Related papers: An ergodic algorithm for generating knots with a p…
We present an application of a genetic algorithmic computational method to the optimization of the concurrence measure of entanglement for the cases of one dimensional chains, as well as square and triangular lattices in a simple…
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an $n$-vertex planar graph and two planar straight-line drawings of the graph…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
In this work, we propose a novel method to synthetically generate realistic 3D representations of wooden logs. Efficient sawmilling heavily relies on accurate measurement of logs and the distribution of knots inside them. Computed…
We study the formation of knots on a macroscopic ball-chain, which is shaken on a horizontal plate at 12 times the acceleration of gravity. We find that above a certain critical length, the knotting probability is independent of chain…
Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
We present computer simulations to examine probability distributions of gyration radius for the no-thickness closed polymers of N straight segments of equal length. We are particularly interested in the conditional distributions when the…
We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…
The design of deep neural networks remains somewhat of an art rather than precise science. By tentatively adopting ergodic theory considerations on top of viewing the network as the time evolution of a dynamical system, with each layer…
We introduce a new combinatorial method to encode knots and links with applications to knot invariants. Clasp diagrams defined in this paper are combinatorial blueprints for building knot diagrams out of full twists on two strings rather…
This article builds on Thurston's height functions. His tiling algorithm is reinterpreted using lattice theory and then generalized in order to generate any tiling of a hole-free region. Combined with a natural encoding of tilings by words,…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
For $N$ compatible substitution rules on $M$ prototiles $t_1,\dots,t_M$, consider tilings and tiling spaces constructed by applying the different substitution rules at random. These give (globally) random substitution tilings. In this paper…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…