We investigate the spectral properties of a differential elliptic operator on $H^1(\barΩ\cup Σ)$, where $Ω$ is a smooth domain surrounded by a layer $Σ$. The thickness of the layer is given by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partial Ω$ and $\varepsilon$ is the ellipticity constant of the operator in $Σ$. We prove that, in the limit for $\varepsilon$ going to $0$, the spectrum converges to the spectrum of a differential elliptic operator in $H^1(Ω)$, and we investigate a first-order asymptotic development.

In this paper we address the issue of stability for the near-inertial Pollard waves, as a model for the halocline in the region of the Arctic Ocean centered around the North Pole, derived in Puntini (2026). Adopting the short-wavelength instability approach, the stability of such flows reduces to study the stability of a system of ODEs along fluid trajectories, leading to the result that, when the steepness of the near-inertial Pollard waves exceeds a specific threshold, those waves are linearly unstable. The explicit dispersion relation of the model allows to easily compute such threshold, knowing the physical properties of the water column.

To enable training of large artificial intelligence (AI) models at the network edge, split federated learning (SFL) has emerged as a promising approach by distributing computation between edge devices and a server. However, while unstable network environments pose significant challenges to SFL, prior schemes often overlook such an effect by assuming perfect client participation, rendering them impractical for real-world scenarios. In this work, we develop an optimization framework for SFL with unstable client participation. We theoretically derive the first convergence upper bound for SFL with unstable client participation by considering activation uploading failures, gradient downloading failures, and model aggregation failures. Based on the theoretical results, we formulate a joint optimization problem for client sampling and model splitting to minimize the upper bound. We then develop an efficient solution approach to solve the problem optimally. Extensive simulations on EMNIST and CIFAR-10 demonstrate the superiority of our proposed framework compared to existing benchmarks.

At least ten emerging providers are developing satellite navigation systems for low Earth orbit (LEO). Compatibility with existing GNSS in L-band is critical to their successful deployment and for the larger ecosystem. Xona is deploying Pulsar, a near 260-satellite LEO constellation offering dual L-band navigation services near L1 and L5. Designed for interoperability, Pulsar provides centimeter-level accuracy, resilience, and authentication, while maintaining a format that existing GNSS receivers can support through a firmware update. This study examines Pulsar's compatibility with GPS and Galileo by evaluating C/N0 degradation caused by the introduction of its X1 and X5 signals. Using spectrally compact QPSK modulation, Pulsar minimizes interference despite higher signal power. Theoretical analysis is supported by hardware testing across a range of commercial GNSS receivers in both lab-based simulation and in-orbit live-sky conditions. The study confirms Pulsar causes no adverse interference effects to existing GNSS, supporting coexistence and integration within the global PNT ecosystem.

In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.

The publications of Gaia DR2 and DR3 have brought major improvements in stellar astrometry and photometry, particularly regarding the description of the white dwarf sequence. Notably, Gaia DR2 enabled the detection of variability in white dwarfs based solely on averaged astrometric and photometric quantities, i.e. the astrometric 5 parameters (positions, proper motion, and parallax) and general photometry properties in the G, BP and RP bands (mean, standard deviation and number of measurements). We identify and classify variable white dwarfs using Gaia DR3 data and Zwicky Transient Facility DR23 observations. The objective is to construct a catalogue of pulsating white dwarf candidates with robust selection criteria. We define a new sample of candidate variable white dwarfs using Gaia DR3 astrometric and photometric data. We cross-match this sample with the ZTF DR23 catalogue and apply a multiband Lomb-Scargle periodogram analysis to detect periodic variability. We then use the OPTICS unsupervised clustering algorithm to to group and classify the confirmed periodic stars. We identify 1423 variable white dwarfs candidates from Gaia DR3, with 864 having ZTF time series. 141 present significant periodicity. We classify these objects into known categories, including ZZ Ceti stars, GW Vir, V777 Her, and white dwarf-main sequence binaries. Our analysis yields several periodic stars, including three ZZ Ceti, 15 GW Vir, one V777 Her, and 24 WD-MS binaries. Furthermore, it reveals a significant population of potentialy variable stars, though without confirmed periodicity. Finally we publish our catalogue of candidate variable white dwarfs including variability status, periodicity, and classification information for the 864 sources with ZTF time series, 519 of them newly identified (including 83 new periodic stars).

Machine learned interaction potentials (MLIPs) have become a critical component of large-scale, high-quality simulations for a range of chemical and biochemical systems. Yet, despite their in-distribution accuracy, molecular dynamics simulations using MLIPs exhibit numerical instabilities due to underlying data insufficiencies when encountering new regions of the potential energy surface. Here we propose a pre-training learning scheme that uses low-quality, practically free, single-molecule non-reactive force field data while all intermolecular interactions and reactive properties are learned at a fine-tuning stage with a small amount of computationally more expensive labels. We show that the force field pre-training approach followed by data efficient ab initio fine tuning allows for stable and accurate molecular dynamics and metadynamics simulations of gas phase molecules, liquid water, and hydrogen combustion reactions compared to models trained from scratch.

We present LubDubDecoder, a system that enables fine-grained monitoring of micro-cardiac vibrations associated with the opening and closing of heart valves across a range of hearables. Our system transforms the built-in speaker, the only transducer common to all hearables, into an acoustic sensor that captures the coarse "lub-dub" heart sounds, leverages their shared temporal and spectral structure to reconstruct the subtle seismocardiography (SCG) and gyrocardiography (GCG) waveforms, and extract the timing of key micro-cardiac events. In an IRB-approved feasibility study with 25 users, our system achieves correlations of 0.88-0.95 compared to chest-mounted reference measurements in within-user and cross-user evaluations, and generalizes to unseen hearables using a zero-effort adaptation scheme with a correlation of 0.91. Our system is robust across remounting sessions and music playback.

We propose using spin-qubit noise magnetometry to probe dynamical signatures of magnetic Berezinskii-Kosterlitz-Thouless (BKT) physics. For a nitrogen-vacancy (NV) center coupled to two-dimensional XY magnets, we predict distinctive features in the magnetic noise spectral density in the sub-MHz to GHz frequency range. In the quasi-long-range ordered phase, the spectrum exhibits a temperature-dependent power law characteristic of algebraic spin correlations. Above the transition, the noise reflects the proliferation of free vortices and enables quantitative extraction of the vortex conductivity, a key parameter of vortex transport. These results highlight NV as a powerful spectroscopic method to resolve magnetic dynamics in the mesoscopic and low-frequency regimes and to probe exotic magnetic phase transitions.

This work explores the prospect of using the plunge to identify potential black hole mimickers. We show that the plunge excites two generic spectral features. (i) At low frequencies, there is a comb of sharp resonances at the real parts of the mimicker quasi-normal modes. (ii) Above a threshold $Mω_{\rm th}\!\approx\!0.39$ (for the dominant mode), the spectrum undergoes a qualitative break: with the black hole mimicker displaying significant deviations from the black hole. Though individual plunge SNRs in extreme mass ratio events are low and detecting them in a sea of noise is difficult, the coherent spectral features identified here may allow for enhancing the SNR by using multiple events.

We investigate the production and suppression of short-lived $K^*(892)$ resonances in p+p and Ar+Sc collisions at CERN-SPS energies ($\sqrt{s_{\mathrm{NN}}} = $ 8.8, 11.9, and 16.8~GeV) using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. We present multiplicities, rapidity and transverse momentum distributions, and analyze the $K^*/K$ yield ratios as a function of energy and centrality. We further estimate the time interval between chemical and kinetic freeze-out using the experimental method. A detailed comparison with recent NA61/SHINE data demonstrates that the UrQMD model captures the essential features of resonance dynamics, although the very strong resonance suppression in central collisions observed in the data cannot be quantitatively reproduced.

The integration of renewable energy via power electronics is transforming power grids into low-inertia systems, heightening the risks of frequency insecurity and widespread outages. Therefore, frequency security assessment (FSA) methods are urgently needed to ensure the reliable system operation. Recently, knowledge-data fusion models attempt to address the limitations of knowledge-driven (accuracy) and data-driven (generalization) FSA methods. However, current methods remain confined to shallow knowledge-data integration due to challenges in representing heterogeneous knowledge and establishing interactive mechanisms. Here, by classifing FSA domain knowledge into physics-guided and physics-constrained categories, we propose a guided learning-constrained network (GL-CN) framework, which deeply integrates domain knowledge across both network architecture and training process. In this framework, a data-driven model with dual input channels combining graph convolutional networks (GCN) and multilayer perceptrons (MLP) is proposed to extract both nodal and system-level power system features. Furthermore, guided learning enhances model generalization through data augmentation in pre-training utilizing physics-guided knowledge, while constrained network encodes physics-constrained knowledge into the network architecture and loss function to ensure physics-consistent and robust predictions. Validated on Yunnan Provincial Power Grid in China, our method reduces FSA time from days to seconds compared to traditional simulation, achieving 98% accuracy, robustness against 39.0% knowledge error, and generalization for 40%-60% renewable penetration. This provides a solid solution for mitigating blackouts caused by frequency insecurity and offers a generalizable paradigm for broader cross-domain problems.

We present an approach to deriving positivity bounds on effective field theories by analyzing the thermodynamic behavior of thermal quantum field systems. Focusing on scalar theories with higher-dimensional operators, we compute the finite-temperature entropy using thermal field theory techniques. We argue that consistency with fundamental thermodynamic principles--specifically, the expectation that entropy increases with the introduction of new degrees of freedom--imposes nontrivial constraints on Wilson coefficients. In particular, we show that the coefficient of the leading dimension-8 operator must be strictly positive. This thermodynamic perspective offers an alternative to traditional S-matrix-based derivations of positivity bounds and provides a complementary perspective into the interplay between entropy, unitarity, and causality in quantum field theory.

We propose a novel fractal based interpolation scheme termed Rational Cubic Trigonometric Zipper Fractal Interpolation Functions (RCTZFIFs) designed to model and preserve the inherent geometric property, positivity, in given datasets. The method employs a combination of rational cubic trigonometric functions within a zipper fractal framework, offering enhanced flexibility through shape parameters and scaling factors. Rigorous error analysis is presented to establish the convergence of the proposed zipper fractal interpolants to the underlying classical fractal functions, and subsequently, to the data-generating function. We derive necessary constraints on the scaling factors and shape parameters to ensure positivity preservation. By carefully selecting the signature, shape parameters, and scaling factors within these bounds, we construct a class of RCTZFIFs that effectively preserve the positive nature of the data, as compared to a reference interpolant that may violate this property. Numerical experiments and visualisations demonstrate the efficacy and robustness of our approach in preserving positivity while offering fractal flexibility.

This paper addresses the dichotomy between the formalization of structural and the formalization of behavioral knowledge by means of semantically lifted programs, which explore an intuitive connection between programs and knowledge graphs. While knowledge graphs and ontologies are eminently useful to represent formal knowledge about a system's individuals and universals, programming languages are designed to describe the system's evolution. To address this dichotomy, we introduce a semantic lifting of the program states of an executing program into a knowledge graph, for an object-oriented programming language. The resulting graph is exposed as a semantic reflection layer within the programming language, allowing programmers to leverage knowledge of the application domain in their programs. In this paper, we formalize semantic lifting and semantic reflection for a small programming language, SMOL, explain the operational aspects of the language, and consider type correctness and virtualisation for runtime program queries through the semantic reflection layer. We illustrate semantic lifting and semantic reflection through a case study of geological modelling and discuss different applications of the technique. The language implementation is open source and available online.

The long-time asymptotics of small Kadomtsev-Petviashvili II (KPII) solutions is derived using the inverse scattering theory and the stationary phase method.

Breaking time-reversal symmetry in integrated photonics without magnetic fields remains a fundamental challenge. We demonstrate phonon-induced non-reciprocity through direct lifting of forward-backward mode degeneracy in microring resonators. Coherent acousto-optic coupling generates differential AC Stark shifts between counter-propagating fundamental optical modes, eliminating the need for intermodal conversion or complex photonic structures. Simple microwave excitation of integrated piezoelectric transducers provides dynamic control of non-reciprocal response, with experimentally demonstrated mode splitting exceeding twice the optical linewidth. The linear relationship between the splitting and acoustic power enables real-time reconfigurability across a wide range of optical wavelengths. This mechanism requires only simple microring resonators and fundamental optical modes, transforming non-reciprocity from a specialized technique requiring careful modal engineering to a universal, electrically-controlled functionality. Our approach establishes a new paradigm for magnetic-free optical isolation and dynamic topological photonics.

Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means to describe observables in terms of their relation to a reference quantum system. We discuss a number of applications of QRFs in the context of quantum field theory on curved spacetimes: 1) A type reduction result for algebras arising from QFTs and QRFs with good thermal properties. 2) Quantisation of boundary electric fluxes and gluing procedures for quantum electromagnetism on spacetimes with boundaries.

Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how such environmental variation influences adaptation, what is learned in the process, and whether memory of past conditions is retained. In this work, we investigate these questions using athermal disordered systems that are subject to cyclic inverse design, enabling them to attain target elastic properties spanning a chosen range. We demonstrate that such systems evolve toward a marginally absorbing manifold (MAM), which encodes memory of the training range that closely resembles return-point memory observed in cyclically driven systems. We further propose a general mechanism for the formation of MAMs and the corresponding memory that is based on gradient discontinuities in the trained quantities. Our model provides a simple and broadly applicable physical framework for understanding how adaptive systems learn under environmental change and how they retain memory of past experiences.

Ultra-fast, precise, and controlled amplitude surrogates are essential for future LHC event generation. First, we investigate the noise reduction and biases of network ensembles and outline a new method to learn well-calibrated systematic uncertainties for them. We also establish evidential regression as a sampling-free method for uncertainty quantification. In a second part, we tackle localized disturbances for amplitude regression and demonstrate that learned uncertainties from Bayesian networks, ensembles, and evidential regression all identify numerical noise or gaps in the training data.

Entanglement entropy (EE) provides a powerful probe of quantum phases, yet its role in identifying topological phase transitions in disordered systems remains underexplored. We introduce an exact EE-based framework that captures topological phase transitions even in the presence of disorder. Specifically, for a class of Su-Schrieffer-Heeger (SSH) model variants, we show that the difference in EE between half-filled and near-half-filled ground states, $ΔS^{\mathcal{A}}$, vanishes in the topological phase but remains finite in the trivial phase, a direct consequence of edge-state localization. This behavior persists even in the presence of quasiperiodic or binary disorder. By analyzing domain-wall configurations in the SSH chain, we further show how subsystem tuning allows one to distinguish genuine topological zero-energy eigenstates from trivial localized states. Exact phase boundaries, derived from Lyapunov exponents via transfer matrices, agree closely with numerical results from $ΔS^{\mathcal{A}}$ and the topological invariant $\mathcal{Q}$, with instances where $ΔS^{\mathcal{A}}$ outperforms $\mathcal{Q}$. Our results highlight EE as a robust diagnostic tool and a potential bridge between quantum information and condensed matter approaches to topological matter.

MnBi$_2$Te$_4$ (MBT) is the first intrinsic magnetic topological insulator, combining a topologically protected surface metallic state and intrinsic magnetic order. A structural compatibility with the nonmagnetic Bi$_2$Te$_3$ (BT) parent compound gives a possibility to create MBT/BT heterostructures and manipulate their magnetic state in view of optimizing the Quantum Anomalous Hall Effect (QAHE). In this work an extensive Nuclear Magnetic Resonance (NMR) study, supported by the bulk magnetization measurements has been performed at 4.2 K on a self-organized single crystal MnBi$_2$Te$_4$/(Bi$_2$Te$_3$)$_n$ heterostructure, obtained from the Mn$_{0.81}$Bi$_{2.06}$Te$_{4.13}$ melt. $^{55}$Mn and $^{209}$Bi NMR signals have been recorded as a function of the out-of-plane magnetic field up to 6 T, covering a spin-flop transition (SFT) from the antiferromagnetic (AFM) to the canted antiferromagnetic (CAFM) configuration of the Mn layers. The canting angle at different external field values has been estimated based on NMR data. Presence of the AFM-coupled Mn antisites has been evidenced and shown to induce an antiparallel magnetic moment on Bi atoms within the host Bi layer. Detection of the induced magnetic moment on bismuth which contributes a new ferromagnetic (FM) component is of utmost importance for understanding the magnetic interactions in the MBT/BT system. These findings have potentially important implications for engineering the QAHE devices.

Superconductivity of a single two-dimensional Dirac fermion offers a natural route to topological superconductivity. While usually considered extrinsic -- arising from proximity to a conventional superconductor -- we investigate when a doped Dirac cone can \emph{spontaneously} develop superconductivity from a short-range repulsive interaction $U$ via the Kohn--Luttinger mechanism. We show that an ideal, linear Dirac cone is immune to pairing at leading order in $U^2$. Superconductivity instead emerges only through higher-order in $k$ corrections to the dispersion, which are unavoidable in any lattice realization and crucially dictate the pairing symmetry. The form of the pairing thus reflects how the well-known obstruction to realizing a single Dirac cone on a lattice is circumvented. When a Dirac cone arises from broken time-reversal symmetry -- for instance, at a transition between Chern insulators or in a valley-polarized phase -- we find a topological $p - ip$ state whose chirality is opposite to that of the parent chiral metal above $T_c$. By contrast, for a surface Dirac cone of a 3D topological insulator, superconductivity is stabilized by anisotropies in the dispersion. For $C_{3v}$-symmetric warping, as in \ce{Bi2Te3}, pairing is strongest when the Fermi surface becomes hexagonal, leading to order in the $(d \pm id)\times(p+ip)$ channel with accidental near-nodes. In the highly anisotropic limit $v_x \gg v_y$, relevant to side surfaces of layered materials, the Fermi surface splits into two branches, and nesting favors a pairing symmetry $Δ\sim \mathrm{sgn}(k_x)\cos(k_y)$ reminiscent of organic superconductors.

We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system $Φ$. This solves an open problem originally asked by Harada--Tymoczko in type A for all Lie types. As an application, we derive a type-uniform formula for the mixed $Φ$-Eulerian numbers.

Efficient and coherent data retrieval and storage are essential for harnessing quantum algorithms' speedup. Such a fundamental task is addressed by a quantum Random Access Memory (qRAM). Despite their promising scaling properties, current qRAM proposals demand excessive resources and rely on operations beyond the capabilities of current hardware requirements, rendering their practical realization inefficient. We introduce a novel architecture that significantly reduces resource requirements while preserving optimal complexity scaling for quantum queries. Moreover, unlike previous proposals, our algorithm design leverages a simple, repeated operational block based exclusively on local unitary operations and short-range interactions between a limited number of quantum walkers traveling over a single binary tree. This novel approach not only simplifies experimental requirements by reducing the complexity of necessary operations but also enhances the architecture's scalability by ensuring a resource-efficient, modular design that maintains optimal quantum query performance.

The advent of massive multiple-input multiple-output (MIMO) technology has provided new opportunities for capacity improvement via strategic antenna deployment, especially when the near-field effect is pronounced due to antenna proliferation. In this paper, we investigate the optimal antenna placement for maximizing the achievable rate of a point-to-point near-field channel, where the transmitter is deployed with massive movable antennas. First, we propose a novel design framework to explore the relationship between antenna positions and achievable data rate. By introducing the continuous antenna position function (APF) and antenna density function (ADF), we reformulate the antenna position design problem from the discrete to the continuous domain, which maximizes the achievable rate functional with respect to ADF. Leveraging functional analysis and variational methods, we derive the optimal ADF condition and propose a gradient-based algorithm for numerical solutions under general channel conditions. Furthermore, for the near-field line-of-sight (LoS) scenario, we present a closed-form solution for the optimal ADF, revealing the critical role of edge antenna density in enhancing the achievable rate. Finally, we propose a flexible antenna array-based deployment method that ensures practical implementation while mitigating mutual coupling issues. Simulation results demonstrate the effectiveness of the proposed framework, with uniform circular arrays emerging as a promising geometry for balancing performance and deployment feasibility in near-field communications.

Jet taggers provide an ideal testbed for applying explainability techniques to powerful ML tools. For theoretically and experimentally challenging quark-gluon tagging, we first identify the leading latent features that correlate strongly with physics observables, both in a linear and a non-linear approach. Next, we show how Shapley values can assess feature importance, although the standard implementation assumes independent inputs and can lead to distorted attributions in the presence of correlations. Finally, we use symbolic regression to derive compact formulas to approximate the tagger output.

Respiration is an essential involuntary function necessary for survival. This poses a challenge for the control of breathing. The preBötzinger complex (preBötC) is a heterogeneous neuronal network responsible for driving the inspiratory rhythm. While neuromodulators such as norepinephrine (NE) allow it to be both robust and flexible for all living beings to interact with their environment, the basis for how neuromodulation impacts neuron-specific properties remains poorly understood. In this work, we examine how NE influences different preBötC neuronal subtypes by modeling its effects through modulating two key parameters: calcium-activated nonspecific cationic current gating conductance ($g_{\rm CAN}$) and inositol-triphosphate ($\rm IP_3$), guided by experimental studies. Our computational model captures the experimentally observed differential effects of NE on distinct preBötC bursting patterns. We show that this dual mechanism is critical for inducing conditional bursting and identify specific parameter regimes where silent neurons remain inactive in the presence of NE. Furthermore, using methods of dynamical systems theory, we uncover the mechanisms by which NE differentially modulates burst frequency and duration in NaP-dependent and CAN-dependent bursting neurons. These results align well with previously reported experimental findings and provide a deeper understanding of cell-specific neuromodulatory responses within the respiratory network.

Using a 1D bilayer system comprised of pairing and metallic layers, the present work proves the striking power of reservoir-mediated boosting of superconductivity. Employing many-body numerics on large systems at zero and finite temperature, we unravel the complex processes by which the tuning of the metal parameters can impact the effective pairing strength as well as the long-range pair-pair-coupling mediated by the metal. It is these two processes that in turn can strongly enhance superconducting susceptibility and thermal superconducting correlation length over those of the isolated system. We show that in this way, even a 1D system can come very close to achieving superconducting long-range order.

We study the critical two-dimensional stochastic heat flow $\mathscr{Z}_t^{\vartheta}$, recently constructed as the scaling limit of directed polymers in a random environment and as the weak limit of the solution to a mollified stochastic heat equation. Focusing on the mass of balls $\mathscr{Z}_t^{\vartheta}(B_r(0),B_r(a))$ ($a\in \mathbb{R}^2$, $r>0$), we establish an upper bound on its lower tail. As a consequence, we prove the integrability of the logarithm of $\mathscr{Z}_t^{\vartheta}(B_r(0),B_r(a))$ and its strict positivity. These results provide partial answers to open questions concerning the local behavior of $\mathscr{Z}_t^\vartheta$.