# Khalegh Mamakani's research while affiliated with University of Victoria and other places

## Publications (6)

Article
A symmetric n-Venn diagram is one that is invariant under n-fold rotation, up to a relabeling of curves. A simple n-Venn diagram is an n-Venn diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer se...
Article
In this paper we are concerned with producing exhaustive lists of simple monotone Venn diagrams that have some symmetry (non-trivial isometry) when drawn on the sphere. A diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. We show that there are 23...
Conference Paper
A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscu...
Article
We show that any permutation of \${1,2,...,N}\$ can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place in parallel in time O(1). In the case where the permutation is the \$k\$-way perfect shuffle we develop two methods for efficiently computing such a pair of involutions...
Conference Paper
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A Venn diagram is convexly-drawable if it can be drawn with all curves convex and it is simple if at most two curves intersect at any point. A Venn diagra...
Conference Paper
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2 n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A k-region in a diagram is a region that is in the interior of precisely k curves. A n-Venn diagram is symmetric if it has a point of rotation about whic...

## Citations

... This influences the insertion strategy so that CO sequences are preferred that have fewer children while still maximizing monotone faces. It is still an open problem to find simple symmetric Venn diagrams for any prime number of sets, and the largest to be produced is a 13-Venn diagram [27]. ...
... However, for a larger number of sets, the result becomes hard to understand as the area of new zones becomes smaller and smaller. Other methods focus on the creation of simple, convex Venn diagrams, e.g., Mamakani et al. [26], which are aesthetically more pleasing. Ruskey et al. [38] use a general Venn construction method to analyze methods that create symmetric Venn diagrams. ...
... In order to provide users a function of viewing the shared clusters between species, we developed a tool named ClusterVenn to visualize this cluster file in OrthoVenn1. This early version was limited to analysis of orthologous clusters for a maximum of six species due to known visualization constraints of Venn diagrams with more than six categories (32). In this update, we used the occurrence table to display the occurrence of cluster groups between species, allowing users to upload and compare clusters without limitations of species number. ...
... In digital signal processing, the method of bit-reversal permutations of the binary numbering of columns and rows in square matrices, which sometimes is termed bit-reversal holography, plays an important role; the method is connected, in particularly, noise-immunity coding and algorithms of fast Fourier transform [Gold and Rader, 1969;Karp, 1996;Lyons, 2010;Shiman, Patsey, 2013;Shishmintsev, 2012;Yang at al., 2013]. In the case of two-dimensional fast Fourier transform -for example, in image processing -algorithms with interleaving in frequency are considered optimal [Lyons, 2010]. ...
... An Euler diagram should only include relations that are present in the data and avoid introducing superfluous areas. Further, the diagram should be monotone [8]. We call Euler diagrams that adhere to these properties semantics-preserving, following the definition of semantics in the domain of linguistics. ...
... The values of R 2 and p in the Permanova signify data variations explained by grouping and the statistical significance level of the difference among groups, respectively. Venn diagrams were drawn in the R package "venn" [49] to visualize the fungi shared by different root age groups. ...