We introduce a novel copy-protection method for industrial control software. With our method, a program executes correctly only on its target hardware and behaves differently on other machines. The hardware-software binding is based on Physically Unclonable Functions (PUFs). We use symbolic execution to guarantee the preservation of safety properties if the software is executed on a different machine, or if there is a problem with the PUF response. Moreover, we show that the protection method is also secure against reverse engineering.

The accretion of metal-poor gas sustains galactic star formation. In the Milky Way, this process is fueled by high-velocity clouds (HVCs), yet their fundamental properties have remained elusive in the absence of stellar tracers. Here we report a binary open cluster within HVC Complex H. With an age of 11.2 +- 0.6 Myr and a subsolar metallicity of 0.05(+0.05-0.02) Zsun, the clusters provide a direct stellar distance anchor to the cloud at 13.8 +- 0.6 kpc. Their proper motions indicate Complex H is on a prograde, south-to-north orbit through the outer Galactic disk. The resulting interaction produces a 'slow-fast-slow' velocity gradient, with the cloud's outer layers decelerating as they merge into the disk. Orbit integration suggests the clusters formed from an internal cloud-cloud collision. This triggering mechanism implies other HVCs could similarly produce high-velocity stars. The scarcity of previous stellar detections in HVCs is explained by the rapid escape of young stars (< 20 Myr), while CO non-detections may stem from weak emission due to low metallicity and gas dispersal. This work reveals that the circumgalactic medium can sustain star formation, offering a tangible laboratory to probe the physical conditions of accreting gas before it merges with the Galactic disk.

High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency bottlenecks, frequently becoming computationally prohibitive when handling high-resolution models. While emerging learning-based approaches offer greater flexibility, they primarily focus on cross-field prediction, often resulting in the loss of critical structural layouts and a lack of editability. In this paper, we propose TopGen, a robust and efficient learning-based framework that mimics professional manual modeling workflows by simultaneously predicting structural layouts and cross-fields. By processing input triangular meshes through point cloud sampling and a shape encoder, TopGen is inherently robust to non-manifold geometries and low-quality initial topologies. We introduce a dual-query decoder using edge-based and face-based sampling points as queries to perform structural line classification and cross-field regression in parallel. This integrated approach explicitly extracts the geometric skeleton while concurrently capturing orientation fields. Such synergy ensures the preservation of geometric integrity and provides an intuitive, editable foundation for subsequent quadrilateral remeshing. To support this framework, we also introduce a large-scale quadrilateral mesh dataset, TopGen-220K, featuring high-quality paired data comprising raw triangular meshes, structural layouts, cross-fields, and their corresponding quad meshes. Experimental results demonstrate that TopGen significantly outperforms existing state-of-the-art methods in both geometric fidelity and topological edge flow rationality.

Nonlinear responses in transport phenomena have attracted significant attention because they can arise even when linear responses are forbidden by symmetry, with the quantum geometry of Bloch wave functions playing an essential role. While such effects have been extensively studied in electric transport, similar quantum-geometric mechanisms are also expected to govern nonlinear thermal transport. In particular, thermal responses are crucial in bosonic systems such as magnons and phonons, which are charge-neutral quasiparticles. However, a consistent theoretical description of nonlinear thermal transport remains challenging because of the difficulty in the treatment of energy magnetization in higher-order responses with Luttinger's gravitational potential method. Here, we formulate the intrinsic nonlinear thermal conductivity of bosonic systems using a quantum kinetic equation approach that avoids Luttinger's method and naturally incorporates contributions from energy magnetization. We identify three distinct contributions to the nonlinear thermal conductivity: two expressed in terms of quantum-geometric quantities, namely the quantum metric and the thermal Berry-connection polarizability (TBCP), and a third determined solely by the band dispersions. Applying our formalism to a specific quantum spin model within linear spin-wave theory, we show that the TBCP term dominates the nonlinear thermal Hall effect in the absence of threefold symmetry. Our results differ quantitatively from those obtained using semiclassical theory, thereby highlighting the importance of quantum corrections beyond the semiclassical picture. These findings establish a general framework for intrinsic nonlinear thermal responses in bosonic systems and reveal quantum-geometric mechanisms underlying thermal transport beyond linear response theory.

The bond incident degree (BID) index of a graph \(G\) is defined as \(\BID(G) = \sum_{u_1u_2\in E(G)} f(d(u_1), d(u_2))\), where \(f(x,y)=f(y,x)\) is a real-valued function. In this paper, using graph transformation methods, we establish the maximum bond incident degree indices of trees and unicyclic graphs with a fixed diameter for the inverse sum indeg (ISI) index. The ISI index corresponds to the function \(f(x,y) = \frac{xy}{x+y}\). We prove that for trees \(T \in \mathbb{T}_{n,d}\) with \(d \geq 3\) and \(n \geq d+3\), the maximum ISI index is attained by the tree \(T_{n,d}^*\). For unicyclic graphs, we characterize the extremal graphs for diameters \(d=2\), \(d=3\), and \(d \geq 4\). Specifically, the maximum ISI index is achieved by \(S_n^+\) for \(d=2\), by \(C_n^*\) for \(d=3\), and by \(\mathcal{U}_{n,d}\) for \(d \geq 4\).

Let $Ω\subset\mathbb{R}^d$ be any open set. We consider solutions of $Hψ_λ=λψ_λ$, $λ\in\mathbb{C}$, where $H$ is an $m$th order complex constant-coefficient elliptic partial differential operator. We prove that either the eigenfunctions satisfy a lower bound on the inner radius of the complement of the zero set of $ψ_λ$ in $Ω$ of order $|λ|^{-1/m}$, or 100% of the $L^2$ mass of $ψ_λ$ concentrates in a boundary layer of width $|λ|^{-1/m}$, as $|λ|\to+\infty$.

In this paper I argue against Carcassi, Calderon, and Aidala's recent claim that the Hilbert spaces are unphysical and should be replaced with the Schwartz spaces in quantum mechanics, since Hilbert spaces include states with infinite expectation values for certain observables. I also review and discuss issues regarding unbounded operators in quantum mechanics raised by Streater and Wightman, Heathcote, and Lemos. I argue that the existence of infinite expectation values does not cause problems in quantum mechanics. On the other hand, replacing the Hilbert spaces with the Schwartz spaces would cause more issues, as it would exclude a class of meaningful Hamiltonian evolutions. I also discuss the question in literature whether reformulating quantum mechanics with essentially self-adjoint operators instead of self-adjoint operators may cause problems. I further analyse the hierarchies of the notions of "physicality" and possibility in fundamental physics, and suggest that "physicality" is a vague concept. Finally, I connect the problem raised by Carcassi, Calderon, and Aidala with the problem of the Hadamard condition in quantum field theory.

The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper, explicit formulas, and compact ones whenever possible, for the M-polynomial under different graph products whose vertex sets are the Cartesian product of the factors are developed. The products studied are the direct, the Cartesian, the strong, the lexicographic, the symmetric-difference, the disjunction, and the Sierpiński product. The obtained formulas yield a unified structural description of how vertex-degree interactions propagate under graph constructions and extend existing results for degree-based indices at the polynomial level.

We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly approximates the entire sequential U-statistic process. The approximation error is explicitly characterized and vanishes under polynomial growth of the dimension. The key technical contribution is a sharp martingale maximal inequality for completely degenerate U-statistics, combined with a high-dimensional strong approximation for independent sums. This coupling yields functional Gaussian limits without relying on $\mathcal{L}^\infty$-type bounds or bootstrap arguments. The theory is illustrated through three representative examples of U-statistics: the spatial Kendall's tau matrix, the multivariate Gini's mean difference, and the characteristic dispersion parameter. As applications, we derive Brownian bridge approximations for U-statistic-based change-point statistics and develop a self-normalized relevant testing procedure whose limiting distribution is fully pivotal. The framework naturally accommodates bounded kernels and therefore remains valid under heavy-tailed distributions. Overall, our results provide a unified probability-theoretic foundation for high-dimensional inference based on U-statistics.

As the first asteroid deflection test, NASA's successfully hit asteroid Dimorphos (secondary of the binary asteroid 65803 Didymos) with the DART kinetic impactor on September 26, 2022. To fully characterise the physical properties of the objects, and measure precisely the effects of this impact in the context of planetary defence, ESA launched the Hera mission on 7 October 2024, with scheduled arrival at Didymos in fall 2026. Among the core payload of the mission, the Asteroid Framing Cameras are two identical imaging systems that will support navigation and scientific activities, by acquiring images from various distances and observing geometries during the course of the mission. Built by ena-Optronik (Germany), the cameras match the requirements designed by the science team and will provide data that supports a wide range of investigations: hazard detection, system dynamics, shape reconstruction, surface morphology and mapping, and surface photometry. Each instrument is a panchromatic camera equipped with a 5.5 x 5.5 degree field of view, and an angular resolution of 93.7 micro-radians per pixel. The cameras shall provide the necessary data to address the mission requirements through a global mapping of the two components of the binary system at spatial scales of 2-3 m/pixel in the Early Characterisation Phase, 1-2 m/pixel in the Detailed Characterisation Phase, and 0.5-2 m/pixel in the Close Operation Phase. Dedicated flybys will bring the resolution down to < 10 cm/pixel on specific areas of interest on Dimorphos, such as the DART impact site and the JUVENTAS cubesat landing site. Here, we present the technical specifications of the camera, as well as the status of the calibration. We then summarise the planned operations in cruise and at the asteroids. Finally, we provide examples of the scientific investigations and products that will make use of the data returned by the cameras

This study explores the heavy-quark contributions to polarized structure functions in deep-inelastic scattering at next-to-leading order. The structure functions $g_1$, $g_4$, $g_5$, $g_6$, and $g_7$ are computed, while $g_2$ and $g_3$ are excluded due to the higher-twist suppression. The calculations are performed within the ACOT renormalization scheme, which ensures theoretical consistency across kinematic regions where heavy quarks transition from being dynamically produced to fully active degrees of freedom. By incorporating heavy-flavor contributions at next-to-leading-order, this work provides deeper insights into their role in polarized structure functions and the spin-dependent dynamics of QCD. Both analytical results and their numerical implementation are presented.

Developed on former gypsum quarries, the Buttes Chaumont Park is a 25-hectare geotechnical complex that is unique in the world. After three years of heavy work to create, in particular, an artificial cave, a lake and an island, the park opened in 1867 and has suffered gravitational hazards ever since (landslides, rockfalls and sinkholes). The BRGM has worked with the Paris City Council since 2021 to characterize the geological and geotechnical context, identify major gravitational hazards, and monitor the evolution of instabilities in slopes and rock/masonry walls. In this context, the BRGM has proposed, defined and followed a geotechnical supervision scheme including four levels of monitoring: detailed quarterly site visits since March 2023, bimonthly tacheometric surveys (operating since December 2022), monthly manual gauges measurements (since January 2024), and automatic extensometers and temperatures measurements (since March 2024). The interpretation of the data allows to confirm and/or complement the gravitational hazard mapping that had been carried out in 2022. By analyzing the correlation between displacement measurements and meteorological conditions, we could also differentiate between seasonal/daily trends mainly associated with temperature variations, and displacements associated with gravitational processes. These results help mitigate risks in the Buttes Chaumont Park in its current state, and adapt works planned in the coming years to restore and secure the park.

This paper presents a reproducible comparison of cubic and radial basis function (RBF) interpolants for multivariate surface analysis. To eliminate evaluation bias, both methods are assessed under a unified slice-wise train/test protocol on the same synthetic function family. Performance is reported using RMSE, MAE, and $R^2$ in two regimes: (i) noise-free observations and (ii) noisy observations. In the noise-free regime, both interpolants achieve high accuracy with output-dependent advantages. In the noisy regime, exact interpolation overfits noisy nodes and degrades out-of-sample performance for both methods; in our experimental setting, the cubic interpolant is comparatively more stable. All experiments are fully reproducible through a single SciPy/NumPy-based script with a fixed random seed, repeated splits, and bootstrap-based uncertainty summaries. From an environmental engineering perspective, the main practical implication is that noisy or apparently inconsistent measurements in thermodynamic process systems should not be discarded by default; instead, they can be structured and interpolated to recover physically meaningful process behavior.

In this paper, a novel QR decomposition-based compression scheme is combined with a volume integral equations method for the fast and efficient numerical computation of the scattering of electromagnetic fields from large scale metasurfaces, via an iterative approach. The underlying problem is of a multiscale nature. Indeed, these metasurfaces are made of a large collection of interacting sub-wavelength scatterers, thus making the numerical computation of the solution very challenging. More specifically, the paper proposes a tailored version of a QR decomposition-based compression for a volume integral equation, together with a proper preconditioner that exploits the geometrical structure of the array, in order to achieve a fast and accurate iterative solver, in view of realistic applications. Numerical examples prove the effectiveness of the method in efficiently modeling metasurfaces made by thousands of particles.

Accurate estimation of the sound speed profile (SSP) is essential for underwater acoustic communication, sonar performance, and navigation, as the acoustic wave propagation depends strongly on the SSP. This work considers SSP estimation in a region of interest using an autonomous underwater vehicle (AUV) equipped with a conductivity-temperature-depth (CTD) sensor and an acoustic receiver measuring transmission loss (TL) from a sonar transmitter. The SSP is modeled using a linear basis-function expansion and is sequentially estimated with an unscented Kalman filter that fuses local CTD measurements with TL measurements. A receding-horizon path planning scheme is also employed to select future AUV positions by minimizing the predicted total sound speed variance. Simulations using the Bellhop acoustic wave propagation solver show that CTD measurements provide accurate local SSP estimates, whereas TL measurements are seen to capture the global characteristics of the SSP, with their joint use improving the reconstruction of both local variations and large-scale SSP behavior. The results also indicate that the proposed path planning strategy reduces the estimation uncertainty compared to constant-velocity motion, thereby enabling improved environmental characterization for underwater acoustic systems.

We develop a quantum teleportation protocol of an unknown optical single rail qubit using a hybrid quantum channel composed of continuous variable (CV) states of certain parity. The quantum channel is characterized by two parameters: a squeezing parameter of single-mode squeezed vacuum (SMSV) state and the beam splitter (BS) parameter used to implement it. The CV part of the hybrid state belongs to Alice, while discrete variable (DV) half is controlled by Bob. The third parameter of the protocol is a parameter of the beam splitter, used to mix the CV components of the hybrid quantum state with unknown optical single-rail qubit. Even though the number of measurement results Alice sends may increase, Bob can obtain the original qubit half the time with an appropriate choice of parameter values. In almost half the remaining cases, Bob obtains the original qubit with distorted amplitudes, and both participants know the value of the distortion factors. This means that as the amount of classical information transmitted by Alice increases, they both gain greater access to partial information about the unitary transformations that the teleported qubits undergo, allowing Bob to continue using them or attempt to recover them to improve the protocol's efficiency. The proposed method is a generalization of quantum teleportation with a nonlocal photon used as a quantum channel and unknown single-rail optical qubit.

We introduce a $p$-adic $L$-function $\mathscr L_{A/L}$ associated to an ordinary elliptic curve $A$ over a global function field $K$ of characteristic $p$ together with a $\mathbb{Z}_{p}^{d}$-extension $L/K$, $d=0$ allowed, unramified outside a finite set of places where $A$ has ordinary (good ordinary or multiplicative) reductions. This $\mathscr L_{A/L}$ is characterized by its interpolation of the special values of twisted Hasse-Weil $L$-functions, we show that it satisfies the desired functional equation and specialization formula in connection with the characteristic ideal of the dual $p^\infty$-Selmer group of $A/L$. The Iwasawa main conjecture having $\mathscr{L}_{A / L}$ as the analytic side is proven in several cases. In the $d\geq 3$ case, %and $A/K$ has semi-stable reductions everywhere, the conjecture holds for $A/L$ if and only if it holds for all intermediate $\Z_p^2$-extensions $A/L'$ belonging to a given non-empty Zariski open subset of the Grassmannian $\mathrm{Gr}(d-2,d)(\Z_p)$.

Let $ϕ$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_ϕf=f\circ ϕ$ on the Hardy space $H^2(\mathbb{D}).$ We mainly characterize all the composition operators induced by linear fractional self-maps of $\mathbb{D}$ that have the positive shadowing property.

We propose two schemes to achieve remote entanglement distribution between two mechanical nodes with a significant frequency mismatch, based on optomechanical systems. The first scheme utilizes the physical mechanism to redistribute the quantum entanglement initially established in a dispersively-coupled optomechanical system with a megahertz mechanical resonance to a distant optomechanical system which embodies the tripleresonant interaction induced by the scattering of gigahertz mechanical phonon. We also provide a fast optical pulse protocol to realize the long-distance entanglement distribution from the optomechanical system supporting the gigahertz mechanical mode to the megahertz mechanical mode included in a distant optomechanical system. Specifically, these two schemes respectively demonstrate the megahertz-to-gigahertz and gigahertz-tomegahertz entanglement distribution in the quantum network of optical photons and phonons. This work may facilitate the application of various mechanical systems in hybrid quantum network-based quantum technologies and fundamental physical research.

We study market making in aggregator-routed RFQ markets where platform routing depends on slowly varying dealer performance scores. We propose a two-tier stochastic control model that separates RFQ-level price competition from a macro routing layer: tier A represents aggregator flow whose opportunity intensity is multiplied by a promotion gate driven by the dealer's win score, while tier B captures background flow that is not gated and does not update the score. RFQs arrive in multiple sizes and the dealer chooses a size-ladder of bid/ask offsets; conditional on winning, trades earn spread minus an adverse selection correction and contribute to inventory risk. The resulting Hamilton-Jacobi-Bellman equation admits a reduced Bergault-Guéant operator form with explicit win/lose branches for the score on tier A. Using the envelope-theorem argument, we express optimal controls through derivatives of the one-dimensional reduced Hamiltonians, yielding an interpretable mapping from optimal win probabilities to optimal offsets. In the long-memory regime, we derive an adiabatic approximation that separates fast inventory dynamics from slow score dynamics. A quadratic inventory ansatz and quadratic Hamiltonian expansion lead to a quasi-stationarity inventory-curvature scaling and a one-dimensional score drift field. For steep (logistic) promotion gates, the score dynamics can exhibit fold bifurcations, bistability, and hysteresis, producing an endogenous "campaign vs. harvest" pattern in optimal quoting. Numerical experiments confirm this behaviour and highlight the stabilizing role of background flow in maintaining inventory-mixing capacity even when the dealer is weakly promoted.

Aims. We aim to determine how ion neutral coupling and ambipolar diffusion affect the linear and the nonlinear growth of the RTinstability under astrophysically relevant conditions, and to identify the coupling regimes in which departures from the classical single fluid picture become significant. Methods. We perform high resolution two fluid numerical simulations using the MPI AMRVAC code, spanning a wide range of perturbation wavelengths, coupling strengths, from uncoupled to strongly coupled passing by intermediate or ambipolar diffusion dominated regimes, and magnetic field configurations. The linear theory is revisited using a physically consistent formulation with different ion neutral coupling strengths across the interface and validated against the simulations. We investigate the physics of the instability using morphology based diagnostics of the mixing layer to compare simulations at equivalent nonlinear stages, complemented by spectral, force, and energy budgets analyses. Results. In the linear regime, theoretical growth rates are recovered over a wide range of wavelengths, from the single fluid limit to intermediate bi fluid coupling. In the nonlinear regime, ambipolar diffusion modifies the classical quadratic growth and introduces a coupling dependent evolution. For multi wavelength perturbations, the nonlinear dynamics becomes strongly scale dependent: intermediate coupling enhances fragmentation in hydrodynamic configurations, while magnetised cases exhibit a non monotonic reorganisation of the interface, with the smoothest morphologies occurring at intermediate coupling. Spectral and energetic diagnostics indicate that these behaviours correlate with changes in the relative contributions of ion neutral drift and magnetic stresses during thenonlinear evolution

In this paper, we improve some transcendence results for $p$--adic continued fractions. In particular, we prove that palindromic and quasi--periodic $p$--adic continued fractions converge either to transcendental numbers or quadratic irrationals, removing any restriction on the $p$--adic norm of the partial quotients (or convergents) considered in other works. Moreover, we provide a quantitative version of Ridout's theorem (the $p$--adic analogue of Roth's theorem), and we study the growth of denominators of convergents of algebraic numbers, establishing a $p$--adic version of a well--known result of Davenport and Roth.

Static Application Security Testing (SAST) tools play a vital role in modern software development by automatically detecting potential vulnerabilities in source code. However, their effectiveness is often limited by a high rate of false positives, which wastes developer's effort and undermines trust in automated analysis. This work presents a Graph Convolutional Network (GCN) model designed to predict SAST reports as true and false positive. The model leverages Code Property Graphs (CPGs) constructed from static analysis results to capture both, structural and semantic relationships within code. Trained on the CamBenchCAP dataset, the model achieved an accuracy of 100% on the test set using an 80/20 train-test split. Evaluation on the CryptoAPI-Bench benchmark further demonstrated the model's practical applicability, reaching an overall accuracy of up to 96.6%. A detailed qualitative inspection revealed that many cases marked as misclassifications corresponded to genuine security weaknesses, indicating that the model effectively reflects conservative, security-aware reasoning. Identified limitations include incomplete control-flow representation due to missing interprocedural connections. Future work will focus on integrating call graphs, applying graph explainability techniques, and extending training data across multiple SAST tools to improve generalization and interpretability.

This paper aims to integrate the concepts of $F$-contraction and $S^B$-contraction within the context of super metric spaces. Specifically, we introduce the concepts of $S^F$-contraction and Bianchini $S^F$-contraction. We demonstrate that these new concepts are genuine generalizations of $S^B$- and $S^K$-contractions by providing nontrivial examples. Furthermore, we establish the existence and uniqueness of fixed points for mappings that satisfy these contractions. Lastly, we apply our findings to a model describing an airplane capable of automatically following a terrain.

Today's massive AI computation loads push heavy data synchronization across sites, i.e., nodes in data centers. Any reduction in such consensus latency can significantly improve the overall performance of desired systems. This consensus challenge explosively peaks at cross-domain sites. In this paper, we proposed CD-Raft to address the cross-domain latency challenge, an optimized Raft protocol for strong consistency in cross-domain sites. CD-Raft can significantly reduce consensus latency by optimizing cross-domain round-trip time (RTT) for reads and writes, as well as carefully positioning the leader node. We verified the correctness of CD-Raft in a formal specification using the TLA+ specification, guaranteeing the strong consistency across sites. We have prototyped CD-Raft and evaluated it using the YCSB benchmark. Empirical results show that compared to the classic Raft, CD-Raft reduces the average latency by 32.90% and (99th percentile) tail latency by 49.24% for renown traces across multiple sites.

We studied the parameter plane of the cosine functions with a fixed critical point. The hyperbolic components can be classified into three types: A, C and D. All the hyperbolic components are bounded and simply connected, except for the unique type-A component, which contains 0 as an isolated boundary point. Using the method of para-puzzle, we constructed a phase-parameter transfer mapping and proved that the boundaries of hyperbolic components are Jordan curves. By a similar idea, the hyperbolic components of type C are quasidisks.

Electric-dipole forbidden spectroscopic transitions in atoms form the basis of many advanced implementations of quantum computers, atomic clocks and quantum sensors. Coherently addressing such transitions in molecules which are among the most ubiquitous and versatile quantum objects has remained a long-standing challenge owing to their complex energy-level structure. Here, we report the search, observation and coherent manipulation of electric-quadrupole rotational-vibrational transitions in single trapped molecules using a quantum-logic-spectroscopy protocol. We identified individual hyperfine-Zeeman-rotational components of the fundamental vibrational transition of the nitrogen molecular ion, N$_2^+$, and performed coherent population transfer between energy levels. Our work opens up new perspectives for precision molecular spectroscopy, for high-fidelity qubits encoded in the rotational-vibrational motion of molecules, for precise infrared molecular clocks and for searches for new physics

Condensed matter systems with strong electronic correlations often manifest a variety of intertwined ordered phases of charge, spin, orbital and other degrees of freedom. As a prototypical strongly correlated electronic system, the Kondo lattice provides fertile soil for many fascinating quantum states, including quantum criticality, unconventional superconductivity, hidden order and topological Kondo insulator/semimetal. The foundation of Kondo physics lies in the hybridization between localized moments and itinerant electrons. Generally, the evolution of Kondo hybridization is characterized as a broad crossover rather than a phase transition. Thus far, an ordered hybridization phase has not been observed. Here, we use scanning tunneling microscopy (STM) to identify a translational-symmetry-breaking order of Kondo hybridization wave(KHW) for the first time on the surface of the spin-triplet heavy-fermion superconductor UTe2. The unprecedented phase of KHW manifests as a periodically modulated Fano lattice, accompanied by a commensurate charge density wave (CDW) and a pronounced energy gap opening near the Fermi level. This KHW-imprinted CDW has an intriguing real-space texture of complementary occupation of the heavy f and conduction charges, thereby forming a Kondo superlattice. The KHW is coexistent with superconductivity in UTe2, which may provide valuable insight into its controversial spin-triplet pairing symmetry and the underlying mechanism. Our first experimental evidence for an ordered hybridization state potentially sheds new light on the strong correlation physics of Kondo lattice system.

We investigate symmetry properties of the first nontrivial eigenfunctions of the fractional Laplacian $(-Δ)^s$, where $s \in (0,1)$, in an $N$-dimensional ball with nonlocal Neumann boundary conditions. By means of a spectral stability result, we prove that, when $s$ is sufficiently close to $1$, the eigenspace associated to the first nontrivial eigenvalue is generated by $N$ antisymmetric eigenfunctions with exactly two nodal domains in the ball.

Physical models aimed to reproduce basic features of the solar sunspot cycle are typically based on the solar dynamo mechanism. Usually qualitative arguments are used to define parameters of the model, among which a challenging component is the nonlinear form of quenching of the alpha-effect governing regeneration of the magnetic field. We propose a novel approach, in which the functional form of the alpha-quenching is represented by a neural network model embedded into neural differential dynamo equations trained on observational data. For demonstration, we consider a low-mode dynamo model and find a wide set of alpha-quenching functions and corresponding dynamo numbers that provide an accurate fit to the average profile of the solar cycle data given by sunspot numbers. Within this set, we observe a strong relationship between the dynamo number and the shape of the alpha-quenching function indicating that additional magnetic field data or constraints are essential to unambiguously infer parameters of the dynamo model. In our opinion, the neural differential approach opens a new prospect for data-driven investigation of the closure problem in dynamo theory.