Uniform infinite planar triangulation and related time-reversed critical branching process

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe

Evaluation of an offshore wind farm computational fluid dynamics model against operational site data

Modelling wind turbine wake effects at a range of wind speeds and directions with actuator disk (AD) models can provide insight but also be challenging. With any model it is important to quantify the level of error, but this can also present a challenge when comparing a steady-state model to measurement data with scatter. This paper models wind flow in a wind farm at a range of wind speeds and directions using an AD implementation. The results from these models are compared to data collected from the actual farm being modelled. An extensive comparison is conducted, constituted from 35 cases where two turbulence models, the standard k-ε and k-ω SST are evaluated. The steps taken in building the models as well as processes for comparing the AD computational fluid dynamics (CFD) results to real-world data using the regression models of ensemble bagging and Gaussian process are outlined. Turbine performance data and boundary conditions are determined using the site data. Modifications to an existing opensource AD code are shown so that the predetermined turbine performance can be implemented into the CFD model. Steady state solutions are obtained with the OpenFOAM CFD solver. Results are compared in terms of velocity deficit at the measurement locations. Using the standard k-ε model, a mean absolute error for all cases together of roughly 8% can be achieved, but this error changes for different directions and methods of evaluating it

A non-constructive proof of the Four Colour Theorem

The approach is through a singularity analysis of generating functions for 3- and 4-connected triangulations, asymptotic analysis, properties of the ${{}_3F_2}$ hypergeometric series, and Tutte's enumerative work on planar maps and chromatic polynomials

Most of the genetic covariation between major depressive and alcohol use disorders is explained by trait measures of negative emotionality and behavioral control

Background Mental health disorders commonly co-occur, even between conceptually distinct syndromes, such as internalizing and externalizing disorders. The current study investigated whether phenotypic, genetic, and environmental variance in negative emotionality and behavioral control account for the covariation between major depressive disorder (MDD) and alcohol use disorder (AUD). Method A total of 3623 members of a national twin registry were administered structured diagnostic telephone interviews that included assessments of lifetime histories of MDD and AUD, and were mailed self-report personality questionnaires that assessed stress reactivity (SR) and behavioral control (CON). A series of biometric models were fitted to partition the proportion of covariance between MDD and AUD into SR and CON. Results A statistically significant proportion of the correlation between MDD and AUD was due to variance specific to SR (men = 0.31, women = 0.27) and CON (men = 0.20, women = 0.19). Further, genetic factors explained a large proportion of this correlation (0.63), with unique environmental factors explaining the rest. SR explained a significant proportion of the genetic (0.33) and environmental (0.23) overlap between MDD and AUD. In contrast, variance specific to CON accounted for genetic overlap (0.32), but not environmental overlap (0.004). In total, SR and CON accounted for approximately 70% of the genetic and 20% of the environmental covariation between MDD and AUD. Conclusions This is the first study to demonstrate that negative emotionality and behavioral control confer risk for the co-occurrence of MDD and AUD via genetic factors. These findings are consistent with the aims of NIMH's RDoC proposal to elucidate how transdiagnostic risk factors drive psychopathology

The Discovery of Cepheids and a New Distance to NGC 2841 Using the Hubble Space Telescope

We report on the discovery of Cepheids in the spiral galaxy NGC 2841, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. NGC 2841 was observed over 12 epochs using the F555W filter, and over 5 epochs using the F814W filter. Photometry was performed using the DAOPHOT/ALLFRAME package. We discovered a total of 29 variables, including 18 high-quality Cepheids with periods ranging from 15 to 40 days. Period-luminosity relations in the V and I bands, based on the high-quality Cepheids, yield an extinction-corrected distance modulus of 30.74 +/- 0.23 mag, which corresponds to a distance of 14.1 +/- 1.5 Mpc. Our distance is based on an assumed LMC distance modulus of 18.50 +/- 0.10 mag (D = 50+/- 2.5 kpc) and a metallicity dependence of the Cepheid P-L relation of gamma (VI) = -0.2 +/- 0.2 mag/dex.Comment: 31 preprint pages including 10 figures. Accepted for publication in ApJ. High-resolution version available from http://cfa-www.harvard.edu/~lmacri/n2841.p

The Asymptotic Number of Irreducible Partitions

A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a union of blocks. We determine the asymptotic relationship between the numbers of irreducible partitions, partitions without singleton blocks, and all partitions when the block sizes must lie in some specified set

Public Interest Immunity: Al Megrahi v HM Advocate

The Lockerbie case has already contributed significantly to the jurisprudence of the law of evidence. Al Megrahi v HM Advocate continues in that vein, shedding some light on how the law relating to public interest immunity now operates following devolution

Avatars of Eurocentrism in the critique of the liberal peace

Recent scholarly critiques of the so-called liberal peace raise important political and ethical challenges to practices of postwar intervention in the global South. However, their conceptual and analytic approaches have tended to reproduce rather than challenge the intellectual Eurocentrism underpinning the liberal peace. Eurocentric features of the critiques include the methodological bypassing of target subjects in research, the analytic bypassing of subjects through frameworks of governmentality, the assumed ontological split between the ‘liberal’ and the ‘local’, and a nostalgia for the liberal subject and the liberal social contract as alternative bases for politics. These collectively produce a ‘paradox of liberalism’ that sees the liberal peace as oppressive but also the only true source of emancipation. However, the article suggests that a repoliticization of colonial difference offers an alternative ‘decolonizing’ approach to critical analysis through repositioning the analytic gaze. Three alternative research strategies for critical analysis are briefly developed