Related papers: Developing Computer Programs for Knot Classificati…

We give a brief survey of some known results on intrinsically linked or knotted graphs.

In the Dimension Embedded in Unified Symmetry (Adrian Sabin Popescu, D.E.U.S. (Dimension Embedded in Unified Symmetry), p. 221-247, Ed. Cartea Universitara, Bucuresti, ISBN 978-973-731-519-9 (arXiv:0704.2670) (2007)) book we made a…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…

The contents of this 6-page paper have been subsumed into the 13-page paper, "A note on closed 3-braids", arXiv:0802.1072 [math.GT]. This paper is correct, but contains less information than the new one. The topological classification of…

This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.

Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering.…

In this paper we explore a new method of analysis of associative algebras.

We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associated element of the pure braid group in terms of the…

We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.

In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification…

The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…

We compose the table of knots in the thickened torus T x I having diagrams with at most 4 crossings. The knots are constructed by the three-step process. First we list regular graphs of degree 4 with at most 4 vertices, then for each graph…

In this paper we give a solution to Zariski's problem of analytic classification of plane branches.

We give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid.