Paint it Black -- A Combinatorial Yawp

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A Probabilistic View of Certain Weighted Fibonacci Sums

In this article, we pursue the reverse strategy of using probability to derive an and develop an exponential generating function for an in Section 3. In Section 4, we present a method for finding an exact, non-recursive, formula for an

Tiling Proofs of Recent Sum Identities Involving Pell Numbers

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities

Bidirectional Scatter Measurements of a Guided-mode Resonant Filter Photonic Crystal Structure

This work investigates the Bidirectional Scatter Distribution Function (BSDF) at incident angles other than normal and at 544-nm wavelength of a Guided Mode Resonance Filter (GMRF) Photonic Crystal (PC) structure designed for normally incident light at 532 nm. Strong out-coupling of PC diffraction orders into both the transmitted and reflected hemispheres was observed specifically at a 25.7° incidence angle, which we attribute to this incident angle/wavelength pair being a good match to the ( ± 1, 0) PC grating mode. BSDF measurements at incident angles of 15° and 35° also displayed some out-coupled diffraction, though much lower in magnitude, and are also attributed to being a weaker match to the ( ± 1, 0) PC grating mode. Three-dimensional finite-difference time-domain Maxwell\u27s equation simulations demonstrate that since this GMRF was designed for complete destructive interference of the transmitted light upon normal incidence, stronger out-coupling of the diffraction is expected for modal solutions as the angle of incidence increases. © 2012 Optical Society of America

Implementing the Simple Biosphere Model (SiB) in a general circulation model: Methodologies and results

The Simple Biosphere MOdel (SiB) of Sellers et al., (1986) was designed to simulate the interactions between the Earth's land surface and the atmosphere by treating the vegetation explicitly and relistically, thereby incorporating biophysical controls on the exchanges of radiation, momentum, sensible and latent heat between the two systems. The steps taken to implement SiB in a modified version of the National Meteorological Center's spectral GCM are described. The coupled model (SiB-GCM) was used with a conventional hydrological model (Ctl-GCM) to produce summer and winter simulations. The same GCM was used with a conventional hydrological model (Ctl-GCM) to produce comparable 'control' summer and winter variations. It was found that SiB-GCM produced a more realistic partitioning of energy at the land surface than Ctl-GCM. Generally, SiB-GCM produced more sensible heat flux and less latent heat flux over vegetated land than did Ctl-GCM and this resulted in the development of a much deeper daytime planetary boundary and reduced precipitation rates over the continents in SiB-GCM. In the summer simulation, the 200 mb jet stream and the wind speed at 850 mb were slightly weakened in the SiB-GCM relative to the Ctl-GCM results and equivalent analyses from observations

Abstracting modelling languages: A reutilization approach

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-31095-9_9Proceedings of 24th International Conference, CAiSE 2012, Gdansk, Poland, June 25-29, 2012Model-Driven Engineering automates the development of information systems. This approach is based on the use of Domain-Specific Modelling Languages (DSMLs) for the description of the relevant aspects of the systems to be built. The increasing complexity of the target systems has raised the need for abstraction techniques able to produce simpler versions of the models, but retaining certain properties of interest. However, developing such abstractions for each DSML from scratch is a time and resource consuming activity. Our solution to this situation is a number of techniques to build reusable abstractions that are defined once and can be reused over families of modelling languages sharing certain requirements. As a proof of concept, we present a catalogue of reusable abstractions, together with an implementation in the MetaDepth multi-level meta-modelling tool.Work funded by the Spanish Ministry of Economy and Competitivity (TIN2011-24139), and the R&D programme of Madrid Region (S2009/TIC-1650)

Empirically Driven Use Case Metamodel Evolution

Metamodel evolution is rarely driven by empirical evidences of metamodel drawbacks. In this paper, the evolution of the use case metamodel used by the publicly available requirements management tool REM is presented. This evolution has been driven by the analysis of empirical data obtained during the assessment of several metrics–based verification heuristics for use cases developed by some of the authors and previously presented in other international fora. The empirical analysis has made evident that some common defects found in use cases developed by software engineering students were caused not only by their lack of experience but also by the expressive limitations imposed by the underlying use case metamodel used in REM. Once these limitations were clearly identified, a number of evolutionary changes were proposed to the REM use case metamodel in order to increase use case quality, i.e. to avoid those situations in which the metamodel were the cause of defects in use case specifications.Ministerio de Ciencia y Tecnología TIC 2003-02737-C02-0

How to Change Behavior in the Context of an FBA-Based Intervention

Teachers implementing behavior interventions are often more effective in eliminating problem behavior and building new skills if they start with functional behavior assessment (FBA). Using FBA, the teacher identifies the purpose, or function, of a problem behavior, then teaches a “replacement skill” that serves the same function. For example, rather than throw a tantrum to avoid a high demand assignment, a teacher teaches a seventh grader to approach an adult in the room to ask for help on particularly difficult problems. Or, instead of making noises to get attention, a teacher teaches a first grader to submit a card with a picture of himself helping the teacher as if to ask “can I be your helper this morning?

Increases in body weight and nutritional status of transplanted Alaskan caribou

Body weight and natality rate in ungulates can be useful indices to nutririon, bur they may also be influenced by genetic and climatic factors. Because caribou {Rangifer tarandus granti) are distributed as discrete populations of metapopulations (i.e., herds) that are usually reproductively isolated from each other for unknown periods, it is difficult to separate the influence of genetics and nutrition on body weight, especially where historical data are lacking. To help elucidate the influence of nutrition on potential variation in body weight and natality of caribou in Alaska, we reviewed data for body weight and natality in 5 populations which resulted from Transplants to previously ungrazed ranges, or to areas where reindeer and caribou had been absent for many decades. In 2 of 5 populations body weight increased significantly, and likely increased in the other 3 populations, but data were insufficient. Natality rate increased in all 5 populations, proportion of fecund yearlings was high and 3 of the 5 newly established herds increased at about the maximum biological potential for the species (lambda=1.35). In the Adak transplant, a lactating yearling was documented. These 5 transplanted populations provide additional evidence that body weight and natality rate in Alaskan caribou are sensitive to changes in population density and relatively short-term (i.e., 10 years) increases in grazing pressure independenr of climate and genetics