Systematics of Aligned Axions

We describe a novel technique that renders theories of $N$ axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes with a number of local minima that scales as $\sqrt{N!}$, and so for large $N$ appear to be analytically and numerically intractable. Our method is based on uncovering a set of approximate symmetries that exist in addition to the $N$ periods. These approximate symmetries, which are exponentially close to exact, allow us to locate the minima very efficiently and accurately and to analyze other characteristics of the potential. We apply our framework to evaluate the diameters of flat regions suitable for slow-roll inflation, which unifies, corrects and extends several forms of "axion alignment" previously observed in the literature. We find that in a broad class of random theories, the potential is smooth over diameters enhanced by $N^{3/2}$ compared to the typical scale of the potential. A Mathematica implementation of our framework is available online.Comment: 68 pages, 17 figure

Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids

The average number of constraints per particle $$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($\rightarrow 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming chain-like face-face clusters with finite extent form in these systems.Comment: 4 pages, 3 figures, 4 tabl

Local Alignment of the BABAR Silicon Vertex Tracking Detector

The BABAR Silicon Vertex Tracker (SVT) is a five-layer double-sided silicon detector designed to provide precise measurements of the position and direction of primary tracks, and to fully reconstruct low-momentum tracks produced in e+e- collisions at the PEP-II asymmetric collider at Stanford Linear Accelerator Center. This paper describes the design, implementation, performance, and validation of the local alignment procedure used to determine the relative positions and orientations of the 340 SVT wafers. This procedure uses a tuned mix of in-situ experimental data and complementary lab-bench measurements to control systematic distortions. Wafer positions and orientations are determined by minimizing a chisquared computed using these data for each wafer individually, iterating to account for between-wafer correlations. A correction for aplanar distortions of the silicon wafers is measured and applied. The net effect of residual mis-alignments on relevant physical variables is evaluated in special control samples. The BABAR data-sample collected between November 1999 and April 2008 is used in the study of the SVT stability.Comment: 21 pages, 20 figures, 3 tables, submitted to Nucl. Instrum. Meth.

Deformable face ensemble alignment with robust grouped-L1 anchors

Many methods exist at the moment for deformable face fitting. A drawback to nearly all these approaches is that they are (i) noisy in terms of landmark positions, and (ii) the noise is biased across frames (i.e. the misalignment is toward common directions across all frames). In this paper we propose a grouped $\mathcal{L}1$-norm anchored method for simultaneously aligning an ensemble of deformable face images stemming from the same subject, given noisy heterogeneous landmark estimates. Impressive alignment performance improvement and refinement is obtained using very weak initialization as "anchors"