Related papers: Encoding and Topological Computation on Textiles
A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
Knitted and woven textile structures are examples of doubly periodic structures in a thickened plane made out of intertwining strands of yarn. Factoring out the group of translation symmetries of such a structure gives rise to a link…
Identification of textile properties is an important milestone toward advanced robotic manipulation tasks that consider interaction with clothing items such as assisted dressing, laundry folding, automated sewing, textile recycling and…
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.
A complete approach for the determination of the complex constitutive behaviour of textile composites through finite element simulation is presented in this paper. In this work, simulations of different loading cases are carried out on…
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
A weave is a type of textile that consists of vertical and horizontal threads, and typically it has a periodic structure. In this paper, we regard a weave as a link in the thickened torus with a diagram consisting of closed geodesics. As…
A periodic weave is the lift of a particular link embedded in a thickened surface to the universal cover. Its components are infinite unknotted simple open curves that can be partitioned in at least two distinct sets of threads. The…
The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
For their resilience and toughness, filamentous entanglements are ubiquitous in both natural and engineered systems across length scales, from polymer-chain- to collagen-networks and from cable-net structures to forest canopies. Textiles…
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the…
Knots, links and entangled filaments appear in many physical systems of interest in biology and engineering. Classifying knots and measuring entanglement is of interest both for advancing knot theory, as well as for analyzing large data…
A potential advantage of quantum machine learning stems from the ability of encoding classical data into high dimensional complex Hilbert space using quantum circuits. Recent studies exhibit that not all encoding methods are the same when…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
Knitted fabrics exemplify a broad class of architected materials capable of large deformations, enabling shape morphing, mechanical biocompatibility, and embedded multifunctionality without material damage. Although geometric nonlinearity…
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code.…