How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Seroprevalence of Toxoplasma gondii and Toxocara canis in a human rural population of Southern Rio Grande do Sul

Due to the growing population of pets, especially homeless dogs and cats, zoonoses still represent a significant public health problem. Toxoplasma gondii and Toxocara spp. are epidemiologically important zoonotic agents as they are etiological factors of human toxoplasmosis and toxocariasis, respectively. These parasites remain neglected even though they are substantially prevalent in rural areas. The aim of this study was to investigate T. gondii and T. canis seroprevalence and risk factors of seropositivity in a rural population in Pelotas municipality, Brazil. The study participants (n=344) were patients of a Basic Healthcare Unit (BHU) located in Cerrito Alegre. Blood samples were collected and tested for T. gondii antibodies by indirect immunofluorescence and T. canis antibodies by an indirect ELISA that targets an excreted-secreted antigen (TES). T. gondii seropositivity was 53.2%, with higher titers (1:256 - 1:1,024) in individuals who habitually eat pork, beef, or chicken, while T. canis seropositivity was 71.8% and concomitant T. gondii and T. canis seropositivity was 38.3%. Among the seropositivity risk factors assessed, only habitual undercooked meat consumption was significant (p = 0.046; OR = 3.7) for T. gondii and none of them were associated with T. canis seropositivity. Both parasites have a high prevalence in rural areas, which reinforces the need to invest in rural community education and health

Do methods for overcoming dormancy affect the physiological quality of okra seeds?

One of the main obstacles in the okra production is the physical dormancy imposed by the tegument of the seeds. Although several methods for overcoming tegumentary dormancy have been proposed, little is known about their effect on the physiological quality of seeds. Thus, this study aimed to verify the effectiveness of methods for overcoming dormancy (control - no treatment; pre-soaking - seed soaking in water at 30 ºC, for 6 h; thermotherapy - immersion in water at 60 ºC, for 3 min; dry heat - oven at 70 ºC, for 5 min; thermal shock - immersion in water at 30 ºC, for 30 min, followed by 5 ºC, for 24 h; and sand scarification - friction between seeds and sand for 20 min), as well as to analyze their impacts on the physiological quality of okra seed lots. After the treatments were applied, images of the outer seed coat were obtained and the moisture content of the seeds, first germination count, germination, emergence, germination speed index and seedling length were measured. The treatments of pre-soaking, thermotherapy and thermal shock remove cell layers in the chalaza region, allowing a greater water absorption and showing to be efficient in overcoming dormancy, without affecting the physiological quality of the seeds. On the other hand, the dry heat treatment can affect the vigor of okra seeds

Geometry and topology of the quasi-plane Szekeres model

This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasi-hyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the $t =$ const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Interpretation of the mass function in the quasi-plane model.Comment: 14 pages, 6 figures; old sections 8, 10 and 11 removed, the remaining ones re-edited for consistency. This is a corrected version that takes into account the erratum published in Phys.Rev. D85, 069903(E) (2012

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy

A Bayesian Belief Network to assess rate of changes in coral reef ecosystems

It is crucial to identify sources of impacts and degradation to maintain functions and services that the physical structure of coral reef provides. Here, a Bayesian Network approach is used to evaluate effects that anthropogenic and climate change disturbances have on coral reef structure. The network was constructed on knowledge derived from the literature and elicited from experts, and parameterised on independent data. Evaluation of the model was conducted through sensitivity analyses and data integration was fundamental to obtain a balanced dataset. Scenario analyses, conducted to assess the effects of stressors on the reef framework state, suggested that calcifying organisms and carbonate production, rather than bioerosion, had the largest influence on the reef carbonate budgetary state. Despite the overall budget remaining positive, anthropogenic pressures, particularly deterioration of water quality, affected reef carbonate production, representing a warning signal for potential changes in the reef state

Participatory modelling for stakeholder involvement in the development of flood risk management intervention options

Advancing stakeholder participation beyond consultation offers a range of benefits for local flood risk management, particularly as responsibilities are increasingly devolved to local levels. This paper details the design and implementation of a participatory approach to identify intervention options for managing local flood risk. Within this approach, Bayesian networks were used to generate a conceptual model of the local flood risk system, with a particular focus on how different interventions might achieve each of nine participant objectives. The model was co-constructed by flood risk experts and local stakeholders. The study employs a novel evaluative framework, examining both the process and its outcomes (short-term substantive and longer-term social benefits). It concludes that participatory modelling techniques can facilitate the identification of intervention options by a wide range of stakeholders, and prioritise a subset for further investigation. They can help support a broader move towards active stakeholder participation in local flood risk management

A Bayesian network to predict coastal vulnerability to sea level rise

This paper is not subject to U.S. copyright. The definitive version was published in Journal of Geophysical Research 116 (2011): F02009, doi:10.1029/2010JF001891.Sea level rise during the 21st century will have a wide range of effects on coastal environments, human development, and infrastructure in coastal areas. The broad range of complex factors influencing coastal systems contributes to large uncertainties in predicting long-term sea level rise impacts. Here we explore and demonstrate the capabilities of a Bayesian network (BN) to predict long-term shoreline change associated with sea level rise and make quantitative assessments of prediction uncertainty. A BN is used to define relationships between driving forces, geologic constraints, and coastal response for the U.S. Atlantic coast that include observations of local rates of relative sea level rise, wave height, tide range, geomorphic classification, coastal slope, and shoreline change rate. The BN is used to make probabilistic predictions of shoreline retreat in response to different future sea level rise rates. Results demonstrate that the probability of shoreline retreat increases with higher rates of sea level rise. Where more specific information is included, the probability of shoreline change increases in a number of cases, indicating more confident predictions. A hindcast evaluation of the BN indicates that the network correctly predicts 71% of the cases. Evaluation of the results using Brier skill and log likelihood ratio scores indicates that the network provides shoreline change predictions that are better than the prior probability. Shoreline change outcomes indicating stability (−1 1 m/yr) was not well predicted. We find that BNs can assimilate important factors contributing to coastal change in response to sea level rise and can make quantitative, probabilistic predictions that can be applied to coastal management decisions.Funding for this work was provided by the USGS Coastal and Marine Geology and Global Change Research programs