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Quadrotors can carry slung loads to hard-to-reach locations at high speed. Since a single quadrotor has limited payload capacities, using a team of quadrotors to collaboratively manipulate a heavy object is a scalable and promising solution. However, existing control algorithms for multi-lifting systems only enable low-speed and low-acceleration operations due to the complex dynamic coupling between quadrotors and the load, limiting their use in time-critical missions such as search and rescue. In this work, we present a solution to significantly enhance the agility of cable-suspended multi-lifting systems. Unlike traditional cascaded solutions, we introduce a trajectory-based framework that solves the whole-body kinodynamic motion planning problem online, accounting for the dynamic coupling effects and constraints between the quadrotors and the load. The planned trajectory is provided to the quadrotors as a reference in a receding-horizon fashion and is tracked by an onboard controller that observes and compensates for the cable tension. Real-world experiments demonstrate that our framework can achieve at least eight times greater acceleration than state-of-the-art methods to follow agile trajectories. Our method can even perform complex maneuvers such as flying through narrow passages at high speed. Additionally, it exhibits high robustness against load uncertainties and does not require adding any sensors to the load, demonstrating strong practicality., Comment: 38 pages, 11 figures

As artificial intelligence systems become increasingly integrated into daily life, the field of explainability has gained significant attention. This trend is particularly driven by the complexity of modern AI models and their decision-making processes. The advent of foundation models, characterized by their extensive generalization capabilities and emergent uses, has further complicated this landscape. Foundation models occupy an ambiguous position in the explainability domain: their complexity makes them inherently challenging to interpret, yet they are increasingly leveraged as tools to construct explainable models. In this survey, we explore the intersection of foundation models and eXplainable AI (XAI) in the vision domain. We begin by compiling a comprehensive corpus of papers that bridge these fields. Next, we categorize these works based on their architectural characteristics. We then discuss the challenges faced by current research in integrating XAI within foundation models. Furthermore, we review common evaluation methodologies for these combined approaches. Finally, we present key observations and insights from our survey, offering directions for future research in this rapidly evolving field.

This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

Uncertainty quantification in text-to-image (T2I) generative models is crucial for understanding model behavior and improving output reliability. In this paper, we are the first to quantify and evaluate the uncertainty of T2I models with respect to the prompt. Alongside adapting existing approaches designed to measure uncertainty in the image space, we also introduce Prompt-based UNCertainty Estimation for T2I models (PUNC), a novel method leveraging Large Vision-Language Models (LVLMs) to better address uncertainties arising from the semantics of the prompt and generated images. PUNC utilizes a LVLM to caption a generated image, and then compares the caption with the original prompt in the more semantically meaningful text space. PUNC also enables the disentanglement of both aleatoric and epistemic uncertainties via precision and recall, which image-space approaches are unable to do. Extensive experiments demonstrate that PUNC outperforms state-of-the-art uncertainty estimation techniques across various settings. Uncertainty quantification in text-to-image generation models can be used on various applications including bias detection, copyright protection, and OOD detection. We also introduce a comprehensive dataset of text prompts and generation pairs to foster further research in uncertainty quantification for generative models. Our findings illustrate that PUNC not only achieves competitive performance but also enables novel applications in evaluating and improving the trustworthiness of text-to-image models., Comment: 28 pages and 22 figures

Existing embodied instance goal navigation tasks, driven by natural language, assume human users to provide complete and nuanced instance descriptions prior to the navigation, which can be impractical in the real world as human instructions might be brief and ambiguous. To bridge this gap, we propose a new task, Collaborative Instance Navigation (CoIN), with dynamic agent-human interaction during navigation to actively resolve uncertainties about the target instance in natural, template-free, open-ended dialogues. To address CoIN, we propose a novel method, Agent-user Interaction with UncerTainty Awareness (AIUTA), leveraging the perception capability of Vision Language Models (VLMs) and the capability of Large Language Models (LLMs). First, upon object detection, a Self-Questioner model initiates a self-dialogue to obtain a complete and accurate observation description, while a novel uncertainty estimation technique mitigates inaccurate VLM perception. Then, an Interaction Trigger module determines whether to ask a question to the user, continue or halt navigation, minimizing user input. For evaluation, we introduce CoIN-Bench, a benchmark supporting both real and simulated humans. AIUTA achieves competitive performance in instance navigation against state-of-the-art methods, demonstrating great flexibility in handling user inputs., Comment: https://intelligolabs.github.io/CoIN/

This paper proposes a novel canonical correlation analysis for semiparametric inference in $I(1)/I(0)$ systems via functional approximation. The approach can be applied coherently to panels of $p$ variables with a generic number $s$ of stochastic trends, as well as to subsets or aggregations of variables. This study discusses inferential tools on $s$ and on the loading matrix $\psi$ of the stochastic trends (and on their duals $r$ and $\beta$, the cointegration rank and the cointegrating matrix): asymptotically pivotal test sequences and consistent estimators of $s$ and $r$, $T$-consistent, mixed Gaussian and efficient estimators of $\psi$ and $\beta$, Wald tests thereof, and misspecification tests for checking model assumptions. Monte Carlo simulations show that these tools have reliable performance uniformly in $s$ for small, medium and large-dimensional systems, with $p$ ranging from 10 to 300. An empirical analysis of 20 exchange rates illustrates the methods.

In this paper, we introduce PASTA (Perceptual Assessment System for explanaTion of Artificial intelligence), a novel framework for a human-centric evaluation of XAI techniques in computer vision. Our first key contribution is a human evaluation of XAI explanations on four diverse datasets (COCO, Pascal Parts, Cats Dogs Cars, and MonumAI) which constitutes the first large-scale benchmark dataset for XAI, with annotations at both the image and concept levels. This dataset allows for robust evaluation and comparison across various XAI methods. Our second major contribution is a data-based metric for assessing the interpretability of explanations. It mimics human preferences, based on a database of human evaluations of explanations in the PASTA-dataset. With its dataset and metric, the PASTA framework provides consistent and reliable comparisons between XAI techniques, in a way that is scalable but still aligned with human evaluations. Additionally, our benchmark allows for comparisons between explanations across different modalities, an aspect previously unaddressed. Our findings indicate that humans tend to prefer saliency maps over other explanation types. Moreover, we provide evidence that human assessments show a low correlation with existing XAI metrics that are numerically simulated by probing the model., Comment: https://github.com/ENSTA-U2IS-AI/Dataset_XAI

While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.

In this letter, we propose a control scheme for rigid bodies designed to optimise transient behaviors. The search space for the optimal control input is parameterized to yield a passive, specifically lossless, nonlinear feedback controller. As a result, it can be combined with other stabilizing controllers without compromising the stability of the closed-loop system. The controller commands torques generating fictitious gyroscopic effects characteristics of 3D rotational rigid body motions, and as such does not inject nor extract kinetic energy from the system. We validate the controller in simulation using a model predictive control (MPC) scheme, successfully combining stability and performance in a stabilization task with obstacle avoidance constraints.

We propose a new multirotor aerial vehicle class of designs composed of a multi-body structure in which a main body is connected by passive joints to links equipped with propellers. We have investigated some instances of such class, some of which are shown to achieve omnidirectionality while having a minimum number of inputs equal to the main body Degrees of Freedom DoF's, only uni-directional positive thrust propellers, and no internal forces generated at steady state. After dynamics are derived following the Euler-Lagrange approach, an I/O dynamic feedback linearization strategy is then used to show the controllability of any desired pose with stable zero dynamics. We finally verify the developed controller with closed-loop simulations.

The increasing demand for highly customized products, as well as flexible production lines, can be seen as trigger for the "fourth industrial revolution", referred to as "Industrie 4.0". Current systems usually rely on wire-line technologies to connect sensors and actuators. To enable a higher flexibility such as moving robots or drones, these connections need to be replaced by wireless technologies in the future. Furthermore, this facilitates the renewal of brownfield deployments to address Industrie 4.0 requirements. This paper proposes representative use cases, which have been examined in the German Tactile Internet 4.0 (TACNET 4.0) research project. In order to analyze these use cases, this paper identifies the main challenges and requirements of communication networks in Industrie 4.0 and discusses the applicability of 5th generation wireless communication systems (5G).

In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_{L^2(B)}.$$In this Note we prove a similar result in any Carnot group $\mathbb{G}$ for a vanishing average $f\in L^p$, $1\le p < Q$, where $Q$ is the so-called homogeneous dimension of $\mathbb{G}$.

Organizing unstructured visual data into semantic clusters is a key challenge in computer vision. Traditional deep clustering (DC) approaches focus on a single partition of data, while multiple clustering (MC) methods address this limitation by uncovering distinct clustering solutions. The rise of large language models (LLMs) and multimodal LLMs (MLLMs) has enhanced MC by allowing users to define clustering criteria in natural language. However, manually specifying criteria for large datasets is impractical. In this work, we introduce the task Semantic Multiple Clustering (SMC) that aims to automatically discover clustering criteria from large image collections, uncovering interpretable substructures without requiring human input. Our framework, Text Driven Semantic Multiple Clustering (TeDeSC), uses text as a proxy to concurrently reason over large image collections, discover partitioning criteria, expressed in natural language, and reveal semantic substructures. To evaluate TeDeSC, we introduce the COCO-4c and Food-4c benchmarks, each containing four grouping criteria and ground-truth annotations. We apply TeDeSC to various applications, such as discovering biases and analyzing social media image popularity, demonstrating its utility as a tool for automatically organizing image collections and revealing novel insights., Comment: Preprint. Project webpage: https://oatmealliu.github.io/smc.html

While biological neurons ensure unidirectional signalling, scalable integrated photonic neurons, such as silicon microresonators, respond the same way regardless of excitation direction due to the Lorentz reciprocity principle. Here, we show that a non-linear Taiji microresonator is a proper optical analogous of a biological neuron showing both a spiking response as well as a direction dependence response., Comment: 4 pages and 2 figures

The rapidly increasing share of fluctuating electricity from photovoltaics calls for accurate approaches to estimate cloud motion, the primary source for the varying power supply. While local sensor networks are prominent in targeting forecast horizons too short for image-based methods, they have minimal spatial coverage. This work presents the first step towards expanding those approaches to spatially scalable sensor networks: With the motivation of using automotive light sensors as a sensor network, two excerpts from a microscopic traffic simulation serve as simulative sensor networks. A fractal-based cloud shadow pattern passes the sensor network areas with defined velocities and directions, which shall be estimated using the cumulative mean absolute error method. The evaluation results indicate that the more extensive observation areas compensate for the dynamics in the sensor network when compared to a reference work with a static sensor grid. Furthermore, this work shows how the estimates deteriorate with lower vehicle penetration rates (PR) and longer building shadows due to a lower solar elevation angle. At a penetration rate of 40 %, the root mean square errors for both sensor networks are still below 5 m/s. In conclusion, the spatio-temporal characteristics of a vehicle network offer some potential for estimating cloud movements., Comment: Submitted to Solar RRL on June 28, 2024

In this paper, we present a novel visual servoing (VS) approach based on latent Denoising Diffusion Probabilistic Models (DDPMs). Opposite to classical VS methods, the proposed approach allows reaching the desired target view, even when the target is initially not visible. This is possible thanks to the learning of a latent representation that the DDPM uses for planning and a dataset of trajectories encompassing target-invisible initial views. The latent representation is learned using a Cross-Modal Variational Autoencoder, and used to estimate the return for conditioning the trajectory generation of the DDPM. Given the current image, the DDPM generates trajectories in the latent space driving the robotic platform to the desired visual target. The approach is applicable to any velocity-based controlled platform. We test our method with simulated and real-world experiments using generic multi-rotor Uncrewed Aerial Vehicles (UAVs). A video of our experiments can be found at https://youtu.be/yu-aTxqceOA.

We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a particular case of our general construction. To avoid a complex likelihood optimization, we combine pseudo-likelihood and pairwise likelihood methods for which asymptotic results are obtained for a single path analysis and also for panel data, using ergodic theorems for multi-indexed partial sums. The latter scenario is particularly important for analyzing absence-presence of species in Ecology, a field where data are often collected from surveys at various locations. Our results also give a theoretical background for such models which are often used by the practitioners but without a probabilistic framework.

Knowledge of the nucleosynthetic isotope composition of the outermost protoplanetary disk is critical to understand the formation and early dynamical evolution of the Solar System. We report the discovery of outer disk material preserved in a pristine meteorite based on its chemical composition, organic-rich petrology, and 15N-rich, deuterium-rich, and 16O-poor isotope signatures. We infer that this outer disk material originated in the comet-forming region. The nucleosynthetic Fe, Mg, Si and Cr compositions of this material reveal that, contrary to current belief, the isotope signature of the comet-forming region is ubiquitous amongst outer Solar System bodies, possibly reflecting an important planetary building block in the outer Solar System. This nucleosynthetic component represents fresh material added to the outer disk by late accretion streamers connected to the ambient molecular cloud. Our results show that most Solar System carbonaceous asteroids accreted material from the comet-forming region, a signature lacking in the terrestrial planet region., Comment: Accepted manuscript, pre-print version

Vision-Language Models seamlessly discriminate among arbitrary semantic categories, yet they still suffer from poor generalization when presented with challenging examples. For this reason, Episodic Test-Time Adaptation (TTA) strategies have recently emerged as powerful techniques to adapt VLMs in the presence of a single unlabeled image. The recent literature on TTA is dominated by the paradigm of prompt tuning by Marginal Entropy Minimization, which, relying on online backpropagation, inevitably slows down inference while increasing memory. In this work, we theoretically investigate the properties of this approach and unveil that a surprisingly strong TTA method lies dormant and hidden within it. We term this approach ZERO (TTA with "zero" temperature), whose design is both incredibly effective and frustratingly simple: augment N times, predict, retain the most confident predictions, and marginalize after setting the Softmax temperature to zero. Remarkably, ZERO requires a single batched forward pass through the vision encoder only and no backward passes. We thoroughly evaluate our approach following the experimental protocol established in the literature and show that ZERO largely surpasses or compares favorably w.r.t. the state-of-the-art while being almost 10x faster and 13x more memory-friendly than standard Test-Time Prompt Tuning. Thanks to its simplicity and comparatively negligible computation, ZERO can serve as a strong baseline for future work in this field. The code is available at https://github.com/FarinaMatteo/zero., Comment: Camera-ready version for NeurIPS 2024

The sixth generation (6G) mobile communication networks are expected to intelligently integrate into various aspects of modern digital society, including smart cities, homes, health-care, transportation, and factories. While offering a multitude of services, it is likely that societies become increasingly reliant on 6G infrastructure. Any disruption to these digital services, whether due to human or technical failures, natural disasters, or terrorism, would significantly impact citizens' daily lives. Hence, 6G networks need not only to provide high-performance services but also to be resilient in maintaining essential services in the face of potentially unknown challenges. This paper provides a general review of the state of the art on resilient systems, definitions, concepts, and approaches. Moreover, it introduces a comprehensive concept, i.e., resilience-by-design (RBD), in three different levels for designing resilient 6G communication networks, summarizing our initial studies within the German Open6GHub project. First, we outline the general RBD enabling principles and discuss their related sub-categories. Next, adopting an interdisciplinary approach, we propose to embed these principles across all 6G layers/perspectives including electronics, physical channel, network components and functions, networks, services, and cross-layer and cross-infrastructure considerations and discuss their challenges. We further elaborate the RBD principles and their realizations along with several 6G use-cases. The paper is concluded by presenting a comprehensive list of open problems for future research on 6G resilience.

Berry picking has long-standing traditions in Finland, yet it is challenging and can potentially be dangerous. The integration of drones equipped with advanced imaging techniques represents a transformative leap forward, optimising harvests and promising sustainable practices. We propose WildBe, the first image dataset of wild berries captured in peatlands and under the canopy of Finnish forests using drones. Unlike previous and related datasets, WildBe includes new varieties of berries, such as bilberries, cloudberries, lingonberries, and crowberries, captured under severe light variations and in cluttered environments. WildBe features 3,516 images, including a total of 18,468 annotated bounding boxes. We carry out a comprehensive analysis of WildBe using six popular object detectors, assessing their effectiveness in berry detection across different forest regions and camera types. We will release WildBe publicly.

On 24 September 2023, the NASA OSIRIS-REx mission dropped a capsule to Earth containing approximately 120 g of pristine carbonaceous regolith from Bennu. We describe the delivery and initial allocation of this asteroid sample and introduce its bulk physical, chemical, and mineralogical properties from early analyses. The regolith is very dark overall, with higher-reflectance inclusions and particles interspersed. Particle sizes range from sub-micron dust to a stone about 3.5 cm long. Millimeter-scale and larger stones typically have hummocky or angular morphologies. A subset of the stones appears mottled by brighter material that occurs as veins and crusts. Hummocky stones have the lowest densities and mottled stones have the highest. Remote sensing of the surface of Bennu detected hydrated phyllosilicates, magnetite, organic compounds, carbonates, and scarce anhydrous silicates, all of which the sample confirms. We also find sulfides, presolar grains, and, less expectedly, Na-rich phosphates, as well as other trace phases. The sample composition and mineralogy indicate substantial aqueous alteration and resemble those of Ryugu and the most chemically primitive, low-petrologic-type carbonaceous chondrites. Nevertheless, we find distinct hydrogen, nitrogen, and oxygen isotopic compositions, and some of the material we analyzed is enriched in fluid-mobile elements. Our findings underscore the value of sample return, especially for low-density material that may not readily survive atmospheric entry, and lay the groundwork for more comprehensive analyses., Comment: 73 pages, 22 figures

Accurate trajectory forecasting is crucial for the performance of various systems, such as advanced driver-assistance systems and self-driving vehicles. These forecasts allow us to anticipate events that lead to collisions and, therefore, to mitigate them. Deep Neural Networks have excelled in motion forecasting, but overconfidence and weak uncertainty quantification persist. Deep Ensembles address these concerns, yet applying them to multimodal distributions remains challenging. In this paper, we propose a novel approach named Hierarchical Light Transformer Ensembles (HLT-Ens) aimed at efficiently training an ensemble of Transformer architectures using a novel hierarchical loss function. HLT-Ens leverages grouped fully connected layers, inspired by grouped convolution techniques, to capture multimodal distributions effectively. We demonstrate that HLT-Ens achieves state-of-the-art performance levels through extensive experimentation, offering a promising avenue for improving trajectory forecasting techniques., Comment: WACV 2025

In this work, we present a model-based optimal boundary control design for an aerial robotic system composed of a quadrotor carrying a flexible cable. The whole system is modeled by partial differential equations (PDEs) combined with boundary conditions described by ordinary differential equations (ODEs). The proper orthogonal decomposition (POD) method is adopted to project the original infinite-dimensional system on a finite low-dimensional space spanned by orthogonal basis functions. Based on such a reduced order model, nonlinear model predictive control (NMPC) is implemented online to realize both position and shape trajectory tracking of the flexible cable in an optimal predictive fashion. The proposed POD-based reduced modeling and optimal control paradigms are verified in simulation using an accurate high-dimensional FDM-based model and experimentally using a real quadrotor and a cable. The results show the viability of the POD-based predictive control approach (allowing closing the control loop on the full system state) and its superior performance compared to an optimally tuned PID controller (allowing closing the control loop on the quadrotor state only).

It is shown that higher degree exact differential forms on compact Riemannian $n$-manifolds possess continuous primitives whose uniform norm is controlled by their $L^n$ norm. A contact sub-Riemannian analogue is proven, with differential forms replaced with Rumin differential forms.

Label smoothing (LS) is a popular regularisation method for training neural networks as it is effective in improving test accuracy and is simple to implement. Hard one-hot labels are smoothed by uniformly distributing probability mass to other classes, reducing overfitting. Prior work has suggested that in some cases LS can degrade selective classification (SC) -- where the aim is to reject misclassifications using a model's uncertainty. In this work, we first demonstrate empirically across an extended range of large-scale tasks and architectures that LS consistently degrades SC. We then address a gap in existing knowledge, providing an explanation for this behaviour by analysing logit-level gradients: LS degrades the uncertainty rank ordering of correct vs incorrect predictions by regularising the max logit more when a prediction is likely to be correct, and less when it is likely to be wrong. This elucidates previously reported experimental results where strong classifiers underperform in SC. We then demonstrate the empirical effectiveness of post-hoc logit normalisation for recovering lost SC performance caused by LS. Furthermore, linking back to our gradient analysis, we again provide an explanation for why such normalisation is effective.

In this letter, we address the problem of re-targeting a commercial under-actuated robotic system to a higher dimensional output task. Commercial platforms are equipped with an on-board low-level internal controller that provides the user some virtual references inputs and cannot be replaced. Such controller may control in practice only a subset of the total degrees-of-freedom of the system. Our primary objective is to augment these systems by introducing supplementary inputs, attaining increased output capability. Integrating such additional inputs into the control framework introduces a layer of complexity, raising questions about the compatibility and cohesiveness of the overall system. We derive necessary and sufficient conditions under which it is possible to extend the controlled outputs by adding extra inputs when one is forced to keep the internal controller unmodified. We underscore the efficacy and universality of our proposed methodology through the presentation of two relevant examples.

This work answers positively the question whether non-stop flights are possible for maintaining constant the pose of cable-suspended objects. Such a counterintuitive answer paves the way for a paradigm shift where energetically efficient fixed-wing flying carriers can replace the inefficient multirotor carriers that have been used so far in precise cooperative cable-suspended aerial manipulation. First, we show that one or two flying carriers alone cannot perform non-stop flights while maintaining a constant pose of the suspended object. Instead, we prove that three flying carriers can achieve this task provided that the orientation of the load at the equilibrium is such that the components of the cable forces that balance the external force (typically gravity) do not belong to the plane of the cable anchoring points on the load. Numerical tests are presented in support of the analytical results.

Scaffolds, also called sidewalk sheds, are intended to be temporary structures to protect pedestrians from construction and repair hazards. However, some sidewalk sheds are left up for years. Long-term scaffolding becomes eyesores, creates accessibility issues on sidewalks, and gives cover to illicit activity. Today, there are over 8,000 active permits for scaffolds in NYC; the more problematic scaffolds are likely expired or unpermitted. This research uses computer vision on street-level imagery to develop a longitudinal map of scaffolding throughout the city. Using a dataset of 29,156,833 dashcam images taken between August 2023 and January 2024, we develop an algorithm to track the presence of scaffolding over time. We also design and implement methods to match detected scaffolds to reported locations of active scaffolding permits, enabling the identification of sidewalk sheds without corresponding permits. We identify 850,766 images of scaffolding, tagging 5,156 active sidewalk sheds and estimating 529 unpermitted sheds. We discuss the implications of an in-the-wild scaffolding classifier for urban tech, innovations to governmental inspection processes, and out-of-distribution evaluations outside of New York City.

We provide a complete description of the set of all solutions to an autoregressive law of motion in a finite-dimensional complex vector space. Every solution is shown to be the sum of three parts, each corresponding to a directed flow of time. One part flows forward from the arbitrarily distant past; one flows backward from the arbitrarily distant future; and one flows outward from time zero. The three parts are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive operator according to whether they are inside, outside or on the unit circle. We provide a finite-dimensional parametrization of the set of all solutions.

In this work, we prove a two-scale homogenization result for a set of diffusion-coagulation Smoluchowski-type equations with transmission boundary conditions. This system is meant to describe the aggregation and diffusion of pathological tau proteins in the cerebral tissue, a process associated with the onset and evolution of a large variety of tauopathies (such as Alzheimer's disease). We prove the existence, positivity and boundedness of solutions to the model equations derived at the microscale (that is the scale of single neurons). Then, we study the convergence of the homogenization process to the solution of a macro-model asymptotically consistent with the microscopic one.

Large-scale infrastructures are prone to deterioration due to age, environmental influences, and heavy usage. Ensuring their safety through regular inspections and maintenance is crucial to prevent incidents that can significantly affect public safety and the environment. This is especially pertinent in the context of electrical power networks, which, while essential for energy provision, can also be sources of forest fires. Intelligent drones have the potential to revolutionize inspection and maintenance, eliminating the risks for human operators, increasing productivity, reducing inspection time, and improving data collection quality. However, most of the current methods and technologies in aerial robotics have been trialed primarily in indoor testbeds or outdoor settings under strictly controlled conditions, always within the line of sight of human operators. Additionally, these methods and technologies have typically been evaluated in isolation, lacking comprehensive integration. This paper introduces the first autonomous system that combines various innovative aerial robots. This system is designed for extended-range inspections beyond the visual line of sight, features aerial manipulators for maintenance tasks, and includes support mechanisms for human operators working at elevated heights. The paper further discusses the successful validation of this system on numerous electrical power lines, with aerial robots executing flights over 10 kilometers away from their ground control stations.

Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are equipped for uncertainty estimation but cannot scale to large DNNs that are highly unstable to train. To address this challenge, we introduce the Adaptable Bayesian Neural Network (ABNN), a simple and scalable strategy to seamlessly transform DNNs into BNNs in a post-hoc manner with minimal computational and training overheads. ABNN preserves the main predictive properties of DNNs while enhancing their uncertainty quantification abilities through simple BNN adaptation layers (attached to normalization layers) and a few fine-tuning steps on pre-trained models. We conduct extensive experiments across multiple datasets for image classification and semantic segmentation tasks, and our results demonstrate that ABNN achieves state-of-the-art performance without the computational budget typically associated with ensemble methods.