Daily Papers

The open road poses many challenges to autonomous perception, including poor visibility from extreme weather conditions. Models trained on good-weather datasets frequently fail at detection in these out-of-distribution settings. To aid adversarial robustness in perception, we introduce WEDGE (WEather images by DALL-E GEneration): a synthetic dataset generated with a vision-language generative model via prompting. WEDGE consists of 3360 images in 16 extreme weather conditions manually annotated with 16513 bounding boxes, supporting research in the tasks of weather classification and 2D object detection. We have analyzed WEDGE from research standpoints, verifying its effectiveness for extreme-weather autonomous perception. We establish baseline performance for classification and detection with 53.87% test accuracy and 45.41 mAP. Most importantly, WEDGE can be used to fine-tune state-of-the-art detectors, improving SOTA performance on real-world weather benchmarks (such as DAWN) by 4.48 AP for well-generated classes like trucks. WEDGE has been collected under OpenAI's terms of use and is released for public use under the CC BY-NC-SA 4.0 license. The repository for this work and dataset is available at https://infernolia.github.io/WEDGE.

Let 1 le k le n, and let v_1,ldots,v_k be integral vectors in Z^n. We consider the wedge map α_{n,k} : (Z^n)^k /SL_k(Z) rightarrow wedge^k(Z^n), (v_1,ldots,v_k) rightarrow v_1 wedge cdots wedge v_k . In his Disquisitiones, Gauss proved that α_{n,2} is injective when restricted to a primitive system of vectors when defining his composition law for binary quadratic forms. He also gave an algorithm for inverting α_{3,2} in a different context on the representation of integers by ternary quadratic forms. We give here an explicit algorithm for inverting α_{n,2}, and observe via Bhargava's composition law for Z^2 otimes Z^2 otimes Z^2 cube that inverting α_{4,2} is the main algorithmic step in Gauss's composition law for binary quadratic forms. This places Gauss's composition as a special case of the geometric problem of inverting a wedge map which may be of independent interests. We also show that a given symmetric positive definite matrix A induces a natural metric on the integral Grassmannian G_{n,k}(Z) so that the map X rightarrow X^TAX becomes norm preserving.

We study a real massless scalar field in d+1 dimensions confined to a wedge of opening angle α, in the presence of a semitransparent circular arc that may oscillate radially. Within the worldline formulation, and for an arbitrary strength λ of the δ-potential that models the arc, we expand the effective action in powers of the radial displacement R of the arc. In this formulation, all the information about the media is contained in the propagator of a non-relativistic point particle, so that known results for that propagator can be used directly. At zeroth order we obtain the Casimir energy of the wedge, with Dirichlet, Neumann or mixed walls, and the contribution of the arc in closed form for arbitrary λ. We show that the worldline integrand is, point by point, the energy density obtained from the energy-momentum tensor of the scalar field with curvature coupling ξ=1/4; with this identification, and using dimensional regularization for the integrated quantities, we recover the known results for the wedge and for the wedge closed by a Dirichlet arc. At second order in R, we reduce the form factor that determines the imaginary part of the in-out effective action, and hence the probability of pair creation by the moving arc, to a one-loop expression involving the radial Green's functions of each angular sector. In the narrow-wedge limit, each angular sector behaves as a field with a mass set by the angular quantization, coupled to a moving δ-mirror; for a Dirichlet arc, the pair creation spectrum of the exterior region approaches that of a planar massive mirror, while the interior region behaves as a tapered cavity. Finally, by decomposing the electromagnetic field into TE and TM scalars, we obtain the Casimir energy of wedges with perfectly conducting, perfectly permeable and mixed walls.

We present a novel approach to determine the constitutive properties of metals under large plastic strains and strain rates that otherwise are difficult to access using conventional materials testing methods. The approach exploits large-strain plastic flow past a sharp wedge, coupled with high-speed photography and image velocimetry to capture the underlying plastic flow dynamics. The inverse problem of estimating material parameters from the flow field is solved using an iterative optimization procedure that minimizes the gap between internal and external plastic work. A major advantage of the method is that it neither makes any assumptions about the flow nor requires computational simulations. To counter the problem of non-unique parameter estimates, we propose a parameterization scheme that takes advantage of the functional form of the constitutive model and reformulates the problem into a more tractable form to identify plasticity parameters uniquely. We present studies to illustrate the principle of the method with two materials with widely different plastic flow characteristics: copper (strain hardening) and a lead-free solder alloy (rate sensitive and deformation history dependent). The results demonstrate the efficacy of the method in reliably determining the material parameters under high strain/strain rate conditions of relevance to a range of practical engineering problems.