Let {X, Y,Z,A,B, C} ∈ Q+ be such that X2 + Y 2 = A2, X2 + Z2 = B2 and Y 2 + Z2 = C2. We consider the problem of finding T ∈ Q+ such that either 1. T 2 −X2 = , T 2 − Y 2 = , T 2 − Z2 = or 2. T 2 −A2 = , T 2 − B2 = , T 2 − C2 = . We show that problem 2 always has a solution and we provide a formula for T . Extensive computation has been unable to find a single solution of problem 1.

We present a Deep Cuboid Detector which takes a consumer-quality RGB image of a cluttered scene and localizes all 3D cuboids (box-like objects). Contrary to classical approaches which fit a 3D model from low-level cues like corners, edges, and vanishing points, we propose an end-to-end deep learning system to detect cuboids across many semantic categories (e.g., ovens, shipping boxes, and furni...

The aim of this work was to use bone anchored external markers to describe the kinematics of the tibia, fibula, talus, calcaneus, navicular, cuboid, medial cuneiform, first and fifth metatarsals during gait. Data were collected from six subjects. There was motion at all the joints studied. Movement between the talus and the tibia showed the expected predominance of sagittal plane motion, but th...

Because a stress fracture is rare and easily missed on an x-ray, it might go undetected. If a patient presents with an activity related injury to the midfoot and x-rays are negative, a computed tomography scan can be helpful in diagnosing a cuboid stress fracture. Also, computed tomography scans graphically show the fracture location and size, in addition to tracking progressive bone changes du...

The recent introduction of the concept of scattering fidelity causes us to revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302 (2003)]. There, the "distortion" of the coda of an acoustic signal is measured under temperature changes. This quantity is, in fact, the negative logarithm of scattering fidelity. We reanalyze their experimental data for two samples, and we find goo...