On strongly normal tesselations

Permutation Groups and Chord Tesselations

Analytical approaches to musical analysis have generally attempted to provide some kind of justification, and, in the last decades, to develop analytical elements based on tesselations of pitch class sets. When applied to atonal music, analytical approaches frequently fail to find internal coherence. Most of the time, tilings of chords are based on a torus representation, which follows the trad...

On spectral radius of strongly connected digraphs

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

Hyperbolic Tesselations and Image Processing I

Self-Organizing Maps on non-euclidean Spaces

We propose a new type of Self-Organizing Map (SOM) that is based on discretizations of curved, non-euclidean spaces. As an introductory example, we brieey discuss \spherical SOMs" on tesselations of the sphere for the display of directional data. We then describe the construction of \hyperbolic SOMs", using regular tesselations of the hyperbolic plane, which is a non-euclidean space characteriz...

Hyperbolic Structures of Arithmetic Type on Some Link Complements

-d) u {00} c= CP = dH, and each a ePSL2(0d) determines an edge which is the geodesic in H having endpoints a//? and y/d. The tesselations 5^ and ^ are by regular ideal octahedra and tetrahedra, respectively, and are classical objects; for example, &\ is constructed in [2]. The tesselations «^, by ideal cuboctahedra, and ST-i, by ideal triangular prisms, are implicit in Chapter 6 of [9]; ^ is a ...