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Generalized Ces\`aro operators $C_t$, for $t\in [0,1)$, are investigated when they act on the disc algebra $A(\mathbb{D})$ and on the Hardy spaces $H^p$, for $1\leq p \leq \infty$. We study the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity on these spaces., Comment: Article accepted for publication in Advances in Operator Theory. arXiv admin note: text overlap with arXiv:2402.04003

For over half a century, statistical mechanics of spin glasses played as a paradigm to model and interpret disparate phenomena, ranging from quantitative biology to computer science. However, despite the extensive body of research in this area, there is still a notable lack of studies addressing the replacement of Ising spins with Boolean spins: as the latter play as bits in Machine Learning, this gap to fill is now mandatory. Purpose of this paper is to address this study by focusing on the mean field assumption, providing a comprehensive description of the results pertaining to these networks, referred to as the Boolean SK model due to their close relationship with the SK one. We provide a comprehensive framework for this model by employing Guerra interpolation: the thermodynamic limit, the replica symmetric and the broken replica free energy expressions are derived. Further, we inspect the onset of the replica symmetry breaking -- i.e., the de Almeida-Thouless line -- and derive Ghirlanda-Guerra fluctuations. All theoretical findings are corroborated by numerical inspections and both highlight crucial differences in the network's behavior if compared with the Ising SK model: as the temperature is lowered, no phase transitions are evidenced and the model continuously moves from a random (ergodic) behavior to a disordered (glassy) phase.

Individuals engaging on social media often tend to establish online communities where interactions predominantly occur among like-minded peers. While considerable efforts have been devoted to studying and delineating these communities, there has been limited attention directed towards individuals who diverge from these patterns. In this study, we examine the community structure of re-post networks within the context of a polarized political environment at two different times. We specifically identify individuals who consistently switch between opposing communities and analyze the key features that distinguish them. Our investigation focuses on two crucial aspects of these users: the topological properties of their interactions and the political bias in the content of their posts. Our analysis is based on a dataset comprising 2 million tweets related to US President Donald Trump, coupled with data from over 100 000 individual user accounts spanning the 2020 US presidential election year. Our findings indicate that individuals who switch communities exhibit disparities compared to those who remain within the same communities, both in terms of the topological aspects of their interaction patterns (pagerank, degree, betweenness centrality.) and in the sentiment bias of their content towards Donald Trump.

Superconducting qubits are one of the most promising physical systems for implementing quantum computers. However, executing quantum algorithms of practical computational advantage requires further improvements in the fidelities of qubit operations, which are currently limited by the energy relaxation and dephasing times of the qubits. Here, we report our measurement results of a high-coherence transmon qubit with energy relaxation and echo dephasing times surpassing those in the existing literature. We measure a qubit frequency of 2.890 GHz, an energy relaxation time with a median of 502 us and a maximum of (765 +/- 82.6) us, and an echo dephasing time with a median of 541 us and a maximum of (1057 +/- 138) us. We report in detail our design, fabrication process, and measurement setup to facilitate the reproduction and wide adoption of high-coherence transmon qubits in the academia and industry., Comment: 13 pages, 8 figures

The development of safe and reliable autonomous unmanned aerial vehicles relies on the ability of the system to recognise and adapt to changes in the local environment based on sensor inputs. State-of-the-art local tracking and trajectory planning are typically performed using camera sensor input to the flight control algorithm, but the extent to which environmental disturbances like rain affect the performance of these systems is largely unknown. In this paper, we first describe the development of an open dataset comprising ~335k images to examine these effects for seven different classes of precipitation conditions and show that a worst-case average tracking error of 1.5 m is possible for a state-of-the-art visual odometry system (VINS-Fusion). We then use the dataset to train a set of deep neural network models suited to mobile and constrained deployment scenarios to determine the extent to which it may be possible to efficiently and accurately classify these `rainy' conditions. The most lightweight of these models (MobileNetV3 small) can achieve an accuracy of 90% with a memory footprint of just 1.28 MB and a frame rate of 93 FPS, which is suitable for deployment in resource-constrained and latency-sensitive systems. We demonstrate a classification latency in the order of milliseconds using typical flight computer hardware. Accordingly, such a model can feed into the disturbance estimation component of an autonomous flight controller. In addition, data from unmanned aerial vehicles with the ability to accurately determine environmental conditions in real time may contribute to developing more granular timely localised weather forecasting.

Replica Symmetry Breaking is a fascinating phenomenon of spin glasses model which could have consequences also in other field of studies. Although there are several studies regarding the stability between the Replica Symmetric and first step of Replica Symmetry Breaking approximations, we have very few results for the following steps (apart from that one by Gardner for P-spin glasses in 1985 and Chen in 2017 and 2021). This is link to the fact that the classic method, based from the work by De Almeida and Thoules (from which the critical stability line takes its name), is cumbersome to generalise for the next assumptions. In this paper we devise a new straightforward method inspired to the work by Toninelli in 2002 to recover the critical line in order to inspect the stability first between the second and the first steps of Replica Symmetry Breaking and then, we generalise to Kth step, with K finite.

We use regression discontinuity design and difference-in-differences methods to estimate the impact of a one-time hiring subsidy for low-educated unemployed youths in Belgium during the recovery from the Great Recession. Within a year of unemployment, the subsidy increases job-finding in the private sector by 10 percentage points. Over six years, high school graduates secure 2.8 more quarters of private employment. However, they transition from public jobs and self-employment, resulting in no net increase in overall employment, albeit with better wages. High school dropouts experience no lasting benefits. Additionally, in tight labor markets near Luxembourg's employment hub, the subsidy results in a complete deadweight loss., Comment: Accepted version

We provide proofs of two theorems stated by Massey in 1961, concerning the obstructions to finding complex structures on real vector bundles. In addition, we determine the second obstruction to a complex structure on a rank six orientable real vector bundle. The obstructions are fractional parts of integral Stiefel-Whitney classes, and a fourth of an appropriate combination of Pontryagin, Chern, and Euler classes., Comment: Comments and suggestions very welcome!

Online platforms host a diverse user base, which can be broadly categorized into "specialist users" with focused interests and "generalist users" who engage in a wide range of topics. This study explores the behavioral differences between these two user types on the popular platform Reddit, focusing on the level of toxicity in their posts and the associated sentiment scores across 24 emotional categories and a neutral state. By employing community embeddings to represent users in a high-dimensional space, we measure activity diversity using the GS score. We analyze a dataset of 16,291,992 posts from 4,926,237 users spanning the period from 2019 to 2021, assessing the degree of toxicity and sentiment scores for each post. Our findings indicate that specialist users exhibit higher levels of toxic behavior compared to generalist users. Furthermore, specialist users demonstrate elevated scores for annoyance, sadness, and fear, while generalist users show higher scores for curiosity, admiration, and love. These insights contribute to a better understanding of user behavior on online platforms and can inform strategies for fostering healthier online communities.

Politics is one of the most prevalent topics discussed on social media platforms, particularly during major election cycles, where users engage in conversations about candidates and electoral processes. Malicious actors may use this opportunity to disseminate misinformation to undermine trust in the electoral process. The emergence of Large Language Models (LLMs) exacerbates this issue by enabling malicious actors to generate misinformation at an unprecedented scale. Artificial intelligence (AI)-generated content is often indistinguishable from authentic user content, raising concerns about the integrity of information on social networks. In this paper, we present a novel taxonomy for characterizing election-related claims. This taxonomy provides an instrument for analyzing election-related claims, with granular categories related to jurisdiction, equipment, processes, and the nature of claims. We introduce ElectAI, a novel benchmark dataset that consists of 9,900 tweets, each labeled as human- or AI-generated. For AI-generated tweets, the specific LLM variant that produced them is specified. We annotated a subset of 1,550 tweets using the proposed taxonomy to capture the characteristics of election-related claims. We explored the capabilities of LLMs in extracting the taxonomy attributes and trained various machine learning models using ElectAI to distinguish between human- and AI-generated posts and identify the specific LLM variant.

In recent years, the availability of multi-omics data has increased substantially. Multi-omics data integration methods mainly aim to leverage different molecular data sets to gain a complete molecular description of biological processes. An attractive integration approach is the reconstruction of multi-omics networks. However, the development of effective multi-omics network reconstruction strategies lags behind. This hinders maximizing the potential of multi-omics data sets. With this study, we advance the frontier of multi-omics network reconstruction by introducing "collaborative graphical lasso" as a novel strategy. Our proposed algorithm synergizes "graphical lasso" with the concept of "collaboration", effectively harmonizing multi-omics data sets integration, thereby enhancing the accuracy of network inference. Besides, to tackle model selection in this framework, we designed an ad hoc procedure based on network stability. We assess the performance of collaborative graphical lasso and the corresponding model selection procedure through simulations, and we apply them to publicly available multi-omics data. This demonstrated collaborative graphical lasso is able to reconstruct known biological connections and suggest previously unknown and biologically coherent interactions, enabling the generation of novel hypotheses. We implemented collaborative graphical lasso as an R package, available on CRAN as coglasso.

The tremendous hype around autonomous driving is eagerly calling for emerging and novel technologies to support advanced mobility use cases. As car manufactures keep developing SAE level 3+ systems to improve the safety and comfort of passengers, traffic authorities need to establish new procedures to manage the transition from human-driven to fully-autonomous vehicles while providing a feedback-loop mechanism to fine-tune envisioned autonomous systems. Thus, a way to automatically profile autonomous vehicles and differentiate those from human-driven ones is a must. In this paper, we present a fully-fledged framework that monitors active vehicles using camera images and state information in order to determine whether vehicles are autonomous, without requiring any active notification from the vehicles themselves. Essentially, it builds on the cooperation among vehicles, which share their data acquired on the road feeding a machine learning model to identify autonomous cars. We extensively tested our solution and created the NexusStreet dataset, by means of the CARLA simulator, employing an autonomous driving control agent and a steering wheel maneuvered by licensed drivers. Experiments show it is possible to discriminate the two behaviors by analyzing video clips with an accuracy of 80%, which improves up to 93% when the target state information is available. Lastly, we deliberately degraded the state to observe how the framework performs under non-ideal data collection conditions.

In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations.

An investigation is made of the generalized Ces\`aro operators $C_t$, for $t\in [0,1]$, when they act on the space $H(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$, on the Banach space $H^\infty$ of bounded analytic functions and on the weighted Banach spaces $H_v^\infty$ and $H_v^0$ with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity., Comment: Accepted and to appear in Collect. Math

We generalize K\"ahler-Ricci solitons to the almost-K\"ahler setting as the zeros of Inoue's moment map \cite{MR4017922}, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-K\"ahler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the $4$-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on $2n$-dimensional compact symplectic Fano manifolds admitting generalized almost-K\"ahler-Ricci solitons. In particular, we partially extend Matsushima's theorem \cite{MR0094478} to compact first-Chern-Einstein almost-K\"ahler manifolds.

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for both the supervised and unsupervised protocols. In these notes, first, we obtain these explicit expressions by relying upon maximum entropy extremization \`a la Jaynes. Beyond providing a formal derivation of these recipes for Hebbian learning, this construction also highlights how Lagrangian constraints within entropy extremization force network's outcomes on neural correlations: these try to mimic the empirical counterparts hidden in the datasets provided to the network for its training and, the denser the network, the longer the correlations that it is able to capture. Next, we prove that, in the big data limit, whatever the presence of a teacher (or its lacking), not only these Hebbian learning rules converge to the original storage prescription of the Hopfield model but also their related free energies (and, thus, the statistical mechanical picture provided by Amit, Gutfreund and Sompolinsky is fully recovered). As a sideline, we show mathematical equivalence among standard Cost functions (Hamiltonian), preferred in Statistical Mechanical jargon, and quadratic Loss Functions, preferred in Machine Learning terminology. Remarks on the exponential Hopfield model (as the limit of dense networks with diverging density) and semi-supervised protocols are also provided.

Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines. Tackling this approach, at the fairly standard replica symmetric level of description, recently Hebbian attractor networks with multi-node interactions (often called Dense Associative Memories) have been shown to outperform their classical pairwise counterparts in a number of tasks, from their robustness against adversarial attacks and their capability to work with prohibitively weak signals to their supra-linear storage capacities. Focusing on mathematical techniques more than computational aspects, in this paper we relax the replica symmetric assumption and we derive the one-step broken-replica-symmetry picture of supervised and unsupervised learning protocols for these Dense Associative Memories: a phase diagram in the space of the control parameters is achieved, independently, both via the Parisi's hierarchy within then replica trick as well as via the Guerra's telescope within the broken-replica interpolation. Further, an explicit analytical investigation is provided to deepen both the big-data and ground state limits of these networks as well as a proof that replica symmetry breaking does not alter the thresholds for learning and slightly increases the maximal storage capacity. Finally the De Almeida and Thouless line, depicting the onset of instability of a replica symmetric description, is also analytically derived highlighting how, crossed this boundary, the broken replica description should be preferred.

In the context of information systems, text sanitization techniques are used to identify and remove sensitive data to comply with security and regulatory requirements. Even though many methods for privacy preservation have been proposed, most of them are focused on the detection of entities from specific domains (e.g., credit card numbers, social security numbers), lacking generality and requiring customization for each desirable domain. Moreover, removing words is, in general, a drastic measure, as it can degrade text coherence and contextual information. Less severe measures include substituting a word for a safe alternative, yet it can be challenging to automatically find meaningful substitutions. We present a zero-shot text sanitization technique that detects and substitutes potentially sensitive information using Large Language Models. Our evaluation shows that our method excels at protecting privacy while maintaining text coherence and contextual information, preserving data utility for downstream tasks.

We discuss the Singer conjecture and Gromov-L\"uck inequality $\chi \geq |\sigma|$ for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface with residually finite fundamental group that does not rely on Gromov's K\"ahler groups theory. Without the residually finiteness assumption, we observe that this conjecture can be proven for all aspherical complex surfaces except possibly those in Class $\mathrm{VII}_0^+$ (a positive answer to the global spherical shell conjecture would rule out the existence of aspherical surfaces in this class). We also sharpen Gromov's inequality for aspherical complex surfaces that are not in Class $\mathrm{VII}_0^+$. This is achieved by connecting the circle of ideas of the Singer conjecture with the study of Reid's conjecture., Comment: Added an application of Theorem 1.4 to a recent Hodge-theoretic version of the Singer-Hopf conjecture due to Arapura-Maxim-Wang [AMW23]

The advent of reconfigurable intelligent surfaces(RISs) brings along significant improvements for wireless technology on the verge of beyond-fifth-generation networks (B5G).The proven flexibility in influencing the propagation environment opens up the possibility of programmatically altering the wireless channel to the advantage of network designers, enabling the exploitation of higher-frequency bands for superior throughput overcoming the challenging electromagnetic (EM) propagation properties at these frequency bands. However, RISs are not magic bullets. Their employment comes with significant complexity, requiring ad-hoc deployments and management operations to come to fruition. In this paper, we tackle the open problem of bringing RISs to the field, focusing on areas with little or no coverage. In fact, we present a first-of-its-kind deep reinforcement learning (DRL) solution, dubbed as D-RISA, which trains a DRL agent and, in turn, obtain san optimal RIS deployment. We validate our framework in the indoor scenario of the Rennes railway station in France, assessing the performance of our algorithm against state-of-the-art (SOA) approaches. Our benchmarks showcase better coverage, i.e., 10-dB increase in minimum signal-to-noise ratio (SNR), at lower computational time (up to -25 percent) while improving scalability towards denser network deployments.

Knowledge distillation (KD) improves the performance of a low-complexity student model with the help of a more powerful teacher. The teacher in KD is a black-box model, imparting knowledge to the student only through its predictions. This limits the amount of transferred knowledge. In this work, we introduce a novel Knowledge Explaining Distillation (KED) framework, which allows the student to learn not only from the teacher's predictions but also from the teacher's explanations. We propose a class of superfeature-explaining teachers that provide explanation over groups of features, along with the corresponding student model. We also present a method for constructing the superfeatures. We then extend KED to reduce complexity in convolutional neural networks, to allow augmentation with hidden-representation distillation methods, and to work with a limited amount of training data using chimeric sets. Our experiments over a variety of datasets show that KED students can substantially outperform KD students of similar complexity.