Related papers: Rendering string diagrams recursively
Program text is rendered using impoverished typographic styles. Beyond choice of fonts and syntax-highlighting colors, code editors and related tools utilize very few text decorations. These limited styles are, furthermore, applied in…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
NodeTrix representations are a popular way to visualize clustered graphs; they represent clusters as adjacency matrices and inter-cluster edges as curves connecting the matrix boundaries. We study the complexity of constructing NodeTrix…
A string graph is the intersection graph of curves in the plane. We prove that there exists an absolute constant $c>0$ such that if $G$ is a string graph on $n$ vertices, then $G$ contains either a clique or an independent set of size at…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
This paper considers 1-string representations of planar graphs that are order-preserving in the sense that the order of crossings along the curve representing vertex $v$ is the same as the order of edges in the clockwise order around $v$ in…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be considered as a specific type of four-regular periodic planar…
Comparing relational languages by their logical expressiveness is well understood. Less well understood is how to compare relational languages by their ability to represent relational query patterns. Indeed, what are query patterns other…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…
An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
As a crucial step in extractive document summarization, learning cross-sentence relations has been explored by a plethora of approaches. An intuitive way is to put them in the graph-based neural network, which has a more complex structure…