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We consider energy-minimizing harmonic maps into trees and we prove the regularity of the singular part of the free interface near triple junction points. Precisely, by proving a new epiperimetric inequality, we show that around any point of frequency $3/2$, the free interface is composed of three $C^{1,\alpha}$-smooth $(d-1)$-dimensional manifolds (composed of points of frequency $1$) with common $C^{1,\alpha}$-regular boundary (made of points of frequency $3/2$) that meet along this boundary at 120 degree angles. Our results also apply to spectral optimal partition problems for the Dirichlet eigenvalues.

Natural language processing skills of Large Language Models (LLMs) are unprecedented, having wide diffusion and application in different tasks. This pilot study focuses on specializing ChatGPT behavior through a Retrieval-Augmented Generation (RAG) system using the OpenAI custom GPTs feature. The purpose of our chatbot, called Unimib Assistant, is to provide information and solutions to the specific needs of University of Milano-Bicocca (Unimib) students through a question-answering approach. We provided the system with a prompt highlighting its specific purpose and behavior, as well as university-related documents and links obtained from an initial need-finding phase, interviewing six students. After a preliminary customization phase, a qualitative usability test was conducted with six other students to identify the strengths and weaknesses of the chatbot, with the goal of improving it in a subsequent redesign phase. While the chatbot was appreciated for its user-friendly experience, perceived general reliability, well-structured responses, and conversational tone, several significant technical and functional limitations emerged. In particular, the satisfaction and overall experience of the users was impaired by the system's inability to always provide fully accurate information. Moreover, it would often neglect to report relevant information even if present in the materials uploaded and prompt given. Furthermore, it sometimes generated unclickable links, undermining its trustworthiness, since providing the source of information was an important aspect for our users. Further in-depth studies and feedback from other users as well as implementation iterations are planned to refine our Unimib Assistant., Comment: Accepted for Italian Workshop on Artificial Intelligence for Human Machine Interaction (AIxHMI 2024), November 26, 2024, Bolzano, Italy

This paper presents the iterative development of Habit Coach, a GPT-based chatbot designed to support users in habit change through personalized interaction. Employing a user-centered design approach, we developed the chatbot using a Retrieval-Augmented Generation (RAG) system, which enables behavior personalization without retraining the underlying language model (GPT-4). The system leverages document retrieval and specialized prompts to tailor interactions, drawing from Cognitive Behavioral Therapy (CBT) and narrative therapy techniques. A key challenge in the development process was the difficulty of translating declarative knowledge into effective interaction behaviors. In the initial phase, the chatbot was provided with declarative knowledge about CBT via reference textbooks and high-level conversational goals. However, this approach resulted in imprecise and inefficient behavior, as the GPT model struggled to convert static information into dynamic and contextually appropriate interactions. This highlighted the limitations of relying solely on declarative knowledge to guide chatbot behavior, particularly in nuanced, therapeutic conversations. Over four iterations, we addressed this issue by gradually transitioning towards procedural knowledge, refining the chatbot's interaction strategies, and improving its overall effectiveness. In the final evaluation, 5 participants engaged with the chatbot over five consecutive days, receiving individualized CBT interventions. The Self-Report Habit Index (SRHI) was used to measure habit strength before and after the intervention, revealing a reduction in habit strength post-intervention. These results underscore the importance of procedural knowledge in driving effective, personalized behavior change support in RAG-based systems., Comment: Accepted for Italian Workshop on Artificial Intelligence for Human Machine Interaction (AIxHMI 2024), November 26, 2024, Bolzano, Italy

In recent years, research in the area of human-robot interaction has focused on developing robots capable of understanding complex human instructions and performing tasks in dynamic and diverse environments. These systems have a wide range of applications, from personal assistance to industrial robotics, emphasizing the importance of robots interacting flexibly, naturally and safely with humans. This paper presents an advanced architecture for robotic action planning that integrates communication, perception, and planning with Large Language Models (LLMs). Our system is designed to translate commands expressed in natural language into executable robot actions, incorporating environmental information and dynamically updating plans based on real-time feedback. The Planner Module is the core of the system where LLMs embedded in a modified ReAct framework are employed to interpret and carry out user commands. By leveraging their extensive pre-trained knowledge, LLMs can effectively process user requests without the need to introduce new knowledge on the changing environment. The modified ReAct framework further enhances the execution space by providing real-time environmental perception and the outcomes of physical actions. By combining robust and dynamic semantic map representations as graphs with control components and failure explanations, this architecture enhances a robot adaptability, task execution, and seamless collaboration with human users in shared and dynamic environments. Through the integration of continuous feedback loops with the environment the system can dynamically adjusts the plan to accommodate unexpected changes, optimizing the robot ability to perform tasks. Using a dataset of previous experience is possible to provide detailed feedback about the failure. Updating the LLMs context of the next iteration with suggestion on how to overcame the issue.

Robots are increasingly being used in dynamic environments like workplaces, hospitals, and homes. As a result, interactions with robots must be simple and intuitive, with robots perception adapting efficiently to human-induced changes. This paper presents a robot control architecture that addresses key challenges in human-robot interaction, with a particular focus on the dynamic creation and continuous update of the robot state representation. The architecture uses Large Language Models to integrate diverse information sources, including natural language commands, robotic skills representation, real-time dynamic semantic mapping of the perceived scene. This enables flexible and adaptive robotic behavior in complex, dynamic environments. Traditional robotic systems often rely on static, pre-programmed instructions and settings, limiting their adaptability to dynamic environments and real-time collaboration. In contrast, this architecture uses LLMs to interpret complex, high-level instructions and generate actionable plans that enhance human-robot collaboration. At its core, the system Perception Module generates and continuously updates a semantic scene graph using RGB-D sensor data, providing a detailed and structured representation of the environment. A particle filter is employed to ensure accurate object localization in dynamic, real-world settings. The Planner Module leverages this up-to-date semantic map to break down high-level tasks into sub-tasks and link them to robotic skills such as navigation, object manipulation (e.g., PICK and PLACE), and movement (e.g., GOTO). By combining real-time perception, state tracking, and LLM-driven communication and task planning, the architecture enhances adaptability, task efficiency, and human-robot collaboration in dynamic environments.

The widespread use of social media has highlighted potential negative impacts on society and individuals, largely driven by recommendation algorithms that shape user behavior and social dynamics. Understanding these algorithms is essential but challenging due to the complex, distributed nature of social media networks as well as limited access to real-world data. This study proposes to use academic social networks as a proxy for investigating recommendation systems in social media. By employing Graph Neural Networks (GNNs), we develop a model that separates the prediction of academic infosphere from behavior prediction, allowing us to simulate recommender-generated infospheres and assess the model's performance in predicting future co-authorships. Our approach aims to improve our understanding of recommendation systems' roles and social networks modeling. To support the reproducibility of our work we publicly make available our implementations: https://github.com/DimNeuroLab/academic_network_project

The purpose of this work is to investigate the soundness and utility of a neural network-based approach as a framework for exploring the impact of image enhancement techniques on visual cortex activation. In a preliminary study, we prepare a set of state-of-the-art brain encoding models, selected among the top 10 methods that participated in The Algonauts Project 2023 Challenge [16]. We analyze their ability to make valid predictions about the effects of various image enhancement techniques on neural responses. Given the impossibility of acquiring the actual data due to the high costs associated with brain imaging procedures, our investigation builds up on a series of experiments. Specifically, we analyze the ability of brain encoders to estimate the cerebral reaction to various augmentations by evaluating the response to augmentations targeting objects (i.e., faces and words) with known impact on specific areas. Moreover, we study the predicted activation in response to objects unseen during training, exploring the impact of semantically out-of-distribution stimuli. We provide relevant evidence for the generalization ability of the models forming the proposed framework, which appears to be promising for the identification of the optimal visual augmentation filter for a given task, model-driven design strategies as well as for AR and VR applications.

We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this framework, since the convergence of the Robin eigenvalues to the Dirichlet ones is known, we address the question of quantifying the rate of such convergence. More precisely, in this work we identify the proper geometric quantity representing (asymptotically) the first term in the expansion of the eigenvalue variation: it is a novel notion of torsional rigidity. Then, by performing a suitable asymptotic analysis of both such quantity and its minimizer, we prove the first-order expansion of any Robin eigenvalue, in the Dirichlet limit. Moreover, the convergence rate of the corresponding eigenfunctions is obtained as well. We remark that all our spectral estimates are explicit and sharp, and cover both the cases of convergence to simple and multiple Dirichlet eigenvalues.

Theory of Mind (ToM), the ability to attribute beliefs, intentions, or mental states to others, is a crucial feature of human social interaction. In complex environments, where the human sensory system reaches its limits, behaviour is strongly driven by our beliefs about the state of the world around us. Accessing others' mental states, e.g., beliefs and intentions, allows for more effective social interactions in natural contexts. Yet, these variables are not directly observable, making understanding ToM a challenging quest of interest for different fields, including psychology, machine learning and robotics. In this paper, we contribute to this topic by showing a developmental synergy between learning to predict low-level mental states (e.g., intentions, goals) and attributing high-level ones (i.e., beliefs). Specifically, we assume that learning beliefs attribution can occur by observing one's own decision processes involving beliefs, e.g., in a partially observable environment. Using a simple feed-forward deep learning model, we show that, when learning to predict others' intentions and actions, more accurate predictions can be acquired earlier if beliefs attribution is learnt simultaneously. Furthermore, we show that the learning performance improves even when observed actors have a different embodiment than the observer and the gain is higher when observing beliefs-driven chunks of behaviour. We propose that our computational approach can inform the understanding of human social cognitive development and be relevant for the design of future adaptive social robots able to autonomously understand, assist, and learn from human interaction partners in novel natural environments and tasks.

We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the presence of a Hardy potential.

We consider the problem of optimal partition of a domain with respect to the sum of the principal eigenvalues and we prove for the first time regularity results for the free interface up to fixed boundary. All our results are quantitative and, in particular, we obtain fine estimates on the continuity of the solutions and the oscillation of the free interface (in terms of the modulus of continuity of the normal vector of the fixed boundary), even in the case of domains with low (Dini-type) regularity. Our analysis is based on an Almgren-type monotonicity formula at boundary points and an epiperimetric inequality at points of low frequency, which, together, yield an explicit rate of convergence for blow-up sequences and the boundary strong unique continuation property. Exploiting our quantitative blow-up analysis, we manage to prove clean-up results near one-phase and two-phase points. We define the notion of free interface inside the fixed boundary, and we prove that the subset of points of minimal frequency is regular and that the interior free interface is approaching the boundary orthogonally in a smooth way.

The aim of the present paper is to investigate the behavior of the spectrum of the Neumann Laplacian in domains with little holes excised from the interior. More precisely, we consider the eigenvalues of the Laplacian with homogeneous Neumann boundary conditions on a bounded, Lipschitz domain. Then, we singularly perturb the domain by removing Lipschitz sets which are "small" in a suitable sense and satisfy a uniform extension property. In this context, we provide an asymptotic expansion for all the eigenvalues of the perturbed problem which are converging to simple eigenvalues of the limit one. The eigenvalue variation turns out to depend on a geometric quantity resembling the notion of (boundary) torsional rigidity: understanding this fact is one of the main contributions of the present paper. In the particular case of a hole shrinking to a point, through a fine blow-up analysis, we identify the exact vanishing order of such a quantity and we establish some connections between the location of the hole and the sign of the eigenvalue variation.

We present an exploration of machine learning architectures for predicting brain responses to realistic images on occasion of the Algonauts Challenge 2023. Our research involved extensive experimentation with various pretrained models. Initially, we employed simpler models to predict brain activity but gradually introduced more complex architectures utilizing available data and embeddings generated by large-scale pre-trained models. We encountered typical difficulties related to machine learning problems, e.g. regularization and overfitting, as well as issues specific to the challenge, such as difficulty in combining multiple input encodings, as well as the high dimensionality, unclear structure, and noisy nature of the output. To overcome these issues we tested single edge 3D position-based, multi-region of interest (ROI) and hemisphere predictor models, but we found that employing multiple simple models, each dedicated to a ROI in each hemisphere of the brain of each subject, yielded the best results - a single fully connected linear layer with image embeddings generated by CLIP as input. While we surpassed the challenge baseline, our results fell short of establishing a robust association with the data., Comment: Submitted to The Algonauts Project 2023 - Exploration and Comparison of Deep Learning Architectures to Predict Brain Response to Realistic Pictures - http://algonauts.csail.mit.edu/

This study examines the modulatory effect of contextual hedonic olfactory stimuli on the visual processing of neutral faces using event-related potentials (ERPs) and effective connectivity analysis. The aim is to investigate how odors' valence influences the cortical connectivity underlying face processing, and the role arousal enhanced by faces plays on such visual-odor multimodal integration. To this goal, a novel methodological approach combining electrodermal activity (EDA) and dynamic causal modeling (DCM) was proposed to examine cortico-cortical interactions changes. The results revealed that EDA sympathetic responses were associated with an increase of the N170 amplitude, which may be suggested as a marker of heightened arousal to faces. Hedonic odors had an impact on early visual ERP components, with increased N1 amplitude during the administration of unpleasant odor and decreased vertex positive potential (VPP) amplitude during the administration of both unpleasant and neutral odors. On the connectivity side, unpleasant odors strengthened the forward connection from the inferior temporal gyrus (ITG) to the middle temporal gyrus (MTG), involved in processing changeable facial features. Conversely, the occurrence of sympathetic responses was correlated with an inhibition of the same connection, and with an enhancement of the backward connection from ITG to the fusiform face gyrus. These findings suggest that negative odors may enhance the interpretation of emotional expressions and mental states, while faces capable of enhancing sympathetic arousal prioritize the processing of identity. The proposed methodology provides insights into the neural mechanisms underlying the integration of visual and olfactory stimuli in face processing.

Artificial intelligence's (AI) progress holds great promise in tackling pressing societal concerns such as health and climate. Large Language Models (LLM) and the derived chatbots, like ChatGPT, have highly improved the natural language processing capabilities of AI systems allowing them to process an unprecedented amount of unstructured data. However, the ensuing excitement has led to negative sentiments, even as AI methods demonstrate remarkable contributions (e.g. in health and genetics). A key factor contributing to this sentiment is the misleading perception that LLMs can effortlessly provide solutions across domains, ignoring their limitations such as hallucinations and reasoning constraints. Acknowledging AI fallibility is crucial to address the impact of dogmatic overconfidence in possibly erroneous suggestions generated by LLMs. At the same time, it can reduce fear and other negative attitudes toward AI. This necessitates comprehensive AI literacy interventions that educate the public about LLM constraints and effective usage techniques, i.e prompting strategies. With this aim, a pilot educational intervention was performed in a high school with 21 students. It involved presenting high-level concepts about intelligence, AI, and LLMs, followed by practical exercises involving ChatGPT in creating natural educational conversations and applying established prompting strategies. Encouraging preliminary results emerged, including high appreciation of the activity, improved interaction quality with the LLM, reduced negative AI sentiments, and a better grasp of limitations, specifically unreliability, limited understanding of commands leading to unsatisfactory responses, and limited presentation flexibility. Our aim is to explore AI acceptance factors and refine this approach for more controlled future studies., Comment: Accepted for AIXIA 2023 22nd International Conference of the Italian Association for Artificial Intelligence 6 - 9 Nov, 2023, Rome, Italy

We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded ``core'', with finitely many unbounded tubes attached to it. We adopt an elementary and purely variational point of view, studying the compactness (or the defect of compactness) of level sets of the relevant constrained Dirichlet integral. As a byproduct of our argument, we also get exponential decay at infinity of variational eigenfunctions. Our analysis includes as a particular case a planar set (sometimes called ``bookcover''), already encountered in the literature on curved quantum waveguides. J. Hersch suggested that this set could provide the sharp constant in the {\it Makai-Hayman inequality} for the bottom of the spectrum of the Dirichlet-Laplacian of planar simply connected sets. We disprove this fact, by means of a singular perturbation technique., Comment: 42 pages, 7 figures. Dedicated to Giuseppe Buttazzo

Educational chatbots come with a promise of interactive and personalized learning experiences, yet their development has been limited by the restricted free interaction capabilities of available platforms and the difficulty of encoding knowledge in a suitable format. Recent advances in language learning models with zero-shot learning capabilities, such as ChatGPT, suggest a new possibility for developing educational chatbots using a prompt-based approach. We present a case study with a simple system that enables mixed-turn chatbot interactions and discuss the insights and preliminary guidelines obtained from initial tests. We examine ChatGPT's ability to pursue multiple interconnected learning objectives, adapt the educational activity to users' characteristics, such as culture, age, and level of education, and its ability to use diverse educational strategies and conversational styles. Although the results are encouraging, challenges are posed by the limited history maintained for the conversation and the highly structured form of responses by ChatGPT, as well as their variability, which can lead to an unexpected switch of the chatbot's role from a teacher to a therapist. We provide some initial guidelines to address these issues and to facilitate the development of effective educational chatbots., Comment: Poster version accepted at the 31st International Conference on Computers in Education (ICCE)

The behavior of simple eigenvalues of Aharonov-Bohm operators with many coalescing poles is discussed. In the case of half-integer circulation, a gauge transformation makes the problem equivalent to an eigenvalue problem for the Laplacian in a domain with straight cracks, laying along the moving directions of poles. For this problem, we obtain an asymptotic expansion for eigenvalues, in which the dominant term is related to the minimum of an energy functional associated with the configuration of poles and defined on a space of functions suitably jumping through the cracks. Concerning configurations with an odd number of poles, an accurate blow-up analysis identifies the exact asymptotic behaviour of eigenvalues and the sign of the variation in some cases. An application to the special case of two poles is also discussed., Comment: Theorem 2.1 improved

In human spatial awareness, 3-D projective geometry structures information integration and action planning through perspective taking within an internal representation space. The way different perspectives are related and transform a world model defines a specific perception and imagination scheme. In mathematics, such collection of transformations corresponds to a 'group', whose 'actions' characterize the geometry of a space. Imbuing world models with a group structure may capture different agents' spatial awareness and affordance schemes. We used group action as a special class of policies for perspective-dependent control. We explored how such geometric structure impacts agents' behavior, comparing how the Euclidean versus projective groups act on epistemic value in active inference, drive curiosity, and exploration behaviors. We formally demonstrate and simulate how the groups induce distinct behaviors in a simple search task. The projective group's nonlinear magnification of information transformed epistemic value according to the choice of frame, generating behaviors of approach toward an object of interest. The projective group structure within the agent's world model contains the Projective Consciousness Model, which is know to capture key features of consciousness. On the other hand, the Euclidean group had no effect on epistemic value : no action was better than the initial idle state. In structuring a priori an agent's internal representation, we show how geometry can play a key role in information integration and action planning.

We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of the perturbed eigenvalues. We detect the proper quantity which sharply measures the perturbation's magnitude. It is a sort of torsional rigidity of the tube's section relative to the domain. This allows us to sharply describe the asymptotic behavior of the perturbed spectrum, even when eigenvalues converge to a multiple one. The final asymptotics of eigenbranches depend on the local behavior near the junction of eigenfunctions chosen in a special way. The present techniques also apply when the perturbation of the Dirichlet eigenvalue problem consists in prescribing homogeneous Neumann boundary conditions on a small portion of the boundary of the domain.

Creating autonomous robots that can actively explore the environment, acquire knowledge and learn skills continuously is the ultimate achievement envisioned in cognitive and developmental robotics. Their learning processes should be based on interactions with their physical and social world in the manner of human learning and cognitive development. Based on this context, in this paper, we focus on the two concepts of world models and predictive coding. Recently, world models have attracted renewed attention as a topic of considerable interest in artificial intelligence. Cognitive systems learn world models to better predict future sensory observations and optimize their policies, i.e., controllers. Alternatively, in neuroscience, predictive coding proposes that the brain continuously predicts its inputs and adapts to model its own dynamics and control behavior in its environment. Both ideas may be considered as underpinning the cognitive development of robots and humans capable of continual or lifelong learning. Although many studies have been conducted on predictive coding in cognitive robotics and neurorobotics, the relationship between world model-based approaches in AI and predictive coding in robotics has rarely been discussed. Therefore, in this paper, we clarify the definitions, relationships, and status of current research on these topics, as well as missing pieces of world models and predictive coding in conjunction with crucially related concepts such as the free-energy principle and active inference in the context of cognitive and developmental robotics. Furthermore, we outline the frontiers and challenges involved in world models and predictive coding toward the further integration of AI and robotics, as well as the creation of robots with real cognitive and developmental capabilities in the future., Comment: 28 pages, 3 figures

In complex environments, where the human sensory system reaches its limits, our behaviour is strongly driven by our beliefs about the state of the world around us. Accessing others' beliefs, intentions, or mental states in general, could thus allow for more effective social interactions in natural contexts. Yet these variables are not directly observable. Theory of Mind (TOM), the ability to attribute to other agents' beliefs, intentions, or mental states in general, is a crucial feature of human social interaction and has become of interest to the robotics community. Recently, new models that are able to learn TOM have been introduced. In this paper, we show the synergy between learning to predict low-level mental states, such as intentions and goals, and attributing high-level ones, such as beliefs. Assuming that learning of beliefs can take place by observing own decision and beliefs estimation processes in partially observable environments and using a simple feed-forward deep learning model, we show that when learning to predict others' intentions and actions, faster and more accurate predictions can be acquired if beliefs attribution is learnt simultaneously with action and intentions prediction. We show that the learning performance improves even when observing agents with a different decision process and is higher when observing beliefs-driven chunks of behaviour. We propose that our architectural approach can be relevant for the design of future adaptive social robots that should be able to autonomously understand and assist human partners in novel natural environments and tasks.

Monitoring crop fields to map features like weeds can be efficiently performed with unmanned aerial vehicles (UAVs) that can cover large areas in a short time due to their privileged perspective and motion speed. However, the need for high-resolution images for precise classification of features (e.g., detecting even the smallest weeds in the field) contrasts with the limited payload and ight time of current UAVs. Thus, it requires several flights to cover a large field uniformly. However, the assumption that the whole field must be observed with the same precision is unnecessary when features are heterogeneously distributed, like weeds appearing in patches over the field. In this case, an adaptive approach that focuses only on relevant areas can perform better, especially when multiple UAVs are employed simultaneously. Leveraging on a swarm-robotics approach, we propose a monitoring and mapping strategy that adaptively chooses the target areas based on the expected information gain, which measures the potential for uncertainty reduction due to further observations. The proposed strategy scales well with group size and leads to smaller mapping errors than optimal pre-planned monitoring approaches.

We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable rotations are included in the constraint, the limit is shown to be the linear elastic equilibrium associated to rotated loads.

The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary deficit in terms of the Fraenkel asymmetry. In addition, we provide the asymptotic behaviour of the $s$-fractional capacity when $s$ goes to $1$ and the stability of our estimate with respect to the parameter $s$.

We deal with eigenvalue problems for the Laplacian with varying mixed boundary conditions, consisting in homogeneous Neumann conditions on a vanishing portion of the boundary and Dirichlet conditions on the complement. By the study of an Almgren type frequency function, we derive upper and lower bounds of the eigenvalue variation and sharp estimates in the case of a strictly star-shaped Neumann region.

In this work we consider an inhomogeneous two-phase obstacle-type problem driven by the fractional Laplacian. In particular, making use of the Caffarelli-Silvestre extension, Almgren and Monneau type monotonicity formulas and blow-up analysis, we provide a classification of the possible vanishing orders, which implies the strong unique continuation property. Moreover, we prove a stratification result for the nodal set, together with estimates on its Hausdorff dimensions, for both the regular and the singular part. The main tools come from geometric measure theory and amount to Whitney's Extension Theorem and Federer's Reduction Principle.

Social media have become an integral part of our lives, expanding our interlinking capabilities to new levels. There is plenty to be said about their positive effects. On the other hand, however, some serious negative implications of social media have been repeatedly highlighted in recent years, pointing at various threats to society and its more vulnerable members, such as teenagers. We thus propose a theoretical framework based on an adaptive "Social Media Virtual Companion" for educating and supporting an entire community, teenage students, to interact in social media environments in order to achieve desirable conditions, defined in terms of a community-specific and participatory designed measure of Collective Well-Being (CWB). This Companion combines automatic processing with expert intervention and guidance. The virtual Companion will be powered by a Recommender System (CWB-RS) that will optimize a CWB metric instead of engagement or platform profit, which currently largely drives recommender systems thereby disregarding any societal collateral effect.We put an emphasis on experts and educators in the educationally managed social media community of the Companion. They play five key roles: (a) use the Companion in classroom-based educational activities; (b) guide the definition of the CWB; (c) provide a hierarchical structure of learning strategies, objectives and activities that will support and contain the adaptive sequencing algorithms of the CWB-RS based on hierarchical reinforcement learning; (d) act as moderators of direct conflicts between the members of the community; and, finally, (e) monitor and address ethical and educational issues that are beyond the intelligent agent's competence and control. Preliminary results on the performance of the Companion's components and studies of the educational and psychological underlying principles are presented.

In this work we consider the homogeneous Neumann eigenvalue problem for the Laplacian on a bounded Lipschitz domain and a singular perturbation of it, which consists in prescribing zero Dirichlet boundary conditions on a small subset of the boundary. We first describe the sharp asymptotic behaviour of a perturbed eigenvalue, in the case in which it is converging to a simple eigenvalue of the limit Neumann problem. The first term in the asymptotic expansion turns out to depend on the Sobolev capacity of the subset where the perturbed eigenfunction is vanishing. Then we focus on the case of Dirichlet boundary conditions imposed on a subset which is scaling to a point; by a blow-up analysis for the capacitary potentials, we detect the vanishing order of the Sobolev capacity of such shrinking Dirichlet boundary portion., Comment: 27 pages

In this paper, we propose a design methodology for one-class classifiers using an ensemble-of-classifiers approach. The objective is to select the best structures created during the training phase using an ensemble of spanning trees. It takes the best classifier, partitioning the area near a pattern into $\gamma^{\gamma-2}$ sub-spaces and combining all possible spanning trees that can be created starting from $\gamma$ nodes. The proposed method leverages on a supervised classification methodology and the concept of minimum distance. We evaluate our approach on well-known benchmark datasets and results obtained demonstrate that it achieves comparable and, in many cases, state-of-the-art results. Moreover, it obtains good performance even with unbalanced datasets., Comment: 8 pages, Dicta Conference

Despite the recent advancement in the social robotic field, important limitations restrain its progress and delay the application of robots in everyday scenarios. In the present paper, we propose to develop computational models inspired by our knowledge of human infants' social adaptive abilities. We believe this may provide solutions at an architectural level to overcome the limits of current systems. Specifically, we present the functional advantages that adaptive Theory of Mind (ToM) systems would support in robotics (i.e., mentalizing for belief understanding, proactivity and preparation, active perception and learning) and contextualize them in practical applications. We review current computational models mainly based on the simulation and teleological theories, and robotic implementations to identify the limitations of ToM functions in current robotic architectures and suggest a possible future developmental pathway. Finally, we propose future studies to create innovative computational models integrating the properties of the simulation and teleological approaches for an improved adaptive ToM ability in robots with the aim of enhancing human-robot interactions and permitting the application of robots in unexplored environments, such as disasters and construction sites. To achieve this goal, we suggest directing future research towards the modern cross-talk between the fields of robotics and developmental psychology.

Great advancements have been achieved in the field of robotics, however, main challenges remain, including building robots with an adaptive Theory of Mind (ToM). In the present paper, seven current robotic architectures for human-robot interactions were described as well as four main functional advantages of equipping robots with an adaptive ToM. The aim of the present paper was to determine in which way and how often ToM features are integrated in the architectures analyzed, and if they provide robots with the associated functional advantages. Our assessment shows that different methods are used to implement ToM features in robotic architectures. Furthermore, while a ToM for false-belief understanding and tracking is often built in social robotic architectures, a ToM for proactivity, active perception and learning is less common. Nonetheless, progresses towards better adaptive ToM features in robots are warranted to provide them with full access to the advantages of having a ToM resembling that of humans.

Proactively perceiving others' intentions is a crucial skill to effectively interact in unstructured, dynamic and novel environments. This work proposes a first step towards embedding this skill in support robots for search and rescue missions. Predicting the responders' intentions, indeed, will enable exploration approaches which will identify and prioritise areas that are more relevant for the responder and, thus, for the task, leading to the development of safer, more robust and efficient joint exploration strategies. More specifically, this paper presents an active intention recognition paradigm to perceive, even under sensory constraints, not only the target's position but also the first responder's movements, which can provide information on his/her intentions (e.g. reaching the position where he/she expects the target to be). This mechanism is implemented by employing an extension of Monte-Carlo-based planning techniques for partially observable environments, where the reward function is augmented with an entropy reduction bonus. We test in simulation several configurations of reward augmentation, both information theoretic and not, as well as belief state approximations and obtain substantial improvements over the basic approach.

One-class classifiers are trained with target class only samples. Intuitively, their conservative modelling of the class description may benefit classical classification tasks where classes are difficult to separate due to overlapping and data imbalance. In this work, three methods are proposed which leverage on the combination of one-class classifiers based on non-parametric models, N-ary Trees and Minimum Spanning Trees class descriptors (MST-CD), to tackle binary classification problems. The methods deal with the inconsistencies arising from combining multiple classifiers and with spurious connections that MST-CD creates in multi-modal class distributions. As shown by our tests on several datasets, the proposed approach is feasible and comparable with state-of-the-art algorithms.

In this work we investigate positivity properties of nonlocal Schr\"odinger type operators, driven by the fractional Laplacian, with multipolar, critical, and locally homogeneous potentials. On one hand, we develop a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions, while, on the other hand, we study the localization of binding for this kind of potentials. Combining these two tools and performing an inductive procedure on the number of poles, we establish necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding Schr\"odinger operator.

In this paper we consider a class of singularly perturbed domains, obtained by attaching a cylindrical tube to a fixed bounded region and letting its section shrink to zero. We use an Almgren-type monotonicity formula to evaluate the sharp convergence rate of perturbed simple eigenvalues, via Courant-Fischer Min-Max characterization and blow-up analysis for scaled eigenfunctions., Comment: 36 pages