How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Branching Ratios for The Radiometric Calibration of EUNIS-2012

The Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS) sounding rocket instrument is a two-channel imaging spectrograph that observes the solar corona and transition region with high spectral resolution and a rapid cadence made possible by unprecedented sensitivity. The upcoming flight will incorporate a new wavelength channel covering the range 524-630 Angstroms, the previously-flown 300-370 Angstroms channel, and the first flight demonstration of cooled active pixel sensor (APS) arrays. The new 524-630 Angstrom channel incorporates a Toroidal Varied Line Space (TVLS) grating coated with B4C/Ir, providing broad spectral coverage and a wide temperature range of 0.025 to 10 MK. Absolute radiometric calibration of the two channels is being performed using a hollow cathode discharge lamp and NIST-calibrated AXUV-100G photodiode. Laboratory observations of He I 584 Angstroms and He II 304 Angstroms provide absolute radiometric calibrations of the two channels at those two respective wavelengths by using the AXUV photodiode as a transfer standard. The spectral responsivity is being determined by observing line pairs with a common upper state in the spectra of Ne I-III and Ar II-III. Calculations of A-values for the observed branching ratios are in progress

Mass Mixing, the Fourth Generation, and the Kinematic Higgs Mechanism

We describe how to construct chiral fermion mass terms using Dirac-Kahler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2) gauge field. Quantization breaks U(2,2) to U(2)xU(2), lifts mass spectrum degeneracy, and generates a non-trivial mass mixing matrix.Comment: 12 pages. No figures. Phys Lett B version. Minor typos fixe

Lagrangian generators of the Poincare gauge symmetries

We have systematically computed the generators of the symmetries arising in Poincare gauge theory formulation of gravity, both in 2+1 and 3+1 dimensions. This was done using a completely Lagrangian approach. The results are expected to be valid in any dimensions, as seen through lifting the results of the 2+1 dimensional example into the 3+1 dimensional one.Comment: Latex2e, 15 pages, 1 figure; (v2) Appendix containing discussion on applications of Lagrangian generators adde

Systematic review of the Exploration, Preparation, Implementation, Sustainment (EPIS) framework

Background: Effective implementation of evidence-based practices (EBPs) remains a significant challenge. Numerous existing models and frameworks identify key factors and processes to facilitate implementation. However, there is a need to better understand how individual models and frameworks are applied in research projects, how they can support the implementation process, and how they might advance implementation science. This systematic review examines and describes the research application of a widely used implementation framework, the Exploration, Preparation, Implementation, Sustainment (EPIS) framework. Methods: A systematic literature review was performed to identify and evaluate the use of the EPIS framework in implementation efforts. Citation searches in PubMed, Scopus, PsycINFO, ERIC, Web of Science, Social Sciences Index, and Google Scholar databases were undertaken. Data extraction included the objective, language, country, setting, sector, EBP, study design, methodology, level(s) of data collection, unit(s) of analysis, use of EPIS (i.e., purpose), implementation factors and processes, EPIS stages, implementation strategy, implementation outcomes, and overall depth of EPIS use (rated on a 1-5 scale). Results: In total, 762 full-text articles were screened by four reviewers, resulting in inclusion of 67 articles, representing 49 unique research projects. All included projects were conducted in public sector settings. The majority of projects (73%) investigated the implementation of a specific EBP. The majority of projects (90%) examined inner context factors, 57% examined outer context factors, 37% examined innovation factors, and 31% bridging factors (i.e., factors that cross or link the outer system and inner organizational context). On average, projects measured EPIS factors across two of the EPIS phases (M = 2.02), with the most frequent phase being Implementation (73%). On average, the overall depth of EPIS inclusion was moderate (2.8 out of 5). Conclusion: This systematic review enumerated multiple settings and ways the EPIS framework has been applied in implementation research projects, and summarized promising characteristics and strengths of the framework, illustrated with examples. Recommendations for future use include more precise operationalization of factors, increased depth and breadth of application, development of aligned measures, and broadening of user networks. Additional resources supporting the operationalization of EPIS are available

Nonlocal lattice fermion models on the 2d torus

Abelian fermion models described by the SLAC action are considered on a finite 2d lattice. It is shown that modification of these models by introducing additional Pauli - Villars regularization supresses nonlocal effects and provides agreement with the continuum results in vectorial U(1) models. In the case of chiral fermions the phase of the determinant differs from the continuum one.Comment: 16 pages, LaTeX, 5 eps figures, uses epsf.sty, rotate.st