相关论文: On phase in scaled graphs

In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase…

We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the…

Recent advent in graph signal processing (GSP) has led to the development of new graph-based transforms and wavelets for image / video coding, where the underlying graph describes inter-pixel correlations. In this paper, we develop a new…

A signed graph $\Sigma = (G, \sigma)$ is a graph where the function $\sigma$ assigns either $1$ or $-1$ to each edge of the simple graph $G$. The adjacency matrix of $\Sigma$, denoted by $A(\Sigma)$, is defined canonically. In a recent…

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…

Let $\mathbb{S}_g$ be the orientable surface of genus $g$. We prove that the component structure of a graph chosen uniformly at random from the class $\mathcal{S}_g(n,m)$ of all graphs on vertex set $[n]=\{1,\dotsc,n\}$ with $m$ edges…

In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

Signed Graph Neural Networks (SGNNs) are effective in learning expressive representations for signed graphs but typically require substantial task-specific labels, limiting their applicability in label-scarce industrial scenarios. In…

Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…

Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a…

In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…

A signed graph is a graph whose edges are labeled positive or negative. The sign of a cycle is the product of the signs of its edges. Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different signed Petersen…

In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables…

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle…

We propose a new framework for the recognition of online handwritten graphics. Three main features of the framework are its ability to treat symbol and structural level information in an integrated way, its flexibility with respect to…

Graph Neural Networks (GNNs) have received increasing attention in many fields. However, due to the lack of prior graphs, their use for semantic labeling has been limited. Here, we propose a novel architecture called the Self-Constructing…

Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…

A biased graph consists of a graph $G$ together with a collection of distinguished cycles of $G$, called balanced cycles, with the property that no theta subgraph contains exactly two balanced cycles. Perhaps the most natural biased graphs…

Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the…