A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...

Given an arbitrary polygon P with holes, we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a cl...

We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O’Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119–128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Be...

BACKGROUND To identify a correlation between the submandibular fossa (SF) visibility and mandibular canal (MC) cortication on panoramic image and the depth of SF measured on CBCT and also correlation between the depth of SF and vertical and horizontal location of MC on CBCT. MATERIAL AND METHODS 500 CBCT scans and panoramic radiographs were evaluated. SF depth types were classified as type I ...

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the fr...

We consider direct visibility in simple orthogonal polygons and derive tight lower and upper bounds on the number of strictly internal and external visibility edges. We also show a lower bound of ⌈n2 ⌉ − 1 on the number of diffuse reflections required for completely illuminating an orthogonal polygon from an arbitrary point inside it. Further, we derive lower bounds on the combinatorial complex...

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We study polar visibility graphs, graphs whose vertices can be represented by arcs of concentric circles with adjacency determined by radial visibility including visibility through the origin. These graphs are more general than the well-studied bar-visibility graphs and are characterized here, when arcs are proper subsets of circles, as the graphs that embed on the plane with all but at most on...

A micro-pulse lidar at eye-safe wavelength is constructed based on an upconversion single-photon detector. The ultralow-noise detector enables using integration technique to improve the signal-to-noise ratio of the atmospheric backscattering even at daytime. With pulse energy of 110 μJ, pulse repetition rate of 15 kHz, optical antenna diameter of 100 mm and integration time of 5 min, a horizont...

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of t...