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Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided., Under review. 17 pages, 5 figures

In this paper, we propose a novel algorithm for energy-efficient, low-latency, accurate inference at the wireless edge, in the context of 6G networks endowed with reconfigurable intelligent surfaces (RISs). We consider a scenario where new data are continuously generated/collected by a set of devices and are handled through a dynamic queueing system. Building on the marriage between Lyapunov stochastic optimization and deep reinforcement learning (DRL), we devise a dynamic learning algorithm that jointly optimizes the data compression scheme, the allocation of radio resources (i.e., power, transmission precoding), the computation resources (i.e., CPU cycles), and the RIS reflectivity parameters (i.e., phase shifts), with the aim of performing energy-efficient edge classification with end-to-end (E2E) delay and inference accuracy constraints. The proposed strategy enables dynamic control of the system and of the wireless propagation environment, performing a low-complexity optimization on a per-slot basis while dealing with time-varying radio channels and task arrivals, whose statistics are unknown. Numerical results assess the performance of the proposed RIS-empowered edge inference strategy in terms of trade-off between energy, delay, and accuracy of a classification task.

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere.

Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relationships among nodes and then they are not able to fully exploit higher-order interactions present in many real world data-sets. In this paper, we introduce Cell Attention Networks (CANs), a neural architecture operating on data defined over the vertices of a graph, representing the graph as the 1-skeleton of a cell complex introduced to capture higher order interactions. In particular, we exploit the lower and upper neighborhoods, as encoded in the cell complex, to design two independent masked self-attention mechanisms, thus generalizing the conventional graph attention strategy. The approach used in CANs is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns {\it edge features} from {\it node features}; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set of features. The experimental results show that CAN is a low complexity strategy that compares favorably with state of the art results on graph-based learning tasks., Preprint, under review

The inference of causal structures from observed data plays a key role in unveiling the underlying dynamics of the system. This paper exposes a novel method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the structure of linear causal relationships occurring at different time scales. Differently from existing approaches, MS-CASTLE takes explicitly into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on stationary wavelet transform and non-convex optimization. MS-CASTLE incorporates, as a special case, a single-scale version named SS-CASTLE, which compares favorably in terms of computational efficiency, performance and robustness with respect to the state of the art onto synthetic data. We used MS-CASTLE to study the multiscale causal structure of the risk of 15 global equity markets, during covid-19 pandemic, illustrating how MS-CASTLE can extract meaningful information thanks to its multiscale analysis, outperforming SS-CASTLE. We found that the most persistent and strongest interactions occur at mid-term time resolutions. Moreover, we identified the stock markets that drive the risk during the considered period: Brazil, Canada and Italy. The proposed approach can be exploited by financial investors who, depending to their investment horizon, can manage the risk within equity portfolios from a causal perspective.

The design of 6th Generation (6G) wireless networks points towards flexible connect-and-compute technologies capable to support innovative services and use cases. Targeting the 2030 horizon, 6G networks are poised to pave the way for sustainable human-centered smart societies and vertical industries, such that wireless networks will be transformed into a distributed smart connectivity infrastructure, where new terminal types are embedded in the daily environment. In this context, the RISE-6G project aims at investigating innovative solutions that capitalize on the latest advances in the emerging technology of Reconfigurable Intelligent Surfaces (RISs), which offers dynamic and goal-oriented radio wave propagation control, enabling the concept of the wireless environment as a service. The project will focus on: i) the realistic modeling of RIS-assisted signal propagation, ii) the investigation of the fundamental limits of RIS-empowered wireless communications and sensing, and iii) the design of efficient algorithms for orchestrating networking RISs, in order to implement intelligent, sustainable, and dynamically programmable wireless environments enabling diverse services that go well beyond the SG capabilities. RISE-6G will offer two unprecedented proof-of-concepts for realizing controlled wireless environments in near-future use cases.

This work merges tools from graph signal processing and linear systems theory to propose sampling strategies for observing the initial state of a process evolving over a graph. The proposed method is ratified by a mathematical analysis that provides insights on the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, conditions when the graph process is observable from a few samples and (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed. Finally, numerical tests are conducted to illustrate the benefits of the proposed approach.

This deliverable defines general framework for consequent technical workpackages in TROPIC. First, scenarios from the business point of view are defined and further transformed to more technical representation. Then, abstraction models are introduced for both communication and computation parts of femto-cloud concept. Furthermore, requirements need to be met to ensure efficient and feasible utilization of the femto-cloud are presented. To enable prove of the femto-cloud concept and to compare the developed techniques and algorithms a set of performance indicators to be considered in all technical workpackages are listed and defined. To that end, the models and simulation settings are defied in the last section of the document

The aim of this paper is to propose a computation offloading strategy for mobile edge computing. We exploit the concept of call graph, which models a generic computer program as a set of procedures related to each other through a weighted directed graph. Our goal is to derive the optimal partition of the call graph establishing which procedures are to be executed locally or remotely. The main novelty of our work is that the optimal partition is obtained jointly with the selection of radio parameters, e.g., transmit power and constellation size, in order to minimize the energy consumption at the mobile handset, under a latency constraint taking into account transmit time and execution time. We consider both single and multi-channel transmission strategies and we prove that a globally optimal solution can be achieved in both cases. Finally, we propose a suboptimal strategy aimed at solving a relaxed version of the original problem in order to tradeoff complexity and performance of the proposed framework. Finally, several numerical results illustrate under what conditions in terms of call graph topology, communication strategy, and computation parameters, the proposed offloading strategy provides large performance gains., Submitted to IEEE Transactions on Signal Processing

There is strong trend, in current research on communication and sensor networks, to study selforganizing, self-healing systems. This poses great challenges to the research on decentralized systems, but at the same offers great potentials for future developments, especially in view of the current trend towards miniaturized systems. Even if the development of self-organizing systems is probably at the beginning, biological systems offers many examples of self-organization and selfhealing. This is as testified, for example, by swarming behaviors, brain activity, and so on. It is then of great interest to derive mathematical models of biological systems and see how they can suggest novel design tools for engineers. Signal Processing can play a big role in this cross-fertilization, as it can help to find out manageable mathematical problems, study their behavior and test the performance in the presence of disturbances. The challenge is to establish a cross-fertilization of ideas from biological to artificial systems, as well as to help understanding biological systems as such. This dissertation considers the problem of dynamic radio access based on sensing in cognitive radio networks. In particular, we follow a rather alternative path with respect to more conventional approaches and, inspired by biological models, we formulate the search for radio resources, i.e. time and frequency slots, as the search for food by a flock of birds swarming in a cooperative manner, but without any centralized control. The interference distribution in the time-frequency plane takes the role of the food spatial distribution: The birds (radio nodes) fly (allocate their resources) over the regions (time-frequency domain) where there is more food (less interference). During the flight, the birds move (choose their time-frequency slots) in a coordinated way, even in the absence of any central control, in order to avoid collisions (conflicts over common radio resources), yet maintaining the swarm cohesion (i.e., avoiding unnecessary spread in the occupancy of the time-frequency plane). This procedure is applied to the dynamic resource allocation in the frequency domain and in the time-frequency domain, where the primary users in a cognitive radio system are modeled as statistically independent homogeneous continuous-time Markov processes. A rigorous mathematical analysis of the proposed algorithm is also derived. First, we study the stability and the cohesiveness of the swarm in case of local interactions among the nodes, providing closed form expressions for the upper and lower bounds of the swarm size as a function of the network connectivity. Then, using stochastic approximation arguments, we derive the convergence properties of the swarming algorithm in the presence of random disturbances introduced by realistic channels, i.e., link failures, quantization, noise and estimation errors. Spectrum sensing is a critical prerequisite in envisioned applications of wireless cognitive radio networks which promise to resolve the perceived bandwidth scarcity versus under-utilization dilemma. Creating an interference map of the operational region plays an instrumental role in enabling spatial frequency reuse and allowing for dynamic spectrum allocation in a hierarchical access model comprising primary and secondary users. For such purpose, a distributed technique for cooperative spectrum estimation in cognitive radio systems is proposed based on a basis expansion model of the power spectral density map in frequency. The proposed method, based on diffusion adaptation algorithms, estimates and learns the interference profile through local cooperation and without the need for a central processor. Convergence and mean square analysis of the diffusion filter applied to the distributed cooperative sensing problem is also derived. Finally, it is proposed a dynamic resource allocation technique combining a distributed diffusion algorithm, for implementing cooperative sensing, with a swarming technique, for allocating resources in a parsimonious way (i.e., avoiding unnecessary spread in the frequency domain), yet avoiding collisions. In particular, the procedure is applied to the dynamic resource allocation problem in the frequency domain. Numerical results show the improvement that results in the resource allocation performance due to the cooperative estimation of the spectrum. Furthermore, it is shown how the proposed technique endows the resulting bio-inspired network with powerful learning and adaptation capabilities.

This document looks into coordinated radio resource allocation algorithms in deployments of huge number of femto-access points (FAP) by exploiting the message exchange at control-plane level through the wired ISP backhaul link. The algorithms present in this document are based on decentralized cooperative strategies supported by Game Theory. Decentralized resource allocation algorithms based on price exchange have been derived under different criteria: guaranteeing a minimum rate with the minimum power, maximizing the weighted sum-rate of the system, maximizing the opportunistic throughput when there are different source of randomness like random link failures and noise quantization or when the activity of macro-users is not known by FAPs (coordinated channel sensing or modelling the activity). Additionally, a genetic-based resource allocation is investigated, providing centralized and decentralized algorithms, to which the Game Theory solutions are challenged. In all cases, the techniques derived require modifications of the current LTE-A standard which are identified. Finally, some of those algorithms have been evaluated in a Realistic corporate scenario elucidating the advantages of coordinated resource allocation techniques proposed.

A series of poly(aryleneethynylene)s functionalized with acetylated glucopyranosyl units were synthesized by the Pd-catalyzed reaction of trimethylsilylethynyl derivatives with aromatic halides in the presence of silver oxide.