Related papers: Frequent Knot Discovery
A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity,…
Motifs are the fundamental components of complex systems. The topological structure of networks representing complex systems and the frequency and distribution of motifs in these networks are intertwined. The complexities associated with…
In this work, we explore Landin's Knot, which is understood as a pattern for encoding general recursion, including non-termination, that is possible after adding higher-order references to an otherwise terminating language. We observe that…
The exponential explosion of the set of patterns is one of the main challenges in pattern mining. This challenge is approached by introducing a constraint for pattern selection. One of the first constraints proposed in pattern mining is…
The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the…
We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…
Knowledge tracing---where a machine models the knowledge of a student as they interact with coursework---is a well established problem in computer supported education. Though effectively modeling student knowledge would have high…
The mining of graphs in terms of their local substructure is a well-established methodology to analyze networks. It was hypothesized that motifs - subgraph patterns which appear significantly more often than expected at random - play a key…
In this paper we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot's embedding for growing…
Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular…
Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the $k$-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as…
In this paper we constructed new model of plastic deformation. The knot theory was used to classify the plastic state.
Using the knowledge discovery framework, it is possible to explore object databases and extract groups of objects with highly heterogeneous movement behavior by efficiently integrating a priori knowledge through interacting with the…
In this paper, we are revisiting pattern mining and especially itemset mining, which allows one to analyze binary datasets in searching for interesting and meaningful association rules and respective itemsets in an unsupervised way. While a…
To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving…
Process mining has emerged as a way to analyze the behavior of an organization by extracting knowledge from event logs and by offering techniques to discover, monitor and enhance real processes. In the discovery of process models,…
Frequent itemset mining is an essential part of data analysis and data mining. Recent works propose interesting SAT-based encodings for the problem of discovering frequent itemsets. Our aim in this work is to define strategies for adapting…
In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our…
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
Discovering the set of closed frequent patterns is one of the fundamental problems in Data Mining. Recent Constraint Programming (CP) approaches for declarative itemset mining have proven their usefulness and flexibility. But the wide use…