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Despite the recent advances in computer vision research, estimating the 3D human pose from single RGB images remains a challenging task, as multiple 3D poses can correspond to the same 2D projection on the image. In this context, depth data could help to disambiguate the 2D information by providing additional constraints about the distance between objects in the scene and the camera. Unfortunately, the acquisition of accurate depth data is limited to indoor spaces and usually is tied to specific depth technologies and devices, thus limiting generalization capabilities. In this paper, we propose a method able to leverage the benefits of depth information without compromising its broader applicability and adaptability in a predominantly RGB-camera-centric landscape. Our approach consists of a heatmap-based 3D pose estimator that, leveraging the paradigm of Privileged Information, is able to hallucinate depth information from the RGB frames given at inference time. More precisely, depth information is used exclusively during training by enforcing our RGB-based hallucination network to learn similar features to a backbone pre-trained only on depth data. This approach proves to be effective even when dealing with limited and small datasets. Experimental results reveal that the paradigm of Privileged Information significantly enhances the model's performance, enabling efficient extraction of depth information by using only RGB images., Comment: ECCV 2024 Workshop T-CAP: TOWARDS A COMPLETE ANALYSIS OF PEOPLE: FINE-GRAINED UNDERSTANDING FOR REAL-WORLD APPLICATIONS

The three-dimensional representation of objects or scenes starting from a set of images has been a widely discussed topic for years and has gained additional attention after the diffusion of NeRF-based approaches. However, an underestimated prerequisite is the knowledge of camera poses or, more specifically, the estimation of the extrinsic calibration parameters. Although excellent general-purpose Structure-from-Motion methods are available as a pre-processing step, their computational load is high and they require a lot of frames to guarantee sufficient overlapping among the views. This paper introduces KRONC, a novel approach aimed at inferring view poses by leveraging prior knowledge about the object to reconstruct and its representation through semantic keypoints. With a focus on vehicle scenes, KRONC is able to estimate the position of the views as a solution to a light optimization problem targeting the convergence of keypoints' back-projections to a singular point. To validate the method, a specific dataset of real-world car scenes has been collected. Experiments confirm KRONC's ability to generate excellent estimates of camera poses starting from very coarse initialization. Results are comparable with Structure-from-Motion methods with huge savings in computation. Code and data will be made publicly available., Comment: Accepted at ECCVW

We use motivic methods to give a quick proof of Berthelot's conjecture stating that the push-forward map in rigid cohomology of the structural sheaf along a smooth and proper map has a canonical structure of overconvergent F-isocrystal on the base., Comment: 28 pages

We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes with power tails statistics, if at a certain time a physical quantity takes on a value much larger than its typical value, this large fluctuation is realised through a single macroscopic jump that exceeds the typical scale of the process by several orders of magnitude. In particular, our estimation focuses on the asymptotic behaviour of the tail of the probability distribution of maxima, a fundamental quantity in a wide class of stochastic models used in chemistry to estimate reaction thresholds, in climatology for earthquake risk assessment, in finance for portfolio management, and in ecology for the collective behaviour of species. We determine the analytical form of the probability distribution of rare events in the extreme value statistics of three jump processes with power tails; L\'evy flights, L\'evy walks and the L\'evy-Lorentz gas. For the L\'evy flights, we re-obtain through the big-jump approach recent analytical results, extending their validity. For the L\'evy-Lorentz gas we show that the topology of the disordered lattice along which the walker moves induces memory effects in its dynamics, which influences the extreme value statistics. Our results are confirmed by extensive numerical simulations., Comment: 9 pages, 6 figures

Human behaviour strongly influences the spread of infectious diseases: understanding the interplay between epidemic dynamics and adaptive behaviours is essential to improve response strategies to epidemics, with the goal of containing the epidemic while preserving a sufficient level of operativeness in the population. Through activity-driven temporal networks, we formulate a general framework which models a wide range of adaptive behaviours and mitigation strategies, observed in real populations. We analytically derive the conditions for a widespread diffusion of epidemics in the presence of arbitrary adaptive behaviours, highlighting the crucial role of correlations between agents behaviour in the infected and in the susceptible state. We focus on the effects of sick-leave, comparing the effectiveness of different strategies in reducing the impact of the epidemic and preserving the system operativeness. We show the critical relevance of heterogeneity in individual behavior: in homogeneous networks, all sick-leave strategies are equivalent and poorly effective, while in heterogeneous networks, strategies targeting the most vulnerable nodes are able to effectively mitigate the epidemic, also avoiding a deterioration in system activity and maintaining a low level of absenteeism. Interestingly, with targeted strategies both the minimum of population activity and the maximum of absenteeism anticipate the infection peak, which is effectively flattened and delayed, so that full operativeness is almost restored when the infection peak arrives. We also provide realistic estimates of the model parameters for influenza-like illness, thereby suggesting strategies for managing epidemics and absenteeism in realistic populations., Comment: 16 pages, 8 figures

Millions of people around the world are infected with mosquito-borne diseases each year. One of the most dangerous species is Aedes aegypti, the main vector of viruses such as dengue, yellow fever, chikungunya, and Zika, among others. Mosquito prevention and eradication campaigns are essential to avoid major public health consequences. In this respect, entomological surveillance is an important tool. At present, this traditional monitoring tool is executed manually and requires digital transformation to help authorities make better decisions, improve their planning efforts, speed up execution, and better manage available resources. Therefore, new technological tools based on proven techniques need to be designed and developed. However, such tools should also be cost-effective, autonomous, reliable, and easy to implement, and should be enabled by connectivity and multi-platform software applications. This paper presents the design, development, and testing of an innovative system named MosquIoT. It is based on traditional ovitraps with embedded Internet of Things (IoT) and Tiny Machine Learning (TinyML) technologies, which enable the detection and quantification of Ae. aegypti eggs. This innovative and promising solution may help dynamically understand the behavior of Ae. aegypti populations in cities, shifting from the current reactive entomological monitoring model to a proactive and predictive digital one.

We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of validity of a recently-derived Bayesian effective action for shallow architectures in the proportional limit. We explore the predictive power of the theory as a function of the parameters (the temperature $T$, the magnitude of the Gaussian priors $\lambda_1$, $\lambda_0$, the size of the hidden layer $N_1$ and the size of the training set $P$) by comparing the experimental and predicted generalization error. The very good agreement between the effective theory and the experiments represents an indication that global rescaling of the infinite-width kernel is a main physical mechanism for kernel renormalization in FC Bayesian standard-scaled shallow networks.

Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed distributions, and rare events are therefore not so rare. We formulate a general approach for estimating the contribution of fast rare events to the exit probabilities in the presence of fat tailed distributions. Using this approach, we study three jump processes that are used to model a wide class of phenomena ranging from biology to transport in disordered systems, ecology and finance: discrete time random-walks, L\'evy walks and the L\'evy-Lorentz gas. We determine the exact form of the scaling function for the probability distribution of fast rare events, in which the jump process exits from an interval in a very short time at a large distance opposite to the starting point. In particular, we show that events occurring on time scales orders of magnitude smaller than the typical time scale of the process can make a significant contribution to the exit probability. Our results are confirmed by extensive numerical simulations., Comment: 6 pages, 4 figures

Technologies to enable safe and effective collaboration and coexistence between humans and robots have gained significant importance in the last few years. A critical component useful for realizing this collaborative paradigm is the understanding of human and robot 3D poses using non-invasive systems. Therefore, in this paper, we propose a novel vision-based system leveraging depth data to accurately establish the 3D locations of skeleton joints. Specifically, we introduce the concept of Pose Nowcasting, denoting the capability of the proposed system to enhance its current pose estimation accuracy by jointly learning to forecast future poses. The experimental evaluation is conducted on two different datasets, providing accurate and real-time performance and confirming the validity of the proposed method on both the robotic and human scenarios.

Neural Radiance Fields (NeRFs) have gained widespread recognition as a highly effective technique for representing 3D reconstructions of objects and scenes derived from sets of images. Despite their efficiency, NeRF models can pose challenges in certain scenarios such as vehicle inspection, where the lack of sufficient data or the presence of challenging elements (e.g. reflections) strongly impact the accuracy of the reconstruction. To this aim, we introduce CarPatch, a novel synthetic benchmark of vehicles. In addition to a set of images annotated with their intrinsic and extrinsic camera parameters, the corresponding depth maps and semantic segmentation masks have been generated for each view. Global and part-based metrics have been defined and used to evaluate, compare, and better characterize some state-of-the-art techniques. The dataset is publicly released at https://aimagelab.ing.unimore.it/go/carpatch and can be used as an evaluation guide and as a baseline for future work on this challenging topic., Comment: Accepted at ICIAP2023

Feature learning, or the ability of deep neural networks to automatically learn relevant features from raw data, underlies their exceptional capability to solve complex tasks. However, feature learning seems to be realized in different ways in fully-connected (FC) or convolutional architectures (CNNs). Empirical evidence shows that FC neural networks in the infinite-width limit eventually outperform their finite-width counterparts. Since the kernel that describes infinite-width networks does not evolve during training, whatever form of feature learning occurs in deep FC architectures is not very helpful in improving generalization. On the other hand, state-of-the-art architectures with convolutional layers achieve optimal performances in the finite-width regime, suggesting that an effective form of feature learning emerges in this case. In this work, we present a simple theoretical framework that provides a rationale for these differences, in one hidden layer networks. First, we show that the generalization performance of a finite-width FC network can be obtained by an infinite-width network, with a suitable choice of the Gaussian priors. Second, we derive a finite-width effective action for an architecture with one convolutional hidden layer and compare it with the result available for FC networks. Remarkably, we identify a completely different form of kernel renormalization: whereas the kernel of the FC architecture is just globally renormalized by a single scalar parameter, the CNN kernel undergoes a local renormalization, meaning that the network can select the local components that will contribute to the final prediction in a data-dependent way. This finding highlights a simple mechanism for feature learning that can take place in overparametrized shallow CNNs, but not in shallow FC architectures or in locally connected neural networks without weight sharing., Comment: 22 pages, 5 figures, 2 tables. Comments are welcome

The ability to leverage heterogeneous robotic experience from different robots and tasks to quickly master novel skills and embodiments has the potential to transform robot learning. Inspired by recent advances in foundation models for vision and language, we propose a multi-embodiment, multi-task generalist agent for robotic manipulation. This agent, named RoboCat, is a visual goal-conditioned decision transformer capable of consuming action-labelled visual experience. This data spans a large repertoire of motor control skills from simulated and real robotic arms with varying sets of observations and actions. With RoboCat, we demonstrate the ability to generalise to new tasks and robots, both zero-shot as well as through adaptation using only 100-1000 examples for the target task. We also show how a trained model itself can be used to generate data for subsequent training iterations, thus providing a basic building block for an autonomous improvement loop. We investigate the agent's capabilities, with large-scale evaluations both in simulation and on three different real robot embodiments. We find that as we grow and diversify its training data, RoboCat not only shows signs of cross-task transfer, but also becomes more efficient at adapting to new tasks., Comment: Transactions on Machine Learning Research (12/2023)

We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo-Kato cohomology without recourse to log-geometry, as predicted by Fontaine, and we produce an induced Clemens-Schmid chain complex., Comment: 51 pages. Minor changes to Section 4.7. To appear in JEMS

We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimension in the presence of long range interactions, $J_{ij}\propto r^{-(d+\sigma)}$. We implement a novel local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\sigma$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\sigma$, highlighting that the onset of short range regime for the dynamical critical properties appears to occur at a value of $\sigma$ which differs from the equilibrium one.

The ability to effectively reuse prior knowledge is a key requirement when building general and flexible Reinforcement Learning (RL) agents. Skill reuse is one of the most common approaches, but current methods have considerable limitations.For example, fine-tuning an existing policy frequently fails, as the policy can degrade rapidly early in training. In a similar vein, distillation of expert behavior can lead to poor results when given sub-optimal experts. We compare several common approaches for skill transfer on multiple domains including changes in task and system dynamics. We identify how existing methods can fail and introduce an alternative approach to mitigate these problems. Our approach learns to sequence existing temporally-extended skills for exploration but learns the final policy directly from the raw experience. This conceptual split enables rapid adaptation and thus efficient data collection but without constraining the final solution.It significantly outperforms many classical methods across a suite of evaluation tasks and we use a broad set of ablations to highlight the importance of differentc omponents of our method.

Wireless networks are commonly used in public spaces, universities and public institutions and provide accurate and easily accessible information to monitor the mobility and behavior of users. Following the application of containment measures during the recent pandemic, we analyse extensive data from the WiFi network in a University Campus in Italy during three periods, corresponding to partial lockdown, partial opening, and almost complete opening. We measure the probability distributions of groups and link activation at Wi-Fi Access Points, investigating how different areas are used in the presence of restrictions. We rank the hotspots and the area they cover according to their crowding and to the probability of link formation, which is the relevant variable in determining potential outbreaks. We consider a recently proposed epidemic model on simplicial temporal networks and we use the measured distributions to infer the change in the reproduction number in the three phases. Our data show that additional measures are necessary to limit the epidemic spreading in the total opening phase, due to the dramatic increase in the number of contacts.

We study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory (also referred to as Wentzel-Kramers-Brillouin (WKB) method in some contexts). We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites, as a function of parameters and network size $N$. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the $q$-susceptible-infected-susceptible ($q-SIS$) model, i.e., a high-order epidemic model requiring of $q$ active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with non-trivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for $[1 \leq q\leq 3]$, with a maximal variability at $q=2$, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability and that the leading-order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states., Comment: 10 pages, 4 figures

Knowing the exact 3D location of workers and robots in a collaborative environment enables several real applications, such as the detection of unsafe situations or the study of mutual interactions for statistical and social purposes. In this paper, we propose a non-invasive and light-invariant framework based on depth devices and deep neural networks to estimate the 3D pose of robots from an external camera. The method can be applied to any robot without requiring hardware access to the internal states. We introduce a novel representation of the predicted pose, namely Semi-Perspective Decoupled Heatmaps (SPDH), to accurately compute 3D joint locations in world coordinates adapting efficient deep networks designed for the 2D Human Pose Estimation. The proposed approach, which takes as input a depth representation based on XYZ coordinates, can be trained on synthetic depth data and applied to real-world settings without the need for domain adaptation techniques. To this end, we present the SimBa dataset, based on both synthetic and real depth images, and use it for the experimental evaluation. Results show that the proposed approach, made of a specific depth map representation and the SPDH, overcomes the current state of the art., Comment: IROS2022 and IEEE Robotics and Automation Letters (RA-L). Accepted June, 2022

We give a proof of the $p$-adic weight monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze's proof in the $\ell$-adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives., Comment: 35 pages

In this paper, we want to speculate about the possibility to model all the currently known/proposed approaches to terminology into a single schema. We will use the Entity-Relationship (ER) diagram as our tool for the conceptual data model of the problem and to express the associations between the objects of the study. We will analyse the onomasiological and semasiological approaches, the ontoterminology paradigm, and the frame-based model, and we will draw the consequences in terms of the conceptual data model. The result of this discussion will be used as the basis of the next step of the data organization in terms of standardized terminological records and Linked Data.

For robots operating in the real world, it is desirable to learn reusable behaviours that can effectively be transferred and adapted to numerous tasks and scenarios. We propose an approach to learn abstract motor skills from data using a hierarchical mixture latent variable model. In contrast to existing work, our method exploits a three-level hierarchy of both discrete and continuous latent variables, to capture a set of high-level behaviours while allowing for variance in how they are executed. We demonstrate in manipulation domains that the method can effectively cluster offline data into distinct, executable behaviours, while retaining the flexibility of a continuous latent variable model. The resulting skills can be transferred and fine-tuned on new tasks, unseen objects, and from state to vision-based policies, yielding better sample efficiency and asymptotic performance compared to existing skill- and imitation-based methods. We further analyse how and when the skills are most beneficial: they encourage directed exploration to cover large regions of the state space relevant to the task, making them most effective in challenging sparse-reward settings.

Recently, learning frameworks have shown the capability of inferring the accurate shape, pose, and texture of an object from a single RGB image. However, current methods are trained on image collections of a single category in order to exploit specific priors, and they often make use of category-specific 3D templates. In this paper, we present an alternative approach that infers the textured mesh of objects combining a series of deformable 3D models and a set of instance-specific deformation, pose, and texture. Differently from previous works, our method is trained with images of multiple object categories using only foreground masks and rough camera poses as supervision. Without specific 3D templates, the framework learns category-level models which are deformed to recover the 3D shape of the depicted object. The instance-specific deformations are predicted independently for each vertex of the learned 3D mesh, enabling the dynamic subdivision of the mesh during the training process. Experiments show that the proposed framework can distinguish between different object categories and learn category-specific shape priors in an unsupervised manner. Predicted shapes are smooth and can leverage from multiple steps of subdivision during the training process, obtaining comparable or state-of-the-art results on two public datasets. Models and code are publicly released., Comment: Accepted at 3DV 2021

Effective contact tracing is crucial to contain epidemic spreading without disrupting societal activities especially in the present time of coexistence with a pandemic outbreak. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that beside forward tracing, which reconstructs to whom disease spreads, and backward tracing, which searches from whom disease spreads, a third "sideward" tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have neither been directly infected by, nor they have directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings in a University Campus., Comment: Main document: 12 pages, 5 figures; Supplementary Material: 14 pages, 4 figures

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks., Comment: 14 pages, 7 figures, 2 tables

Gesture recognition is a fundamental tool to enable novel interaction paradigms in a variety of application scenarios like Mixed Reality environments, touchless public kiosks, entertainment systems, and more. Recognition of hand gestures can be nowadays performed directly from the stream of hand skeletons estimated by software provided by low-cost trackers (Ultraleap) and MR headsets (Hololens, Oculus Quest) or by video processing software modules (e.g. Google Mediapipe). Despite the recent advancements in gesture and action recognition from skeletons, it is unclear how well the current state-of-the-art techniques can perform in a real-world scenario for the recognition of a wide set of heterogeneous gestures, as many benchmarks do not test online recognition and use limited dictionaries. This motivated the proposal of the SHREC 2021: Track on Skeleton-based Hand Gesture Recognition in the Wild. For this contest, we created a novel dataset with heterogeneous gestures featuring different types and duration. These gestures have to be found inside sequences in an online recognition scenario. This paper presents the result of the contest, showing the performances of the techniques proposed by four research groups on the challenging task compared with a simple baseline method., Comment: 12 pages, to be published on Computers & Graphics

Many advances that have improved the robustness and efficiency of deep reinforcement learning (RL) algorithms can, in one way or another, be understood as introducing additional objectives or constraints in the policy optimization step. This includes ideas as far ranging as exploration bonuses, entropy regularization, and regularization toward teachers or data priors. Often, the task reward and auxiliary objectives are in conflict, and in this paper we argue that this makes it natural to treat these cases as instances of multi-objective (MO) optimization problems. We demonstrate how this perspective allows us to develop novel and more effective RL algorithms. In particular, we focus on offline RL and finetuning as case studies, and show that existing approaches can be understood as MO algorithms relying on linear scalarization. We hypothesize that replacing linear scalarization with a better algorithm can improve performance. We introduce Distillation of a Mixture of Experts (DiME), a new MORL algorithm that outperforms linear scalarization and can be applied to these non-standard MO problems. We demonstrate that for offline RL, DiME leads to a simple new algorithm that outperforms state-of-the-art. For finetuning, we derive new algorithms that learn to outperform the teacher policy.

We show how to attach to any rigid analytic variety $V$ over a perfectoid space $P$ a rigid analytic motive over the Fargues-Fontaine curve $\mathcal{X}(P)$ functorially in $V$ and $P$. We combine this construction with the overconvergent relative de Rham cohomology to produce a complex of solid quasi-coherent sheaves over $\mathcal{X}(P)$, and we show that its cohomology groups are vector bundles if $V$ is smooth and proper over $P$ or if $V$ is quasi-compact and $P$ is a perfectoid field, thus proving and generalizing a conjecture of Scholze. The main ingredients of the proofs are explicit $\mathbb{B}^1$-homotopies, the motivic proper base change and the formalism of solid quasi-coherent sheaves., Comment: Minor edits. Published version

We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises, characterized by scale free avalanches. The origin of this phenomenon in the c-LIF can be related to the order symmetry breaking in neurons spike-times, which corresponds to the onset of a broad activity distribution. Our analysis uncovers a general mechanism through which networks of simple neurons can be attracted to a complex basin in the phase space., Comment: 10 pages, 9 figures; to appear in Chaos, Solitons & Fractals

Robot manipulation requires a complex set of skills that need to be carefully combined and coordinated to solve a task. Yet, most ReinforcementLearning (RL) approaches in robotics study tasks which actually consist only of a single manipulation skill, such as grasping an object or inserting a pre-grasped object. As a result the skill ('how' to solve the task) but not the actual goal of a complete manipulation ('what' to solve) is specified. In contrast, we study a complex manipulation goal that requires an agent to learn and combine diverse manipulation skills. We propose a challenging, highly under-actuated peg-in-hole task with a free, rotational asymmetrical peg, requiring a broad range of manipulation skills. While correct peg (re-)orientation is a requirement for successful insertion, there is no reward associated with it. Hence an agent needs to understand this pre-condition and learn the skill to fulfil it. The final insertion reward is sparse, allowing freedom in the solution and leading to complex emerging behaviour not envisioned during the task design. We tackle the problem in a multi-task RL framework using Scheduled Auxiliary Control (SAC-X) combined with Regularized Hierarchical Policy Optimization (RHPO) which successfully solves the task in simulation and from scratch on a single robot where data is severely limited.

We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry., Comment: 188 pages. This version incorporates an erratum to the journal version of the article (the hypotheses of Lemma 2.1.4 have been modified; all the other results are unaffected)

Isolation of symptomatic individuals, tracing and testing of their nonsymptomatic contacts are fundamental strategies for mitigating the current COVID-19 pandemic. The breaking of contagion chains relies on two complementary strategies: manual reconstruction of contacts based on interviews and a digital (app-based) privacy-preserving contact tracing. We compare their effectiveness using model parameters tailored to describe SARS-CoV-2 diffusion within the activity-driven model, a general empirically validated framework for network dynamics. We show that, even for equal probability of tracing a contact, manual tracing robustly performs better than the digital protocol, also taking into account the intrinsic delay and limited scalability of the manual procedure. This result is explained in terms of the stochastic sampling occurring during the case-by-case manual reconstruction of contacts, contrasted with the intrinsically prearranged nature of digital tracing, determined by the decision to adopt the app or not by each individual. The better performance of manual tracing is enhanced by heterogeneity in agent behavior: superspreaders not adopting the app are completely invisible to digital contact tracing, while they can be easily traced manually, due to their multiple contacts. We show that this intrinsic difference makes the manual procedure dominant in realistic hybrid protocols., Comment: Main document: 11 pages, 6 figures; Supplementary Information: 18 pages, 5 figures

We consider an epidemic process on adaptive activity-driven temporal networks, with adaptive behaviour modelled as a change in activity and attractiveness due to infection. By using a mean-field approach, we derive an analytical estimate of the epidemic threshold for SIS and SIR epidemic models for a general adaptive strategy, which strongly depends on the correlations between activity and attractiveness in the susceptible and infected states. We focus on strong social distancing, implementing two types of quarantine inspired by recent real case studies: an active quarantine, in which the population compensates the loss of links rewiring the ineffective connections towards non-quarantining nodes, and an inactive quarantine, in which the links with quarantined nodes are not rewired. Both strategies feature the same epidemic threshold but they strongly differ in the dynamics of active phase. We show that the active quarantine is extremely less effective in reducing the impact of the epidemic in the active phase compared to the inactive one, and that in SIR model a late adoption of measures requires inactive quarantine to reach containment., Comment: 6 pages, 4 figures

The use of benchmarks is a widespread and scientifically meaningful practice to validate performance of different approaches to the same task. In the context of robot grasping the use of common object sets has emerged in recent years, however no dominant protocols and metrics to test grasping pipelines have taken root yet. In this paper, we present version 1.0 of GRASPA, a benchmark to test effectiveness of grasping pipelines on physical robot setups. This approach tackles the complexity of such pipelines by proposing different metrics that account for the features and limits of the test platform. As an example application, we deploy GRASPA on the iCub humanoid robot and use it to benchmark our grasping pipeline. As closing remarks, we discuss how the GRASPA indicators we obtained as outcome can provide insight into how different steps of the pipeline affect the overall grasping performance., Comment: To cite this work, please refer to the journal reference entry. For more information, code, pictures and video please visit https://github.com/robotology/GRASPA-benchmark

Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations. The principle has been rigorously proved for sums of independent and identically distributed random variables and it has recently been extended to more complex stochastic processes involving L\'evy distributions, such as L\'evy walks and the L\'evy-Lorentz gas, using an effective rate approach. We review the general rate formalism and we extend its applicability to continuous time random walks and to the Lorentz gas, both with stretched exponential distributions, further enlarging its applicability. We derive an analytic form for the probability density functions for rare events in the two models, which clarify specific properties of stretched exponentials., Comment: 9 pages, 5 figures

The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare events. According to the principle, in heavy-tailed processes a rare huge fluctuation is caused by a single event and not by the usual coherent accumulation of small deviations. We consider generalized L\'evy walks, a class of stochastic processes with power law distributed step durations, which model complex microscopic dynamics in the single stretch. We derive the bulk of the probability distribution and using the big jump principle, the exact form of the tails that describes rare events. We show that the tails of the distribution present non-universal and non-analytic behaviors, which depend crucially on the dynamics of the single step. The big jump estimate also provides a physical explanation of the processes driving the rare events, opening new possibilities for their correct prediction., Comment: 14 pages, 6 figures

In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits super-diffusion. In the context of glass forming systems, super cooled glasses and contamination spreading in porous medium it was suggested to model this behavior with a biased continuous time random walk. Here we analyze the plume of particles far lagging behind the mean, with the single big jump principle. Revealing the mechanism of the anomaly, we show how a single trapping time, the largest one, is responsible for the rare fluctuations in the system. These non typical fluctuations still control the behavior of the mean square displacement, which is the most basic quantifier of the dynamics in many experimental setups. We show how the initial conditions, describing either stationary state or non-equilibrium case, persist for ever in the sense that the rare fluctuations are sensitive to the initial preparation. To describe the fluctuations of the largest trapping time, we modify Fr\'{e}chet's law from extreme value statistics, taking into consideration the fact that the large fluctuations are very different from those observed for independent and identically distributed random variables., Comment: 14 pages, 9 figures

Exploration is an extremely challenging problem in reinforcement learning, especially in high dimensional state and action spaces and when only sparse rewards are available. Effective representations can indicate which components of the state are task relevant and thus reduce the dimensionality of the space to explore. In this work, we take a representation learning viewpoint on exploration, utilizing prior experience to learn effective latent representations, which can subsequently indicate which regions to explore. Prior experience on separate but related tasks help learn representations of the state which are effective at predicting instantaneous rewards. These learned representations can then be used with an entropy-based exploration method to effectively perform exploration in high dimensional spaces by effectively lowering the dimensionality of the search space. We show the benefits of this representation for meta-exploration in a simulated object pushing environment., Comment: 7 pages, 8 figures, workshop

The critical behaviour of statistical models with long-range interactions exhibits distinct regimes as a function of $\rho$, the power of the interaction strength decay. For $\rho$ large enough, $\rho>\rho_{\rm sr}$, the critical behaviour is observed to coincide with that of the short-range model. However, there are controversial aspects regarding this picture, one of which is the value of the short-range threshold $\rho_{\rm sr}$ in the case of the long-range XY model in two dimensions. We study the 2d XY model on the {\it diluted} graph, a sparse graph obtained from the 2d lattice by rewiring links with probability decaying with the Euclidean distance of the lattice as $|r|^{-\rho}$, which is expected to feature the same critical behavior of the long range model. Through Monte Carlo sampling and finite-size analysis of the spontaneous magnetisation and of the Binder cumulant, we present numerical evidence that $\rho_{\rm sr}=4$. According to such a result, one expects the model to belong to the Berezinskii-Kosterlitz-Thouless (BKT) universality class for $\rho\ge 4$, and to present a $2^{nd}$-order transition for $\rho<4$., Comment: 28 pages, 9 figures

We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness., Comment: 23 pages, 11 figures

The cortex exhibits self-sustained highly-irregular activity even under resting conditions, whose origin and function need to be fully understood. It is believed that this can be described as an "asynchronous state" stemming from the balance between excitation and inhibition, with important consequences for information-processing, though a competing hypothesis claims it stems from critical dynamics. By analyzing a parsimonious neural-network model with excitatory and inhibitory interactions, we elucidate a noise-induced mechanism called "Jensen's force" responsible for the emergence of a novel phase of arbitrarily-low but self-sustained activity, which reproduces all the experimental features of asynchronous states. The simplicity of our framework allows for a deep understanding of asynchronous states from a broad statistical-mechanics perspective and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronous-state and critical-state hypotheses. We argue that Jensen's forces are measurable experimentally and might be relevant in contexts beyond neuroscience.

Can faces acquired by low-cost depth sensors be useful to catch some characteristic details of the face? Typically the answer is no. However, new deep architectures can generate RGB images from data acquired in a different modality, such as depth data. In this paper, we propose a new \textit{Deterministic Conditional GAN}, trained on annotated RGB-D face datasets, effective for a face-to-face translation from depth to RGB. Although the network cannot reconstruct the exact somatic features for unknown individual faces, it is capable to reconstruct plausible faces; their appearance is accurate enough to be used in many pattern recognition tasks. In fact, we test the network capability to hallucinate with some \textit{Perceptual Probes}, as for instance face aspect classification or landmark detection. Depth face can be used in spite of the correspondent RGB images, that often are not available due to difficult luminance conditions. Experimental results are very promising and are as far as better than previously proposed approaches: this domain translation can constitute a new way to exploit depth data in new future applications., Comment: Accepted at ICPR 2018

Event cameras are biologically-inspired sensors that gather the temporal evolution of the scene. They capture pixel-wise brightness variations and output a corresponding stream of asynchronous events. Despite having multiple advantages with respect to traditional cameras, their use is partially prevented by the limited applicability of traditional data processing and vision algorithms. To this aim, we present a framework which exploits the output stream of event cameras to synthesize RGB frames, relying on an initial or a periodic set of color key-frames and the sequence of intermediate events. Differently from existing work, we propose a deep learning-based frame synthesis method, consisting of an adversarial architecture combined with a recurrent module. Qualitative results and quantitative per-pixel, perceptual, and semantic evaluation on four public datasets confirm the quality of the synthesized images., Comment: Accepted as full oral at the 15th International Conference on Computer Vision Theory and Applications (VISAPP) 2020

In this paper we prove the Rigidity Theorem for motives of rigid analytic varieties over a non-Archimedean valued field $K$. We prove this theorem both for motives with transfers and without transfers in a relative setting. Applications include the construction of \'etale realization functors, an upgrade of the known comparison between motives with and without transfers and an upgrade of the rigid analytic motivic tilting equivalence, extending them to $\mathrm{Z}[1/p]$-coefficients., Comment: Minor changes. Accepted for publication in J. Inst. Math. Jussieu. 24 pages

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use Scholze's uniformization theorem to prove that the aforementioned moduli space satisfies a non-archimedean analogue of the "Theorem of the Fixed Part" in mixed characteristic., Comment: 31 pages. Final version

Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favouring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks., Comment: 10 pages, 8 fogures

In this paper, an adversarial architecture for facial depth map estimation from monocular intensity images is presented. By following an image-to-image approach, we combine the advantages of supervised learning and adversarial training, proposing a conditional Generative Adversarial Network that effectively learns to translate intensity face images into the corresponding depth maps. Two public datasets, namely Biwi database and Pandora dataset, are exploited to demonstrate that the proposed model generates high-quality synthetic depth images, both in terms of visual appearance and informative content. Furthermore, we show that the model is capable of predicting distinctive facial details by testing the generated depth maps through a deep model trained on authentic depth maps for the face verification task.

The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the same as the distribution of the largest summand. In practice, it means that when in a stochastic process the relevant quantity is a sum of variables, the mechanism leading to rare events is peculiar: instead of being caused by a set of many small deviations all in the same direction, one jump, the biggest of the lot, provides the main contribution to the rare large fluctuation. We reformulate and elevate the big jump principle beyond its current status to allow it to deal with correlations, finite cutoffs, continuous paths, memory and quenched disorder. Doing so we are able to predict rare events using the extended big jump principle in L\'evy walks, in a model of laser cooling, in a scattering process on a heterogeneous structure and in a class of L\'evy walks with memory. We argue that the generalized big jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy tailed distributions, ranging from contamination spreading to active transport in the cell., Comment: 23 pages, 11 figures

Multi-People Tracking in an open-world setting requires a special effort in precise detection. Moreover, temporal continuity in the detection phase gains more importance when scene cluttering introduces the challenging problems of occluded targets. For the purpose, we propose a deep network architecture that jointly extracts people body parts and associates them across short temporal spans. Our model explicitly deals with occluded body parts, by hallucinating plausible solutions of not visible joints. We propose a new end-to-end architecture composed by four branches (visible heatmaps, occluded heatmaps, part affinity fields and temporal affinity fields) fed by a time linker feature extractor. To overcome the lack of surveillance data with tracking, body part and occlusion annotations we created the vastest Computer Graphics dataset for people tracking in urban scenarios by exploiting a photorealistic videogame. It is up to now the vastest dataset (about 500.000 frames, almost 10 million body poses) of human body parts for people tracking in urban scenarios. Our architecture trained on virtual data exhibits good generalization capabilities also on public real tracking benchmarks, when image resolution and sharpness are high enough, producing reliable tracklets useful for further batch data association or re-id modules., Comment: Accepted at ECCV 2018

Depth cameras allow to set up reliable solutions for people monitoring and behavior understanding, especially when unstable or poor illumination conditions make unusable common RGB sensors. Therefore, we propose a complete framework for the estimation of the head and shoulder pose based on depth images only. A head detection and localization module is also included, in order to develop a complete end-to-end system. The core element of the framework is a Convolutional Neural Network, called POSEidon+, that receives as input three types of images and provides the 3D angles of the pose as output. Moreover, a Face-from-Depth component based on a Deterministic Conditional GAN model is able to hallucinate a face from the corresponding depth image. We empirically demonstrate that this positively impacts the system performances. We test the proposed framework on two public datasets, namely Biwi Kinect Head Pose and ICT-3DHP, and on Pandora, a new challenging dataset mainly inspired by the automotive setup. Experimental results show that our method overcomes several recent state-of-art works based on both intensity and depth input data, running in real-time at more than 30 frames per second., Comment: Submitted to IEEE Transactions on PAMI, updated version (second round). arXiv admin note: substantial text overlap with arXiv:1611.10195

To precisely reach for an object with a humanoid robot, it is of central importance to have good knowledge of both end-effector, object pose and shape. In this work we propose a framework for markerless visual servoing on unknown objects, which is divided in four main parts: I) a least-squares minimization problem is formulated to find the volume of the object graspable by the robot's hand using its stereo vision; II) a recursive Bayesian filtering technique, based on Sequential Monte Carlo (SMC) filtering, estimates the 6D pose (position and orientation) of the robot's end-effector without the use of markers; III) a nonlinear constrained optimization problem is formulated to compute the desired graspable pose about the object; IV) an image-based visual servo control commands the robot's end-effector toward the desired pose. We demonstrate effectiveness and robustness of our approach with extensive experiments on the iCub humanoid robot platform, achieving real-time computation, smooth trajectories and sub-pixel precisions.