Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Nitrogen forms affect root structure and water uptake in the hybrid poplar

The study analyses the effects of two different forms of nitrogen fertilisation (nitrate and ammonium) on root structure and water uptake of two hybrid poplar (Populus maximowiczii x P. balsamifera) clones in a field experiment. Water uptake was studied using sap flow gauges on individual proximal roots and coarse root structure was examined by excavating 18 whole-root systems. Finer roots were scanned and analyzed for architecture. Nitrogen forms did not affect coarse-root system development, but had a significant effect on fine-root development. Nitrate-treated trees presented higher fine:coarse root ratios and higher specific root lengths than control or ammonium treated trees. These allocation differences affected the water uptake capacity of the plants as reflected by the higher sapflow rate in the nitrate treatment. The diameter of proximal roots at the tree base predicted well the total root biomass and length. The diameter of smaller lateral roots also predicted the lateral root mass, length, surface area and the number of tips. The effect of nitrogen fertilisation on the fine root structure translated into an effect on the functioning of the fine roots forming a link between form (architecture) and function (water uptake)

Evaluation of the health-related quality of life of children in Schistosoma haematobium-endemic communities in Kenya: a cross-sectional study.

BACKGROUND: Schistosomiasis remains a global public health challenge, with 93% of the ~237 million infections occurring in sub-Saharan Africa. Though rarely fatal, its recurring nature makes it a lifetime disorder with significant chronic health burdens. Much of its negative health impact is due to non-specific conditions such as anemia, undernutrition, pain, exercise intolerance, poor school performance, and decreased work capacity. This makes it difficult to estimate the disease burden specific to schistosomiasis using the standard DALY metric. METHODOLOGY/PRINCIPAL FINDINGS: In our study, we used Pediatric Quality of Life Inventory (PedsQL), a modular instrument available for ages 2-18 years, to assess health-related quality of life (HrQoL) among children living in a Schistosoma haematobium-endemic area in coastal Kenya. The PedsQL questionnaires were administered by interview to children aged 5-18 years (and their parents) in five villages spread across three districts. HrQoL (total score) was significantly lower in villages with high prevalence of S. haematobium (-4.0%, p<0.001) and among the lower socioeconomic quartiles (-2.0%, p<0.05). A greater effect was seen in the psychosocial scales as compared to the physical function scale. In moderate prevalence villages, detection of any parasite eggs in the urine was associated with a significant 2.1% (p<0.05) reduction in total score. The PedsQL reliabilities were generally high (Cronbach alphas ≥0.70), floor effects were acceptable, and identification of children from low socioeconomic standing was valid. CONCLUSIONS/SIGNIFICANCE: We conclude that exposure to urogenital schistosomiasis is associated with a 2-4% reduction in HrQoL. Further research is warranted to determine the reproducibility and responsiveness properties of QoL testing in relation to schistosomiasis. We anticipate that a case definition based on more sensitive parasitological diagnosis among younger children will better define the immediate and long-term HrQoL impact of Schistosoma infection

An SO(10) Grand Unified Theory of Flavor

We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based on an $S_4$ family symmetry. It makes use of our recent proposal to use SO(10) with type II seesaw mechanism for neutrino masses combined with a simple ansatz that the dominant Yukawa matrix (the {\bf 10}-Higgs coupling to matter) has rank one. In this paper, we show how the rank one model can arise within some plausible assumptions as an effective field theory from vectorlike {\bf 16} dimensional matter fields with masses above the GUT scale. In order to obtain the desired fermion flavor texture we use $S_4$ flavon multiplets which acquire vevs in the ground state of the theory. By supplementing the $S_4$ theory with an additional discrete symmetry, we find that the flavon vacuum field alignments take a discrete set of values provided some of the higher dimensional couplings are small. Choosing a particular set of these vacuum alignments appears to lead to an unified understanding of observed quark-lepton flavor: (i) the lepton mixing matrix that is dominantly tri-bi-maximal with small corrections related to quark mixings; (ii) quark lepton mass relations at GUT scale: $m_b\simeq m_{\tau}$ and $m_\mu\simeq 3 m_s$ and (iii) the solar to atmospheric neutrino mass ratio $m_\odot/m_{\rm atm}\simeq \theta_{\rm Cabibbo}$ in agreement with observations. The model predicts the neutrino mixing parameter, $U_{e3} \simeq \theta_{\rm Cabibbo}/(3\sqrt2) \sim 0.05$, which should be observable in planned long baseline experiments.Comment: Final version of the paper as it will appear in JHEP

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

A realistic pattern of fermion masses from a five-dimensional SO(10) model

We provide a unified description of fermion masses and mixing angles in the framework of a supersymmetric grand unified SO(10) model with anarchic Yukawa couplings of order unity. The space-time is five dimensional and the extra flat spatial dimension is compactified on the orbifold $S^1/(Z_2 \times Z_2')$, leading to Pati-Salam gauge symmetry on the boundary where Yukawa interactions are localised. The gauge symmetry breaking is completed by means of a rather economic scalar sector, avoiding the doublet-triplet splitting problem. The matter fields live in the bulk and their massless modes get exponential profiles, which naturally explain the mass hierarchy of the different fermion generations. Quarks and leptons properties are naturally reproduced by a mechanism, first proposed by Kitano and Li, that lifts the SO(10) degeneracy of bulk masses in terms of a single parameter. The model provides a realistic pattern of fermion masses and mixing angles for large values of $\tan\beta$. It favours normally ordered neutrino mass spectrum with the lightest neutrino mass below 0.01 eV and no preference for leptonic CP violating phases. The right handed neutrino mass spectrum is very hierarchical and does not allow for thermal leptogenesis. We analyse several variants of the basic framework and find that the results concerning the fermion spectrum are remarkably stable.Comment: 30 pages, 7 figures, 4 table

Decision and Discovery in Defining “Disease”

This version (May 17, 2005) was published in its final form as: Schwartz PH. Decision and discovery in defining 'disease'. In: Kincaid H, McKitrick J, editors. Establishing medical reality: essays in the metaphysics and epistemology of biomedical science. Dordrecht: Springer; 2007. p. 47-63. http://dx.doi.org/10.1007/1-4020-5216-2_5The debate over how to analyze the concept of disease has often centered on the question of whether to include a reference to values, in particular the ‘disvalue’of diseases, or whether to avoid such notions. ‘Normativists,’such as King ([1954], 1981) and Culver and Gert (1982) emphasize the undesirability of diseases, while ‘Naturalists,’ most prominently Christopher Boorse (1977, 1987, 1997), instead require just the presence of biological dysfunction. The debate between normativism and naturalism often deteriorates into stalemate, with each side able to point out significant problems with the other. It starts to look as if neither approach can work. In this paper, I argue that the standoff stems from deeply questionable assumptions that have been used to formulate the opposing positions and guide the debate. In the end, I propose an alternative set of guidelines that offer a more constructive way to devise and compare theories