v/v) between the digesta and dialyzing medium, to simulate gradient absorption from the duodenum. The feed/water ratio was kept within physiological limits and a constant feed weight to digestive enzymes was maintained. There was a linear response to increasing dosages of phytase up to 1000 FTU/kg feed, and to increasing phosphate concentration in feeds. In vivo validation was performed with growing turkeys (1-3 wk) fed diets containing 12 g/kg of calcium; 0, 500, 1000 FTU/kg of phytase in a factorial arrangement with 0, 1, 2, 3 g/kg of supplemental phosphate (from KH2PO4). After a simple transformation (variable/in vitro phosphorus = f (in vitro phosphorus)) amounts of phosphorus hydrolyzed from feed samples by in vitro digestions correlated with the 3 week body weight gains (R= 0.986 P [less than] 0.0001), toe ash (R=0.952 P [less than] 0.0001), feed intake (R=0.994 P [less than] 0.0001) and feed efficiency (R=0.992 P [less than] 0.0001). The dephosphorylating ability of phytase in vitro was significantly enhanced (P [less than] 0.05) by the addition of acid phosphatase. Fungal acid protease and Aspergillus niger cellulase also enhanced the dephosphorylation process in vitro.Project # G-2029-01 Agreement # 14-08-0001-G-2029-0

Similar dissection of sets

In 1994, Martin Gardner stated a set of questions concerning the dissection of a square or an equilateral triangle in three similar parts. Meanwhile, Gardner's questions have been generalized and some of them are already solved. In the present paper, we solve more of his questions and treat them in a much more general context. Let $D\subset \mathbb{R}^d$ be a given set and let $f_1,...,f_k$ be injective continuous mappings. Does there exist a set $X$ such that $D = X \cup f_1(X) \cup ... \cup f_k(X)$ is satisfied with a non-overlapping union? We prove that such a set $X$ exists for certain choices of $D$ and $\{f_1,...,f_k\}$. The solutions $X$ often turn out to be attractors of iterated function systems with condensation in the sense of Barnsley. Coming back to Gardner's setting, we use our theory to prove that an equilateral triangle can be dissected in three similar copies whose areas have ratio $1:1:a$ for $a \ge (3+\sqrt{5})/2$

Oral health, sugary drink consumption and the soft drink industry levy: using spatial microsimulation to understand tooth decay

Spatial microsimulation is a powerful tool for creating large-scale population datasets that can be used to assess spatial phenomena in health-related outcomes. Despite this, it remains underutilized within dental public health. This paper outlines the development of an oral health focused microsimulation model for Sheffield (UK, SimSheffield), and how this can be used to assess potential socio-spatial impacts of a sugar tax which was introduced in the United Kingdom in 2016 and is known as the Soft Drink Industry Levy (SDIL). Exploratory analysis showed areas paying more SDIL were not those with the highest tooth decay or deprivation scores as might be hoped (in the first case) and expected from the literature (in the second)

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993