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The accurate diagnosis of machine breakdowns is crucial for maintaining operational safety in smart manufacturing. Despite the promise shown by deep learning in automating fault identification, the scarcity of labeled training data, particularly for equipment failure instances, poses a significant challenge. This limitation hampers the development of robust classification models. Existing methods like model-agnostic meta-learning (MAML) do not adequately address variable working conditions, affecting knowledge transfer. To address these challenges, a Related Task Aware Curriculum Meta-learning (RT-ACM) enhanced fault diagnosis framework is proposed in this paper, inspired by human cognitive learning processes. RT-ACM improves training by considering the relevance of auxiliary sensor working conditions, adhering to the principle of ``paying more attention to more relevant knowledge", and focusing on ``easier first, harder later" curriculum sampling. This approach aids the meta-learner in achieving a superior convergence state. Extensive experiments on two real-world datasets demonstrate the superiority of RT-ACM framework.

Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme seamlessly supports general elements resulting from the cutting of a background mesh along the interface. Interface conditions are enforced weakly \`a la Nitsche. We provide a rigorous convergence of analysis of the scheme for a steady model problem and showcase an application to a physical problem inspired by the Leaky Dielectric Model.

In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-robustness refers to the fact that, under suitable regularity assumptions, the right-hand side of the velocity error estimate does not depend on the inverse of the viscosity. This property is obtained here through a penalty term which involves a subtle projection of the convective term on a subgrid space constructed element by element. The estimated convergence order for the $L^\infty(L^2)$- and $L^2(\text{energy})$-norm of the velocity is $h^{k+\frac12}$, which matches the best results for continuous and discontinuous Galerkin methods and corresponds to the one expected for HHO methods in convection-dominated regimes. Two-dimensional numerical results on a variety of polygonal meshes complete the exposition.

For each pair of positive integers $(a,b)$ such that $a \geq 0$ and $b > 1$, the present paper provides a necessary and sufficient condition for the existence of Hamiltonian cycles visiting all the vertices of any $k$-dimensional grid $\{0,1\}^k \subset \mathbb{R}^k$ and whose associated Euclidean distance is equal to $\sqrt{a^2+b^2}$. Our solution extends previously stated results in fairy chess on the existence of closed Euclidean $(a,b)$-leapers tours for $2 \times 2 \times \cdots \times 2$ chessboards, where the (Euclidean) knight identifies the $(1,2)$-leaper., Comment: 6 pages. Names of Lemma 2.3 and Corollary 2.5 fixed

Blockchains have gained substantial attention from academia and industry for their ability to facilitate decentralized trust and communications. However, the rapid progress of quantum computing poses a significant threat to the security of existing blockchain technologies. Notably, the emergence of Shor's and Grover's algorithms raises concerns regarding the compromise of the cryptographic systems underlying blockchains. Consequently, it is essential to develop methods that reinforce blockchain technology against quantum attacks. In response to this challenge, two distinct approaches have been proposed. The first approach involves post-quantum blockchains, which aim to utilize classical cryptographic algorithms resilient to quantum attacks. The second approach explores quantum blockchains, which leverage the power of quantum computers and networks to rebuild the foundations of blockchains. This paper aims to provide a comprehensive overview and comparison of post-quantum and quantum blockchains while exploring open questions and remaining challenges in these domains. It offers an in-depth introduction, examines differences in blockchain structure, security, privacy, and other key factors, and concludes by discussing current research trends.

In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by extension and reduction maps, generates a fourth complex with cohomology isomorphic to the former three. This construction is used to devise new serendipity versions of rot-rot and Stokes complexes derived in the Discrete de Rham spirit.

Oxygen deficient titanium dioxide (TiO$_{2-x}$) is a very attractive material for several applications ranging from photocatalysis to resistive switching. Oxygen vacancies turn insulating anatase titanium dioxide into a polaronic conductor, while creating a defect state band below the ultraviolet semiconducting gap. Here we employ a combination of broadband infrared (IR) reflectivity and THz-pump/IR-probe measurements to investigate the relationship between localized defect states and delocalized conducting polaronic states. We show that the THz pump allows to convert deeply localized electrons into metastable polarons with a lifetime in the ns range. These long-lived metastable states may find application in novel opto-electronic applications exploiting the interplay of dc resistivity, with terahertz and infrared signals.

We study Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. As observed in [1] this implies a deconfinement-confinement transition as the radius is increased. We gather hints on the nature of this transition using perturbation theory. We compute the anomalous dimensions of the lightest scalar operators in the boundary theory, which are negative for the singlet and positive for non-trivial representations. We also compute the correction to the coefficient $C_J$ and we estimate that the singlet operator reaches marginality before the value of the coupling at which $C_J=0$. These results favor the scenario of merger and annihilation as the most promising candidate for the transition. For the Neumann boundary condition, the lightest scalar operator is found to have a positive anomalous dimension, in agreement with the idea that this boundary condition extrapolates smoothly to flat space. The perturbative calculations are made possible by a drastic simplification of the gauge field propagator in Fried-Yennie gauge. We also derive a general result for the leading-order anomalous dimension of the displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings., Comment: 49 pages, 4 figures, 1 table, 7 boxed equations

The present paper aims to extend the knight's tour problem for $k$-dimensional grids of the form $\{0,1\}^k$ to other fairy chess leapers. Accordingly, we constructively show the existence of closed tours in $2 \times 2 \times \cdots \times 2$ ($k$ times) chessboards concerning the wazir, the threeleaper, and the zebra, for all $k \geq 15$. Our result considers the three above-mentioned leapers and replicates for each of them the recent discovery of Euclidean knight's tours for the same set of $2 \times 2 \times \cdots \times 2$ grids, opening a new research path on the topic by studying different fairy chess leapers that perform jumps of fixed Euclidean length on given regular grids, visiting all their vertices exactly once before coming back to the starting one., Comment: 9 pages

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

Polarized X-rays allow for imaging birefringent or dichroic properties of materials with nanometric resolution. To disentangle these properties from the electronic density, either a polarization analyzer or several measurements with different polarizations (typically two, or more) are needed. Here we demonstrate that ptychography can disentangle these from a single-polarization measurement by using a multimodal analysis. This new method provides an alternative to obtain polarization-resolved images of a sample when manipulating the incident polarization is not possible nor sufficient., Comment: 6 pages, 3 figures

In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions that yield inf-sup stability as well as error estimates which distinguish the velocity- and pressure-related contributions to the error. We additionally identify the key properties under which the pressure-related contributions vanish in the estimate of the velocity, thus leading to pressure-robustness. Several examples of existing and new schemes that fit into the framework are provided, and extensive numerical validation of the theoretical properties is provided.

The growth potential of a crypto(currency) project can be measured by the use cases spurred by the underlying technology. However, these projects are usually distributed, with a weak feedback schemes. Hence, a metric that is widely used as a proxy for their healthiness is the number of transactions and related volumes. Nevertheless, such a metric can be subject to manipulation (the crypto market being an unregulated one magnifies such a risk). To address the cited gap we design a comprehensive methodology to process large cryptocurrency transaction graphs that, after clustering user addresses of interest, derives a compact representation of the network that highlights clusters interactions. To show the viability of our solution, we bring forward a use case centered on Polkadot, which has gained significant attention in the digital currency landscape due to its pioneering approach to interoperability and scalability. However, little is known about how many and to what extent its wide range of enabled use cases have been adopted by end-users so far. The answer to this type of question means mapping Polkadot (or any analyzed crypto project) on a palette that ranges from a thriving ecosystem to a speculative coin without compelling use cases. Our findings demonstrate that crypto exchanges exert considerable influence on the Polkadot network, owning nearly 40% of all addresses in the ledger and absorbing at least 80% of all transactions. In addition, the high volume of inter-exchange transactions (> 20%) underscores the strong interconnections among just a couple of prominent exchanges, prompting further investigations into the behavior of these actors to uncover potential unethical activities, such as wash trading. These results, while characterized by a high level of scalability and adaptability, are at the same time immune from the drawbacks of currently used metrics.

We prove the uniform convergence of the geometric multigrid V-cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously established results for HDG methods, and our multigrid method uses standard smoothers and local solvers that are bounded, convergent, and consistent. We use a weak version of elliptic regularity in our proofs. Numerical experiments confirm our theoretical results.

We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local P\'eclet numbers. A set of numerical tests supports the theoretical derivations.

Recent advances in AI technologies have notably expanded device intelligence, fostering federation and cooperation among distributed AI agents. These advancements impose new requirements on future 6G mobile network architectures. To meet these demands, it is essential to transcend classical boundaries and integrate communication, computation, control, and intelligence. This paper presents the 6G-GOALS approach to goal-oriented and semantic communications for AI-Native 6G Networks. The proposed approach incorporates semantic, pragmatic, and goal-oriented communication into AI-native technologies, aiming to facilitate information exchange between intelligent agents in a more relevant, effective, and timely manner, thereby optimizing bandwidth, latency, energy, and electromagnetic field (EMF) radiation. The focus is on distilling data to its most relevant form and terse representation, aligning with the source's intent or the destination's objectives and context, or serving a specific goal. 6G-GOALS builds on three fundamental pillars: i) AI-enhanced semantic data representation, sensing, compression, and communication, ii) foundational AI reasoning and causal semantic data representation, contextual relevance, and value for goal-oriented effectiveness, and iii) sustainability enabled by more efficient wireless services. Finally, we illustrate two proof-of-concepts implementing semantic, goal-oriented, and pragmatic communication principles in near-future use cases. Our study covers the project's vision, methodologies, and potential impact.

X-ray magnetic circular dichroism is an efficient contrast mechanism allowing for a direct sensitivity to magnetization. Combined with an imaging technique such as photoemission electron microscopy, it has been successfully applied to high-resolution investigations of ferromagnetic thin films but also of three-dimensional systems thanks to the transmission-type contrast in their shadow. Our focus in this work is the wave-optics scattering pattern that can be observed near such a shadow's rim. Taking advantage of non-uniform magnetic states present in near-micron-size Co$_{1-x}$Gd$_x$ beads, we first show how X-ray resonant magnetic scattering affects the Fresnel diffraction at the Co L$_3$ edge. In order to confirm this observation, we then turn to the Co M$_{2,3}$ edges. There, we measure magnetic scattering patterns with a significantly increased spatial extent (due to the larger wavelength), despite the signal's weakness. The patterns' origin is supported by a comparison between our experimental data and a simple analytical model, then numerical simulations., Comment: 13 pages, 11 figures

Spin waves, known for their ability to propagate without the involvement of moving charges, hold immense promise for on-chip information transfer and processing, offering a path toward post-CMOS computing technologies. This study investigates the potential synergy between propagating Damon-Eshbach spin waves and voltage-controlled magnetization in the pursuit of environmentally sustainable computing solutions. Employing micromagnetic simulations, we assess the feasibility of utilizing spin waves in DE mode in conjunction with localized voltage-induced alterations in surface anisotropy to enable low-energy logic operations. Our findings underscore the critical importance of selecting an optimal excitation frequency and gate width, which significantly influence the efficiency of the phase shift induced in propagating spin waves. Notably, we demonstrate that a realistic phase shift of 2.5$\left[ \pi \ \text{mrad}\right]$ can be achieved at a Co(5nm)/MgO material system via the VCMA effect. Moreover, by tuning the excitation frequency, Co layer thickness, gate width, and the use of a GdO\textsubscript{x} dielectric, we illustrate the potential to enhance the phase shift by a factor of 200 when compared to MgO dielectrics. This research contributes valuable insights towards developing next-generation computing technologies with reduced energy consumption.

In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using serendipity techniques. The main features of the DDR approach are the support of general meshes and arbitrary approximation orders. The method we develop is based on the curl-curl formulation of the momentum equation and, through compatibility with the Helmholtz-Hodge decomposition, delivers pressure-robust error estimates for the velocity. It also enables non-standard boundary conditions, such as imposing the value of the pressure on the boundary. In-depth numerical validation on a complete panel of tests including general polyhedral meshes is provided. The paper also contains an appendix where bounds on DDR potential reconstructions and differential operators are proved in the more general framework of Polytopal Exterior Calculus.

We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an equilibrated stress reconstruction in the Arnold--Falk--Winther space that includes a guaranteed upper bound distinguishing the different components of the error. This analysis is the starting point for the development of an adaptive algorithm including a stopping criterion for the generalized Newton method. This algorithm is then used to perform numerical simulations that validate the theoretical results., Comment: 33 pages, 15 figures

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and late-time four-point functions. Explicit computations reveal that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we compute the late-time four-point functions of vector fields at large $N$, demonstrating that their spectral density is meromorphic in the spectral plane and positive along the principal series. These results offer highly nontrivial checks of unitarity and analyticity for cosmological correlators., Comment: 25 pages, 3 figures

We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $\mu$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $\mu=0$ we show that a certain $\mathbb{Z}_2$-valued 't Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any $N$ and any $T>0$. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for $T>0$ of the inhomogeneous chiral phase configuration found at $T=0$ for any $N$ and any $\mu$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $\mu$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings., Comment: 28+23 pages; v2: Several clarifications and improvements, reference added

We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k\neq 0$. To obtain this result we compute the $\beta$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds., Comment: 33 pages, 14 figures. v2: minor modifications, comments and references added

Anti-de-Sitter space acts as an infra-red cut off for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. We scrutinize the interpolation for theories in two dimensions from the perspective of boundary conformal theories. We show that the appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space. We conjecture a similar mechanism for confinement in gauge theories., Comment: 13 pages, 5 figures; v2: typo corrected, reference added; v3: typos corrected

We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d $\mathcal{N}=2$ SCFTs with $\frac{1}{2}$-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial $S^3$. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d $\mathcal{N}=2$ SCFTs on the boundary. In particular we derive the action of the SL(2,$\mathbb{Z}$) duality on the one-point functions., Comment: 62 pages, 7 figures; v3: corrected mistake in the boundary term, modified accordingly the derivation of the one-point function, version accepted in JHEP

Thanks to its tunable infrared band-gap and to its anisotropic conduction properties, black phosphorus represents a very unique 2D material, whose potential in the engineering of new devices still needs to be fully explored. We investigate here the nonlinear terahertz (THz) electrodynamics of black phosphorus along the more conducting armchair direction. Similarly to the case of other 2D systems like graphene and topological insulators, the THz saturable absorption properties of black phosphorus can be understood within a thermodynamic model by assuming a fast thermalization of the electron bath. While black phosphorus does not display the presence of massless fermions at ambient pressure and temperature, our analysis shows that its anomalous THz nonlinear properties can be accounted for by a relativistic massive Dirac dispersion, provided the Fermi temperature is low enough. An optimal tuning of the Fermi level therefore represents a strategy to engineer strong THz nonlinear response in other massive Dirac materials as in transition metal dichalchogenides or high-temperature superconductors., Comment: Accepted for publication in Physical Review Applied