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Reconstructing complex curvilinear structures such as neural circuits, road networks, and blood vessels is a key challenge in many scientific and engineering fields. It has a broad range of applications, from the delineation of micrometer-sized neurons in ...
Various practical applications of the average (A) and difference (D) of Friedel opposites are described. Techniques based on the resonant-scattering contribution to Friedel differences are applied to see whether a crystal is centrosymmetric or not, and to ...
Non-adaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most d d ...
We consider graphs that admit polyline drawings where all crossings occur at the same angle alpha is an element of (0, pi/2]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This r ...
In conventional group testing, the goal is to detect a small subset of defecting items D in a large population N by grouping \textit{arbitrary} subset of N into different pools. The result of each group test $\mathcal{T} ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conj ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
We study some variants of Conway’s thrackle conjecture. A tangle is a graph drawn in the plane such that its edges are represented by continuous arcs, and any two edges share precisely one point, which is either a common endpoint or an interior point at wh ...
Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...
Given a collection C of curves in the plane, its string graph is defined as the graph with vertex set C, in which two curves in C are adjacent if and only if they intersect. Given a partially ordered set (P,
