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The Linked Open Data (LOD) cloud diagram is a picture that helps us grasp the contents and the links of globally available data sets. Such diagram has been a powerful dissemination method for the Linked Data movement, allowing people to…
In this thesis, we introduce novel methods for analyzing pulsar populations using a variety of mathematical techniques. These tools-particularly graph theory-have been thoroughly validated in advanced mathematics, enabling us to overcome…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
Network architecture plays a key role in the deep learning-based computer vision system. The widely-used convolutional neural network and transformer treat the image as a grid or sequence structure, which is not flexible to capture…
Following DeMeyer, Ford & Miranda [DFM93], we define a topology on a fan by declaring open sets to be its subfans. Then, like Kato [Kat94], we make our fans into monoided spaces by associating a sheaf of monoids to each fan. (Our sheaf of…
There is a limitation in the size of an image that can be processed using computationally demanding methods such as e.g. Convolutional Neural Networks (CNNs). Some imaging modalities - notably biological and medical - can result in images…
In many social networks, several different link relations will exist between the same set of users. Additionally, attribute or textual information will be associated with those users, such as demographic details or user-generated content.…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Graph neural networks (GNNs) have received remarkable success in link prediction (GNNLP) tasks. Existing efforts first predefine the subgraph for the whole dataset and then apply GNNs to encode edge representations by leveraging the…
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
Recently, Graph Neural Network (GNN) has achieved remarkable progresses in various real-world tasks on graph data, consisting of node features and the adjacent information between different nodes. High-performance GNN models always depend…
The large domain discrepancy between faces captured in polarimetric (or conventional) thermal and visible domain makes cross-domain face recognition quite a challenging problem for both human-examiners and computer vision algorithms.…
Most existing graph visualization methods based on dimension reduction are limited to relatively small graphs due to performance issues. In this work, we propose a novel dimension reduction method for graph visualization, called…
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
We introduce geoplotlib, an open-source python toolbox for visualizing geographical data. geoplotlib supports the development of hardware-accelerated interactive visualizations in pure python, and provides implementations of dot maps,…
B$_0$-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B$_0$-VPG permutation graphs. We respond here by…
This paper introduces provGen, a generator aimed at producing large synthetic provenance graphs with predictable properties and of arbitrary size. Synthetic provenance graphs serve two main purposes. Firstly, they provide a variety of…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
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,…