An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $\Theta(n)$ such tilings exist.Comment: In proceedings of ISAAC 201

Mechanism of age-dependent susceptibility and novel treatment strategy in glutaric acidemia type I

Glutaric acidemia type I (GA-I) is an inherited disorder of lysine and tryptophan metabolism presenting with striatal lesions anatomically and symptomatically similar to Huntington disease. Affected children commonly suffer acute brain injury in the context of a catabolic state associated with nonspecific illness. The mechanisms underlying injury and age-dependent susceptibility have been unknown, and lack of a diagnostic marker heralding brain injury has impeded intervention efforts. Using a mouse model of GA-I, we show that pathologic events began in the neuronal compartment while enhanced lysine accumulation in the immature brain allowed increased glutaric acid production resulting in age-dependent injury. Glutamate and GABA depletion correlated with brain glutaric acid accumulation and could be monitored in vivo by proton nuclear magnetic resonance (1H NMR) spectroscopy as a diagnostic marker. Blocking brain lysine uptake reduced glutaric acid levels and brain injury. These findings provide what we believe are new monitoring and treatment strategies that may translate for use in human GA-I

Methods for Rapidly Processing Angular Masks of Next-Generation Galaxy Surveys

As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angular masks of the Sloan Digital Sky Survey contain about N=300,000 distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time O(N^2) with a naive algorithm, such as finding which polygons overlap each other. Here we present a "divide-and-conquer" solution to this challenge: we first split the angular mask into predefined regions called "pixels," such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces O(N^2) tasks to O(N), and also reduces the important task of determining in which polygon(s) a point on the sky lies from O(N) to O(1), resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular HEALPix format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the mangle software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/, along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since mangle is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.Comment: New version 2.1 of the mangle software now available at http://space.mit.edu/home/tegmark/mangle/ - includes galaxy survey masks and galaxy lists for the latest SDSS data release and the 2dFGRS final data release as well as extensive documentation and examples. 14 pages, 9 figures, matches version accepted by MNRA

Probing conformational states of glutaryl-CoA dehydrogenase by fragment screening

The first crystal structure is reported of a glutaryl-CoA dehydrogenase in the apo state without flavin adenine dinucleotide cofactor bound. Additional structures with small molecules complexed in the catalytic active site were obtained by fragment-based screening

Geocentrism reexamined

The universe is nearly isotropic on very large scales. It is much more difficult to show that the universe is radially homogeneous (independent of distance), or equivalently, that it is isotropic about distant points. This taken as an axiom, since if it were not true, then we would occupy a preferred position. This paper considers several empirical arguments for radial homogeneity based on the cosmic microwave background (CMB). The tightest limits on inhomogeneity on the scale of the horizon are of order ten percent but will improve soon. These limits involve the Sunyaev-Zel'dovich effect in clusters of galaxies, excitation of low-energy atomic transitions, and the accurately thermal spectrum of the CMB. Weaker limits from primordial nucleosynthesis are discussed briefly.Comment: RevTeX source, 14 pages, no figs. To appear Phys Rev

Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 2: The Physics Program for DUNE at LBNF

The Physics Program for the Deep Underground Neutrino Experiment (DUNE) at the Fermilab Long-Baseline Neutrino Facility (LBNF) is described