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As testified by new regulations like the European AI Act, worries about the human and societal impact of (autonomous) software technologies are becoming of public concern. Human, societal, and environmental values, alongside traditional software quality, are increasingly recognized as essential for sustainability and long-term well-being. Traditionally, systems are engineered taking into account business goals and technology drivers. Considering the growing awareness in the community, in this paper, we argue that engineering of systems should also consider human, societal, and environmental drivers. Then, we identify the macro and technological challenges by focusing on humans and their role while co-existing with digital systems. The first challenge considers humans in a proactive role when interacting with digital systems, i.e., taking initiative in making things happen instead of reacting to events. The second concerns humans having a reactive role in interacting with digital systems, i.e., humans interacting with digital systems as a reaction to events. The third challenge focuses on humans with a passive role, i.e., they experience, enjoy or even suffer the decisions and/or actions of digital systems. The fourth challenge concerns the duality of trust and trustworthiness, with humans playing any role. Building on the new human, societal, and environmental drivers and the macro and technological challenges, we identify a research roadmap of digital systems for humanity. The research roadmap is concretized in a number of research directions organized into four groups: development process, requirements engineering, software architecture and design, and verification and validation.

We present the results of the second commissioning phase of the short-focal-length area of the Apollon laser facility (located in Saclay, France), which was performed with the main laser beam (F1), scaled to a peak power of 2 PetaWatt. Under the conditions that were tested, this beam delivered on-target pulses of maximum energy up to 45 J and 22 fs duration. Several diagnostics were fielded to assess the performance of the facility. The on-target focal spot and its spatial stability, as well as the secondary sources produced when irradiating solid targets, have all been characterized, with the goal of helping users design future experiments. The laser-target interaction was characterized, as well as emissions of energetic ions, X-ray and neutrons recorded, all showing good laser-to-target coupling efficiency. Moreover, we demonstrated the simultaneous fielding of F1 with the auxiliary 0.5 PW F2 beam of Apollon, enabling dual beam operation. The present commissioning will be followed in 2025 by a further commissioning stage of F1 at the 8 PW level, en route to the final 10 PW goal.

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential equations. To obtain an analytical solution, modified Bessel functions are utilized and closed-form solutions for the displacement and microdistortion are obtained. We show how certain limit cases (classical linear elasticity), which are naturally included in the relaxed micromorphic model, can be efficiently achieved. Furthermore, numerical results are calculated and the effects of various parameters are examined. The results can be used to calibrate and check corresponding finite element codes.

This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two switching rules are presented relying on the solution of differential Lyapunov inequalities and Lyapunov-Metzler inequalities, from which the stability conditions are expressed. The first one allows to regulate the state of linear switched systems to zero, whereas the second one is designed for switched affine systems proving practical stability of the origin. In both cases, the determination of a guaranteed cost associated with each control strategy is shown. In the cases of linear and affine systems, the existence of the solution for the Lyapunov-Metzler condition is discussed and guidelines for the selection of a solution ensuring suitable performance of the system evolution are provided. The theoretical results are finally assessed by means of three examples., Comment: 12 pages, 10 figures

In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that \begin{equation*} \langle\frac{\mathrm{D}^{\circ}}{\mathrm{D} t}[\sigma] , D \rangle > 0 \quad \forall \ D \in \text{Sym}(3)\setminus \{0\} \, , \end{equation*} where $\frac{\mathrm{D}^{\circ}}{\mathrm{D} t}$ is any corotational stress rate, $\sigma$ is the Cauchy stress and $D = \text{Sym} \, L$, condition $L= \dot{F} \, F^{-1}$ is the deformation rate tensor. For $\widehat{\sigma}(\log V) := \sigma (V)$ it is equivalent to the monotonicity (TSTS-M$^+$) \begin{equation*} \langle \widehat{\sigma} (\log V_1) - \widehat{\sigma} (\log V_2) , \log V_1 - \log V_2 \rangle > 0 \quad \forall \ V_1, V_2 \in \text{Sym}^{++}(3), \ V_1 \neq V_2 \, . \end{equation*} For hyperelasticity, (CSP) is in general independent of convexity of the mapping $F \mapsto \mathrm{W}(F)$ or $U \mapsto \widehat{\mathrm{W}}(U)$. Considering a family of diagonal, homogeneous deformations $t \mapsto F(t)$ one can, nevertheless, show that (CSP) implies positive incremental Cauchy stress moduli for this deformation family, including the incremental Young's modulus, the incremental equibiaxial modulus, the incremental planar tension modulus and the incremental bulk modulus. Aside, (CSP) is sufficient for the Baker-Ericksen and tension-extension inequality. Moreover, it implies local invertibility of the Cauchy stress-stretch relation. Together, this shows that (CSP) is a reasonable constitutive stability postulate in nonlinear elasticity, complementing local material stability viz. LH-ellipticity.

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 to appear in Mathematics and Mechanics of Solids

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