Related papers: Frequent Knot Discovery
Object-oriented database systems proved very valuable at handling and administrating complex objects. In the following guidelines for embedding neural networks into such systems are presented. It is our goal to treat networks as normal data…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Now a days, data mining and knowledge discovery methods are applied to a variety of enterprise and engineering disciplines to uncover interesting patterns from databases. The study of Sequential patterns is an important data mining problem…
Anomaly detection is a fundamental problem in data mining field with many real-world applications. A vast majority of existing anomaly detection methods predominately focused on data collected from a single source. In real-world…
Finding an optimal set of critical nodes in a complex network has been a long-standing problem in the fields of both artificial intelligence and operations research. Potential applications include epidemic control, network security, carbon…
It is a major unsolved problem as to whether unknot recognition - that is, testing whether a given closed loop in R^3 can be untangled to form a plain circle - has a polynomial time algorithm. In practice, trivial knots (which can be…
Data mining is a new concept & an exploration and analysis of large data sets, in order to discover meaningful patterns and rules. Many organizations are now using the data mining techniques to find out meaningful patterns from the…
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…
A powerful way to study groups is via their actions on suitable spaces. Classifying spaces for families of subgroups are a type of these spaces, obtained by imposing some strict conditions on the fixed-point sets. We show how in the…
High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…
It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended…
Although most knots are nonalternating, modern research in knot theory seems to focus on alternating knots. We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones…
Relationship-aware sequential pattern mining is the problem of mining frequent patterns in sequences in which the events of a sequence are mutually related by one or more concepts from some respective hierarchical taxonomies, based on the…
The exponential growth of data in current times and the demand to gain information and knowledge from the data present new challenges for database researchers. Known database systems and algorithms are no longer capable of effectively…
Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent developments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
This paper presents and analysis the common existing sequential pattern mining algorithms. It presents a classifying study of sequential pattern-mining algorithms into five extensive classes. First, on the basis of Apriori-based algorithm,…
The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.