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Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapes

Krzysztof Gdawiec, Diana Domańska (2011)

International Journal of Applied Mathematics and Computer Science

One of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using partitioned iterated function systems with division. Moreover, we introduce a new fractal recognition method based on a dependence graph obtained from...

Paths through fixed vertices in edge-colored graphs

W. S. Chou, Y. Manoussakis, O. Megalakaki, M. Spyratos, Zs. Tuza (1994)

Mathématiques et Sciences Humaines

We study the problem of finding an alternating path having given endpoints and passing through a given set of vertices in edge-colored graphs (a path is alternating if any two consecutive edges are in different colors). In particular, we show that this problem in NP-complete for 2-edge-colored graphs. Then we give a polynomial characterization when we restrict ourselves to 2-edge-colored complete graphs. We also investigate on (s,t)-paths through fixed vertices, i.e. paths of length s+t such that...

Pattern avoidance in partial words over a ternary alphabet

Adam Gągol (2015)

Annales UMCS, Mathematica

Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with m distinct variables and of length at least 2m is avoidable over a ternary alphabet and if the length is at least 3 2m−1 it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words - sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words

PDF Enhancements Tools for a Digital Library

Hatlapatka, Radim, Sojka, Petr (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

This paper describes several innovative PDF document enhancements and tools that can be used when building a digital library. The main result presented in this paper is the PDF re-compression tool, developed using the jbig2enc encoder called pdfJbIm. This re-compression tool enables the size of the original bitonal PDFs to be, on average, downsized by one third. Some modifications to the jbig2enc encoder that increase the compression ratio even further are also described here. Together with another...

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