Related papers: Cross-Laplacians Based Topological Signal Processi…

Topological deep learning has emerged as a powerful paradigm for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. While combinatorial complexes (CCs) offer a…

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…

Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…

Multi-cell cooperation (MCC) mitigates intercell interference and improves throughput at the cell edge. This paper considers a cooperative downlink, whereby cell-edge mobiles are served by multiple cooperative base stations. The cooperating…

We investigate the influence of topology on the magnetic response of inductively coupled superconducting flux-qubit networks. Using exact diagonalization methods and linear response theory, we compare the magnetic response of linear and…

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each…

Multilayer networks provide a more advanced and comprehensive framework for modeling real-world systems compared to traditional single-layer and multiplex networks. Unlike single-layer models, multilayer networks have multiple interacting…

Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges…

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…

We propose a novel computational framework leveraging hypergraph theory to analyse cancer stem cell markers (CSCMs) across multiple organs. Hypergraphs provide a robust representation of CSCM co-expression patterns, capturing their complex…

Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…

Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…

This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…

Artificial intelligence (AI) is reshaping computational and network biology by enabling new approaches to decode cellular communication networks. We introduce Hierarchical Molecular Language Models (HMLMs), a novel framework that models…

We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a…

Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in…

The design and engineering of molecular communication (MC) components capable of processing chemical concentration signals is the key to unleashing the potential of MC for interdisciplinary applications. By controlling the signaling pathway…

Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance…