Abstract We construct a simplicial complex, the rectangle complex of relation R , and show that it is homotopy equivalent to Dowker $$R$$ R . This results in short conceptual proof functorial versions Dowker’s Theorem used topological data analysis.

1. Six octopuses were trained on a series of visual discrimination tasks where the discriminanda were presented simultaneously, and where different tasks alternated in a single training session. 2. All the octopuses could make discriminations based on brightness and orientation over the same period of time. 3. Over a period in which all octopuses discriminated a black from a white vertical rect...

We study complete minimal graphs in IH × IR, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon Γ in IH. We give necessary and sufficient conditions on the ”lenghts” of the sides of the polygon (and all inscribed polygons in Γ) that ensure the existence of such a graph. We then apply this to construct entire minimal graphs in IH× IR ...

Given a set of rectangles with fixed orientations, we want to find an enclosing rectangle of minimum area that contains them all with no overlap. Many simple scheduling tasks can be modelled by this NP-complete problem. We use an anytime branch-and-bound algorithm to solve the problem optimally. Our main contributions are a lower-bound on the amount of wasted space in a partial solution, based ...

A latin rectangle is an m × n array, m ≤ n, from the numbers 1, 2, . . . , n such that each of these numbers occur in each row and in each column at most once. A critical set in an m×n array is a set S of given entries, such that there exists a unique extension of S to a latin rectangle of size m×n. If we index the rows and columns of an m×n array, m ≤ n, by the sets M = {1, 2, . . . ,m} and N ...

the inscribed monument belonged to ancient times can be regarded us a documents to study the thoughts ,ideas ,cultural and communication arts of ancient civilizations ziwiye, hasanlu, qaychi and rabat2 areas belong to iron age and mannea era, in wich many inscribed monuments have been obtained. the discovery of many inscribed monuments show the importance of these art works, stencils and were u...

In the weighted rectangle stabbing problem we are given a grid in ]R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is...

This paper proposes a new algorithm to extract the rectangle in images. It’s goal is to meet the requirement of the truck’s compartment positioning and assure that some work are done inside the truck’s compartment. Firstly, the Canny operator is used to calculate the edge of the image, because it is sensitive to the image texture features. Secondly, the Canny edge is transformed with the Hough ...