Entanglement entropy of (3+1)D topological orders with excitations

Excitations in (3+1)D topologically ordered phases have very rich structures. (3+1)D topological phases support both point-like and string-like excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the question how different types of topological excitations contribute to the entanglement entropy, or alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological orders? We are mainly interested in (3+1)D topological orders that can be realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite group $G$ and its group 4-cocycle $\omega\in\mathcal{H}^4[G;U(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant $\ln d_i$ to the entanglement entropy, where $d_i$ is the quantum dimension that depends on both the structure of the excitation and the data $(G,\,\omega)$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\,\omega)$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\omega$ from the others.Comment: 12 pages, 4 figures; v2: minor changes, published versio

Integration, Testing, And Analysis Of Multispectral Imager On Small Unmanned Aerial System For Skin Detection

Small Unmanned Aerial Systems (SUAS) have been utilized by the military, geological researchers, and first responders, to provide information about the environment in real time. Hyperspectral Imagery (HSI) provides high resolution data in the spatial and spectral dimension; all objects, including skin have unique spectral signatures. However, little research has been done to integrate HSI into SUAS due to their cost and form factor. Multispectral Imagery (MSI) has proven capable of dismount detection with several distinct wavelengths. This research proposes a spectral imaging system that can detect dismounts on SUAS. Also, factors that pertain to accurate dismount detection with an SUAS are explored. Dismount skin detection from an aerial platform also has an inherent difficulty compared to ground-based platforms. Computer vision registration, stereo camera calibration, and geolocation from autopilot telemetry are utilized to design a dismount detection platform with the Systems Engineering methodology. An average 5.112% difference in ROC AUC values that compared a line scan spectral imager to the prototype area scan imager was recorded. Results indicated that an SUAS-based Spectral Imagers are capable tools in dismount detection protocols. Deficiencies associated with the test expedient prototype are discussed and recommendations for further improvements are provided

Anomalies and entanglement renormalization

We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.Comment: 12+18 pages, 6+5 figures, 0+2 tables, v2 published versio

Automatic Detection of Calibration Grids in Time-of-Flight Images

It is convenient to calibrate time-of-flight cameras by established methods, using images of a chequerboard pattern. The low resolution of the amplitude image, however, makes it difficult to detect the board reliably. Heuristic detection methods, based on connected image-components, perform very poorly on this data. An alternative, geometrically-principled method is introduced here, based on the Hough transform. The projection of a chequerboard is represented by two pencils of lines, which are identified as oriented clusters in the gradient-data of the image. A projective Hough transform is applied to each of the two clusters, in axis-aligned coordinates. The range of each transform is properly bounded, because the corresponding gradient vectors are approximately parallel. Each of the two transforms contains a series of collinear peaks; one for every line in the given pencil. This pattern is easily detected, by sweeping a dual line through the transform. The proposed Hough-based method is compared to the standard OpenCV detection routine, by application to several hundred time-of-flight images. It is shown that the new method detects significantly more calibration boards, over a greater variety of poses, without any overall loss of accuracy. This conclusion is based on an analysis of both geometric and photometric error.Comment: 11 pages, 11 figures, 1 tabl

The nature of shape constancy mechanisms as revealed by shape priming

Five shape priming experiments are reported in which the target was either a five- or six-sided line-drawn figure and participants made a speeded 2AFC judgment about the target’s number of sides. On priming trials, the target was preceded by a briefly presented smaller line figure (the prime) and performance on these trials was gauged relative to a no prime condition. In the first two experiments, primes were rendered invisible by the presentation of a backwards visual noise mask, respectively for a short (~40 ms) or long duration (~93 ms). No reliable priming effects arose under masked conditions. When these experiments were repeated without the mask, participants were speeded when the prime and target were related by a rigid through-the-plane rotation but not when the prime was a non-rigid, stretched version of the target. The same pattern of priming effects arose when, in a final experiment, novel irregular shapes were used. Collectively, the data reveal the operation of shape constancy mechanisms that are particularly sensitive to shape rigidity. The findings suggest that the visual system attempts to secure a correspondence between the rapid and successive presentations of the prime and the target by matching shapes according to a rigidity constraint

A perceptual-statistics shading model

The process of surface perception is complex and based on several influencing factors, e.g., shading, silhouettes, occluding contours, and top down cognition. The accuracy of surface perception can be measured and the influencing factors can be modified in order to decrease the error in perception. This paper presents a novel concept of how a perceptual evaluation of a visualization technique can contribute to its redesign with the aim of improving the match between the distal and the proximal stimulus. During analysis of data from previous perceptual studies, we observed that the slant of 3D surfaces visualized on 2D screens is systematically underestimated. The visible trends in the error allowed us to create a statistical model of the perceived surface slant. Based on this statistical model we obtained from user experiments, we derived a new shading model that uses adjusted surface normals and aims to reduce the error in slant perception. The result is a shape-enhancement of visualization which is driven by an experimentally-founded statistical model. To assess the efficiency of the statistical shading model, we repeated the evaluation experiment and confirmed that the error in perception was decreased. Results of both user experiments are publicly-available datasets

Representations of celestial coordinates in FITS

In Paper I, Greisen & Calabretta (2002) describe a generalized method for assigning physical coordinates to FITS image pixels. This paper implements this method for all spherical map projections likely to be of interest in astronomy. The new methods encompass existing informal FITS spherical coordinate conventions and translations from them are described. Detailed examples of header interpretation and construction are given.Comment: Consequent to Paper I: "Representations of world coordinates in FITS". 45 pages, 38 figures, 13 tables, aa macros v5.2 (2002/Jun). Both papers submitted to Astronomy & Astrophysics (2002/07/19). Replaced to try to get figure and table placement right (no textual changes