Endoscopic images do not contain sharp edges to segment using the traditional segmentation methods for obtaining edges. Therefore, the active contours or ‘snakes’ using level set method with the energy minimization algorithm is adopted here to segment these images. The results obtained from the above segmentation process will be number of segmented regions. The boundary of each region is consid...

We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three crossings, but does not contain K6 as a subgraph, then it is also 5-colorable. We also consider the question of whether the result can be extended to graphs with more crossings.

Subgap states are responsible for the low-bias transport features of hybrid superconducting--semiconducting devices. Here, we analyze local and nonlocal differential conductance Coulomb-blockaded multiterminal superconducting islands that host subgap with different spatial structures. The emerging patterns their spectroscopy used to characterize possible topological nature these devices offer p...

We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^d$, for $d\geq3$, and give sharp bounds probability that radius of a finite cluster in excursion set $\{\varphi \geq h\}$ exceeds large value $N$, any height $h \neq h_*$, where $h_*$ refers to corresponding percolation critical parameter. In dimension $d=3$, we prove this is sub-exponential $N$ decays as $\exp\{-\frac{\pi}{6}(h-h_*)^...

The syntactic structure of a sentence can be modelled as a tree, where vertices correspond to words and edges indicate syntactic dependencies. It has been claimed recurrently that the number of edge crossings in real sentences is small. However, a baseline or null hypothesis has been lacking. Here we quantify the amount of crossings of real sentences and compare it to the predictions of a serie...

Introduction The overall aim of this study is to compare daytime driving with night-time driving looking at line crossings during self-reported sleepiness and long blinks. The hypothesis is that high levels of self-reported sleepiness (KSS 9) and long blink duration (>0.15 s) will be less associated with critical events during the day-time compared to night-time. Method The study is based on da...

Generalised Hermite polynomials are employed for the reconstruction of an unknown signal from a knowledge of its zero-crossings, under certain conditions on its spatial/spectral width, but dispensing with the assumption of bandlimitedness. A computational implementation of the proposed method is given for one-variable (or one-dimensional) signals, featuring an application of simulated annealing...

In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions. A drawing of a clustered graph is c-planar if it has no edge-edge, edge-region, or region-region crossings. Determining the complexity of testing whether a clustered graph admits a c-planar drawing is a long-standing open problem in the Grap...