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We recall in this note that the induced tangent stiffness tensor $\mathbb{H}^{\text{ZJ}}_{\tau}(\tau)$ appearing in a hypoelastic formulation based on the Zaremba-Jaumann corotational derivative and the rate constitutive equation for the Kirchhoff stress tensor $\tau$ is minor and major symmetric if the Kirchhoff stress $\tau$ is derived from an elastic potential $\mathrm{W}(F)$. This result is vaguely known in the literature. Here, we expose two different notational approaches which highlight the full symmetry of the tangent stiffness tensor $\mathbb{H}^{\text{ZJ}}_{\tau}(\tau)$. The first approach is based on the direct use of the definition of each symmetry (minor and major), i.e., via contractions of the tensor with the deformation rate tensor $D$. The second approach aims at finding an absolute expression of the tensor $\mathbb{H}^{\text{ZJ}}_{\tau}(\tau)$, by means of special tensor products and their symmetrisations. In some past works, the major symmetry of $\mathbb{H}^{\text{ZJ}}_{\tau}(\tau)$ has been missed because not all necessary symmetrisations were applied. The approach is exemplified for the isotropic Hencky energy. Corresponding stability checks of software packages are shortly discussed., Comment: arXiv admin note: text overlap with arXiv:2409.20051

Kibble balances are energy-conversion devices currently employed to realize the metrological redefinition of the kilogram unit of mass. The authors, noticing that the literature lacks a fundamental mathematical description of the Kibble balance working principle, propose a differential geometric approach to study general non-linear electromagneto-mechanical systems. Based on the application of Finsler geometry, the mathematical apparatus introduced in the paper is used to analyze the limits of modern Kibble balances, with particular attention to the magnetic design. The authors review the formalism introduced by G. Kron (who proposed a unified theory of electrical machines) and extend it to non-linear systems. Numerical simulations are presented to show the difference between a linear and non-linear analysis of Kibble balance machines, with attention to the hysteretic behaviour of the permanent magnet system., Comment: 10 pages, 6 figures, Original Research Paper

We combine the rate-formulation for the objective, corotational Zaremba-Jaumann rate \begin{align} \frac{{\rm D}^{\rm ZJ}}{{\rm D} t} [\sigma] = \mathbb{H}^{\rm ZJ}(\sigma).D, \qquad D = {\rm sym} {\rm D} v\,, \end{align} operating on the Cauchy stress $\sigma$, the Eulerian strain rate $D$ and the spatial velocity $v$ with the novel \enquote{corotational stability postulate} (CSP)\begin{equation} \Bigl\langle \frac{{\rm D}^{\rm ZJ}}{{\rm D} t}[\sigma], D \Bigr\rangle > 0 \qquad \forall \, D\in{\rm Sym}(3)\setminus\{0\} \end{equation} to show that for a given isotropic Cauchy-elastic constitutive law $B \mapsto \sigma(B)$ in terms of the left Cauchy-Green tensor $B = F F^T$, the induced fourth-order tangent stiffness tensor $\mathbb{H}^{\rm ZJ}(\sigma)$ is positive definite if and only if for $\widehat{\sigma}(\log B):=\sigma(B)$, the strong monotonicity condition (TSTS-M$^{++}$) in the logarithmic strain is satisfied. Thus (CSP) implies (TSTS-M^{++}) and vice-versa, and both imply the invertibility of the hypo-elastic material law between the stress and strain rates given by the tensor $\mathbb{H}^{\rm ZJ}(\sigma)$. The same characterization remains true for the corotational Green-Naghdi rate as well as the corotational logarithmic rate, conferring the corotational stability postulate (CSP) together with the monotonicity in the logarithmic strain tensor (TSTS-M^{++}) a far reaching generality. It is conjectured that this characterization of (CSP) holds for a large class of reasonable corotational rates. The result for the logarithmic rate is based on a novel chain rule for corotational derivatives of isotropic tensor functions.

We investigate objective corotational rates satisfying an additional, physically plausible assumption. More precisely, we require for \begin{equation*} \frac{{\rm D}^{\circ}}{{\rm D} t}[B] = \mathbb{A}^{\circ}(B).D \end{equation*} that $\mathbb{A}^{\circ}(B)$ is positive definite. Here, $B = F \, F^T$ is the left Cauchy-Green tensor, $\frac{{\rm D}^{\circ}}{{\rm D}t}$ is a specific objective corotational rate, $D = {\rm sym} \, {\rm D} v$ is the Eulerian stretching and $\mathbb{A}^{\circ}(B)$ is the corresponding induced fourth order tangent stiffness tensor. Well known corotational rates like the Zaremba-Jaumann rate, the Green-Naghdi rate and the logarithmic rate belong to this family of ``positive'' corotational rates. For general objective corotational rates $\frac{{\rm D}^{\circ}}{{\rm D} t}$ we determine several conditions characterizing positivity. Among them an explicit condition on the material spin-functions of Xiao, Bruhns and Meyers (2004). We also give a geometrical motivation for invertibility and positivity and highlight the structure preserving properties of corotational rates that distinguish them from more general objective stress rates. Applications of this novel concept are indicated.

A thorough understanding of the small-signal response of solar cells can reveal intrinsic device characteristics and pave the way for innovations. This study investigates the impedance of crystalline silicon PN junction devices using TCAD simulations, focusing on the impact of frequency, bias voltage, and the presence of a low-high (LH) junction. It is shown that the PN junction exhibits a fixed $RC$-loop behavior at low frequencies, but undergoes relaxation in both resistance $R_j$ and capacitance $C_j$ as frequency increases. Moreover, it is revealed that the addition of a LH junction impacts the impedance by altering $R_j$, $C_j$, and the series resistance $R_s$. Contrary to conventional modeling approaches, which often include an additional $RC$-loop to represent the LH junction, this study suggests that such a representation does not represent the underlying physics, particularly the frequency-dependent behavior of $R_j$ and $C_j$.

Following Hill and Leblond, the aim of our work is to show, for isotropic nonlinear elasticity, a relation between the corotational Zaremba-Jaumann objective derivative of the Cauchy stress $\sigma$, i.e. \begin{equation} \frac{{\rm D}^{\rm ZJ}}{{\rm D} t}[\sigma] = \frac{{\rm d}}{{\rm d}{t}}[\sigma] - W \, \sigma + \sigma \, W, \qquad W = {\rm skew}(\dot F \, F^{-1}) \end{equation} and a constitutive requirement involving the logarithmic strain tensor. Given the deformation tensor $F ={\rm D} \varphi$, the left Cauchy-Green tensor $B = F \, F^T$, and the strain-rate tensor $D = {\rm sym}(\dot F \, F^{-1})$, we show that \begin{equation} \label{eqCPSdef} \begin{alignedat}{2} \forall \,D\in{\rm Sym}(3) \! \setminus \! \{0\}: ~ \langle{\frac{{\rm D}^{\rm ZJ}}{{\rm D} t}[\sigma]},{D}\rangle > 0 \quad &\iff \quad \log B \longmapsto \widehat\sigma(\log B) \;\textrm{is strongly Hilbert-monotone} &\iff \quad {\rm sym} {\rm D}_{\log B} \widehat \sigma(\log B) \in{\rm Sym}^{++}_4(6) \quad \text{(TSTS-M$^{++}$)}, \end{alignedat} \tag{1} \end{equation} where ${\rm Sym}^{++}_4(6)$ denotes the set of positive definite, (minor and major) symmetric fourth order tensors. We call the first inequality ``corotational stability postulate'' (CSP), a novel concept, which implies the \textbf{T}rue-\textbf{S}tress \textbf{T}rue-\textbf{S}train strict Hilbert-\textbf{M}onotonicity (TSTS-M$^+$) for $B \mapsto \sigma(B) = \widehat \sigma(\log B)$, i.e. \begin{equation} \langle \widehat\sigma(\log B_1)-\widehat\sigma(\log B_2),{\log B_1-\log B_2} \rangle> 0 \qquad \forall \, B_1\neq B_2\in{\rm Sym}^{++}(3) \, . \end{equation} In this paper we expand on the ideas of Hill and Leblond, extending Leblonds calculus to the Cauchy elastic case.

Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most $k$ times for some integer $k \ge 1$. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that upward-$k$-planarity testing is NP-complete already for $k =1$ and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward $1$-planar drawing in which all vertices are incident to the outer face., Comment: This is the extended version, with full appendix, of a paper to appear in the Proc. 32nd Int. Symp. Graph Drawing & Network Visualization (GD 2024)

We report the machine learning (ML)-based approach allowing thermoelectric generator (TEG) efficiency evaluation directly from 5 parameters: 2 physical properties - carriers density and energy gap, and 3 engineering parameters - external load resistance, TEG hot side temperature and leg height. Then, we propose to use genetic algorithm to optimize the proposed parameters in a way to maximize TEG efficiency. To prepare data, physical properties of n- and p-type materials were computed by coupling Density Functional Theory to Boltzmann Transport, and used for Finite Elements simulations. TEG efficiency was evaluated from a finite elements model considering design, radiative heat loss, contacts, external load resistance and different combinations of materials, resulting in 5300 different scenarios. For ML model, physical properties and engineering parameters were used as input features, skipping transport coefficients, while TEG efficiency was a target. Model was built on gradient boosting algorithm, its performance was evaluated using the coefficient of determination that reached a value of 0.98 on test dataset. Features importance analysis revealed the most crucial features for Half-Heusler-based TEG efficiency: carriers density or Fermi level, indicating the predominant role of electrical conductivity and electronic part of electrical conductivity. Features that were less important, but able to increase model performance were: energy gap, lattice thermal conductivity, charge carrier relaxation time and carriers conductivity effective mass. Features showed no impact were: density of states effective mass, heat capacity, density, relative permittivity and leg width. The proposed approach can be applied for the identification of the most important physical properties and their optimal values, the optimization of TEG design and operation conditions in a way to maximize TEG efficiency.

The aim of the paper is to recall the importance of the study of invertibility and monotonicity of stress-strain relations for investigating the non-uniqueness and bifurcation of homogeneous solutions of the equilibrium problem of a hyperelastic cube subjected to equiaxial tensile forces. In other words, we reconsider a remarkable possibility in this nonlinear scenario: Does symmetric loading lead only to symmetric deformations or also to asymmetric deformations? If so, what can we say about monotonicity for these homogeneous solutions, a property which is less restrictive than the energetic stability criteria of homogeneous solutions for Rivlin's cube problem. For the Neo-Hooke type materials we establish what properties the volumetric function $h$ depending on ${\rm det}\, F$ must have to ensure the existence of a unique radial solution (i.e. the cube must continue to remain a cube) for any magnitude of radial stress acting on the cube. The function $h$ proposed by Ciarlet and Geymonat satisfies these conditions. However, discontinuous equilibrium trajectories may occur, characterized by abruptly appearing non-symmetric deformations with increasing load, and a cube can instantaneously become a parallelepiped. Up to the load value for which the bifurcation in the radial solution is realized local monotonicity holds true. However, after exceeding this value, monotonicity no longer occurs on homogeneous deformations which, in turn, preserve the cube shape.

We study Schr\"odinger operators on compact finite metric graphs subject to $\delta'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing $\delta'$-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in [arXiv:2212.12531]. ., Comment: 12 pages, 1 figure; comments are welcome!

We have developed a first-principles method to calculate the electron-phonon coupling for specific modes and q-points in the Brillouin Zone for crystalline organic semiconductors. Using the obtained coupling strengths, we propose an approach to compute the temperature-dependent mobilities of electrons and holes. This methodology is applied to both bulk and thin-film polymorphs of tetracene. To validate our treatment of the electronic structures and vibrational properties, we calculate the Raman spectra in the lattice-phonon region and compare them with experimental data. We then compare the computed mobilities with available data for single crystals, finding good agreement within the experimental range, especially when accounting for possible charged impurities. Finally, we discuss the observed differences between the polymorphs.

Marine in-situ data is collected by sensors mounted on fixed or mobile systems deployed into the ocean. This type of data is crucial both for the ocean industries and public authorities, e.g., for monitoring and forecasting the state of marine ecosystems and/or climate changes. Various public organizations have collected, managed, and openly shared in-situ marine data in the past decade. Recently, initiatives like the Ocean Decade Corporate Data Group have incentivized the sharing of marine data of public interest from private companies aiding in ocean management. However, there is no clear understanding of the impact of data quality in the engineering of systems, as well as on how to manage and exploit the collected data. In this paper, we propose main architectural decisions and a data flow-oriented component and connector view for marine in-situ data streams. Our results are based on a longitudinal empirical software engineering process, and driven by knowledge extracted from the experts in the marine domain from public and private organizations, and challenges identified in the literature. The proposed software architecture is instantiated and exemplified in a prototype implementation., Comment: The paper is accepted at the 21st IEEE International Conference on Software Architecture (ICSA 2024)

We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental degrees of freedom intact. Consequently, the degrees of freedom intrinsically agree even at the interface with a domain of a different dimensionality. Thus, this approach circumvents the need for intermediate finite elements or mortar methods. We introduce the derivations of all models of various dimensions using tangential differential calculus. The coupling itself is then achieved by defining a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples involving a three-dimensional silicone-rubber block reinforced with a curved graphite shell on its lower surface, a three-dimensional silver block reinforced with a graphite plate and beams, and lastly, intersecting silver shells reinforced with graphite beams.

Quantifying the uncertainty of predictions made by large language models (LLMs) in binary text classification tasks remains a challenge. Calibration, in the context of LLMs, refers to the alignment between the model's predicted probabilities and the actual correctness of its predictions. A well-calibrated model should produce probabilities that accurately reflect the likelihood of its predictions being correct. We propose a novel approach that utilizes the inductive Venn--Abers predictor (IVAP) to calibrate the probabilities associated with the output tokens corresponding to the binary labels. Our experiments on the BoolQ dataset using the Llama 2 model demonstrate that IVAP consistently outperforms the commonly used temperature scaling method for various label token choices, achieving well-calibrated probabilities while maintaining high predictive quality. Our findings contribute to the understanding of calibration techniques for LLMs and provide a practical solution for obtaining reliable uncertainty estimates in binary question answering tasks, enhancing the interpretability and trustworthiness of LLM predictions., Comment: Accepted to COPA 2024 (13th Symposium on Conformal and Probabilistic Prediction with Applications)

For plane strain linear elasticity, given any anisotropic elasticity tensor $\mathbb{C}_{\rm aniso}$, we determine a best approximating isotropic counterpart $\mathbb{C}_{\rm iso}$. This is not done by using a distance measure on the space of positive definite elasticity tensors (Euclidean or logarithmic distance) but by considering two simple isotropic analytic solutions (center of dilatation and concentrated couple) and best fitting these radial solutions to the numerical anisotropic solution based on $\mathbb{C}_{\rm aniso}$. The numerical solution is done via a finite element calculation, and the fitting via a subsequent quadratic error minimization. Thus, we obtain the two Lam\'e-moduli $\mu$, $\lambda$ (or $\mu$ and the bulk-modulus $\kappa$) of $\mathbb{C}_{\rm aniso}$. We observe that our so-determined isotropic tensor $\mathbb{C}_{\rm iso}$ coincides with neither the best logarithmic fit of Norris nor the best Euclidean fit. Our result calls into question the very notion of a best-fit isotropic elasticity tensor to a given anisotropic material.

Cyber-physical systems (CPS) development requires verifying whether system behaviors violate their requirements. This analysis often considers system behaviors expressed by execution traces and requirements expressed by signal-based temporal properties. When an execution trace violates a requirement, engineers need to solve the trace diagnostic problem: They need to understand the cause of the breach. Automated trace diagnostic techniques aim to support engineers in the trace diagnostic activity. This paper proposes search-based trace-diagnostic (SBTD), a novel trace-diagnostic technique for CPS requirements. Unlike existing techniques, SBTD relies on evolutionary search. SBTD starts from a set of candidate diagnoses, applies an evolutionary algorithm iteratively to generate new candidate diagnoses (via mutation, recombination, and selection), and uses a fitness function to determine the qualities of these solutions. Then, a diagnostic generator step is performed to explain the cause of the trace violation. We implemented Diagnosis, an SBTD tool for signal-based temporal logic requirements expressed using the Hybrid Logic of Signals (HLS). We evaluated Diagnosis by performing 34 experiments for 17 trace-requirements combinations leading to a property violation and by assessing the effectiveness of SBTD in producing informative diagnoses and its efficiency in generating them on a time basis. Our results confirm that Diagnosis can produce informative diagnoses in practical time for most of our experiments (33 out of 34)., Comment: 14 pages plus two for references

In this paper we extend the micromagnetic theory of magnetostatic surface waves in insulating ferromagnetic thin films to include the applied electric field effects. We start by identifying the two main effects on the dispersion relation: the first one is of relativistic nature and emerges as a consequence of the Ahronov-Casher effect, while the second one is a consequence of the electric field induced symmetry breaking operating at the level of magnetic exchange interactions. We support our theory by comparing its predictions with experimental data on ittrium iron garnet thin films taken from the literature. The main result is to evidence the limitations of using the same value of the applied electric field to address both effects and to emphasize that crystal symmetry breaking due to the applied electric field brings about the contributions of the crystal field and determines different amplitudes for the two effects., Comment: 6 pages, 6 figures presented at the conference HMM 2023 Vienna

As testified by new regulations like the European AI act, the worries about the societal impact of (autonomous) software technologies are becoming of public concern. Social and human values, besides the traditional software behaviour and quality, are increasingly recognized as important for sustainability and long-term well-being. In this paper, we identify the macro and technological challenges and opportunities of present and future digital systems that should be engineered for humanity. Our specific perspective in identifying the challenges is to focus on humans and on their role in their co-existence with digital systems. The first challenge considers humans in a proactive role when interacting with the digital systems, i.e., taking initiative in making things happening instead of reacting to events. The second concerns humans having an active role in the interaction with the digital systems i.e., on humans that interact with digital systems as a reaction to events. The third challenge focuses on humans that have a passive role i.e., they experience, enjoy or even suffer the decisions and/or actions of digital systems. Two further transversal challenges are considered: the duality of trust and trustworthiness and the compliance to legislation that both may seriously affect the deployment and use of digital systems.

The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.

In this work we present a consistent reduction of the relaxed micromorphic model to its corresponding two-dimensional planar model, such that its capacity to capture discontinuous dilatation fields is preserved. As a direct consequence of our approach, new conforming finite elements for $H^\mathrm{dev}(\mathrm{Curl},A)$ become necessary. We present two novel $H^\mathrm{dev}(\mathrm{Curl},A)$-conforming finite element spaces, of which one is a macro element based on Clough--Tocher splits, as well as primal and mixed variational formulations of the planar relaxed micromorphic model. Finally, we demonstrate the effectiveness of our approach with two numerical examples.

Time series clustering is fundamental in data analysis for discovering temporal patterns. Despite recent advancements, learning cluster-friendly representations is still challenging, particularly with long and complex time series. Deep temporal clustering methods have been trying to integrate the canonical k-means into end-to-end training of neural networks but fall back on surrogate losses due to the non-differentiability of the hard cluster assignment, yielding sub-optimal solutions. In addition, the autoregressive strategy used in the state-of-the-art RNNs is subject to error accumulation and slow training, while recent research findings have revealed that Transformers are less effective due to time points lacking semantic meaning, to the permutation invariance of attention that discards the chronological order and high computation cost. In light of these observations, we present LoSTer which is a novel dense autoencoder architecture for the long-sequence time series clustering problem (LSTC) capable of optimizing the k-means objective via the Gumbel-softmax reparameterization trick and designed specifically for accurate and fast clustering of long time series. Extensive experiments on numerous benchmark datasets and two real-world applications prove the effectiveness of LoSTer over state-of-the-art RNNs and Transformer-based deep clustering methods., Comment: Under review in IEEE Transactions on Pattern Analysis and Machine Intelligence

The shift from Cloud Computing to a Cloud-Edge continuum presents new opportunities and challenges for data-intensive and interactive applications. Edge computing has garnered a lot of attention from both industry and academia in recent years, emerging as a key enabler for meeting the increasingly strict demands of Next Generation applications. In Edge computing the computations are placed closer to the end-users, to facilitate low-latency and high-bandwidth applications and services. However, the distributed, dynamic, and heterogeneous nature of Edge computing, presents a significant challenge for service placement. A critical aspect of Edge computing involves managing the placement of applications within the network system to minimize each application's runtime, considering the resources available on system devices and the capabilities of the system's network. The placement of application images must be proactively planned to minimize image tranfer time, and meet the strict demands of the applications. In this regard, this paper proposes an approach for proactive image placement that combines Graph Neural Networks and actor-critic Reinforcement Learning, which is evaluated empirically and compared against various solutions. The findings indicate that although the proposed approach may result in longer execution times in certain scenarios, it consistently achieves superior outcomes in terms of application placement.

This position paper introduces Urgent Edge Computing (UEC) as a paradigm shift addressing the evolving demands of time-sensitive applications in distributed edge environments, in time-critical scenarios. With a focus on ultra-low latency, availability, resource management, decentralization, self-organization, and robust security, UEC aims to facilitate operations in critical scenarios such as disaster response, environmental monitoring, and smart city management. This paper outlines and discusses the key requirements, challenges, and enablers along with a conceptual architecture. The paper also outlines the potential applications of Urgent Edge Computing

Robotic systems are becoming pervasive and adopted in increasingly many domains, such as manufacturing, healthcare, and space exploration. To this end, engineering software has emerged as a crucial discipline for building maintainable and reusable robotic systems. The robotics software engineering research field has received increasing attention, fostering autonomy as a fundamental goal. However, robotics developers are still challenged to achieve this goal because simulation cannot realistically deliver solutions to emulate real-world phenomena. Robots also need to operate in unpredictable and uncontrollable environments, which require safe and trustworthy self-adaptation capabilities implemented in software. Typical techniques to address the challenges are runtime verification, field-based testing, and mitigation techniques that enable fail-safe solutions. However, no clear guidance exists for architecting ROS-based systems to enable and facilitate runtime verification and field-based testing. This paper aims to fill this gap by providing guidelines to help developers and quality assurance (QA) teams develop, verify, or test their robots in the field. These guidelines are carefully tailored to address the challenges and requirements of testing robotics systems in real-world scenarios. We conducted (i) a literature review on studies addressing runtime verification and field-based testing for robotic systems, (ii) mined ROS-based applications repositories, and (iii) validated the applicability, clarity, and usefulness via two questionnaires with 55 answers overall. We contribute 20 guidelines: 8 for developers and 12 for QA teams formulated for researchers and practitioners in robotic software engineering. Finally, we map our guidelines to open challenges in runtime verification and field-based testing for ROS-based systems, and we outline promising research directions in the field.

Compact laser-plasma acceleration of fast ions has made great strides since its discovery over two decades ago, resulting in the current generation of high-energy ($\geq 100\,\rm MeV$) ultracold beams over ultrashort ($\leq 1\,\rm ps$) durations. To unlock broader applications of these beams, we need the ability to tailor the ion energy spectrum. Here, we present a scheme that achieves precisely this by accelerating protons in a "lighthouse" fashion, whereby the highest-energy component of the beam is emitted in a narrow cone, well separated from the lower-energy components. This is made possible by a two-stage interaction in which the rear surface of the target is first set into rapid motion before the main acceleration phase. This approach offers the additional advantages of leveraging a robust sheath acceleration process in standard micron-thick targets and being optically controllable., Comment: 9 pages, 6 figures

Excess mortality is defined as an increase in the number of deaths above what is expected based on historical trends, hereafter called baseline. In a previous paper, we introduced a statistical method that allows an unbiased and robust determination of the baseline to be used for the computation of excesses. A good determination of the baseline allows us to efficiently evaluate the excess of casualties that occurred in Italy in the last 12 years and in particular in the last 3 years due to the Coronavirus Disease 2019 (COVID-19) epidemic. To this extent, we have analyzed the data on mortality in Italy in the period January 1st 2011 to December 31th 2022, provided by the Italian National Institute of Statistics (ISTAT). The dataset contains information on deaths for all possible causes, without specific reference to any particular one. The data exhibit strikingly evident periodicity in the number of deaths with pronounced maxima in the winter and minima in the summer, repeating itself in amplitude along the whole twelve-year sample. Superimposed on this wave-like structure are often present excesses of casualties, most likely due to occasional causes of death such as the flu epidemics (in winter) and heat waves (in summer). The very accurate periodicity along the seasons (the "baseline"), allows us to determine with great accuracy and confidence the number of expected deaths for each day of the year in the absence of occasional contributions. Each of the latter can be modeled with an additional function that parameterizes the deviation from the baseline.

In this paper, we investigate the global higher regularity properties of weak solutions for a linear elliptic system coupled with a nonlinear Maxwell-type system defined on Lipschitz domains. The regularity result is established using a modified finite difference approach. These adjusted finite differences involve inner variations in conjunction with a Piola-type transformation to preserve the curl-structure within the matrix Maxwell system. The proposed method is further applied to the linear relaxed micromorphic model. As a result, for a physically nonlinear version of the relaxed micromorphic model, we demonstrate that for arbitrary $\epsilon > 0$, the displacement vector $u$ belongs to $H^{\frac{3}{2}-\epsilon}(\Omega)$, and the microdistortion tensor $P$ belongs to $H^{\frac{1}{2}-\epsilon}(\Omega)$ while $\Curl P$ belongs to $H^{\frac{1}{2}-\epsilon}(\Omega)$.

LoRaWAN is a wireless technology that enables high-density deployments of IoT devices. Designed for Low Power Wide Area Networks (LPWAN), LoRaWAN employs large cells to service a potentially extremely high number of devices. The technology enforces a centralized architecture, directing all data generated by the devices to a single network server for data processing. End-to-end encryption is used to guarantee the confidentiality and security of data. In this demo, we present \edgelora, a system architecture designed to incorporate edge processing in LoRaWAN without compromising security and confidentiality of data. \edgelora maintains backward compatibility and addresses scalability issues arising from handling large amounts of data sourced from a diverse range of devices. The demo provides evidence on the advantages in terms of reduced latency, lower network bandwidth requirements, higher scalability, and improved security and privacy resulting from the application of the Edge processing paradigm to LoRaWAN., Comment: This paper is a pre-print version of the conference paper that has been accepted to ACM MobiCom 2023: Proceedings of the 29th Annual International Conference on Mobile Computing and Networking

We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squares fitting of the total energy of the relaxed micromorphic homogeneous continuum to the total energy of the fully-resolved heterogeneous microstructure, governed by classical linear elasticity. The relaxed micromorphic model is a generalized continuum that utilizes the $\Curl$ of a micro-distortion field instead of its full gradient as in the classical micromorphic theory, leading to several advantages and differences. The most crucial advantage is that it operates between two well-defined scales. These scales are determined by linear elasticity with microscopic and macroscopic elasticity tensors, which respectively bound the stiffness of the relaxed micromorphic continuum from above and below. While the macroscopic elasticity tensor is established a priori through standard periodic first-order homogenization, the microscopic elasticity tensor remains to be determined. Additionally, the characteristic length parameter, associated with curvature measurement, controls the transition between the micro- and macro-scales. Both the microscopic elasticity tensor and the characteristic length parameter are here determined using a computational approach based on the least squares fitting of energies. This process involves the consideration of an adequate number of quadratic deformation modes and different specimen sizes. We conduct a comparative analysis between the least square fitting results of the relaxed micromorphic model, the fitting of a skew-symmetric micro-distortion field (Cosserat-micropolar model), and the fitting of the classical micromorphic model with two different formulations for the curvature...

While nanoalloys are of paramount scientific and practical interests, the main processes leading to their formation are still poorly understood. Key structural features in the alloy systems, including crystal phase, chemical ordering, and morphology, are challenging to control at the nanoscale, making it difficult to transfer their usage to industrial applications. In this contribution, we focus on the gold/silver system that has two of the most prevalent noble metals, and combine experiments with simulations to uncover the formation mechanisms at the atomic-level. Nanoparticles are produced using state-of-the-art inert-gas aggregation source and analyzed using transmission electron microscopy and energy-dispersive x-ray spectroscopy. Machine-learning-assisted molecular dynamics simulations are employed to model the crystallization process from liquid droplets to nanocrystals. Our study finds a preponderance of nanoparticles with five-fold symmetric morphology, including icosahedron and decahedron which is consistent with previous results on mono-metallic nanoparticles. However, we observe that gold atoms, rather than silver atoms, segregate at the surface of the obtained nanoparticles for all the considered alloy compositions. These segregation tendencies are in contrast to previous studies and have consequences on the crystallization dynamics and the subsequent crystal ordering. We finally show that the underpinnings of this surprising segregation dynamics is due to charge transfer and electrostatic interactions rather than surface energy considerations.

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements belonging to these classes, and we extend this computation to fourth-order elasticity tensors acting on non-symmetric matrices. These tensors naturally appear in generalized continuum models. Based on tensor symmetrization, we provide the most general forms of these tensors for orthotropic, transversely isotropic, cubic, and isotropic materials. We present a self-contained discussion and provide detailed calculations for simple examples.

We study the $p$-\emph{torsion function} and the corresponding $p$-\emph{torsional rigidity} associated with $p$-Laplacians and, more generally, $p$-Schr\"odinger operators, for $1

It has become commonplace for the stored energy function of any realistic shell model to align ``within first order" with the classical Koiter membrane-bending (flexural) shell model. In this paper, we assess whether certain extended Cosserat shell models are consistent with the classical linear Koiter model. In doing this, we observe that there are numerous reasons why a modified version of the classical Koiter model should be considered, a consensus reached not only by Koiter himself but also by Sanders and Budiansky, who independently developed the same theory during the same period. To provide a comprehensive overview of the strain measures employed in our Cosserat shell models, this paper presents them in a unified manner and compares them with the strain measures previously utilized in the literature. We show that all our new strain tensors either generalize (in the case of nonlinear constrained or unconstrained models) or coincide (in the case of the linear constrained model) with the strain tensors recognized as the ``best" or those possessing a well-defined geometric interpretation connected to bending or curvature.

The rise of AI-based and autonomous systems is raising concerns and apprehension due to potential negative repercussions stemming from their behavior or decisions. These systems must be designed to comply with the human contexts in which they will operate. To this extent, Townsend et al. (2022) introduce the concept of SLEEC (social, legal, ethical, empathetic, or cultural) rules that aim to facilitate the formulation, verification, and enforcement of the rules AI-based and autonomous systems should obey. They lay out a methodology to elicit them and to let philosophers, lawyers, domain experts, and others to formulate them in natural language. To enable their effective use in AI systems, it is necessary to translate these rules systematically into a formal language that supports automated reasoning. In this study, we first conduct a linguistic analysis of the SLEEC rules pattern, which justifies the translation of SLEEC rules into classical logic. Then we investigate the computational complexity of reasoning about SLEEC rules and show how logical programming frameworks can be employed to implement SLEEC rules in practical scenarios. The result is a readily applicable strategy for implementing AI systems that conform to norms expressed as SLEEC rules., Comment: In proceedings of the 38th Annual AAAI Conference on Artificial Intelligence

One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank invariants), is among the most studied metrics in this context, particularly in 2-parameter persistence. The main reason for this interest is that, in the 2-parameter case, the foliation method allows for an effective computation of the matching distance, based on filtering the space along lines of positive slope. Our work provides a qualitative analysis, based on a construction called extended Pareto grid, of the filtering lines that actually contribute to the computation of the matching distance. Under certain genericity assumptions, we show that these lines must either be horizontal, vertical, of slope 1 or belong to a finite collection of special lines associated with discontinuity phenomena., Comment: Theorem 5 is now a stronger result and Appendix B has been added

The large variety of complex electronic structure materials and their alloys, offer highly promising directions for improvements in thermoelectric (TE) power factors (PF). Their electronic structure contains rich features, referred to as 'surface complexity', one of them being the highly anisotropic warped energy surface shapes with elongated features and threads in some cases. In this work we use Boltzmann transport simulations to quantify the influence that the shape of the electronic structure energy surfaces has on the PF. Using both analytical ellipsoidal bands, as well as realistic bands from the group of half-Heuslers, we show that band shape complexity alone can offer an advantage to the PF of ~3x in realistic cases. The presence of anisotropic scattering mechanisms such as ionized impurity or polar optical phonon scattering, however, can reduce these improvements by up to ~50%. We show that expressions based on the simple ratio of the density-of-states to the conductivity effective masses, mDOS/mC, together with the number of valleys, can capture the anisotropy shape with a moderate to high degree of correlation. For this, we use a convenient way to extract these masses by mapping the complex bandstructures of materials to parabolic electronic structures, without the need for Boltzmann transport codes. Despite the fact that the PF depends on many parameters, information about the benefits of the band shape alone, would be very useful for identifying and understanding the performance of novel thermoelectric materials.

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.