相关论文: Developing a Mathematical Model for Bobbin Lace
We formalize Italian smocking, an intricate embroidery technique that gathers flat fabric into pleats along meandering lines of stitches, resulting in pleats that fold and gather where the stitching veers. In contrast to English smocking,…
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…
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…
This paper aims to develop a mathematical foundation to model knitting with graphs. We provide a precise definition for knit objects with a knot theoretic component and propose a simple undirected graph, a simple directed graph, and a…
We develop an optimization-based method to model smocking, a surface embroidery technique that provides decorative geometric texturing while maintaining stretch properties of the fabric. During smocking, multiple pairs of points on the…
A barcode is a finite multiset of intervals on the real line. Jaramillo-Rodriguez (2023) previously defined a map from the space of barcodes with a fixed number of bars to a set of multipermutations, which presented new combinatorial…
Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\mathfrak{A}=$$\{\rightarrow,$ $\nearrow,$ $\searrow,$ $\uparrow,$ $\downarrow\}$ with the restriction that…
In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates…
In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on,…
We describe a general algorithm for generating various families of ribbon tableaux and computing their spin polynomials. This algorithm is derived from a new matricial coding. An advantage of this new notation lies in the fact that it…
While textiles have existed throughout much of human history as complex mechanical metamaterials, textile science has largely been overlooked by the physics community until recently. In this review, we consider the symmetry, topology, and…
From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide…
Concept lattice drawings are an important tool to visualize complex relations in data in a simple manner to human readers. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although those methods are…
In the last few years, the amount of collected data, in various computer science applications, has grown considerably. These large volumes of data need to be analyzed in order to extract useful hidden knowledge. This work focuses on…
This work proves that the process of gluing finite lattices to form a larger lattice is bijective, that is each lattice is the glued sum of a unique system of finite lattices, provided the class of lattices is constrained to modular,…
A knotted ribbon is one of physical aspect of a knot. A folded ribbon knot is a depiction of a knot obtained by folding a long and thin rectangular strip to become flat. The ribbonlength of a knot type can be defined as the minimum length…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
This paper describes some biologically-inspired processes that could be used to build the sort of networks that we associate with the human brain. New to this paper, a 'refined' neuron will be proposed. This is a group of neurons that by…
The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…