Related papers: Generalized signals on simplicial complexes
Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach…
Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…
In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a…
Despite the success of sequence-to-sequence (seq2seq) models in semantic parsing, recent work has shown that they fail in compositional generalization, i.e., the ability to generalize to new structures built of components observed during…
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph…
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…
We develop unbiased strategies to probabilistic T-wave snowball sampling from graphs, where the interest of estimation may concern finite-order subgraphs such as triangles, cycles or stars. Our approaches encompass also the…
We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and…
Graph signal processing (GSP) studies graph-structured data, where the central concept is the vector space of graph signals. To study a vector space, we have many useful tools up our sleeves. However, uncertainty is omnipresent in practice,…
Following the recent progress in Terahertz (THz) signal generation and radiation methods, joint THz communications and sensing applications are shaping the future of wireless systems. Towards this end, THz spectroscopy is expected to be…
In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor…
Graph signal processing (GSP) deals with the representation, analysis, and processing of structured data, i.e. graph signals that are defined on the vertex set of a generic graph. A crucial prerequisite for applying various GSP and graph…
We are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in these two directions that can be viewed as improvements on…
We describe a procedure for constructing a model of a smooth data spectrum using Gaussian processes rather than the historical parametric description. This approach considers a fuller space of possible functions, is robust at increasing…
We generalize triadic closure, along with previous generalizations of triadic closure, under an intuitive umbrella generalization: the Subgraph-to-Subgraph Transition (SST). We present algorithms and code to model graph evolution in terms…
This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…