Attractor Flows from Defect Lines

Deforming a two dimensional conformal field theory on one side of a trivial defect line gives rise to a defect separating the original theory from its deformation. The Casimir force between these defects and other defect lines or boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns out, that these flows are constant reparametrizations of gradient flows of the g-functions of the chosen defect or boundary condition. The special flows associated to supersymmetric boundary conditions in N=(2,2) superconformal field theories agree with the attractor flows studied in the context of black holes in N=2 supergravity.Comment: 28 page

Fusion of conformal interfaces

We study the fusion of conformal interfaces in the c=1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological interfaces, which (a) minimize the entropy function, (b) fix through an attractor mechanism one or both of the bulk radii, and (c) are (marginally) stable under splitting. One significant difference is that the conserved charges are logarithms of natural numbers, rather than vectors in a charge lattice, as for BPS states. Besides potential applications to condensed-matter physics and number theory, these results point to the existence of large solution-generating algebras in string theory.Comment: 28 pages, 4 figures. Minor clarifications in v2. Sign Mistakes corrected and reference added in v

Websites as Facilities Under ADA Title III

Title III of the Americans with Disabilities Act requires public accommodations—private entities that offer goods or services to the public—to be accessible to individuals with disabilities. There is an ongoing debate about whether Title III applies to websites that offer services to the public, but this debate may be resolved in the coming years by litigation or Department of Justice regulations. Assuming for the sake of argument that Title III will eventually be applied to websites, the next inquiry is what that application should look like. The regulatory definition of “facilities” should be amended to include nonphysical places of public accommodations. This change would open the door to a multilayered approach to accessible websites, wherein existing websites are subject to relatively lax requirements but new and altered websites are subject to stricter requirements

The SDSS Galaxy Angular Two-Point Correlation Function

We present the galaxy two-point angular correlation function for galaxies selected from the seventh data release of the Sloan Digital Sky Survey. The galaxy sample was selected with $r$-band apparent magnitudes between 17 and 21; and we measure the correlation function for the full sample as well as for the four magnitude ranges: 17-18, 18-19, 19-20, and 20-21. We update the flag criteria to select a clean galaxy catalog and detail specific tests that we perform to characterize systematic effects, including the effects of seeing, Galactic extinction, and the overall survey uniformity. Notably, we find that optimally we can use observed regions with seeing < 1\farcs5, and $r$-band extinction < 0.13 magnitudes, smaller than previously published results. Furthermore, we confirm that the uniformity of the SDSS photometry is minimally affected by the stripe geometry. We find that, overall, the two-point angular correlation function can be described by a power law, $\omega(\theta) = A_\omega \theta^{(1-\gamma)}$ with $\gamma \simeq 1.72$, over the range 0\fdg005--10\degr. We also find similar relationships for the four magnitude subsamples, but the amplitude within the same angular interval for the four subsamples is found to decrease with fainter magnitudes, in agreement with previous results. We find that the systematic signals are well below the galaxy angular correlation function for angles less than approximately 5\degr, which limits the modeling of galaxy angular correlations on larger scales. Finally, we present our custom, highly parallelized two-point correlation code that we used in this analysis.Comment: 22 pages, 17 figures, accepted by MNRA

Superconformal defects in the tricritical Ising model

We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the folding trick, a superconformal defect is mapped to a superconformal boundary of the N=1 superconformal unitary minimal model of c=7/5 with D_6-E_6 modular invariant. It turns out that the complete set of the boundary states of c=7/5 D_6-E_6 model cannot be interpreted as the consistent set of superconformal defects in the tricritical Ising model since it does not contain the "no defect" boundary state. Instead, we find a set of 18 consistent superconformal defects including "no defect" and satisfying the Cardy condition. This set also includes some defects which are not purely transmissive or purely reflective.Comment: 25 pages, 3 figures. v2: typos corrected. v3: clarification about spin structure aligned theory added, references adde

Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Marker based Thermal-Inertial Localization for Aerial Robots in Obscurant Filled Environments

For robotic inspection tasks in known environments fiducial markers provide a reliable and low-cost solution for robot localization. However, detection of such markers relies on the quality of RGB camera data, which degrades significantly in the presence of visual obscurants such as fog and smoke. The ability to navigate known environments in the presence of obscurants can be critical for inspection tasks especially, in the aftermath of a disaster. Addressing such a scenario, this work proposes a method for the design of fiducial markers to be used with thermal cameras for the pose estimation of aerial robots. Our low cost markers are designed to work in the long wave infrared spectrum, which is not affected by the presence of obscurants, and can be affixed to any object that has measurable temperature difference with respect to its surroundings. Furthermore, the estimated pose from the fiducial markers is fused with inertial measurements in an extended Kalman filter to remove high frequency noise and error present in the fiducial pose estimates. The proposed markers and the pose estimation method are experimentally evaluated in an obscurant filled environment using an aerial robot carrying a thermal camera.Comment: 10 pages, 5 figures, Published in International Symposium on Visual Computing 201

Spin relaxation in diluted magnetic semiconductor quantum dots

Electron spin relaxation induced by phonon-mediated s-d exchange interaction in a II-VI diluted magnetic semiconductor quantum dot is investigated theoretically. The electron-acoustic phonon interaction due to piezoelectric coupling and deformation potential is included. The resulting spin lifetime is typically on the order of microseconds. The effectiveness of the phonon-mediated spin-flip mechanism increases with increasing Mn concentration, electron spin splitting, vertical confining strength and lateral diameter, while it shows non-monotonic dependence on the magnetic field and temperature. An interesting finding is that the spin relaxation in a small quantum dot is suppressed for strong magnetic field and low Mn concentration at low temperature.Comment: 11 pages, 11 figures, to be published in Phys. Rev.