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We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In particular: we extend the modal characterizations of a finite number of well known conditions on normative and permission systems, as well as on subordination, precontact, and dual precontact algebras developed in \cite{de2024obligations}, to those corresponding to the infinite class of {\em clopen-analytic inequalities} in a modal language consisting both of positive and of negative unary modal operators; we characterize the syntactic shape of first-order conditions on algebras endowed with subordination, precontact, and dual precontact relations which guarantees these conditions to be the first-order correspondents of axioms in the modal language above; we introduce algorithms for computing the first-order correspondents of modal axioms on algebras endowed with subordination, precontact, and dual precontact relations, and conversely, for computing the modal axioms of which the conditions satisfying the suitable syntactic shape are the first-order correspondents; finally, we extend Celani's dual characterization results between subordination lattices and subordination spaces to a wider environment which also encompasses precontact and dual precontact relations, and relative to an infinite class of first order conditions relating subordination, precontact and dual precontact relations on distributive lattices. The modal characterizations established in the present paper pave the way to establishing faithful embeddings for infinite classes of input/output logics, and hence to their implementation in LogiKEy, Isabelle/HOL, Lean, or other interactive systems.

The drive toward automating cellular network operations has grown with the increasing complexity of these systems. Despite advancements, full autonomy currently remains out of reach due to reliance on human intervention for modeling network behaviors and defining policies to meet target requirements. Network Digital Twins (NDTs) have shown promise in enhancing network intelligence, but the successful implementation of this technology is constrained by use case-specific architectures, limiting its role in advancing network autonomy. A more capable network intelligence, or "telecommunications brain", is needed to enable seamless, autonomous management of cellular network. Large Language Models (LLMs) have emerged as potential enablers for this vision but face challenges in network modeling, especially in reasoning and handling diverse data types. To address these gaps, we introduce Hermes, a chain of LLM agents that uses "blueprints" for constructing NDT instances through structured and explainable logical steps. Hermes allows automatic, reliable, and accurate network modeling of diverse use cases and configurations, thus marking progress toward fully autonomous network operations.

To address an ever-increasing demand for ubiquitous high-speed connectivity, mobile networks have intensified their deployment process. However, achieving this target has proven to be a challenge and has led to a surge in overall energy consumption. In recent years, non-terrestrial networks (NTNs) have been endorsed as a potential solution to these problems by complementing the coverage of the terrestrial network in areas with limited network deployment. To this end, this paper proposes an integrated terrestrial and non-terrestrial network (TN-NTN) that utilises the overall available communication resources to expand coverage and meet Quality of Service (QoS) requirements during high-traffic hours in any deployment scenario. Importantly, our framework allows to drastically reduce the terrestrial network energy consumption during low-traffic hours. Specifically, we introduce a novel radio resource management algorithm, BLASTER (Bandwidth SpLit, User ASsociation, and PowEr ContRol), which integrates bandwidth allocation, user equipment (UE) association, power control, and base station activation within the TN-NTN. This algorithm aims to optimize network resource allocation fairness and energy consumption dynamically, demonstrating new opportunities in deploying satellite networks in legacy cellular systems. Our study offers a comprehensive analysis of the integrated network model, emphasizing the effective balance between energy saving and QoS, and proposing practical solutions to meet the fluctuating traffic demands of cellular networks., Comment: Submitted to IEEE Transactions on Wireless Communications

Despite the remarkable success of Large Language Models (LLMs), they still exhibit a limited capability to align their outputs to the user instructions. In this work, we introduce a simple and effective method, which we name GUIDE, that mechanistically increases attention scores in instruction tokens. To support this operation, we present Influence, a novel metric that highlights how the user's instructions propagate through the transformer layers and impact the LLM output. Our results show that GUIDE improves the accuracy of following instructions 29.4 % to 60.4%, outperforming natural prompting alternatives and Supervised Fine-Tuning up to 1M tokens.

Due to an ever-expansive network deployment, numerous questions are being raised regarding the energy consumption of the mobile network. Recently, Non-Terrestrial Networks (NTNs) have proven to be a useful, and complementary solution to Terrestrial Networks (TN) to provide ubiquitous coverage. In this paper, we consider an integrated TN-NTN, and study how to maximize its resource usage in a dynamic traffic scenario. We introduce BLASTER, a framework designed to control User Equipment (UE) association, Base Station (BS) transmit power and activation, and bandwidth allocation between the terrestrial and non-terrestrial tiers. Our proposal is able to adapt to fluctuating daily traffic, focusing on reducing power consumption throughout the network during low traffic and distributing the load otherwise. Simulation results show an average daily decrease of total power consumption by 45% compared to a network model following 3GPP recommendation, as well as an average throughput increase of roughly 250%. Our paper underlines the central and dynamic role that the NTN plays in improving key areas of concern for network flexibility., Comment: To be published in IEEE International Symposium on Personal, Indoor and Mobile Radio Communications 2024

The adoption of digital twins (DTs) in precision medicine is increasingly viable, propelled by extensive data collection and advancements in artificial intelligence (AI), alongside traditional biomedical methodologies. However, the reliance on black-box predictive models, which utilize large datasets, presents limitations that could impede the broader application of DTs in clinical settings. We argue that hypothesis-driven generative models, particularly multiscale modeling, are essential for boosting the clinical accuracy and relevance of DTs, thereby making a significant impact on healthcare innovation. This paper explores the transformative potential of DTs in healthcare, emphasizing their capability to simulate complex, interdependent biological processes across multiple scales. By integrating generative models with extensive datasets, we propose a scenario-based modeling approach that enables the exploration of diverse therapeutic strategies, thus supporting dynamic clinical decision-making. This method not only leverages advancements in data science and big data for improving disease treatment and prevention but also incorporates insights from complex systems and network science, quantitative biology, and digital medicine, promising substantial advancements in patient care.

This paper introduces Waste Factor (W), also denoted as Waste Figure (WF) in dB, a promising new metric for quantifying energy efficiency in a wide range of circuits and systems applications, including data centers and RANs. Also, the networks used to connect data centers and AI computing engines with users for ML applications must become more power efficient. This paper illustrates the limitations of existing energy efficiency metrics that inadequately capture the intricate energy dynamics of RAN components. We delineate the methodology for applying W across various network configurations, including MISO, SIMO, and MIMO systems, and demonstrate the effectiveness of W in identifying energy optimization opportunities. Our findings reveal that W not only offers nuanced insights into the energy performance of RANs but also facilitates informed decision-making for network design and operational efficiency. Furthermore, we show how W can be integrated with other KPIs to guide the development of optimal strategies for enhancing network energy efficiency under different operational conditions. Additionally, we present simulation results for a distributed multi-user MIMO system at 3.5, 17, and 28 GHz, demonstrating overall network power efficiency on a per square kilometer basis, and show how overall W decreases with an increasing number of base stations and increasing carrier frequency. This paper shows that adopting W as a figure of merit can significantly contribute to the sustainability and energy optimization of next-generation wireless communication networks, paving the way for greener and more sustainable, energy-efficient 5G and 6G technologies., Comment: 28 pages, 21 figures, 5 tables

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing diversity-stability debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as, if not more, important to consider when studying the stability of large ecological systems., Comment: 19 pages, 17 figures, journal submission

The application of Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) systems in the telecommunication domain presents unique challenges, primarily due to the complex nature of telecom standard documents and the rapid evolution of the field. The paper introduces Telco-RAG, an open-source RAG framework designed to handle the specific needs of telecommunications standards, particularly 3rd Generation Partnership Project (3GPP) documents. Telco-RAG addresses the critical challenges of implementing a RAG pipeline on highly technical content, paving the way for applying LLMs in telecommunications and offering guidelines for RAG implementation in other technical domains., Comment: 6 pages, 5 Figure, 4 Tables, accepted to IEEE Globecom 2024 (see https://github.com/netop-team/telco-rag)

A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are modeled as compartments. Due to interactions and intrinsic dynamics, individuals are allowed to change category, leading to concentrations varying over time with complex behavior, typical of reaction-diffusion systems. While compartmental modeling provides a powerful framework for studying the dynamics of such populations and describe the spatiotemporal evolution of a system, it mostly relies on deterministic mean-field descriptions to deal with systems with many degrees of freedom. Here, we propose a method to alleviate some of the limitations of compartmental models by capitalizing on tools originating from quantum physics to systematically reduce multi-dimensional systems to an effective one-dimensional representation. Using this reduced system, we are able to not only investigate the mean-field dynamics and their critical behavior, but we can additionally study stochastic representations that capture fundamental features of the system. We demonstrate the validity of our formalism by studying the critical behavior of models widely adopted to study epidemic, ecological and economic systems., Comment: 28 pages, 13 figures

Empirical complex systems are widely assumed to be characterized not only by pairwise interactions, but also by higher-order (group) interactions that affect collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks' superior descriptive power -- compared to classical pairwise networks -- comes with a much increased model complexity and computational cost. Consequently, it is of paramount importance to establish a quantitative method to determine when such a modeling framework is advantageous with respect to pairwise models, and to which extent it provides a parsimonious description of empirical systems. Here, we propose a principled method, based on information compression, to analyze the reducibility of higher-order networks to lower-order interactions, by identifying redundancies in diffusion processes while preserving the relevant functional information. The analysis of a broad spectrum of empirical systems shows that, although some networks contain non-compressible group interactions, others can be effectively approximated by lower-order interactions -- some technological and biological systems even just by pairwise interactions. More generally, our findings mark a significant step towards minimizing the dimensionality of models for complex systems

The increasing interest in Large Language Models (LLMs) within the telecommunications sector underscores their potential to revolutionize operational efficiency. However, the deployment of these sophisticated models is often hampered by their substantial size and computational demands, raising concerns about their viability in resource-constrained environments. Addressing this challenge, recent advancements have seen the emergence of small language models that surprisingly exhibit performance comparable to their larger counterparts in many tasks, such as coding and common-sense reasoning. Phi-2, a compact yet powerful model, exemplifies this new wave of efficient small language models. This paper conducts a comprehensive evaluation of Phi-2's intrinsic understanding of the telecommunications domain. Recognizing the scale-related limitations, we enhance Phi-2's capabilities through a Retrieval-Augmented Generation approach, meticulously integrating an extensive knowledge base specifically curated with telecom standard specifications. The enhanced Phi-2 model demonstrates a profound improvement in accuracy, answering questions about telecom standards with a precision that closely rivals the more resource-intensive GPT-3.5. The paper further explores the refined capabilities of Phi-2 in addressing problem-solving scenarios within the telecom sector, highlighting its potential and limitations.

We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In particular, we consider precontact algebras as a suitable algebraic environment for negative permission, and we characterize properties of several types of permission (negative, static, dynamic), as well as their interactions with normative systems, by means of suitable modal languages encoding outputs., Comment: arXiv admin note: text overlap with arXiv:2205.13903

Large Language Models (LLMs) have emerged as a significant advancement in the field of Natural Language Processing (NLP), demonstrating remarkable capabilities in language generation and other language-centric tasks. Despite their evaluation across a multitude of analytical and reasoning tasks in various scientific domains, a comprehensive exploration of their knowledge and understanding within the realm of natural language tasks in the telecommunications domain is still needed. This study, therefore, seeks to evaluate the knowledge and understanding capabilities of LLMs within this domain. To achieve this, we conduct an exhaustive zero-shot evaluation of four prominent LLMs-Llama-2, Falcon, Mistral, and Zephyr. These models require fewer resources than ChatGPT, making them suitable for resource-constrained environments. Their performance is compared with state-of-the-art, fine-tuned models. To the best of our knowledge, this is the first work to extensively evaluate and compare the understanding of LLMs across multiple language-centric tasks in this domain. Our evaluation reveals that zero-shot LLMs can achieve performance levels comparable to the current state-of-the-art fine-tuned models. This indicates that pretraining on extensive text corpora equips LLMs with a degree of specialization, even within the telecommunications domain. We also observe that no single LLM consistently outperforms others, and the performance of different LLMs can fluctuate. Although their performance lags behind fine-tuned models, our findings underscore the potential of LLMs as a valuable resource for understanding various aspects of this field that lack large annotated data.

We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper, we introduce and discuss the generalizations of several types of permission (negative, dual negative, static, dynamic), as well as their interactions with normative systems, to various families of selfextensional logics, thereby proposing a systematic approach to the definition of normative and permission systems on nonclassical propositional bases., Comment: 21 pages

Participants in socio-economic systems are often ranked based on their performance. Rankings conveniently reduce the complexity of such systems to ordered lists. Yet, it has been shown in many contexts that those who reach the top are not necessarily the most talented, as chance plays a role in shaping rankings. Nevertheless, the role played by chance in determining success, i.e., serendipity, is underestimated, and top performers are often imitated by others under the assumption that adopting their strategies will lead to equivalent results. We investigate the tradeoff between imitation and serendipity in an agent-based model. Agents in the model receive payoffs based on their actions and may switch to different actions by either imitating others or through random selection. When imitation prevails, most agents coordinate on a single action, leading to non-meritocratic outcomes, as a minority of them accumulates the majority of payoffs. Yet, such agents are not necessarily the most skilled ones. When serendipity dominates, instead, we observe more egalitarian outcomes. The two regimes are separated by a sharp transition, which we characterise analytically in a simplified setting. We discuss the implications of our findings in a variety of contexts, ranging from academic research to business.

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple distinct ways, simultaneously -- was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymer networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after the publication of one of the most seminal papers on this topic, we review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics, and function. We discuss potential frontiers for this topic and the corresponding challenges in the field for the future., Comment: Published in Cambridge Elements. Cambridge University Press; 2022

The energy consumption of mobile networks poses a critical challenge. Mitigating this concern necessitates the deployment and optimization of network energy-saving solutions, such as carrier shutdown, to dynamically manage network resources. Traditional optimization approaches encounter complexity due to factors like the large number of cells, stochastic traffic, channel variations, and intricate trade-offs. This paper introduces the simulated reality of communication networks (SRCON) framework, a novel, data-driven modeling paradigm that harnesses live network data and employs a blend of machine learning (ML)- and expert-based models. These mix of models accurately characterizes the functioning of network components, and predicts network energy efficiency and user equipment (UE) quality of service for any energy carrier shutdown configuration in a specific network. Distinguishing itself from existing methods, SRCON eliminates the reliance on expensive expert knowledge, drive testing, or incomplete maps for predicting network performance. This paper details the pipeline employed by SRCON to decompose the large network energy efficiency modeling problem into ML and expert-based submodels. It demonstrates how, by embracing stochasticity, and carefully crafting the relationship between such submodels, the overall computational complexity can be reduced and prediction accuracy enhanced. Results derived from real network data underscore the paradigm shift introduced by SRCON, showcasing significant gains over a state-of-the art method used by a operator for network energy efficiency modeling. The reliability of this local, data-driven modeling of the network proves to be a key asset for network energy-saving optimization., Comment: 24 pages, 13 figures, submitted to IEEE Transactions on Machine Learning in Communications and Networking

As deep learning models become increasingly large, they pose significant challenges in heterogeneous devices environments. The size of deep learning models makes it difficult to deploy them on low-power or resource-constrained devices, leading to long inference times and high energy consumption. To address these challenges, we propose FlexTrain, a framework that accommodates the diverse storage and computational resources available on different devices during the training phase. FlexTrain enables efficient deployment of deep learning models, while respecting device constraints, minimizing communication costs, and ensuring seamless integration with diverse devices. We demonstrate the effectiveness of FlexTrain on the CIFAR-100 dataset, where a single global model trained with FlexTrain can be easily deployed on heterogeneous devices, saving training time and energy consumption. We also extend FlexTrain to the federated learning setting, showing that our approach outperforms standard federated learning benchmarks on both CIFAR-10 and CIFAR-100 datasets., Comment: Workshop on Advancing Neural Network Training (WANT) at NeurIPS 2023

We introduce TeleQnA, the first benchmark dataset designed to evaluate the knowledge of Large Language Models (LLMs) in telecommunications. Comprising 10,000 questions and answers, this dataset draws from diverse sources, including standards and research articles. This paper outlines the automated question generation framework responsible for creating this dataset, along with how human input was integrated at various stages to ensure the quality of the questions. Afterwards, using the provided dataset, an evaluation is conducted to assess the capabilities of LLMs, including GPT-3.5 and GPT-4. The results highlight that these models struggle with complex standards related questions but exhibit proficiency in addressing general telecom-related inquiries. Additionally, our results showcase how incorporating telecom knowledge context significantly enhances their performance, thus shedding light on the need for a specialized telecom foundation model. Finally, the dataset is shared with active telecom professionals, whose performance is subsequently benchmarked against that of the LLMs. The findings illustrate that LLMs can rival the performance of active professionals in telecom knowledge, thanks to their capacity to process vast amounts of information, underscoring the potential of LLMs within this domain. The dataset has been made publicly accessible on GitHub.

In past years, non-terrestrial networks (NTNs) have emerged as a viable solution for providing ubiquitous connectivity for future wireless networks due to their ability to reach large geographical areas. However, the efficient integration and operation of an NTN with a classic terrestrial network (TN) is challenging due the large amount of parameters to tune. In this paper, we consider the downlink scenario of an integrated TN-NTN transmitting over the S band, comprised of low-earth orbit (LEO) satellites overlapping a large-scale ground cellular network. We propose a new resource management framework to optimize the user equipment (UE) performance by properly controlling the spectrum allocation, the UE association and the transmit power of ground base stations (BSs) and satellites. Our study reveals that, in rural scenarios, NTNs, combined with the proposed radio resource management framework, reduce the number of UEs that are out of coverage, highlighting the important role of NTNs in providing ubiquitous connectivity, and greatly improve the overall capacity of the network. Specifically, our solution leads to more than 200% gain in terms of mean data rate with respect to a network without satellites and a standard integrated TN-NTN when the resource allocation setting follows 3GPP recommendation., Comment: To be published in IEEE International Conference on Communications Workshops 2023

During the COVID-19 pandemic, the behavioral response to reported case numbers changed drastically over time. While a few dozen cases were enough to trigger government-induced and voluntary contact reduction in early 2020, less than a year later, much higher case numbers were required to induce behavioral change. Little attention has been paid to understand, and mathematically model, this effect of decreasing risk perception over longer time-scales. Here, first we show that weighing the number of cases with a time-varying factor of the form $t^{a}\;,\;a<0$ explains real-world mobility patterns from several European countries during 2020 when introduced into a very simple behavior model. Subsequently, we couple our behavior model with an SIR epidemic model. Remarkably, decreasing risk perception can produce complex dynamics, including multiple waves of infection. We find two regimes for the total number of infected individuals that are explained by the interplay of initial attention and the rate of attention decrease. Our results show that including adaption into non-equilibrium models is necessary to understand behavior change over long time scales and the emergence of non-trivial infection dynamics., Comment: 14 pages, 11 figures

Large Language Models (LLMs), AI-driven models that can achieve general-purpose language understanding and generation, have emerged as a transformative force, revolutionizing fields well beyond Natural Language Processing (NLP) and garnering unprecedented attention. As LLM technology continues to progress, the telecom industry is facing the prospect of its impact on its landscape. To elucidate these implications, we delve into the inner workings of LLMs, providing insights into their current capabilities and limitations. We also examine the use cases that can be readily implemented in the telecom industry, streamlining tasks, such as anomalies resolutions and technical specifications comprehension, which currently hinder operational efficiency and demand significant manpower and expertise. Furthermore, we uncover essential research directions that deal with the distinctive challenges of utilizing the LLMs within the telecom domain. Addressing them represents a significant stride towards fully harnessing the potential of LLMs and unlocking their capabilities to the fullest extent within the telecom domain.

We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from Formal Concept Analysis (FCA). The description logic LE-ALC allows us to formally describe databases with objects, features, and formal concepts, represented according to FCA as Galois-stable sets of objects and features. We describe ABoxes and TBoxes in LE-ALC, provide a tableaux algorithm for checking the consistency of LE-ALC knowledge bases with acyclic TBoxes, and show its termination, soundness and completeness. Interestingly, consistency checking for LE-ALC is in PTIME for acyclic and completely unravelled TBoxes, while the analogous problem in the classical ALC setting is PSPACE-complete., Comment: In the new version, some of the proofs have been corrected and simplified, We also improved the exposition of the complexity results

This paper proposes the utilization of cell-free massive MIMO (CF-M-MIMO) processing on top of the regular micro/macrocellular deployments typically found in current 5G networks. Towards this end, it contemplates the connection of all base stations to a central processing unit (CPU) through fronthaul links, thus enabling the joint processing of all serviced user equipment (UE), yet avoiding the expensive deployment and maintenance of dozens of randomly scattered access points (APs). Moreover, it allows the implementation of centralized strategies to exploit the sleep mode capabilities of current baseband/RF hardware to (de)activate selected Base Stations (BSs) in order to maximize the network energy efficiency and to react to changes in UE behaviour and/or operator requirements. In line with current cellular network deployments, it considers the use of multiple antennas at the UE side that unavoidably introduces the need to effectively manage the number of streams to be directed to each UE in order to balance multiplexing gains and increased pilot contamination., Comment: 14 pages, 12 figures

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the components' individual degrees of freedom and reduce their collective dynamical range. Here, we show that real-world networks are formed to optimize the gain in information flow and loss in response diversity. Encoding network states as density matrices, we demonstrate that such a trade-off mathematically resembles the thermodynamic efficiency characterized by heat and work in physical systems. Our findings explain, analytically and numerically, the sparsity and the empirical scaling law observed in hundreds of real-world networks across multiple domains. We show, through numerical experiments in synthetic and biological networks, that ubiquitous topological features such as modularity and small-worldness emerge to optimize the above trade-off for middle- to large-scale information exchange between system's units. Our results highlight that the emergence of some of the most prevalent topological features of real-world networks have a thermodynamic origin.

The statistical field theory of information dynamics on complex networks concerns the dynamical evolution of large classes of models of complex systems. Previous work has focused on networks where nodes carry an information field, which describes the internal state of the node, and its dynamical evolution. In this work, we propose a more general mathematical framework to model information dynamics on complex networks, where the internal node states are vector valued, thus allowing each node to carry multiple types of information. This setup is relevant for many biophysical and socio-technological models of complex systems, ranging from viral dynamics on networks to models of opinion dynamics and social contagion. The full dynamics of these systems is described in the space of all possible network configurations, as opposed to a node-based perspective. Here, we illustrate the mathematical framework presented in an accompanying letter, while focusing on an exemplary application of epidemic spreading on a low-dimensional network., Comment: 10 pages, 5 figures

The information implicitly represented in the state of physical systems allows one to analyze them with analytical techniques from statistical mechanics and information theory. In the case of complex networks such techniques are inspired by quantum statistical physics and have been used to analyze biophysical systems, from virus-host protein-protein interactions to whole-brain models of humans in health and disease. Here, instead of node-node interactions, we focus on the flow of information between network configurations. Our numerical results unravel fundamental differences between widely used spin models on networks, such as voter and kinetic dynamics, which cannot be found from classical node-based analysis. Our model opens the door to adapting powerful analytical methods from quantum many-body systems to study the interplay between structure and dynamics in interconnected systems., Comment: 7 pages, 3 figures

It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard approach to risk management and option pricing. Yet, there is no consensus on what class of probability distributions should be adopted to describe financial returns and different models used in the literature have demonstrated, to varying extent, an ability to reproduce empirically observed stylized facts. In order to provide some clarity, in this paper we perform a thorough study of the most popular models of return distributions as obtained in the empirical analyses of high-frequency financial data. We compare the statistical properties and simulate the dynamics of non-Gaussian financial fluctuations by means of Monte Carlo sampling from the different models in terms of realistic tail exponents. Our findings show a noticeable consistency between the considered return distributions in the modeling of the scaling properties of large price changes. We also discuss the convergence rate to the asymptotic distributions of the non-Gaussian stochastic processes and we study, as a first example of possible applications, the impact of our results on option pricing in comparison with the standard Black and Scholes approach., Comment: 20 pages, 9 figures

Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and man-made systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these non-trivial topological structures in the context of human transportation in cities. We propose a minimal model for spatial networks generation, where a network lattice acts as a spatial substrate and edge velocities and distances define an effective temporal distance which quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of joint network paths and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain Origin-Destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from tree-like structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer range ones typical of commuting. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London Area subway network.

In this article, we advocate for the design of ad hoc artificial intelligence (AI)/machine learning (ML) models to facilitate their usage in future smart infrastructures based on communication networks. To motivate this, we first review key operations identified by the 3GPP for transferring AI/ML models through 5G networks and the main existing techniques to reduce their communication overheads. We also present a novel communication-aware ML framework, which we refer to as Accordion, that enables an efficient AI/ML model transfer thanks to an overhauled model training and communication protocol. We demonstrate the communication-related benefits of Accordion, analyse key performance trade-offs, and discuss potential research directions within this realm.

Explainability is a key challenge and a major research theme in AI research for developing intelligent systems that are capable of working with humans more effectively. An obvious choice in developing explainable intelligent systems relies on employing knowledge representation formalisms which are inherently tailored towards expressing human knowledge e.g., interrogative agendas. In the scope of this work, we focus on formal concept analysis (FCA), a standard knowledge representation formalism, to express interrogative agendas, and in particular to categorize objects w.r.t. a given set of features. Several FCA-based algorithms have already been in use for standard machine learning tasks such as classification and outlier detection. These algorithms use a single concept lattice for such a task, meaning that the set of features used for the categorization is fixed. Different sets of features may have different importance in that categorization, we call a set of features an agenda. In many applications a correct or good agenda for categorization is not known beforehand. In this paper, we propose a meta-learning algorithm to construct a good interrogative agenda explaining the data. Such algorithm is meant to call existing FCA-based classification and outlier detection algorithms iteratively, to increase their accuracy and reduce their sample complexity. The proposed method assigns a measure of importance to different set of features used in the categorization, hence making the results more explainable.

The fifth generation of the Radio Access Network (RAN) has brought new services, technologies, and paradigms with the corresponding societal benefits. However, the energy consumption of 5G networks is today a concern. In recent years, the design of new methods for decreasing the RAN power consumption has attracted interest from both the research community and standardization bodies, and many energy savings solutions have been proposed. However, there is still a need to understand the power consumption behavior of state-ofthe-art base station architectures, such as multi-carrier active antenna units (AAUs), as well as the impact of different network parameters. In this paper, we present a power consumption model for 5G AAUs based on artificial neural networks. We demonstrate that this model achieves good estimation performance, and it is able to capture the benefits of energy saving when dealing with the complexity of multi-carrier base stations architectures. Importantly, multiple experiments are carried out to show the advantage of designing a general model able to capture the power consumption behaviors of different types of AAUs. Finally, we provide an analysis of the model scalability and the training data requirements.

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct microstates compatible with given topology and dynamical evolution. In this Letter, we propose a maximum entropy principle to characterize network states for systems with heterogeneous, generally correlated, connectivity patterns and non-trivial dynamics. We focus on three distinct coalescence processes, widely encountered in the analysis of empirical interconnected systems, and characterize their entropy and transitions between distinct dynamical regimes across distinct temporal scales. Our framework allows one to study the statistical physics of systems that aggregate, such as in transportation infrastructures serving the same geographic area, or correlate, such as inter-brain synchrony arising in organisms that socially interact, and active matter that swarm or synchronize.

The description of complex human mobility patterns is at the core of many important applications ranging from urbanism and transportation to epidemics containment. Data about collective human movements, once scarce, has become widely available thanks to new sources such as Phone CDR, GPS devices, or Smartphone apps. Nevertheless, it is still common to rely on a single dataset by implicitly assuming that it is a valid instance of universal dynamics, regardless of factors such as data gathering and processing techniques. Here, we test such an overarching assumption on an unprecedented scale by comparing human mobility datasets obtained from 7 different data-sources, tracing over 500 millions individuals in 145 countries. We report wide quantifiable differences in the resulting mobility networks and, in particular, in the displacement distribution previously thought to be universal. These variations -- that do not necessarily imply that the human mobility is not universal -- also impact processes taking place on these networks, as we show for the specific case of epidemic spreading. Our results point to the crucial need for disclosing the data processing and, overall, to follow good practices to ensure the robustness and the reproducibility of the results.

Recurrent networks are a special class of artificial neural systems that use their internal states to perform computing tasks for machine learning. One of its state-of-the-art developments, i.e. reservoir computing (RC), uses the internal structure -- usually a static network with random structure -- to map an input signal into a nonlinear dynamical system defined in a higher dimensional space. Reservoirs are characterized by nonlinear interactions among their units and their ability to store information through recurrent loops, allowing to train artificial systems to learn task-specific dynamics. However, it is fundamentally unknown how the random topology of the reservoir affects the learning performance. Here, we fill this gap by considering a battery of synthetic networks -- characterized by different topological features -- and 45 empirical connectomes -- sampled from brain regions of organisms belonging to 8 different species -- to build the reservoir and testing the learning performance against a prediction task with a variety of complex input signals. We find nontrivial correlations between RC performances and both the number of nodes and rank of the covariance matrix of activation states, with performance depending on the nature -- stochastic or deterministic -- of input signals. Remarkably, the modularity and the link density of the reservoir are found to affect RC performances: these results cannot be predicted by models only accounting for simple topological features of the reservoir. Overall, our findings highlight that the complex topological features characterizing biophysical computing systems such as connectomes can be used to design efficient bio-inspired artificial neural networks., Comment: 14 pages, 4 figures, 3 supplementary figures

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer networks from characterizing emergent network states to performing multiscale analysis. However, this framework is usually limited to diffusion dynamics on undirected networks. Here, to overcome some limitations, we propose an approach to derive density matrices based on dynamical systems and information theory, that allows for encapsulating a much wider range of linear and non-linear dynamics and richer classes of structure, such as directed and signed ones. We use our framework to study the response to local stochastic perturbations of synthetic and empirical networks, including neural systems consisting of excitatory and inhibitory links and gene-regulatory interactions. Our findings demonstrate that topological complexity does not lead, necessarily, to functional diversity -- i.e., complex and heterogeneous response to stimuli or perturbations. Instead, functional diversity is a genuine emergent property which cannot be deduced from the knowledge of topological features such as heterogeneity, modularity, presence of asymmetries or dynamical properties of a system.

In recent years, statistical physics' methodologies have proven extremely successful in offering insights into the mechanisms that govern social interactions. However, the question of whether these models are able to capture trends observed in real-world datasets is hardly addressed in the current literature. With this work we aim at bridging the gap between theoretical modeling and validation with data. In particular, we propose a model for opinion dynamics on a social network in the presence of external triggers, framing the interpretation of the model in the context of misbehavior spreading. We divide our population in aware, unaware and zealot/educated agents. Individuals change their status according to two competing dynamics, referred to as behavioral dynamics and broadcasting. The former accounts for information spreading through contact among individuals whereas broadcasting plays the role of an external agent, modeling the effect of mainstream media outlets. Through both simulations and analytical computations we find that the stationary distribution of the fraction of unaware agents in the system undergoes a phase transition when an all-to-all approximation is considered. Surprisingly, such a phase transition disappears in the presence of a minimum fraction of educated agents. Finally, we validate our model using data collected from the public discussion on Twitter, including millions of posts, about the potential adverse effects of the AstraZeneca vaccine against COVID-19. We show that the intervention of external agents, as accounted for in our model, is able to reproduce some key features that are found in this real-world dataset.

Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from entropy measures. Here, we introduce a ranking of edges based on how each edge's removal would change a system's von Neumann entropy (VNE), which is a spectral-entropy measure that has been adapted from quantum information theory to quantify the complexity of information dynamics over networks. We show that a direct calculation of such rankings is computationally inefficient (or unfeasible) for large networks: e.g.\ the scaling is $\mathcal{O}(N^3)$ per edge for networks with $N$ nodes. To overcome this limitation, we employ spectral perturbation theory to estimate VNE perturbations and derive an approximate edge-ranking algorithm that is accurate and fast to compute, scaling as $\mathcal{O}(N)$ per edge. Focusing on a form of VNE that is associated with a transport operator $e^{-\beta{ L}}$, where ${ L}$ is a graph Laplacian matrix and $\beta>0$ is a diffusion timescale parameter, we apply this approach to diverse applications including a network encoding polarized voting patterns of the 117th U.S. Senate, a multimodal transportation system including roads and metro lines in London, and a multiplex brain network encoding correlated human brain activity. Our experiments highlight situations where the edges that are considered to be most important for information diffusion complexity can dramatically change as one considers short, intermediate and long timescales $\beta$ for diffusion., Comment: 27 pages, 9 figures. Revision based on submission to SIAM MMS journal

The energy consumption of the fifth generation(5G) of mobile networks is one of the major concerns of the telecom industry. However, there is not currently an accurate and tractable approach to evaluate 5G base stations (BSs) power consumption. In this article, we propose a novel model for a realistic characterisation of the power consumption of 5G multi-carrier BSs, which builds on a large data collection campaign. At first, we define a machine learning architecture that allows modelling multiple 5G BS products. Then, we exploit the knowledge gathered by this framework to derive a realistic and analytically tractable power consumption model, which can help driving both theoretical analyses as well as feature standardisation, development and optimisation frameworks. Notably, we demonstrate that such model has high precision, and it is able of capturing the benefits of energy saving mechanisms. We believe this analytical model represents a fundamental tool for understanding 5G BSs power consumption, and accurately optimising the network energy efficiency., Comment: Accepted by IEEE Communications Magazine