Related papers: Visualising Quantum Product Codes
Engineering a product-line is more than just describing a product-line: to be correct, every variant that can be generated must satisfy some constraints. To ensure that all such variants will be correct (e.g. well-typed) there are only two…
In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…
We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the $(m+1)$-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We…
Researchers in the humanities are among the many who are now exploring the world of big data. They have begun to use programming languages like Python or R and their corresponding libraries to manipulate large data sets and discover brand…
Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order…
Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum…
The generalized $k$-edge-connectivity $\lambda_k(G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$, denoted by $G\circ H$, is an important graph product. In this…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
Image/video data is usually represented with multiple visual features. Fusion of multi-source information for establishing the attributes has been widely recognized. Multi-feature visual recognition has recently received much attention in…
We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our…
Visualizing time series in a dense spatial context such as a geographical map is a challenging task, which requires careful balance between the amount of depicted data and perceptual precision. Horizon graphs are a well-known technique for…
To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution…
Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data…
We introduce the 2-sorted counting logic $GC^k$ that expresses properties of hypergraphs. This logic has available k variables to address hyperedges, an unbounded number of variables to address vertices, and atomic formulas E(e,v) to…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
Vector-Quantized Generative Models (VQGMs) have emerged as powerful tools for image generation. However, the key component of VQGMs -- the codebook of discrete tokens -- is still not well understood, e.g., which tokens are critical to…
Classical Hamming graphs are Cartesian products of complete graphs, and two vertices are adjacent if they differ in exactly one coordinate. Motivated by connections to unitary Cayley graphs, we consider a generalization where two vertices…
We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of $K_n\times G$ is found, provided that $G$…
This paper investigates the theoretical analysis of intrinsic message passing decoding for generalized product codes (GPCs) with irregular degree distributions, a generalization of product codes that allows every code bit to be protected by…
Understanding and navigating large-scale codebases remains a significant challenge in software engineering. Existing methods often treat code as flat text or focus primarily on local structural relationships, limiting their ability to…