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We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes both the Helmholtz equation and the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide Hadamard-type formulas for the shape derivatives under weak regularity assumptions on the domain and its perturbations. Proofs are based on abstract results adapted to varying Hilbert complexes. As a bypass product of our analysis we give a proof of the celebrated Helmann-Feynman theorem for simple eigenvalues assuming differentiability of the corresponding eigenvectors. In a forthcoming publication we aim for a more general result involving also multiple eigenvalues of suitable families of self-adjoint operators in Hilbert spaces depending on possibly infinite dimensional parameters.

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unit-disk maximum independent set problem. Numerical simulations were performed for instances of 6, 8 and 10-qubits graphs. We have found that the failure probability of the procedure is relatively small and rapidly decreases with the number of shots. In addition, a theoretical upper bound for the failure probability of the procedure was obtained., Comment: 19 pages, 13 figures

We study random interpolating sequences with prescribed radii in the Nevanlinna and Smirnov classes. As it turns out these are characterized by the Blaschke condition. This follows from a more general result. Indeed, we show that this characterization is true in so-called big Hardy-Orlicz spaces. It is noteworthy to mention that conditions for deterministic interpolation in these spaces are given by harmonic majorants, the existence of which is difficult to check in general.

Embodied artificial intelligence (AI) requires pushing complex multi-modal models to the extreme edge for time-constrained tasks such as autonomous navigation of robots and vehicles. On small form-factor devices, e.g., nano-sized unmanned aerial vehicles (UAVs), such challenges are exacerbated by stringent constraints on energy efficiency and weight. In this paper, we explore embodied multi-modal AI-based perception for Nano-UAVs with the Kraken shield, a 7g multi-sensor (frame-based and event-based imagers) board based on Kraken, a 22 nm SoC featuring multiple acceleration engines for multi-modal event and frame-based inference based on spiking (SNN) and ternary (TNN) neural networks, respectively. Kraken can execute SNN real-time inference for depth estimation at 1.02k inf/s, 18 {\mu}J/inf, TNN real-time inference for object classification at 10k inf/s, 6 {\mu}J/inf, and real-time inference for obstacle avoidance at 221 frame/s, 750 {\mu}J/inf., Comment: 5 pages, 5 figures

We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn inequality doesn't hold., Comment: references added; 9 pages, 2 figures

Nano-sized unmanned aerial vehicles (UAVs) are ideal candidates for flying Internet-of-Things smart sensors to collect information in narrow spaces. This requires ultra-fast navigation under very tight memory/computation constraints. The PULP-Dronet convolutional neural network (CNN) enables autonomous navigation running aboard a nano-UAV at 19 frame/s, at the cost of a large memory footprint of 320 kB -- and with drone control in complex scenarios hindered by the disjoint training of collision avoidance and steering capabilities. In this work, we distill a novel family of CNNs with better capabilities than PULP-Dronet, but memory footprint reduced by up to 168x (down to 2.9 kB), achieving an inference rate of up to 139 frame/s; we collect a new open-source unified collision/steering 66 k images dataset for more robust navigation; and we perform a thorough in-field analysis of both PULP-Dronet and our tiny CNNs running on a commercially available nano-UAV. Our tiniest CNN, called Tiny-PULP-Dronet v3, navigates with a 100% success rate a challenging and never-seen-before path, composed of a narrow obstacle-populated corridor and a 180{\deg} turn, at a maximum target speed of 0.5 m/s. In the same scenario, the SoA PULP-Dronet consistently fails despite having 168x more parameters., Comment: 13 pages, 6 figures, 7 tables, accepted for publication at IEEE Internet of Things Journal, July 2024

Social networks are creating a digital world in which the cognitive, emotional, and pragmatic value of the imagery of human faces and bodies is arguably changing. However, researchers in the digital humanities are often ill-equipped to study these phenomena at scale. This work presents FRESCO (Face Representation in E-Societies through Computational Observation), a framework designed to explore the socio-cultural implications of images on social media platforms at scale. FRESCO deconstructs images into numerical and categorical variables using state-of-the-art computer vision techniques, aligning with the principles of visual semiotics. The framework analyzes images across three levels: the plastic level, encompassing fundamental visual features like lines and colors; the figurative level, representing specific entities or concepts; and the enunciation level, which focuses particularly on constructing the point of view of the spectator and observer. These levels are analyzed to discern deeper narrative layers within the imagery. Experimental validation confirms the reliability and utility of FRESCO, and we assess its consistency and precision across two public datasets. Subsequently, we introduce the FRESCO score, a metric derived from the framework's output that serves as a reliable measure of similarity in image content., Comment: Accepted at CVIU journal 2024

Pocket-sized autonomous nano-drones can revolutionize many robotic use cases, such as visual inspection in narrow, constrained spaces, and ensure safer human-robot interaction due to their tiny form factor and weight -- i.e., tens of grams. This compelling vision is challenged by the high level of intelligence needed aboard, which clashes against the limited computational and storage resources available on PULP (parallel-ultra-low-power) MCU class navigation and mission controllers that can be hosted aboard. This work moves from PULP-Dronet, a State-of-the-Art convolutional neural network for autonomous navigation on nano-drones. We introduce Tiny-PULP-Dronet: a novel methodology to squeeze by more than one order of magnitude model size (50x fewer parameters), and number of operations (27x less multiply-and-accumulate) required to run inference with similar flight performance as PULP-Dronet. This massive reduction paves the way towards affordable multi-tasking on nano-drones, a fundamental requirement for achieving high-level intelligence., Comment: 3 Figures, 1 table. Accepted for publication at IEEE Artificial Intelligence Circuits and Systems (AICAS), 2022

We study sub and supersolutions for the $p$-Laplace type elliptic equation of the form $$-\Delta_p u-V|u|^{p-2}u=0\quad\text{in $\Omega$},$$ where $\Omega$ is a radially symmetric domain in ${\mathbb{R}}^N$ and $V(x)\ge 0$ is a continuous potential such that the solutions of the equation satisfy the comparison principle on bounded subdomains of $\Omega$. In this work we establish a superposition principle and then use it to develop a version of a Phragm\'{e}n-Lindel\"{o}f comparison principle in the case $p\ge 2$. Moreover, by applying this principle to the case of Hardy-type potentials we recover and improve a number of known lower and upper estimates for sub and supersolutions.

We give a capacitary type characterization of Carleson measures for a class of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel upper half-space, introduced by Arcozzi et al. This answers in part a question raised by the same authors.

Deep neural networks are increasingly used in a wide range of technologies and services, but remain highly susceptible to out-of-distribution (OOD) samples, that is, drawn from a different distribution than the original training set. A common approach to address this issue is to endow deep neural networks with the ability to detect OOD samples. Several benchmarks have been proposed to design and validate OOD detection techniques. However, many of them are based on far-OOD samples drawn from very different distributions, and thus lack the complexity needed to capture the nuances of real-world scenarios. In this work, we introduce a comprehensive benchmark for OOD detection, based on ImageNet and Places365, that assigns individual classes as in-distribution or out-of-distribution depending on the semantic similarity with the training set. Several techniques can be used to determine which classes should be considered in-distribution, yielding benchmarks with varying properties. Experimental results on different OOD detection techniques show how their measured efficacy depends on the selected benchmark and how confidence-based techniques may outperform classifier-based ones on near-OOD samples.

We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an ellipsoidal density that is H\"older continuous with respect to the position variable.

Generative techniques for image anonymization have great potential to generate datasets that protect the privacy of those depicted in the images, while achieving high data fidelity and utility. Existing methods have focused extensively on preserving facial attributes, but failed to embrace a more comprehensive perspective that considers the scene and background into the anonymization process. This paper presents, to the best of our knowledge, the first approach to image anonymization based on Latent Diffusion Models (LDMs). Every element of a scene is maintained to convey the same meaning, yet manipulated in a way that makes re-identification difficult. We propose two LDMs for this purpose: CAMOUFLaGE-Base exploits a combination of pre-trained ControlNets, and a new controlling mechanism designed to increase the distance between the real and anonymized images. CAMOFULaGE-Light is based on the Adapter technique, coupled with an encoding designed to efficiently represent the attributes of different persons in a scene. The former solution achieves superior performance on most metrics and benchmarks, while the latter cuts the inference time in half at the cost of fine-tuning a lightweight module. We show through extensive experimental comparison that the proposed method is competitive with the state-of-the-art concerning identity obfuscation whilst better preserving the original content of the image and tackling unresolved challenges that current solutions fail to address.

A critical challenge in deploying unmanned aerial vehicles (UAVs) for autonomous tasks is their ability to navigate in an unknown environment. This paper introduces a novel vision-depth fusion approach for autonomous navigation on nano-UAVs. We combine the visual-based PULP-Dronet convolutional neural network for semantic information extraction, i.e., serving as the global perception, with 8x8px depth maps for close-proximity maneuvers, i.e., the local perception. When tested in-field, our integration strategy highlights the complementary strengths of both visual and depth sensory information. We achieve a 100% success rate over 15 flights in a complex navigation scenario, encompassing straight pathways, static obstacle avoidance, and 90{\deg} turns., Comment: 5 pages, 2 figures, 1 table, 1 video

We study the Kolmogorov 0-1 law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the 0-1 law for a random sequence to be partitioned into M separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely.

The LiFr diatomic represents a promising candidate for indirect laser cooling that has not yet been investigated not theoretically or experimentally. The potential energy curves of the ground and low_lying excited states of the LiFr heteronuclear alkali metal dimer are calculated using the Fock_space relativistic coupled cluster theory for the first time. A number of properties such as the electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck_Condon factors, and radiative lifetimes (including bound and free transitions) are predicted. The probabilities of the two_step schemes (optical cycles) for the transfer process of the LiFr molecules from high excited vibrational states to the ground vibronic state are also predicted. The data obtained would be useful for laser cooling and spectral experiments with LiFr molecules., Comment: 10 pages, 11 figures

This work presents a multi-sensory anti-collision system design to achieve robust autonomous exploration capabilities for a swarm of 10 cm-side nano-drones operating on object detection missions. We combine lightweight single-beam laser ranging to avoid proximity collisions with a long-range vision-based obstacle avoidance deep learning model (i.e., PULP-Dronet) and an ultra-wide-band (UWB) based ranging module to prevent intra-swarm collisions. An in-field study shows that our multisensory approach can prevent collisions with static obstacles, improving the mission success rate from 20% to 80% in cluttered environments w.r.t. a State-of-the-Art (SoA) baseline. At the same time, the UWB-based sub-system shows a 92.8% success rate in preventing collisions between drones of a four-agent fleet within a safety distance of 65 cm. On a SoA robotic platform extended by a GAP8 multi-core processor, the PULP-Dronet runs interleaved with an objected detection task, which constraints its execution at 1.6 frame/s. This throughput is sufficient for avoiding obstacles with a probability of about 40% but shows a need for more capable processors for the next-generation nano-drone swarms.

Autonomous drone racing competitions are a proxy to improve unmanned aerial vehicles' perception, planning, and control skills. The recent emergence of autonomous nano-sized drone racing imposes new challenges, as their ~10cm form factor heavily restricts the resources available onboard, including memory, computation, and sensors. This paper describes the methodology and technical implementation of the system winning the first autonomous nano-drone racing international competition: the IMAV 2022 Nanocopter AI Challenge. We developed a fully onboard deep learning approach for visual navigation trained only on simulation images to achieve this goal. Our approach includes a convolutional neural network for obstacle avoidance, a sim-to-real dataset collection procedure, and a navigation policy that we selected, characterized, and adapted through simulation and actual in-field experiments. Our system ranked 1st among seven competing teams at the competition. In our best attempt, we scored 115m of traveled distance in the allotted 5-minute flight, never crashing while dodging static and dynamic obstacles. Sharing our knowledge with the research community, we aim to provide a solid groundwork to foster future development in this field., Comment: 8 pages, 10 Figures, 3 Tables, This paper has been accepted for publication in the IEEE Robotics and Automation Letters (RAL). Copyright 2023 IEEE

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $\alpha$-$z$-R\'enyi relative entropies, which comprise known relevant quantities such as the R\'enyi relative entropy and the sandwiched R\'enyi relative entropy, we establish the Holevo-R\'enyi inequality. This result leads to a quantum bound for the $\alpha$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

Neuro-symbolic integration aims at harnessing the power of symbolic knowledge representation combined with the learning capabilities of deep neural networks. In particular, Logic Tensor Networks (LTNs) allow to incorporate background knowledge in the form of logical axioms by grounding a first order logic language as differentiable operations between real tensors. Yet, few studies have investigated the potential benefits of this approach to improve zero-shot learning (ZSL) classification. In this study, we present the Fuzzy Logic Visual Network (FLVN) that formulates the task of learning a visual-semantic embedding space within a neuro-symbolic LTN framework. FLVN incorporates prior knowledge in the form of class hierarchies (classes and macro-classes) along with robust high-level inductive biases. The latter allow, for instance, to handle exceptions in class-level attributes, and to enforce similarity between images of the same class, preventing premature overfitting to seen classes and improving overall performance. FLVN reaches state of the art performance on the Generalized ZSL (GZSL) benchmarks AWA2 and CUB, improving by 1.3% and 3%, respectively. Overall, it achieves competitive performance to recent ZSL methods with less computational overhead. FLVN is available at https://gitlab.com/grains2/flvn., Comment: Accepted for publication at ICIAP 2023

The Jensen-Shannon divergence has been successfully applied as a segmentation tool for symbolic sequences, that is to separate the sequence into subsequences with the same symbolic content. In this work, we propose a method, based on the the Jensen-Shannon divergence, for segmentation of what we call \textit{quantum generated sequences}, which consist in symbolic sequences generated from measuring a quantum system. For one-qubit and two-qubit systems, we show that the proposed method is adequate for segmentation.