Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Limit theorems for weakly subcritical branching processes in random environment

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, 'supercritical'. This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on non-extinction. Also a functional limit theorem is proven, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.Comment: 35 page

Comparison of the ICare® rebound tonometer with the Goldmann tonometer in a normal population

The aim of this study was to evaluate the accuracy of measurement of intraocular pressure (IOP) using a new induction/impact rebound tonometer (ICare) in comparison with the Goldmann applanation tonometer (AT). The left eyes of 46 university students were assessed with the two tonometers, with induction tonometry being performed first. The ICare was handled by an optometrist and the Goldmann tonometer by an ophthalmologist. In this study, statistically significant differences were found when comparing the ICare rebound tonometer with applanation tonometry (AT) (p < 0.05). The mean difference between the two tonometers was 1.34 +/- 2.03 mmHg (mean +/- S.D.) and the 95% limits of agreement were +/-3.98 mmHg. A frequency distribution of the differences demonstrated that in more than 80% of cases the IOP readings differed by <3 mmHg between the ICare and the AT. In the present population the ICare overestimates the IOP value by 1.34 mmHg on average when compared with Goldmann tonometer. Nevertheless, the ICare tonometer may be helpful as a screening tool when Goldmann applanation tonometry is not applicable or not recommended, as it is able to estimate IOP within a range of +/-3.00 mmHg in more than 80% of the populatio

Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetization is obtained through finite-size scaling, using a corner transfer matrix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen model. Through a conformal mapping of the system onto a strip, the gap-exponent relation is shown to remain valid for such an aperiodic defect.Comment: 12 pages, TeX file + 4 figures, epsf neede

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

Staalkaarten stadslandbouw+; ontwikkelstrategieën om te komen tot stadslandbouw in Almere Oosterwold

Dit rapport verkent de vraag hoe stadslandbouw economisch, ecologisch en sociaal gezien kan bijdragen aan de ambities van Almere Oosterwold. De vraag concentreert zich rond mogelijke bedrijfstypen, mogelijke verbindingen met de stad, organisatievormen en mogelijke locaties. Maar het is ook belangrijk meer te weten over randvoorwaarden, kansen en potentiële belemmeringen van het beoogde productieve landschap. En uiteindelijk de kernvraag, wat wordt de ontwikkelingsroute naar stadslandbouw in Almere Oosterwold

Surface Magnetization and Critical Behavior of Aperiodic Ising Quantum Chains

We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the couplings. Using substitution rules to generate the aperiodic sequences, we derive functional equations for the surface magnetization. These equations are solved by iteration and the surface magnetic exponent can be determined exactly. The method is applied to three specific aperiodic sequences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for which the modulation is an irrelevant perturbation, the surface magnetization vanishes with a square root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is marginal and the surface magnetic exponent varies continuously with the modulation amplitude. Finally, the Rudin-Shapiro sequence, which corresponds to the relevant case, displays an anomalous surface critical behavior which is analyzed via scaling considerations: Depending on the value of the modulation, the surface magnetization either vanishes with an essential singularity or remains finite at the bulk critical point, i.e., the surface phase transition is of first order.Comment: 8 pages, 7 eps-figures, uses RevTex and epsf, minor correction

Presence of celiac disease epitopes in modern and old hexaploid wheat varieties: wheat breeding may have contributed to increased prevalence of celiac disease

Gluten proteins from wheat can induce celiac disease (CD) in genetically susceptible individuals. Specific gluten peptides can be presented by antigen presenting cells to gluten-sensitive T-cell lymphocytes leading to CD. During the last decades, a significant increase has been observed in the prevalence of CD. This may partly be attributed to an increase in awareness and to improved diagnostic techniques, but increased wheat and gluten consumption is also considered a major cause. To analyze whether wheat breeding contributed to the increase of the prevalence of CD, we have compared the genetic diversity of gluten proteins for the presence of two CD epitopes (Glia-α9 and Glia-α20) in 36 modern European wheat varieties and in 50 landraces representing the wheat varieties grown up to around a century ago. Glia-α9 is a major (immunodominant) epitope that is recognized by the majority of CD patients. The minor Glia-α20 was included as a technical reference. Overall, the presence of the Glia-α9 epitope was higher in the modern varieties, whereas the presence of the Glia-α20 epitope was lower, as compared to the landraces. This suggests that modern wheat breeding practices may have led to an increased exposure to CD epitopes. On the other hand, some modern varieties and landraces have been identified that have relatively low contents of both epitopes. Such selected lines may serve as a start to breed wheat for the introduction of ‘low CD toxic’ as a new breeding trait. Large-scale culture and consumption of such varieties would considerably aid in decreasing the prevalence of CD

A Universal Approach to Eliminate Antigenic Properties of Alpha-Gliadin Peptides in Celiac Disease

Celiac disease is caused by an uncontrolled immune response to gluten, a heterogeneous mixture of wheat storage proteins, including the α-gliadins. It has been shown that α-gliadins harbor several major epitopes involved in the disease pathogenesis. A major step towards elimination of gluten toxicity for celiac disease patients would thus be the elimination of such epitopes from α-gliadins. We have analyzed over 3,000 expressed α-gliadin sequences from 11 bread wheat cultivars to determine whether they encode for peptides potentially involved in celiac disease. All identified epitope variants were synthesized as peptides and tested for binding to the disease-associated HLA-DQ2 and HLA-DQ8 molecules and for recognition by patient-derived α-gliadin specific T cell clones. Several specific naturally occurring amino acid substitutions were identified for each of the α-gliadin derived peptides involved in celiac disease that eliminate the antigenic properties of the epitope variants. Finally, we provide proof of principle at the peptide level that through the systematic introduction of such naturally occurring variations α-gliadins genes can be generated that no longer encode antigenic peptides. This forms a crucial step in the development of strategies to modify gluten genes in wheat so that it becomes safe for celiac disease patients. It also provides the information to design and introduce safe gluten genes in other cereals, which would exhibit improved quality while remaining safe for consumption by celiac disease patients

The undebated issue of justice: silent discourses in Dutch flood risk management

Flood risk for all types of flooding is projected to increase based on climate change projections and increases in damage potential. These challenges are likely to aggravate issues of justice in flood risk management (henceforth FRM). Based on a discursive-institutionalist perspective, this paper explores justice in Dutch FRM: how do institutions allocate the responsibilities and costs for FRM for different types of flooding? What are the underlying conceptions of justice? What are the future challenges with regard to climate change? The research revealed that a dichotomy is visible in the Dutch approach to FRM: despite an abundance of rules, regulations and resources spent, flood risk or its management, are only marginally discussed in terms of justice. Despite that the current institutional arrangement has material outcomes that treat particular groups of citizens differently, depending on the type of flooding they are prone to, area they live in (unembanked/embanked) or category of user (e.g. household, industry, farmer). The paper argues that the debate on justice will (re)emerge, since the differences in distributional outcomes are likely to become increasingly uneven as a result of increasing flood risk. The Netherlands should be prepared for this debate by generating the relevant facts and figures. An inclusive debate on the distribution of burdens of FRM could contribute to more effective and legitimate FRM