Related papers: Developing Computer Programs for Knot Classificati…
Neural network approaches have been applied to computational morphology with great success, improving the performance of most tasks by a large margin and providing new perspectives for modeling. This paper starts with a brief introduction…
Malware classification is a difficult problem, to which machine learning methods have been applied for decades. Yet progress has often been slow, in part due to a number of unique difficulties with the task that occur through all stages of…
We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots. We determine the set of knot projections with the unknotting-type number at most two, and this result implies classical…
We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,\xi_std), we associate a corresponding multi-pointed nice…
The online programing services, such as Github,TopCoder, and EduCoder, have promoted a lot of social interactions among the service users. However, the existing social interactions is rather limited and inefficient due to the rapid…
We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many positive knots.
Empirical results in software engineering have long started to show that findings are unlikely to be applicable to all software systems, or any domain: results need to be evaluated in specified contexts, and limited to the type of systems…
We propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to…
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties…
As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations ap-pear in research papers, books, lecture notes, blog posts,…
Knot theory is the Mathematical study of knots. In this paper we have studied the Composition of two knots. Knot theory belongs to Mathematical field of Topology, where the topological concepts such as topological spaces, homeomorphisms,…
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The…
We present the complete classification of the subgroup of the classical knot concordance group generated by knots with eight or fewer crossings. Proofs are presented in summary. We also describe extensions of this work to the case of nine…
Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…
We examine computer experiments that can be performed to understand the dynamics of knots under self-repulsion. In the course of specific computer exploration we use the knot theory of rational knots and rational tangles to produce classes…
Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…
Real-world events exhibit a high degree of interdependence and connections, and hence data points generated also inherit the linkages. However, the majority of AI/ML techniques leave out the linkages among data points. The recent surge of…
We deal with the problem of semantic classification of challenging and highly-cluttered dataset. We present a novel, and yet a very simple classification technique by leveraging the ease of classifiability of any existing well separable…