To atten a set partition (with apologies to Mathematica r ) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing|increasing entries in each block and blocks arranged in increasing order of their rst entries|we count the partitions of [n] whose attening avoids a single 3-letter pattern. Five coun...

Virtual colonoscopy is a well-known screening modality for colon cancer, and virtual colon flattening techniques have been proposed to map the 3D surface to the 2D domain. Performing this flattening with conformal geometry allows for the local shapes to be preserved. We explore here how these shape preserving flattened maps can be used for visualization of the colon and to enhance the VC enviro...

Droplets made of a mixture two liquids with different volatilities take on pancake shape.

If massive compact halo objects (MACHOs) are detected in ongoing searches, then τSMC/τLMC, the ratio of the optical depth toward the Small and Large Magellanic Clouds, will be a robust indicator of the flattening of the Galactic dark matter halo. For a spherical halo, τSMC/τLMC is about 1.45, independent of details of the shape of the Galactic rotation curve, the assumed mass of the Galactic di...

Breast cyst fluid (BCF) contained in gross cists is involved with its many biomolecules in different stages of breast cystic development. Type I apocrine and type II flattened cysts are classified based on biochemical, morphological and hormonal differences, and their different patterns of growth factors and active biocompounds may require different regulation. In a previous paper, hyaluronic a...

We present flattened convolutional neural networks that are designed for fast feedforward execution. The redundancy of the parameters, especially weights of the convolutional filters in convolutional neural networks has been extensively studied and different heuristics have been proposed to construct a low rank basis of the filters after training. In this work, we train flattened networks that ...

The flattening filter free (FFF) X-rays can provide much higher dose rate at the treatment target compared to the conventional flattened X-rays. However, the substantial increase of dose rate for FFF beams may affect the ion recombination correction factor, which is required for accurate measurements using ionization chambers in clinical dosimetry. The purpose of this work is to investigate the...