DimStiller is a system for dimensionality reduction and analysis. It frames the task of understanding and transforming input dimensions as a series of analysis steps where users transform data tables by chaining together different techniques, called operators, into pipelines of expressions. The individual operators have controls and views that are linked together based on the structure of the expression. Users interact with the operator controls to tune parameter choices, with immediate visual feedback guiding the exploration of local neighborhoods of the space of possible data tables. DimStiller also provides global guidance for navigating data-table space through expression templates called workflows, which permit re-use of common patterns of analysis.

Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research on the topology of textiles and braid theory form a base for the current work and is briefly summarized. We define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search. Results of this new approach are presented and, by comparison to existing bobbin lace patterns, it is demonstrated that this model reveals new patterns that have never been seen before. Finally, we apply our new patterns to an original bookmark design and propose future areas for exploration.Keywords: Fibre Art; Bobbin Lace; 2-in 2-out Directed Graphs; Toroidal Graphs; Braid Theory; Exhaustive Enumeration 00A06; 00A66; 05B45; 05C63; 05C20 Bobbin lace is a fibre art form constructed by braiding together many threads. A very small set of actions is used in its production but the plethora of ways in which these actions can be combined results in the complex organization of threads into lace. Over the past 500 years, lacemakers have explored this rich domain relying primarily on trial and error. The goal of our research is to develop a mathematical model as a systematic way of examining the myriad of possibilities.In this paper we start with an overview of bobbin lace: what it is and how it is made. A simple, traditional pattern is provided for the reader who wishes to experiment with this art form. We then look at related work on the topology of textiles, its application to lace and key ideas that form a basis for our model. The main contribution of this paper is the definition of a model that uses braid theory and graph theory to describe workable patterns. An intelligent combinatorial search algorithm is used to enumerate and exhaustively generate patterns consistent with this model, and the results are discussed. Finally, we provide a second pattern for the reader to try. This original design makes use of new, algorithmically generated patterns which we believe have not been previously discovered.

In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to (1, 0), that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.Research supported by NSERC. Thank you to Anna Lubiw for helpful input.

Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors A ={→, , , ↑, ↓} with the restriction that vertical steps (↑, ↓) cannot be consecutive. The set A is the union of the well known Motzkin step vectors M ={→, , } with the vertical steps {↑, ↓}. An explicit bijection φ between the exhaustive set of vertically constrained *

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