An action of a finite group $G$ is a pair $(S,\hat{G})$, where $S$ is a compact Riemann surface of genus $g \geqslant 2$ and $\hat{G} \leqslant {\rm Aut}(S)$ is isomorphic to $G$. To each action $(S,\hat{G})$ there is associated a signature $(γ;k_{1},\ldots,k_{r})$ that codifies the orbifold structure of $S/\hat{G}$. Two actions of $G$, say $(S_{1},G_{1})$ and $(S_{2},G_{2})$, are topologically equivalent if there is an orientation-preserving homeomorphism $φ:S_{1} \to S_{2}$ such that $φG_{1} φ^{-1}=G_{2}$. Topologically equivalent actions necessarily must have the same signature. The problem of determining the number of different topological actions of $G$ for a given signature is in general a difficult task. In this article, we describe, up to topological equivalence, those actions when $G$ is an abelian group and quotient genus $γ=0$. We are particularly interested in the case $G={\mathbb Z}_{k}^{m}$ and the quotient signature of the action to be of the form $(0;k,\stackrel{n+1}{\ldots},k)$.

Two confluent rewriting systems in noncommutatives polynomials are constructed using the equations allowing the identification of the local coordinates (of second kind) of the graphs of the $ζ$ polymorphism as being (shuffle or quasi-shuffle) characters and bridging two algebraic structures of polyzetas. In each system, the left side of each rewriting rule corresponds to the leading monomial of the associated homogeneous in weight polynomial while the right side is canonically represented on the Q-algebra generated by irreducible terms which encode an algebraic basis of the Q-algebra of polyzetas. These polynomials are totally lexicographically ordered and generate the kernels of the $ζ$ polymorphism meaning that the Q-free algebra of polyzetas is graded and the irreducible polyzetas are transcendent numbers, Q-algebraically independent, and then $π$ 2 is Q-algebraically independent on odd zeta values (so does $π$).

In the realm of spatiotemporal chaos, unstable periodic orbits play a major role in understanding the dynamics. Their stability changes and bifurcations in general are thus of central interest. Here, coupled map lattice discretizations of nonlinear partial differential equations, exhibiting a variety of behaviors depending on the coupling strength, are considered. In particular, the linear stability analysis of synchronized states is performed by evaluating the Bravais lattice orbit Jacobian in its reciprocal space first Brillouin zone, with space and time treated on equal grounds. The eigenvalues of the orbit Jacobian operator, computed as functions of the coupling strength, tell us about the stability of the periodic orbit under a perturbation of a certain time- and space frequency. Moreover, the stability under aperiodic, that is, incoherent perturbations, is revealed by integrating the sum of the stability exponents over all space-time frequencies.

The query optimizer is a fundamental component of database management systems. Recent studies have shown that learned query optimizers outperform traditional cost-based query optimizers. However, they fail to exploit valuable runtime observations generated during query execution to dynamically re-optimize the plan, thereby limiting further improvements in query performance. To address this issue, we propose learned query re-optimization, which allows optimization decisions to be deferred to execution time and guided by actual runtime observations. We realize this idea through LQRS, a learned query re-optimization framework that builds upon Spark SQL, exploiting runtime observations for dynamic plan refinement. Specifically, LQRS employs a curriculum reinforcement learning strategy and jointly supports pre-execution and in-execution optimization, allowing knowledge learned during execution to directly benefit pre-execution planning. Furthermore, we design a plug-and-play planner extension built upon the extensibility interfaces of Spark SQL, enabling online plan modification. Experiments on Spark SQL demonstrate that LQRS reduces end-to-end execution time by up to 90% compared to other learned query optimizers and query re-optimization methods.

One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on symbolic provers. Recently, large language models (LLMs) have demonstrated strong capabilities in theorem proving, complementing symbolic provers. Nonetheless, prompting LLMs can be expensive and may pose security risks for confidential codebases. As a result, purely symbolic approaches remain important even in the LLM era, as they are cost-effective, secure, and complement the strengths of LLMs. Motivated by these considerations, we pose a new research question: can the internal proof strategies of LLMs be extracted to enhance the capabilities of symbolic provers? As an initial step, we introduce Strat2Rocq. In an offline stage, Strat2Rocq extracts proof strategies from LLMs and formalizes them as lemmas in Rocq. In an online stage, given a theorem to be proved, Strat2Rocq augments the proof context with these extracted lemmas, enabling CoqHammer to leverage the LLM-derived strategies for more effective automated proving. Our evaluation demonstrates that, on open-source Rocq projects for software verification, Strat2Rocq enhances the success rate of CoqHammer by 13.41%. A side discovery is that the extracted lemmas are also beneficial to LLM proof agents, improving the success rate of an LLM proof agent by 4.00%.

We perform 3 dimensional moving-mesh hydrodynamical simulations of bubble nebulae around ultraluminous X-ray sources, using state-of-the-art software AREPO. We use a Monte-Carlo method to inject outflows with uniform mass outflow rate and momentum, in a conical funnel with a specific half opening angle. Simulation results show that the morphology of the bubble is determined by the initial momentum of the outflows, while the mechanical power of the outflows only influences the size of the bubble without changing its shape. Low mechanical power also results in a short cooling timescale of the system, leading to an early collapse of the bubble shell. The half opening angle of the outflows and the viewing angle of the system determine the observed bubble eccentricity together. Compared with the observational morphology of the ULX bubble sources NGC 55 ULX-1 and NGC 1313 X-2, our simulation favors the fact that the high velocity outflows of the accretion disks in these two systems are confined in a narrow funnel region.

In this work, we present the program MOLLId (MOLecular Line Identification) for automated molecular lines approximation with gaussian profile. Molecular identification was performed using multi-level comparison of the lines' center frequencies and rest frequencies from the spectroscopic database. The program was tested using identification of the molecular lines in observational spectra of young stellar objects RCW 120 YSO S1 and RCW 120 YSO S2, located near the border of the RCW 120 PDR. In the spectra of the RCW 120 YSO S1 source, 100 lines of 41 molecules were identified over the level of 4-6 sigma. In the spectra of the RCW 120 YSO S2 source, 407 lines of 79 molecules were identified over the level 3-5 sigma. Using Intel Core i7-12700K CPU, identification time is equal to 6 and 8 minutes per spectral range for the YSOs S1 and S2, respectively. From the analysis of CH3OH, CH3CN, CH3CCH molecules identified in RCW 120 YSO S2 we found a two-component structure and estimated the physical parameters in the LTE approximation for each of the components.

We report on the epitaxial growth of nm-thick films of bismuth-substituted yttrium iron garnet (BiYIG) by high-temperature off-axis radio-frequency magnetron sputtering. We demonstrate accurate control of the magnetic properties by tuning of the sputtering parameters and epitaxial strain on various (111)-oriented garnet substrates. BiYIG films with up to -0.80\% lattice mismatch with the substrate remain fully strained up to 60~nm-thick, maintaining a high crystalline quality. Transmission electron microscopy and energy-dispersive X-ray spectroscopy confirm coherent epitaxial growth, the absence of defects, and limited interdiffusion at the BiYIG/substrate interface. Varying the tensile or compressive strain between -0.80\% and +0.56\% in BiYIG allows for accurate compensation of the total magnetic anisotropy through magneto-elastic coupling. The effective magnetic anisotropy of sputtered BiYIG films can be further tuned via the off-axis deposition angle and the oxygen flow during growth, which determine the cation stoichiometry. Under optimized growth conditions, a ferromagnetic resonance (FMR) linewidth of 1~mT at 10~GHz is reliably obtained even for thicknesses as low as 10~nm. We also report small FMR linewidths in ultrathin (2-5~nm) BiYIG films grown on diamagnetic substrate yttrium scandium gallium garnet. These findings highlight the promise of low-damping, strain-engineered nm-thick BiYIG films for implementing advanced functionalities in spin-orbitronic and magnonic devices. Specifically, the magnetic-anisotropy compensation and low damping enable large cone-angle magnetization dynamics immune to magnon-magnon nonlinear scattering.

Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model accuracy by relaxing these assumptions and including additional terms in the formulation. However, such models are sensitive to large surface gradients which lead the assumptions of the model to break down. In this paper, we present a formulation of extended lubrication theory, and compare our model with several existing models, along with the numerical solution to the Stokes equations. The error in pressure and velocity is characterized for a variety of fluid domain geometries. Our results indicate that the new solution is suitable for a wide range of geometries. The magnitude of surface variation and the length scale ratio are both important factors influencing the accuracy of the extended lubrication theory models.

Turbulence is most commonly associated with high Reynolds number flow, however the framework of turbulent dynamics has been conceptually extended to many other fields, such as magnetohydrodynamic turbulence, elastic wave turbulence in solids, and more recently to low Reynolds number active turbulence in biological fluids. Here we report a form of solid turbulent dynamics in a self-propelled two-dimensional elastic sheet. We show numerically that the polar ordering dynamics in the active elastic solid model (AES) exhibit hallmark features of turbulent dynamics: power-law scaling of the energy spectrum and non-Gaussian statistics of velocity increments. However, there is no energy cascade, in line with previous findings for active turbulence in fluids. These results extend the concept of active turbulence to solid-state active matter, and can be important for understanding collective dynamics in biological active solids such as bacterial colonies and epithelial cell layers.

The supernova remnant (SNR) S147 contains the pulsar PSR J0538+2817 and a likely unbound binary companion, HD 37424. It is the only good Galactic candidate for a binary unbound by a core-collapse supernova (SN). Using Gaia DR3 parallaxes and photometry, we select the stars local to SNR S147 in a cylinder with a projected radius of $100$ pc and a parallax range of $0.614 < \varpi < 0.787$ mas (a length of $\simeq 360$ pc). We individually model the most luminous of these stars. The two most luminous single stars are the unbound binary companion, HD 37424, and HD 37367, with estimated masses of $(13.51\pm0.05) M_{\odot}$ and $(14.30\pm0.09) M_{\odot}$, respectively. The two most luminous binary systems are the spectroscopic binary HD 37366 and the eclipsing binary ET Tau that have primary masses of $(20.9\pm0.12) M_{\odot}$ and $(16.7\pm0.09) M_{\odot}$, respectively. We model the Gaia color-magnitude diagram (CMD) of this local stellar population using both single stars and a model consisting of noninteracting binaries using Solar metallicity PARSEC isochrones. For both models, the estimated age distributions of the $439$ $M_{G} < 0$ mag stars favor a high mass progenitor of $21.5M_{\odot}-41.1M_{\odot}$ for the SN.

Spiking Neural Networks (SNNs) offer low-latency and energy-efficient decision-making on neuromorphic hardware by mimicking the event-driven dynamics of biological neurons. However, the discrete and non-differentiable nature of spikes leads to unstable gradient propagation in directly trained SNNs, making Batch Normalization (BN) an important component for stabilizing training. In online Reinforcement Learning (RL), imprecise BN statistics hinder exploitation, resulting in slower convergence and suboptimal policies. While Artificial Neural Networks (ANNs) can often omit BN, SNNs critically depend on it, limiting the adoption of SNNs for energy-efficient control on resource-constrained devices. To overcome this, we propose Confidence-adaptive and Re-calibration Batch Normalization (CaRe-BN), which introduces (i) a confidence-guided adaptive update strategy for BN statistics and (ii) a re-calibration mechanism to align distributions. By providing more accurate normalization, CaRe-BN stabilizes SNN optimization without disrupting the RL training process. Importantly, CaRe-BN does not alter inference, thus preserving the energy efficiency of SNNs in deployment. Extensive experiments on both discrete and continuous control benchmarks demonstrate that CaRe-BN improves SNN performance by up to $22.6\%$ across different spiking neuron models and RL algorithms. Remarkably, SNNs equipped with CaRe-BN even surpass their ANN counterparts by $5.9\%$. These results highlight a new direction for BN techniques tailored to RL, paving the way for neuromorphic agents that are both efficient and high-performing. Code is available at https://github.com/xuzijie32/CaRe-BN.

This competition in high-energy physics (HEP) and machine learning was the first to strongly emphasise uncertainties in $(H \rightarrow τ^+ τ^-)$ cross-section measurement. Participants were tasked with developing advanced analysis techniques capable of dealing with uncertainties in the input training data and providing credible confidence intervals. The accuracy of these intervals was evaluated using pseudo-experiments to assess correct coverage. The dataset is now published in Zenodo, and the winning submissions are fully documented.

In the thin wall approximation, we study a class of asymptotically AdS black holes which contain a spherically symmetric vacuum bubble with a different (positive or negative) cosmological constant. Collapsing, expanding, and static bubble solutions are considered. Among these, expanding bubbles with positive cosmological constant can provide a way to apply the AdS/CFT correspondence to describe the physics of an expanding universe. We systematically study the causal structure of the solutions as a function of the cosmological constant, the mass of the black hole, and the tension of the bubble. We then compute the holographic entanglement entropy for a class of boundary subregions using extremal codimension-two surfaces as a probe. For collapsing bubbles, we find examples in which the entanglement entropy also explores the geometry inside the black hole bifurcation surface. As a complementary way to probe the interior of the bubble, we investigate almost-null radial geodesics related to the bulk-cone singularities of boundary two-point correlators. While the bulk-cone singularities for collapsing and expanding bubbles are consistent with thermalization at late time, static bubbles violate thermalization and exhibit properties similar to those of scar states.

We ask how quantum correlations can be distributed among many subsystems. To address this, we define entanglement sharing schemes (ESS) where certain pairs of subsystems allow entanglement to be recovered via local operations, while other pairs must not. ESS schemes come in two variants, one where the partner system with which entanglement should be prepared is known, and one where it is not. In the case of known partners, we fully characterize the access structures realizable for ESS when using stabilizer states, and construct efficient schemes for threshold access structures, and give a conjecture for the access structures realizable with general states. In the unknown partner case, we again give a complete characterization in the stabilizer setting, additionally give a complete characterization of the case where there are no restrictions on unauthorized pairs, and we prove a set of necessary conditions on general schemes which we conjecture are also sufficient. Finally, we give an application of the theory of entanglement sharing to resolve an open problem related to the distribution of entanglement in response to time-sensitive requests in quantum networks.

We investigate the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma systems with analytic initial data. This result is the first to establish analyticity persistence in such coupled KdV systems.

Forward and backward scattering provide complementary volumetric and interfacial information, yet conventional three-dimensional (3D) imaging typically accesses only one. In this Letter, we present a substrate-enhanced diffraction tomography approach that simultaneously recovers both channels under multi-angle epi-illumination.This geometry captures one forward- and two backward-scattering bands in axially symmetric Fourier regions, where their complementary coverage enables phase-absorption separation in a non-Hermitian spectrum. Explicit 3D transfer functions are derived for both channels, and an axial Kramers-Kronig relation is established to incorporate substrate-induced boundary conditions in a unified framework. Our results establish a label-free, high-resolution 3D imaging modality that surpasses the limits of existing methods.

Multi-stage disease histories derived from longitudinal data are becoming increasingly available as registry data and biobanks expand. Multi-state models are suitable to investigate transitions between different disease stages in presence of competing risks. In this context, however, their estimation is complicated by dependent left-truncation, multiple time scales, index event bias, and interval-censoring. In this work, we investigate the extension of piecewise exponential additive models (PAMs) to this setting and their applicability given the above challenges. In simulation studies we show that PAMs can handle dependent left-truncation and accommodate multiple time scales. Compared to a stratified single time scale model, a multiple time scales model is found to be less robust to the data generating process. We also quantify the extent of index event bias in multiple settings, demonstrating its dependence on the completeness of covariate adjustment. In general, PAMs recover baseline and fixed effects well in most settings, except for baseline hazards in interval-censored data. Finally, we apply our framework to estimate multi-state transition hazards and probabilities of chronic kidney disease (CKD) onset and progression in a UK Biobank dataset (n=142,667). We observe CKD progression risk to be highest for individuals with early CKD onset and to further increase over age. In addition, the well-known genetic variant rs77924615 in the UMOD locus is found to be associated with CKD onset hazards, but not with risk of further CKD progression.

Magnonics offers nanometer-scale wave propagation and strong nonlinearities, making it attractive for neuromorphic applications such as artificial neurons. Yet, magnonic elements with interconnections solely within the magnonic system remain challenging, preventing the realization of interconnected magnonic neurons to date. Here, we experimentally demonstrate an all-magnonic neuron that reacts to magnon inputs with thresholded, amplified magnon firing and subsequent self-reset, enabling all-magnonic operation and cascading. Our approach is based on micro-antenna excitation on an ultra-low damping garnet with perpendicular magnetic anisotropy (PMA), where we exploit the positive magnon frequency shift to realize nonlinear activation. Using Brillouin light scattering spectroscopy, we uncover a transient neuron response with tunable fading memory: A 25% change in pump power results in a 3-order-of-magnitude tuning in memory time, which we harness, demonstrating temporal integration of up to 50 magnon pulses. Finally, we realize neuron triggering in a cascade of 3 neurons, highlighting its potential for connected magnonic circuits.

We consider a 331 model, based on $β=-1/\sqrt{3}$, with three $SU(3)$ triplets with a softly broken $\mathbb{Z}_2$ symmetry. The resulting scalar potential is commonly used in phenomenology. We systematically determine all the potential minima and obtain the conditions under which the electroweak vacuum is global with the help of orbit space methods. For the case the electroweak vacuum is not global, we calculate bounds on the scalar couplings from metastability. We find a parametrisation of the potential couplings in terms of physical quantities and use it to show the available parameter space.

We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching processes at a sufficiently large generation in this asymptotic can be approximated by a compound Poisson-gamma distribution. Numerical experiments revealed that the compound Poisson-gamma models were in good agreement with the corresponding GW models for sufficiently large generations under a reasonable parameter regime. Our results can be regarded as supporting the use of the compound Poisson-gamma model as a model for cascaded multiplication processes, such as detection signals of electron multipliers and population sizes of individuals with specific biological characteristics.

Let $I$ be a monomial ideal in a polynomial ring $S=K[x_1,\ldots,x_n]$ over a field $K$ with $n=2$ or $3$, and let $\overline{I}$ be its integral closure. We will show that $\text{reg} (\overline{I}) \le \text{reg} (I)$. Furthermore, if $I$ is generated by elements of degree $d$, then $\text{reg} (I)=d$ if and only if $I$ has linear quotients.

Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective attacks and coherent attacks under suitable assumptions. Here we consider continuous-variable communication protocols, where the sender Alice encodes information using a discrete modulation of phase-shifted coherent states, and the receiver Bob decodes by homodyne or heterodyne detection. We compute the Petz-Rényi and sandwiched Rényi conditional entropies associated with these setups, assuming either a passive eavesdropper or one that injects thermal photons into the channel, who gathers the quantum information leaked through a lossy communication line of known or bounded transmittance. Whereas our results do not directly provide reliable key-rate estimates, they do represent useful ball-park figures. We obtain analytical or semi-analytical expressions that do not require intensive numerical calculations. These expressions serve as bounds on the key rates that may be tight in certain scenarios. We compare different estimates, including known bounds that have already appeared in the literature and new bounds. The latter are found to be tighter for very short block sizes.

The uniqueness of purifications of quantum states on a system $A$ up to local unitary transformations on a purifying system $B$ is central to quantum information theory. We show that, if the two systems are modelled by commuting von Neumann algebras $M_A$ and $M_B$ on a Hilbert space $\mathcal H$, then uniqueness of purifications is equivalent to Haag duality $M_A = M_B'$. In particular, the uniqueness of purifications can fail in systems with infinitely many degrees of freedom -- even when $M_A$ and $M_B$ are commuting factors that jointly generate $B(\mathcal H)$ and hence allow for local tomography of all density matrices on $\mathcal H$.

We study a system of fully nonlinear elliptic equations, depending on a small parameter $\eps$, that models long-range segregation of populations. The diffusion is governed by the negative Pucci operator. In the linear case, this system was previously investigated by Caffarelli, the second author, and Quitalo in \cite{CL2} as a model in population dynamics. We establish the existence of solutions and prove convergence as $\eps\to0^+$ to a free boundary problem in which populations remain segregated at a positive distance. In addition, we show that the supports of the limiting functions are sets of finite perimeter and satisfy a semi-convexity property.

We investigate the trade-off between vacuum insensitivity and sensitivity to excitations in finite-size detectors, taking measurement locality as a fundamental constraint. We derive an upper bound on the detectability of vacuum excitation, given a small but nonzero probability of false positives in the vacuum state. The result is independent of the specific details of the measurement or the underlying physical mechanisms of the detector and relies only on the assumption of locality. Experimental confirmation or violation of the inequality would provide a test of the axioms of algebraic quantum field theory, offer new insights into the measurement problem in relativistic quantum physics, and establish a fundamental technological limit in local particle detection.

We study the spatial distributions of pressure, energy density, and shear forces inside the nucleon within the two-flavor Skyrme model including vector mesons. This framework has the advantage that nucleon configurations can be stabilized without the Skyrme term. In contrast to the model without vector mesons, however, we realize that the energy-momentum tensor (EMT) becomes pseudo-gauge dependent. We explicitly demonstrate that all these distributions differ between the canonical and Belinfante forms of the EMTs. We identify the pseudo-gauge ambiguity as originating from nonvanishing surface terms associated with spin currents generated by the vector-meson field strength tensors. Furthermore, we show that the pressure and shear-force distributions in the canonical EMT develop singularities at the nucleon center, whereas the corresponding Belinfante distributions remain finite. Finally, we discuss the implications of pseudo-gauge dependence for extracting the confining force and for constructing the equation of state inside the nucleon.

Via the spin-Hall effect and its inverse, in-plane charge currents in a normal metal$-$ferromagnet (N$|$F) bilayer can be used to excite and detect magnetization dynamics in F. Using a magneto-electric circuit approach, we here consider the current response to quadratic order in the applied electric field, which is resonantly enhanced for driving frequencies close to frequencies of coherent magnetization modes. Our theory can be applied to bilayers with a magnetic insulator or with a magnetic metal. It focuses on the contribution of coherent magnetization dynamics to spin currents collinear with the equilibrium magnetization direction, but also takes into account relaxation of spin accumulation via spin currents carried by incoherent magnons and conduction electrons in F.

In this letter, we analyse and interpret the kinematic power corrections to deeply virtual Compton scattering dispersion relation. We show that the kinematic corrections at twist-4 can be connected to other form factors of the Energy-Momentum Tensor beyond the pressure distribution involved at leading-power, namely the ones related to Momentum and total Angular Momentum distributions. In the nucleon case, these corrections are not negligible at presently accessible virtualities. The DVCS subtraction constant becomes an experimental constraint on momentum distributions, pressure forces distributions, and total angular momentum distributions. Finally, we use continuum and lattice-QCD results to predict the expected size of the DVCS subtraction constant, and conclude that momentum distributions are responsible of roughly one-third of the experimental signal at $Q^2 = 2\textrm{GeV}^2$.

Amorphous interfacial complexions have been shown to restrict grain growth and improve damage tolerance in nanocrystalline alloys, with increased chemical complexity stabilizing the complexions themselves. Here, we investigate local chemical composition and structural short-range order in Cu-rich, multi-component nanocrystalline alloys to understand how dopants self-organize within these amorphous complexions and how local structure is altered. High resolution scanning transmission electron microscopy and elemental analysis are used to study both grain boundaries and interphase boundaries, with chemical partitioning observed for both. Notably, the amorphous-crystalline transition region is observed to be enriched in certain dopant species and depleted of others as compared to the interior of the amorphous complexions. This chemical patterning can be explained in terms of the elemental preference for ordered or disordered grain boundary environments. As only a qualitative measure of structural short-range order can be obtained with nanobeam electron diffraction for these specimens, atomistic simulations with a custom-built machine learning interatomic potential are then used to probe how dopant patterning affects local structural state. Increased grain boundary chemical complexity is found to result in a more disordered complexion structure, with segregation to the amorphous-crystalline transition regions driving changes in local structure that are sensitive to dopant ratios. As a whole, the intimate connection between local chemistry and order in amorphous interfacial complexions is demonstrated, opening the door for microstructural engineering within the amorphous complexions themselves.