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Cytoarchitectonic maps provide microstructural reference parcellations of the brain, describing its organization in terms of the spatial arrangement of neuronal cell bodies as measured from histological tissue sections. Recent work provided…
In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms,…
Unsupervised graph representation learning has emerged as a powerful tool to address real-world problems and achieves huge success in the graph learning domain. Graph contrastive learning is one of the unsupervised graph representation…
In this paper, we explore the topic of graph learning from the perspective of the Irregularity-Aware Graph Fourier Transform, with the goal of learning the graph signal space inner product to better model data. We propose a novel method to…
Graph representation learning has long been an important yet challenging task for various real-world applications. However, their downstream tasks are mainly performed in the settings of supervised or semi-supervised learning. Inspired by…
A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. It is proved that…
In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few…
Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area. However, for the nodes in graph, their ST patterns can vary greatly in difficulties for…
In this paper, we introduce a self-supervised learning method to enhance the graph-level representations with the help of a set of subgraphs. For this purpose, we propose a universal framework to generate subgraphs in an auto-regressive way…
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…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
The hippocampal formation is thought to learn spatial maps of environments, and in many models this learning process consists of forming a sensory association for each location in the environment. This is inefficient, akin to learning a…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult,…
Let $G$ be a planar $3$-graph (i.e., a planar graph with vertex degree at most three) with $n$ vertices. We present the first $O(n^2)$-time algorithm that computes a planar orthogonal drawing of $G$ with the minimum number of bends in the…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
We introduce and study a notion of co-radiantness for set-valued mappings between nonnegative orthants of Euclidean spaces. We analyze them from an abstract convexity perspective. Our main results consist in representations, in terms of…