Multidimensional Farey partitions

Interpretation and Comparison of Multidimensional Data Partitions

In this paper, a novel visualization method for partitions of multidimensional data is presented. It can be used for characterization of one or comparison of two partitions. The method nds the variables that best describe a partition or di erence between partitions. It is especially useful when the data set size is large and there are many variables, i.e., the data dimension is high. The method...

A Multidimensional Data Structure for Maintaining XML Data Partitions

To achieve good performance of processing queries on huge XML data in cluster machines, data partitioning and placement strategy is one of the key factors. In this paper we propose a multidimensional data structure for maintaining XML data partitions, specifically for holistic twig join processing. Initially, we construct the multidimensional data structure from statistical information on vario...

Farey Curves

^nr", Hn , INTRODUCTION 4. Observations and Questions References Consider the family of quadratic polynomials PA : C —> C, where A is a complex number with |A| < 1, defined by Px(z) = Xz + z. We will examine this polynomial from a dynamical point of view; that is, we will be interested in its behaviour under iteration. The first observation is that the polynomial Px has a fixed point at zero: P...

Products of Farey Fractions

A Farey Fraction Spin Chain

We introduce a new number–theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation–invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and exhibits a unique phase transition at inverse temperature β = 2. The free energy i...