Related papers: Cross-Laplacians Based Topological Signal Processi…
In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian…
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering…
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…
Future communication networks must address the scarce spectrum to accommodate extensive growth of heterogeneous wireless devices. Wireless signal recognition is becoming increasingly more significant for spectrum monitoring, spectrum…
This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1)…
Signal processing over single-layer graphs has become a mainstream tool owing to its power in revealing obscure underlying structures within data signals. However, many real-life datasets and systems, {including those in Internet of Things…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Recent breakthroughs in natural language processing show that attention mechanism in Transformer networks, trained via masked-token prediction, enables models to capture the semantic context of the tokens and internalize the grammar of…
Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
We study synchronization of $N$ oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…
Deep features have been proven powerful in building accurate dense semantic correspondences in various previous works. However, the multi-scale and pyramidal hierarchy of convolutional neural networks has not been well studied to learn…
High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…
The stack in various forms has been widely used as an architectural template for networking systems. Recently the stack has been subject to criticism for a lack of flexibility. However, when it comes right down to it nobody has offered a…
Both biological cortico-thalamic networks and artificial transformer networks use canonical computations to perform a wide range of cognitive tasks. In this work, we propose that the structure of cortico-thalamic circuits is well suited to…
The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…
We propose a novel deep layer cascade (LC) method to improve the accuracy and speed of semantic segmentation. Unlike the conventional model cascade (MC) that is composed of multiple independent models, LC treats a single deep model as a…