Tube formulas and complex dimensions of self-similar tilings

We use the self-similar tilings constructed by the second author in "Canonical self-affine tilings by iterated function systems" to define a generating function for the geometry of a self-similar set in Euclidean space. This tubular zeta function encodes scaling and curvature properties related to the complement of the fractal set, and the associated system of mappings. This allows one to obtain the complex dimensions of the self-similar tiling as the poles of the tubular zeta function and hence develop a tube formula for self-similar tilings in \$\mathbb{R}^d$. The resulting power series in $\epsilon$ is a fractal extension of Steiner's classical tube formula for convex bodies K \ci \bRd. Our sum has coefficients related to the curvatures of the tiling, and contains terms for each integer $i=0,1,...,d-1$, just as Steiner's does. However, our formula also contains terms for each complex dimension. This provides further justification for the term "complex dimension". It also extends several aspects of the theory of fractal strings to higher dimensions and sheds new light on the tube formula for fractals strings obtained in "Fractal Geometry and Complex Dimensions" by the first author and Machiel van Frankenhuijsen.Comment: 41 pages, 6 figures, incorporates referee comments and references to new result

Minkowski measurability results for self-similar tilings and fractals with monophase generators

In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for certain fractals under rather general conditions. Based on these formulas, we give here a characterization of Minkowski measurability of a certain class of self-similar tilings and self-similar sets. Under appropriate hypotheses, self-similar tilings with simple generators (more precisely, monophase generators) are shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type. Under a natural geometric condition on the tiling, the result is transferred to the associated self-similar set (i.e., the fractal itself). Also, the latter is shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type.Comment: 18 pages, 1 figur

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling (specifically, the inner tube formula for each generator of the fractal spray is required to be polynomial). Now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators, and also by giving a proof which holds pointwise, rather than distributionally. Hence, our results for fractal sprays extend to higher dimensions the pointwise tube formula for (1-dimensional) fractal strings obtained earlier by Lapidus and van Frankenhuijsen. Our pointwise tube formulas are expressed as a sum of the residues of the "tubular zeta function" of the fractal spray in $\mathbb{R}^d$. This sum ranges over the complex dimensions of the spray, that is, over the poles of the geometric zeta function of the underlying fractal string and the integers $0,1,...,d$. The resulting "fractal tube formulas" are applied to the important special case of self-similar tilings, but are also illustrated in other geometrically natural situations. Our tube formulas may also be seen as fractal analogues of the classical Steiner formula.Comment: 43 pages, 13 figures. To appear: Advances in Mathematic

Sandhill Crane Roost Selection, Human Disturbance, and Forage Resources

Sites used for roosting represent a key habitat requirement for many species of birds because availability and quality of roost sites can influence individual fitness. Birds select roost sites based on numerous factors, requirements, and motivations, and selection of roosts can be dynamic in time and space because of various ecological and environmental influences. For sandhill cranes (Antigone canadensis) at their main spring staging area along the Platte River in south-central Nebraska, USA, past investigations of roosting cranes focuse donphysical channel characteristics related to perceived security as motivating roost distribution.We used 6,310 roost sites selected by 313 sandhill cranes over 5 spring migration seasons (2003–2007) to quantify resource selection functions of roost sites on the central Platte River using a discrete choice analysis. Sandhill cranes generally showed stronger selection for wider channels with shorter bank vegetation situated farther from potential human disturbance features such as roads, bridges, and dwellings.Furthermore, selection for roost sites with preferable physical characteristics (wide channels with short bank vegetation) was more resilient to nearby disturbance features than more narrow channels with taller bank vegetation. The amount of cornfields surrounding sandhill crane roost sites positively influenced relative probability of use but only for more narrow channels \u3c100m and those with shorter bank vegetation. We confirmed key resource features that sandhill cranes selected at river channels along the Platte River, and after incorporating spatial variation due to human disturbance, our understanding of roost site selection was more robust, providing insights on how disturbance may interact with physical habitat features. Managers can use information on roost-site selection when developing plans to increase probability of crane use at existing roost sites and to identify new areas for potential use if existing sites become limited

Irrigation Scheduling Program for Sugarcane

An estimate of potential evapotranspiration is acquired to implement an irrigation scheduling program. Four equations, which estimate potential evapotranspiration (evaporation) were evaluated for prediction of Class A Pan evaporation. The equations used were Penman\u27s combination equation, the Jensen-Haise temperature and radiation equation, and two of the Christiansen-Hargreaves polynomial regression type equations. Measured and calculated radiation was used together with two values of albedo. Four years of daily climate data from Rhodesia was evaluated by general linear regression methods. Despite the significant variations between the four annual regression lines of each equation, the use of confidence intervals indicate that the Penman and Christiansen-Hargreaves equation adequately predict Class A pan evaporation for irrigation control purposes. Using class A pan evaporation as the measure of potential evapotranspiration for sugarcane, a computerized irrigation scheduling model was developed. Controlled plant moisture stress was incorporated in the program with an irrigation coefficient related to the limiting effects of low soil moisture on plant transpiration. Five soil moisture regimes and two levels of irrigation were studied. Within the limits of the defined soil moisture assumptions, the program exhibited considerable flexibility in computation and the control of desired plant moisture stress

Pre-specification of statistical analysis approaches in published clinical trial protocols was inadequate

OBJECTIVES: Results from randomized trials can depend on the statistical analysis approach used. It is important to prespecify the analysis approach in the trial protocol to avoid selective reporting of analyses based on those which provide the most favourable results. We undertook a review of published trial protocols to assess how often the statistical analysis of the primary outcome was adequately prespecified. METHODS: We searched protocols of randomized trials indexed in PubMed in November 2016. We identified whether the following aspects of the statistical analysis approach for the primary outcome were adequately prespecified: (1) analysis population; (2) analysis model; (3) use of covariates; and (4) method of handling missing data. RESULTS: e identified 99 eligible protocols. Very few protocols adequately prespecified the analysis population (8/99, 8%), analysis model (27/99, 27%), covariates (40/99, 40%), or approach to handling missing data (10/99, 10%). Most protocols did not adequately predefine any of these four aspects of their statistical analysis approach (39%) or predefined only one aspect (36%). No protocols adequately predefined all four aspects of the analysis. CONCLUSION: The statistical analysis approach is rarely prespecified in published trial protocols. This may allow selective reporting of results based on different analyses

Lost in translation: how can education about dementia be effectively integrated into medical school contexts? A realist synthesis

\ua9 Author(s) (or their employer(s)) 2023. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ. OBJECTIVES: The prevalence of dementia in both community and hospital settings requires a clinical workforce that is skilled in diagnosis and management of the condition to competently care for patients. Though evidence of successful educational interventions about dementia exists, effective translation into medical school curricula is the exception rather than the norm. DESIGN: We adopted a realist synthesis approach following Realist And MEta-narrative Evidence Syntheses: Evolving Standards (RAMESES) guidelines to answer the following questions: (1) what are the barriers to integrating effective interventions about dementia into medical school curricula and (2) where they are successfully delivered, what are the contextual factors that allow for this enactment? DATA SOURCES: We searched PubMed, Embase, CINAHL and PsycINFO using the MesH terms Schools, Medical; Students, Medical; Education, Medical AND Neurocognitive disorders or the closest possible set of terms within each database. ELIGIBILITY CRITERIA: Undergraduate or graduate entry medical school programme, teaching and learning focussing on dementia, evaluating student outcomes (satisfaction, knowledge, skills, attitudes or behaviours), interventions described clearly enough to classify teaching method, any research design (quantitative and qualitative), English language. DATA EXTRACTION AND SYNTHESIS: We used a shared spreadsheet to enter key information about eligible studies and the reasons for excluding studies that did not fit eligibility criteria. We extracted descriptive data about the nature of educational interventions and narrative information as to barriers and facilitators to implementing those interventions. RESULTS: Our initial literature search identified 16 relevant papers for review. Systematic extraction of data informed the development of an initial programme theory (IPT) structured around four contextual barriers: \u27culture\u27, \u27concern for patient welfare\u27, \u27student attitudes\u27 and \u27logistics\u27 with associated facilitatory mechanisms embed medical education about dementia. CONCLUSIONS: We outline the process of generating our IPT, including overlap with Cultural Historical Activity Theory. We outline our intention to refine our programme theory through ongoing review of the evidence base and collaboration with stakeholders, with the aim of finalising a model for successful integration of dementia education