Search

We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model particularises into the microstretch, Cosserat (micropolar), couple-stress, and linear elasticity model for certain choices of material parameters, we recover the fundamental solutions in all these cases.

Since it has often been claimed by academics that reconfiguration is essential, many approaches to reconfiguration, especially of robotic systems, have been developed. Accordingly, the literature on robotics is rich in techniques for reconfiguring robotic systems. However, when talking to researchers in the domain, there seems to be no common understanding of what exactly reconfiguration is and how it relates to other concepts such as adaptation. Beyond this academic perspective, robotics frameworks provide mechanisms for dynamically loading and unloading parts of robotics applications. While we have a fuzzy picture of the state-of-the-art in robotic reconfiguration from an academic perspective, we lack a picture of the state-of-practice from a practitioner perspective. To fill this gap, we survey the literature on reconfiguration in robotic systems by identifying and analyzing 98 relevant papers, review how four major robotics frameworks support reconfiguration, and finally investigate the realization of reconfiguration in 48 robotics applications. When comparing the state-of-the-art with the state-of-practice, we observed a significant discrepancy between them, in particular, the scientific community focuses on complex structural reconfiguration, while in practice only parameter reconfiguration is widely used. Based on our observations, we discuss possible reasons for this discrepancy and conclude with a takeaway message for academics and practitioners interested in robotics.

In this paper, we show that a general method introduced by Fu and Mielke allows to give a complete answer on the existence and uniqueness of a subsonic solution describing the propagation of surface waves in an isotropic half space modelled with the linear theory of isotropic elastic materials with micro-voids. Our result is valid for the entire class of materials admitting real wave propagation which include auxetic materials (negative Poisson's ration) and composite materials with negative-stiffness inclusions (negative Young's modulus). Moreover, the used method allows to formulate a simple and complete numerical strategy for the computation of the solution., Comment: arXiv admin note: text overlap with arXiv:2104.13143

The time varying reproduction number R is a critical variable for situational awareness during infectious disease outbreaks, but delays between infection and reporting hinder its accurate estimation in real time. We propose a nowcasting method for improving the timeliness and accuracy of R estimates, based on comparisons of successive versions of surveillance databases. The method was validated against COVID-19 surveillance data collected in Italy over an 18-month period. Compared to traditional methods, the nowcasted reproduction number reduced the estimation delay from 13 to 8 days, while maintaining a better accuracy. Moreover, it allowed anticipating the detection of periods of epidemic growth by between 6 and 23 days. The method offers a simple and generally applicable tool to improve situational awareness during an epidemic outbreak, allowing for informed public health response planning.

Information Forensics and Security (IFS) is an active R&D area whose goal is to ensure that people use devices, data, and intellectual properties for authorized purposes and to facilitate the gathering of solid evidence to hold perpetrators accountable. For over a quarter century since the 1990s, the IFS research area has grown tremendously to address the societal needs of the digital information era. The IEEE Signal Processing Society (SPS) has emerged as an important hub and leader in this area, and the article below celebrates some landmark technical contributions. In particular, we highlight the major technological advances on some selected focus areas in the field developed in the last 25 years from the research community and present future trends.

Nowadays, as the need for capacity continues to grow, entirely novel services are emerging. A solid cloud-network integrated infrastructure is necessary to supply these services in a real-time responsive, and scalable way. Due to their diverse characteristics and limited capacity, communication and computing resources must be collaboratively managed to unleash their full potential. Although several innovative methods have been proposed to orchestrate the resources, most ignored network resources or relaxed the network as a simple graph, focusing only on cloud resources. This paper fills the gap by studying the joint problem of communication and computing resource allocation, dubbed CCRA, including function placement and assignment, traffic prioritization, and path selection considering capacity constraints and quality requirements, to minimize total cost. We formulate the problem as a non-linear programming model and propose two approaches, dubbed B\&B-CCRA and WF-CCRA, based on the Branch \& Bound and Water-Filling algorithms to solve it when the system is fully known. Then, for partially known systems, a Double Deep Q-Learning (DDQL) architecture is designed. Numerical simulations show that B\&B-CCRA optimally solves the problem, whereas WF-CCRA delivers near-optimal solutions in a substantially shorter time. Furthermore, it is demonstrated that DDQL-CCRA obtains near-optimal solutions in the absence of request-specific information., Comment: in IEEE Transactions on Mobile Computing, 2023. arXiv admin note: text overlap with arXiv:2309.09763

Mechanical metamaterials have recently gathered increasing attention for their uncommon mechanical responses enabling unprecedented applications for elastic wave control. To model the mechanical response of large metamaterials' samples made up of base unit cells, so-called homogenization or upscaling techniques come into play trying to establish an equivalent continuum model describing these macroscopic metamaterials' characteristics. A common approach is to assume a priori that the target continuum model is a classical linear Cauchy continuum featuring the macroscopic displacement as the only kinematical field. This implies that the parameters of such continuum models (density and/or elasticity tensors) must be considered to be frequency-dependent to capture the complex metamaterials' response in the frequency domain. These frequency-dependent models can be useful to describe some of the aforementioned macroscopic metamaterials' properties, yet, they suffer some drawbacks such as featuring negative masses and/or elastic coefficients in some frequency ranges. More than being counter-intuitive, this implies that the considered Cauchy continuum is not positive-definite for all the considered frequencies. In this paper, we present a procedure, based on the definition of extra kinematical variables (with respect to displacement alone) and the use of the inverse Fourier transform in time, to convert a frequency-dependent model into an enriched continuum model of the micromorphic type. All the parameters of the associated enriched model are constant (i.e., frequency-independent) and the model itself remains positive-definite for all the considered frequency ranges. The response of the frequency-dependent model and the associated micromorphic model coincide in the frequency domain, in particular when looking at the dispersion curves., Comment: 37 pages, 10 figures

We study the low temperature $(2+1)$D Solid-On-Solid model on $[[1, L ]]^2$ with zero boundary conditions and nonnegative heights (a floor at height $0$). Caputo et al. (2016) established that this random surface typically admits either $\mathfrak h $ or $\mathfrak h+1$ many nested macroscopic level line loops $\{\mathcal L_i\}_{i\geq 0}$ for an explicit $\mathfrak h\asymp \log L$, and its top loop $\mathcal L_0$ has cube-root fluctuations: e.g., if $\rho(x)$ is the vertical displacement of $\mathcal L_0$ from the bottom boundary point $(x,0)$, then $\max \rho(x) = L^{1/3+o(1)}$ over $x\in I_0:=L/2+[[-L^{2/3},L^{2/3}]]$. It is believed that rescaling $\rho$ by $L^{1/3}$ and $I_0$ by $L^{2/3}$ would yield a limit law of a diffusion on $[-1,1]$. However, no nontrivial lower bound was known on $\rho(x)$ for a fixed $x\in I_0$ (e.g., $x=\frac L2$), let alone on $\min\rho(x)$ in $I_0$, to complement the bound on $\max\rho(x)$. Here we show a lower bound of the predicted order $L^{1/3}$: for every $\epsilon>0$ there exists $\delta>0$ such that $\min_{x\in I_0} \rho(x) \geq \delta L^{1/3}$ with probability at least $1-\epsilon$. The proof relies on the Ornstein--Zernike machinery due to Campanino-Ioffe-Velenik, and a result of Ioffe, Shlosman and Toninelli (2015) that rules out pinning in Ising polymers with modified interactions along the boundary. En route, we refine the latter result into a Brownian excursion limit law, which may be of independent interest. We further show that in a $ K L^{2/3}\times K L^{2/3}$ box with boundary conditions $\mathfrak h-1,\mathfrak h,\mathfrak h,\mathfrak h$ (i.e., $\mathfrak h-1$ on the bottom side and $\mathfrak h$ elsewhere), the limit of $\rho(x)$ as $K,L\to\infty$ is a Ferrari--Spohn diffusion., Comment: 63 pages, 2 figures. Final version

In many fields of robotics, knowing the relative position and orientation between two sensors is a mandatory precondition to operate with multiple sensing modalities. In this context, the pair LiDAR-RGB cameras offer complementary features: LiDARs yield sparse high quality range measurements, while RGB cameras provide a dense color measurement of the environment. Existing techniques often rely either on complex calibration targets that are expensive to obtain, or extracted virtual correspondences that can hinder the estimate's accuracy. In this paper we address the problem of LiDAR-RGB calibration using typical calibration patterns (i.e. A3 chessboard) with minimal human intervention. Our approach exploits the planarity of the target to find correspondences between the sensors measurements, leading to features that are robust to LiDAR noise. Moreover, we estimate a solution by solving a joint non-linear optimization problem. We validated our approach by carrying on quantitative and comparative experiments with other state-of-the-art approaches. Our results show that our simple schema performs on par or better than other approches using complex calibration targets. Finally, we release an open-source C++ implementation at \url{https://github.com/srrg-sapienza/ca2lib}, Comment: 7 pages, 10 figures

We show how to explicitly compute the homogenized curvature energy appearing in the isotropic $\Gamma$-limit for flat and for curved initial configuration Cosserat shell models, when a parental three-dimensional minimization problem on $\Omega \subset \mathbb{R}^3$ for a Cosserat energy based on the second order dislocation density tensor $\alpha:=\overline{R} ^T {\rm Curl}\,\overline{R} \in \mathbb{R}^{3\times 3}$, $\overline{R}\in {\rm SO}(3)$ is used.

In this paper we establish spectral comparison results for Schr\"odinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite quantum graphs such as a modified local Weyl law. In this sense, we regard this paper as a starting point for a more thorough investigation of spectral comparison results on more general infinite metric graphs., Comment: 11 pages, 3 figures, comments welcome!

In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of transformations, in a non-expansive way. If the set of transformations acting is a group, then we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subject to the action of certain self-maps, and the space of P-GENEOs between these spaces. We define pseudo-metrics on them and show some properties of the resulting spaces. In particular, we show how such spaces have convenient approximation and convexity properties.

Based on the main result presented in a recent paper, we derive Ambarzumian-type theorems for Schr\"odinger operators defined on quantum graphs. We recover existing results such as the classical theorem by Ambarzumian and establish some seemingly new statements, too., Comment: 5 pages, comments welcome!

In this work we construct novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the $\mathrm{div} \mathrm{Div}$-sequence with respect to the $H(\mathrm{sym} \mathrm{Curl})$-space. The elements respect $H(\mathrm{Curl})$-regularity and their lowest order versions converge optimally for $[H(\mathrm{sym} \mathrm{Curl}) \setminus H(\mathrm{Curl})]$-fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model.

Over the last two decades a plethora of new thermoelectric materials, their alloys, and their nanostructures were synthesized. The ZT figure of merit, which quantifies the thermoelectric efficiency of these materials increased from values of unity to values consistently beyond two across material families. At the same time, the ability to identify and optimize such materials, has stressed the need for advanced numerical tools for computing electronic transport in materials with arbitrary bandstructure complexity, multiple scattering mechanisms, and a large degree of nanostructuring. Many computational methods have been developed, the majority of which utilize the Boltzmann transport equation (BTE) formalism, spanning from fully ab initio to empirical treatment, with varying degree of computational expense and accuracy. In this paper we describe a suitable computational process that we have recently developed specifically for thermoelectric materials. The method consists of three independent software packages that we have developed and: 1) begins from ab initio calculation of the electron-phonon scattering rates, 2) to then be used within a Boltzmann transport simulator, and 3) calculated quantities from BTE are then passed on to a Monte Carlo simulator to examine electronic transport in highly nanostructured material configurations. The method we describe is computationally significantly advantageous compared to current fully ab initio and existing Monte Carlo methods, but with a similar degree of accuracy, thus making it truly enabling in understanding and assessing thermoelectric transport in complex band, nanostructured materials., Comment: 39 pages, 9 figures

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and quantum graphs, to Laplacians on a class of fractals including the Sierpi\'nski gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed.

In the modern digital world users need to make privacy and security choices that have far-reaching consequences. Researchers are increasingly studying people's decisions when facing with privacy and security trade-offs, the pressing and time consuming disincentives that influence those decisions, and methods to mitigate them. This work aims to present a systematic review of the literature on privacy categorization, which has been defined in terms of profile, profiling, segmentation, clustering and personae. Privacy categorization involves the possibility to classify users according to specific prerequisites, such as their ability to manage privacy issues, or in terms of which type of and how many personal information they decide or do not decide to disclose. Privacy categorization has been defined and used for different purposes. The systematic review focuses on three main research questions that investigate the study contexts, i.e. the motivations and research questions, that propose privacy categorisations; the methodologies and results of privacy categorisations; the evolution of privacy categorisations over time. Ultimately it tries to provide an answer whether privacy categorization as a research attempt is still meaningful and may have a future.

In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that underpins the financial interdependencies between different organizations constitutes the backbone of the financial system. A failure in one or more of these organizations can lead the propagation of the financial collapse onto other organizations in a domino effect. Paramount importance is therefore given to the mitigation of these failures. Motivated by the relevance of this problem and recent prominent events connected to it, we develop a framework that allows us to investigate under what conditions organizations remain healthy or are involved in the propagation of the failures in the network. The contribution of this paper is the following: i) we develop a dynamical model that describes the equity values of financial organizations and their evolution over time given an initial condition; ii) we characterize the equilibria for this model by proving the existence and uniqueness of these equilibria, and by providing an explicit expression for them; and iii) we provide a computational method via sign-space iteration to analyze the propagation of failures and the attractive equilibrium point.

We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic system of partial differential equations that is coupled with a system of Maxwell-type. The result is obtained by combining a Helmholtz decomposition argument with regularity results for linear elliptic systems and the classical embedding of $H(\mathrm{div};\Omega)\cap H_0(\mathrm{curl};\Omega)$ into $H^1(\Omega)$., Comment: 14 pages

A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.

Effectively specifying and implementing robotic missions poses a set of challenges to software engineering for robotic systems. These challenges stem from the need to formalize and execute a robot's high-level tasks while considering various application scenarios and conditions, also known as contexts, in real-world operational environments. Writing correct mission specifications that explicitly account for multiple contexts can be tedious and error-prone. Furthermore, as the number of contexts, and consequently the complexity of the specification, increases, generating a correct-by-construction implementation (e.g., by using synthesis methods) can become intractable. A viable approach to address these issues is to decompose the mission specification into smaller, manageable sub-missions, with each sub-mission tailored to a specific context. Nevertheless, this compositional approach introduces its own set of challenges in ensuring the overall mission's correctness. In this paper, we propose a novel compositional framework for specifying and implementing contextual robotic missions using assume-guarantee contracts. The mission specification is structured in a hierarchical and modular fashion, allowing for each sub-mission to be synthesized as an independent robot controller. We address the problem of dynamically switching between sub-mission controllers while ensuring correctness under predefined conditions.

Research in 3D semantic segmentation has been increasing performance metrics, like the IoU, by scaling model complexity and computational resources, leaving behind researchers and practitioners that (1) cannot access the necessary resources and (2) do need transparency on the model decision mechanisms. In this paper, we propose SCENE-Net, a low-resource white-box model for 3D point cloud semantic segmentation. SCENE-Net identifies signature shapes on the point cloud via group equivariant non-expansive operators (GENEOs), providing intrinsic geometric interpretability. Our training time on a laptop is 85~min, and our inference time is 20~ms. SCENE-Net has 11 trainable geometrical parameters and requires fewer data than black-box models. SCENE--Net offers robustness to noisy labeling and data imbalance and has comparable IoU to state-of-the-art methods. With this paper, we release a 40~000 Km labeled dataset of rural terrain point clouds and our code implementation.

This paper presents a new approach for assessing uncertainty in machine translation by simultaneously evaluating translation quality and providing a reliable confidence score. Our approach utilizes conformal predictive distributions to produce prediction intervals with guaranteed coverage, meaning that for any given significance level $\epsilon$, we can expect the true quality score of a translation to fall out of the interval at a rate of $1-\epsilon$. In this paper, we demonstrate how our method outperforms a simple, but effective baseline on six different language pairs in terms of coverage and sharpness. Furthermore, we validate that our approach requires the data exchangeability assumption to hold for optimal performance., Comment: Accepted at the 12th Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2023

We report the Astrorivelatore Gamma ad Immagini LEggero (AGILE) observations of solar flares, detected by the on board anticoincidence system in the 80-200 keV energy range, from 2007 May 1st to 2022 August 31st. In more than 15 yr, AGILE detected 5003 X-ray, minute-lasting transients, compatible with a solar origin. A cross-correlation of these transients with the Geostationary Operational Environmental Satellites (GOES) official solar flare database allowed to associate an intensity class (i.e., B, C, M, or X) to 3572 of them, for which we investigated the main temporal and intensity parameters. The AGILE data clearly revealed the solar activity covering the last stages of the 23rd cycle, the whole 24th cycle, and the beginning of the current 25th cycle. In order to compare our results with other space missions operating in the high-energy range, we also analyzed the public lists of solar flares reported by RHESSI and Fermi Gamma-ray Burst Monitor. This catalog reports 1424 events not contained in the GOES official dataset, which, after statistical comparisons, are compatible with low-intensity, short-duration solar flares. Besides providing a further dataset of solar flares detected in the hard X-ray range, this study allowed to point out two main features: a longer persistence of the decay phase in the high-energy regime, with respect to the soft X-rays, and a tendency of the flare maximum to be reached earlier in the soft X-rays with respect to the hard X-rays. Both these aspects support a two-phase acceleration mechanism of electrons in the solar atmosphere., Comment: 22 pages, 10 figures

In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a special class of large graphs, called social graphs, that might prove interesting for applications. In addition, we derive spectral estimates involving the surface area and, as a main result, present an upper bound on the second eigenvalue for planar graphs which in some cases improves upon existing bounds from D. A. Spielman and S.-H. Teng, Spectral partitioning works: Planar graphs and finite element meshes, and M. Pl\"umer, Upper eigenvalue bounds for the Kirchhoff Laplacian on embedded metric graphs., Comment: 15 pages; six figures; comments welcome!

We investigate discretizations of a geometrically nonlinear elastic Cosserat shell with nonplanar reference configuration originally introduced by B\^irsan, Ghiba, Martin, and Neff in 2019. The shell model includes curvature terms up to order 5 in the shell thickness, which are crucial to reliably simulate high-curvature deformations such as near-folds or creases. The original model is generalized to shells that are not homeomorphic to a subset of $\mathbb{R}^2$. For this, we replace the originally planar parameter domain by an abstract two-dimensional manifold, and verify that the hyperelastic shell energy and three-dimensional reconstruction are invariant under changes of the local coordinate systems. This general approach allows to determine the elastic response for even non-orientable surfaces like the M\"obius strip and the Klein bottle. We discretize the model with a geometric finite element method and, using that geometric finite elements are $H^1$-conforming, prove that the discrete shell model has a solution. Numerical tests then show the general performance and versatility of the model and discretization method.

The zero and first order Gamma-limit of vanishing internal length scale are studied for the mechanical energy of a shear problem in geometrically nonlinear Cosserat elasticity. The convergence of the minimizers is shown and the limit functionals are characterized., Comment: 27 pages, 6 figures

Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines (layers), and their relationships (edges) are represented by segments connecting vertices. Methods for constructing 2-layer drawings often try to minimize the number of edge crossings. We use vertex splitting to reduce the number of crossings, by replacing selected vertices on one layer by two (or more) copies and suitably distributing their incident edges among these copies. We study several optimization problems related to vertex splitting, either minimizing the number of crossings or removing all crossings with fewest splits. While we prove that some variants are \NP-complete, we obtain polynomial-time algorithms for others. We run our algorithms on a benchmark set of bipartite graphs representing the relationships between human anatomical structures and cell types.

The relaxed micromorphic model is a generalized continuum model that is well-posed in the space $X = [H^1]^3 \times [H(\textrm{curl})]^3$. Consequently, finite element formulations of the model rely on $H^1$-conforming subspaces and N\'ed\'elec elements for discrete solutions of the corresponding variational problem. This work applies the recently introduced polytopal template methodology for the construction of N\'ed\'elec elements. This is done in conjunction with Bernstein-B\'ezier polynomials and dual numbers in order to compute hp-FEM solutions of the model. Bernstein-B\'ezier polynomials allow for optimal complexity in the assembly procedure due to their natural factorization into univariate Bernstein base functions. In this work, this characteristic is further augmented by the use of dual numbers in order to compute their values and their derivatives simultaneously. The application of the polytopal template methodology for the construction of the N\'ed\'elec base functions allows them to directly inherit the optimal complexity of the underlying Bernstein-B\'ezier basis. We introduce the Bernstein-B\'ezier basis along with its factorization to univariate Bernstein base functions, the principle of automatic differentiation via dual numbers and a detailed construction of N\'ed\'elec elements based on Bernstein-B\'ezier polynomials with the polytopal template methodology. This is complemented with a corresponding technique to embed Dirichlet boundary conditions, with emphasis on the consistent coupling condition. The performance of the elements is shown in examples of the relaxed micromorphic model.