Related papers: Frequent Knot Discovery
In this paper, we introduce a new type of relation between knots called the descendant relation. One knot $H$ is a descendant of another knot $K$ if $H$ can be obtained from a minimal crossing diagram of $K$ by some number of crossing…
Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…
This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.
The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to…
In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…
Data mining algorithms are now able to efficiently deal with huge amount of data. Various kinds of patterns may be discovered and may have some great impact on the general development of knowledge. In many domains, end users may want to…
Mining association rules is a popular and well researched method for discovering interesting relations between variables in large databases. A practical problem is that at medium to low support values often a large number of frequent…
We explore free knot diagrams, which are projections of knots into the plane which don't record over/under data at crossings. We consider the combinatorial question of which free knot diagrams give which knots and with what probability.…
Frequent Pattern Mining is a one field of the most significant topics in data mining. In recent years, many algorithms have been proposed for mining frequent itemsets. A new algorithm has been presented for mining frequent itemsets based on…
In this paper we introduce a new type of pattern -- a flipping correlation pattern. The flipping patterns are obtained from contrasting the correlations between items at different levels of abstraction. They represent surprising…
Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be…
In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We construct an infinite collection of knots with the property that any knot in this family has $n$-string essential tangle decompositions for arbitrarily high $n$.
In recent years, due to the wide applications of uncertain data, mining frequent itemsets over uncertain databases has attracted much attention. In uncertain databases, the support of an itemset is a random variable instead of a fixed…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
The problem of frequent pattern mining from non-temporal databases is studied extensively by various researchers working in areas of data mining, temporal databases and information retrieval. However, Conventional frequent pattern…
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
In general frequent itemsets are generated from large data sets by applying association rule mining algorithms like Apriori, Partition, Pincer-Search, Incremental, Border algorithm etc., which take too much computer time to compute all the…