Four bugs on a rectangle

The problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10^427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth’s double-arrow notation and level-index arithmetic are discussed

Spectral properties of quantized barrier billiards

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics.Comment: 8 pages, 9 figure

Labeling Subway Lines

Graphical features on map, charts, diagrams and graph drawings usually must be annotated with text labels in order to convey their meaning. In this paper we focus on a problem that arises when labeling schematized maps, e.g. for subway networks. We present algorithms for labeling points on a line with axis-parallel rectangular labels of equal height. Our aim is to maximize label size under the constraint that all points must be labeled. Even a seemingly strong simplification of the general point-labeling problem, namely to decide whether a set of points on a horizontal line can be labeled with sliding rectangular labels, turns out to be weakly NPcomplete. This is the first labeling problem that is known to belong to this class. We give a pseudo-polynomial time algorithm for it. In case of a sloping line points can be labeled with maximum-size square labels in O(n log n) time if four label positions per point are allowed and in O(n 3 log n) time if labels can slide. We also investigate rectangular labels

Spinal cord gray matter segmentation using deep dilated convolutions

Gray matter (GM) tissue changes have been associated with a wide range of neurological disorders and was also recently found relevant as a biomarker for disability in amyotrophic lateral sclerosis. The ability to automatically segment the GM is, therefore, an important task for modern studies of the spinal cord. In this work, we devise a modern, simple and end-to-end fully automated human spinal cord gray matter segmentation method using Deep Learning, that works both on in vivo and ex vivo MRI acquisitions. We evaluate our method against six independently developed methods on a GM segmentation challenge and report state-of-the-art results in 8 out of 10 different evaluation metrics as well as major network parameter reduction when compared to the traditional medical imaging architectures such as U-Nets.Comment: 13 pages, 8 figure

Modelling and Experimental Investigation of Hexagonal Nacre-Like Structure Stiffness

A highly ordered, hexagonal, nacre-like composite stiffness is investigated using experiments, simulations, and analytical models. Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination. A simulation geometry is made by digital microscope measurements of the specimens, and a simulation is conducted using material data based on component material characterization. Available analytical models are compared to the experimental results, and a more accurate model is derived specifically for highly ordered hexagonal tablets with relatively large in-plane gaps. The influence of hexagonal width, cut width, and interface thickness are analyzed using the hexagonal nacre-like composite stiffness model. The proposed analytical model converges within 1% with the simulation and experimental result

Anchored Rectangle and Square Packings

For points p_1,...,p_n in the unit square [0,1]^2, an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles r_1,...,r_n in [0,1]^2 such that point p_i is a corner of the rectangle r_i (that is, r_i is anchored at p_i) for i=1,...,n. We show that for every set of n points in [0,1]^2, there is an anchored rectangle packing of area at least 7/12-O(1/n), and for every n, there are point sets for which the area of every anchored rectangle packing is at most 2/3. The maximum area of an anchored square packing is always at least 5/32 and sometimes at most 7/27. The above constructive lower bounds immediately yield constant-factor approximations, of 7/12 -epsilon for rectangles and 5/32 for squares, for computing anchored packings of maximum area in O(n log n) time. We prove that a simple greedy strategy achieves a 9/47-approximation for anchored square packings, and 1/3 for lower-left anchored square packings. Reductions to maximum weight independent set (MWIS) yield a QPTAS and a PTAS for anchored rectangle and square packings in n^{O(1/epsilon)} and exp(poly(log (n/epsilon))) time, respectively

A simple beam model for the shear failure of interfaces

We propose a novel model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.Comment: 11 pages, 13 figure

The curvHDR Method for Gating Flow Cytometry Samples

Motivation: High-throughput flow cytometry experiments produce hundreds of large multivariate samples of cellular characteristics. These samples require specialized processing to obtain clinically meaningful measurements. A major component of this processing is a form of cell subsetting known as gating. Manual gating is time-consuming and subjective. Good automatic and semi-automatic gating algorithms are very beneficial to high-throughput flow cytometry. Results: We develop a statistical procedure, named curvHDR, for automatic and semi-automatic gating. The method combines the notions of significant high negative curvature regions and highest density regions and has the ability to adapt well to human-perceived gates. The underlying principles apply to dimension of arbitrary size, although we focus on dimensions up to three. Accompanying software, compatible with contemporary flow cytometry informatics, is developed. Availability: Software for Bioconductor within R is available