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In this article we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator $\Delta_\gamma^p$. We extend to a generic $p>1$ a result which was proved only when $p=2$. When $p\neq 2$, the nonlinear operator $-\Delta_\gamma^p$ has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem which is not based on linear subspaces. We also prove a new abstract result based on a pseudo-index related to the $\mathbf{Z}_2$-cohomological index that is applicable here. We provide a version of the Lions' Concentration-Compactness Principle for our operator.

In this paper we study the embedding properties for the weighted Sobolev space $H^1_V(\mathbb{R}^N)$ into the Lebesgue weighted space $L^\tau_W(\mathbb{R}^N)$. Here $V$ and $W$ are diverging weight functions. The different behaviour of $V$ with respect to $W$ at infinity plays a crucial role. Particular attention is paid to the case $V=W$. This situation is very delicate since it depends strongly on the dimension and, in particular, $N=2$ is somewhat a limit case. As an application, an existence result for a planar nonlinear Schr\"odinger equation in presence of coercive potentials is provided.

We consider the initial-boundary value problem in the quarter space for the system of equations of ideal Magneto-Hydrodynamics for compressible fluids with perfectly conducting wall boundary conditions. On the two parts of the boundary the solution satisfies different boundary conditions, which make the problem an initial-boundary value problem with non-uniformly characteristic boundary. We identify a subspace ${{\mathcal H}}^3(\Omega)$ of the Sobolev space $H^3(\Omega)$, obtained by addition of suitable boundary conditions on one portion of the boundary, such that for initial data in ${{\mathcal H}}^3(\Omega)$ there exists a solution in the same space ${{\mathcal H}}^3(\Omega)$, for all times in a small time interval. This yields the well-posedness of the problem combined with a persistence property of full $H^3$-regularity, although in general we expect a loss of normal regularity near the boundary. Thanks to the special geometry of the quarter space the proof easily follows by the "reflection technique".

Holes in Si quantum dots are being investigated for the implementation of electrically addressable spin qubits. In this perspective, the attention has been focused on the electric-field induced transitions between the eigenstates belonging to the ground doublet. Here we theoretically extend the analysis to the first excited doublet. We show that - in a prototypical quantum dot structure - transitions involving the lowest excited states display Rabi frequencies that are several orders of magnitude larger than those occurring in the ground doublet. A clear relation with the symmetries of the eigenstates emerges, and a wide tunability of the Rabi frequencies by means of the applied bias. Possible implications for multilevel manipulation schemes and for multi-hole qubit encodings can be envisioned.

The analysis of the transportation usage rate provides opportunities for evaluating the efficacy of the transportation service offered by proposing an indicator that integrates actual demand and capacity. This study aims to develop a methodology for analyzing the occupancy rate from large-scale datasets to identify gaps between supply and demand in public transportation. Leveraging the spatio-temporal granularity of data from Automatic People Counting (APC) and relying on the Generalized Linear Mixed Effects Model and the Generalized Mixed-Effect Random Forest, in this study we propose a methodology for analyzing factors determining undercrowding. The results of the model are examined at both the segment and ride levels. Initially, the analysis focuses on identifying segments more likely associated with undercrowding, understanding factors influencing the probability of undercrowding, and exploring their relationships. Subsequently, the analysis extends to the temporal distribution of undercrowding, encompassing its impact on the entire journey. The proposed methodology is applied to analyze APC data, provided by the company responsible for public transport management in Milan, on a radial route of the surface transportation network., Comment: Pre-print version

We demonstrate that, contrary to common wisdom, genuine multipartite entanglement (GME) can be abundantly generated from simple non-correlated many-electron states. We show that the extracted GME can be maximized via spin-independent transformations derived from the quantum Fourier transform. We further demonstrate the possibility of maximizing the GME through localized orbitals in a variety of realistic systems and correlated states. Towards the exploitation of potentially useful entanglement, we rationalize system-specific and universal features of the extracted GME.

This paper presents a Human-Robot Blind Handover architecture within the context of Human-Robot Collaboration (HRC). The focus lies on a blind handover scenario where the operator is intentionally faced away, focused in a task, and requires an object from the robot. In this context, it is imperative for the robot to autonomously manage the entire handover process. Key considerations include ensuring safety while handing the object to the operator's hand, and detect the proper timing to release the object. The article explores strategies to navigate these challenges, emphasizing the need for a robot to operate safely and independently in facilitating blind handovers, thereby contributing to the advancement of HRC protocols and fostering a natural and efficient collaboration between humans and robots.

In the context of Human-Robot Collaboration (HRC), it is crucial that the two actors are able to communicate with each other in a natural and efficient manner. The absence of a communication interface is often a cause of undesired slowdowns. On one hand, this is because unforeseen events may occur, leading to errors. On the other hand, due to the close contact between humans and robots, the speed must be reduced significantly to comply with safety standard ISO/TS 15066. In this paper, we propose a novel architecture that enables operators and robots to communicate efficiently, emulating human-to-human dialogue, while addressing safety concerns. This approach aims to establish a communication framework that not only facilitates collaboration but also reduces undesired speed reduction. Through the use of a predictive simulator, we can anticipate safety-related limitations, ensuring smoother workflows, minimizing risks, and optimizing efficiency. The overall architecture has been validated with a UR10e and compared with a state of the art technique. The results show a significant improvement in user experience, with a corresponding 23% reduction in execution times and a 50% decrease in robot downtime.

In the rapidly evolving landscape of Human-Robot Collaboration (HRC), effective communication between humans and robots is crucial for complex task execution. Traditional request-response systems often lack naturalness and may hinder efficiency. This study emphasizes the importance of adopting human-like communication interactions to enable fluent vocal communication between human operators and robots simulating a collaborative human-robot industrial assembly. We propose a novel approach that employs human-like interactions through natural dialogue, enabling human operators to engage in vocal conversations with robots. Through a comparative experiment, we demonstrate the efficacy of our approach in enhancing task performance and collaboration efficiency. The robot's ability to engage in meaningful vocal conversations enables it to seek clarification, provide status updates, and ask for assistance when required, leading to improved coordination and a smoother workflow. The results indicate that the adoption of human-like conversational interactions positively influences the human-robot collaborative dynamic. Human operators find it easier to convey complex instructions and preferences, resulting in a more productive and satisfying collaboration experience.

For $N\ge 3$ we study the following semipositone problem $$ -\Delta_\gamma u = g(z) f_a(u) \quad \hbox{in $\mathbb{R}^N$}, $$ where $\Delta_\gamma$ is the Grushin operator $$ \Delta_ \gamma u(z) = \Delta_x u(z) + \vert x \vert^{2\gamma} \Delta_y u (z) \quad (\gamma\ge 0), $$ $g\in L^1(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)$ is a positive function, $a>0$ is a parameter and $f_a$ is a continuous function on $\mathbb{R}$ that coincides with $f(t) -a$ for $t\in\mathbb{R}^+$, where $f$ is a continuous function with subcritical and Ambrosetti-Rabinowitz type growth and which satisfies $f(0) = 0$. Depending on the range of $a$, we obtain the existence of positive mountain pass solutions in $D_\gamma(\mathbb{R}^N)$

We consider the initial-boundary value problem in the halfspace for the system of equations of ideal Magneto-Hydrodynamics with a perfectly conducting wall boundary condition. We show the convergence of solutions to the solution of the equations of incompressible MHD as the Mach number goes to zero. Because of the characteristic boundary, where a loss of regularity in the normal direction to the boundary may occur, the convergence is shown in suitable anisotropic Sobolev spaces which take account of the singular behavior at the boundary.

We revisit granular models that represent the size of a firm as the sum of the sizes of multiple constituents or sub-units. Originally developed to address the unexpectedly slow reduction in volatility as firm size increases, these models also explain the shape of the distribution of firm growth rates. We introduce new theoretical insights regarding the relationship between firm size and growth rate statistics within this framework, directly linking the growth statistics of a firm to how diversified it is. The non-intuitive nature of our results arises from the fat-tailed distributions of the size and the number of sub-units, which suggest the categorization of firms into three distinct diversification types: well-diversified firms with sizes evenly distributed across many sub-units, firms with many sub-units but concentrated size in just a few, and poorly diversified firms consisting of only a small number of sub-units. Inspired by our theoretical findings, we identify new empirical patterns in firm growth. Our findings show that growth volatility, when adjusted by average size-conditioned volatility, has a size-independent distribution, but with a tail that is much too thin to be in agreement with the predictions of granular models. Furthermore, the predicted Gaussian distribution of growth rates, even when rescaled for firm-specific volatility, remains fat-tailed across all sizes. Such discrepancies not only challenge the granularity hypothesis but also underscore the need for deeper exploration into the mechanisms driving firm growth.

We consider the boundary value problem $$ \cases{ -\Delta_\gamma u = \lambda u + \left\vert u \right\vert^{2^*_\gamma-2}u &in $\Omega$\cr u = 0 &on $\partial\Omega$,\cr } $$ where $\Omega$ is an open bounded domain in $\mathbb{R}^N$, $N \geq 3$, while $\Delta_\gamma$ is the Grushin operator $$ \Delta_ \gamma u(z) = \Delta_x u(z) + \vert x \vert^{2\gamma} \Delta_y u (z) \quad (\gamma\ge 0). $$ We prove a multiplicity and bifurcation result for this problem, extending the results of Cerami, Fortunato and Struwe and of Fiscella, Molica Bisci and Servadei.

Abdominal Aortic Aneurysm consists of a permanent dilation in the abodminal portion of the aorta and, along with its associated pathologies like calcifications and intraluminal thrombi, is one of the most important pathologies of the circulatory system. The shape of the aorta is among the primary drivers for these health issues, with particular reference to all the characteristics which affects the hemodynamics. Starting from the computed tomography angiography of a patient, we propose to summarize such information using tools derived from Topological Data Analysis, obtaining persistence diagrams which describe the irregularities of the lumen of the aorta. We showcase the effectiveness of such shape-related descriptors with a series of supervised and unsupervised case studies.

This paper aims to explore the factors stimulating different tourism behaviours, with specific reference to same-day visits and overnight stays. To this aim, we employ mobile network data referred to the area of Lombardy. The paper highlights that larger availability of tourism accommodations, cultural and natural endowments are relevant factors explaining overnight stays. Conversely, temporary entertainment and transportation facilities increase municipalities attractiveness for same-day visits. The results also highlight a trade-off in the capability of municipalities of being attractive in connection to both the tourism behaviours, with higher overnight stays in areas with more limited same-day visits. Mobile data offer a spatial and temporal granularity allowing to detect relevant patterns and support the design of tourism precision policies.

Strain represents an ubiquitous feature in semiconductor heterostructures, and can be engineered by different means in order to improve the properties of various devices, including advanced MOSFETs and spin-based qubits. However, its treatment within the envelope function framework is well established only for the homogeneous case, thanks to the theory of Bir and Pikus. Here, we generalize such theory to the case of inhomogeneous strain. By fully accounting for the relativistic effects and metric aspects of the problem, we derive a complete envelope-function Hamiltonian, including the terms that depend on first and second spatial derivatives of the strain tensor., Comment: 4.75 pages + Appendices and Supplementary Material (all references at the end); 4 figures. Revised version

Accurately estimating Origin-Destination (OD) matrices is a topic of increasing interest for efficient transportation network management and sustainable urban planning. Traditionally, travel surveys have supported this process; however, their availability and comprehensiveness can be limited. Moreover, the recent COVID-19 pandemic has triggered unprecedented shifts in mobility patterns, underscoring the urgency of accurate and dynamic mobility data supporting policies and decisions with data-driven evidence. In this study, we tackle these challenges by introducing an innovative pipeline for estimating dynamic OD matrices. The real motivating problem behind this is based on the Trenord railway transportation network in Lombardy, Italy. We apply a novel approach that integrates ticket and subscription sales data with passenger counts obtained from Automated Passenger Counting (APC) systems, making use of the Iterative Proportional Fitting (IPF) algorithm. Our work effectively addresses the complexities posed by incomplete and diverse data sources, showcasing the adaptability of our pipeline across various transportation contexts. Ultimately, this research bridges the gap between available data sources and the escalating need for precise OD matrices. The proposed pipeline fosters a comprehensive grasp of transportation network dynamics, providing a valuable tool for transportation operators, policymakers, and researchers. Indeed, to highlight the potentiality of dynamic OD matrices, we showcase some methods to perform anomaly detection of mobility trends in the network through such matrices and interpret them in light of events that happened in the last months of 2022., Comment: Codes available. Synthetic Data available. Application to train network data. 27 pages, 6 Tables, 16 Figures

In the rapidly evolving landscape of human-robot collaboration, effective communication between humans and robots is crucial for complex task execution. Traditional request-response systems often lack naturalness and may hinder efficiency. In this study, we propose a novel approach that employs human-like conversational interactions for vocal communication between human operators and robots. The framework emphasizes the establishment of a natural and interactive dialogue, enabling human operators to engage in vocal conversations with robots. Through a comparative experiment, we demonstrate the efficacy of our approach in enhancing task performance and collaboration efficiency. The robot's ability to engage in meaningful vocal conversations enables it to seek clarification, provide status updates, and ask for assistance when required, leading to improved coordination and a smoother workflow. The results indicate that the adoption of human-like conversational interactions positively influences the human-robot collaborative dynamic. Human operators find it easier to convey complex instructions and preferences, fostering a more productive and satisfying collaboration experience., Comment: IRIM 3D 2023

The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot and its surroundings have to be executed along with other nominal tasks. In such cases, it is also important to prioritize the former over the latter. In this paper, we formalize the definition of extended set-based tasks, i.e., tasks which can be executed by rendering subsets of the task space asymptotically stable or forward invariant. We propose a mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present and analyze an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations and experiments with robotic manipulators.

Time-of-Flight Positron Emission Tomography is a medical imaging technique, based on the detection of two back-to-back {\gamma}-photons generated from radiotracers injected in the body. Its limit is the ability of employed scintillation detectors to discriminate in time the arrival of {\gamma}-pairs, i.e. the coincidence time resolution (CTR). A CTR < 50 ps that would enable fast imaging with ultralow radiotracer dose. Monolithic materials do not have simultaneously the required high light output and fast emission characteristics, thus the concept of scintillating heterostructure is proposed, where the device is made of a dense scintillator coupled to a fast-emitting light material. Here we present a composite polymeric scintillator, whose density has been increased upon addition of hafnium oxide nanoparticles. This enhanced by +300% its scintillation yield, surpassing commercial plastic scintillators. The nanocomposite is coupled to bismuth germanate oxide (BGO) realizing a multilayer scintillator. We observed the energy sharing between its components, which activate the nanocomposite fast emission enabling a net CTR improvement of 25% with respect to monolithic BGO. These results demonstrate that a controlled loading with dense nanomaterials is an excellent strategy to enhance the performance of polymeric scintillators for their use in advanced radiation detection and imaging technologies.

The new industrial settings are characterized by the presence of human and robots that work in close proximity, cooperating in performing the required job. Such a collaboration, however, requires to pay attention to many aspects. Firstly, it is crucial to enable a communication between this two actors that is natural and efficient. Secondly, the robot behavior must always be compliant with the safety regulations, ensuring always a safe collaboration. In this paper, we propose a framework that enables multi-channel communication between humans and robots by leveraging multimodal fusion of voice and gesture commands while always respecting safety regulations. The framework is validated through a comparative experiment, demonstrating that, thanks to multimodal communication, the robot can extract valuable information for performing the required task and additionally, with the safety layer, the robot can scale its speed to ensure the operator's safety.

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation $$ (-\Delta)^su + V(|x|)u = K(|x|)f(u), \quad \text{ in } \mathbb{R}^N, $$ where the two measurable functions $K > 0$ and $V \geq 0$ could vanish at infinity.

We are concerned with nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-boundary value problem with characteristic free boundary. It is well-known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions that yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. We first identify a sufficient condition ensuring the weak stability of the linearized current-vortex sheets problem. Under this stability condition for the background state, we show that the linearized problem obeys an energy estimate in anisotropic weighted Sobolev spaces with a loss of derivatives. Based on the weakly linear stability results, we then establish the local-in-time existence and nonlinear stability of current-vortex sheets by a suitable Nash-Moser iteration, provided the stability condition is satisfied at each point of the initial discontinuity. This result gives a new confirmation of the stabilizing effect of sufficiently strong magnetic fields on Kelvin-Helmholtz instabilities., Comment: The paper has been accepted for publication in "Archive for Rational Mechanics and Analysis"

The technical specification ISO/TS 15066 provides the foundational elements for assessing the safety of collaborative human-robot cells, which are the cornerstone of the modern industrial paradigm. The standard implementation of the ISO/TS 15066 procedure, however, often results in conservative motions of the robot, with consequently low performance of the cell. In this paper, we propose an energy tank-based approach that allows to directly satisfy the energetic bounds imposed by the ISO/TS 15066, thus avoiding the introduction of conservative modeling and assumptions. The proposed approach has been successfully validated in simulation.