Papers

Topological states are renowned for their robustness against perturbations. Recent advances have further introduced momentum-gap (or time) topology in time-varying media, enabling temporal topological states. However, existing studies for momentum-gap topology are largely confined to non-propagating interface states; their potential for wave transport, especially at moving boundaries, has yet to be realized. Here, we experimentally demonstrate topological streams in space-time: space-time topological edge states that propagate along a moving boundary in a dynamically modulated time-synthetic photonic lattice. These streams arise from the coexistence of energy-gap and momentum-gap topologies and break both spatial and temporal translation symmetries, conserving neither energy nor momentum. Remarkably, they reconstruct their wave profiles after strong localized spatiotemporal obstacles, enabled by an imaginary quasienergy gap and kinematic decoupling from radiative bulk channels. Our results establish a form of self-healing spatiotemporal non-Hermitian protection, showing that the temporal dimension can transform topology from pinned states and isolated events into robust, directional and self-restoring wave transport.

We construct a continuous family of inequality and social stratification indices based on the curvature of the Lorenz curve. We study the inequality axioms of the family and find that they are satisfied only with the so-called stratification-aversion parameter $\alpha$ set to 0 – in all other cases, these constraints cannot be satisfied in a strict sense. With $\alpha = 0$, the index has a very simple closed form and its value can be easily approximated. We study the values of the index on World Bank inequality data and see how the rankings across a wide selection of countries change as $\alpha$ is varied. Spearman and Kendall rank-correlation matrices with other common indices are also computed and analyzed. We find the curvature index to deviate consistently from the comparison indices, albeit less so for consumption- than income-based countries.

This work validates the Lyapunov–Liouville framework and its non-diffusive closures in decaying homogeneous isotropic turbulence (HIT) by numerically integrating the closed von Kármán–Howarth and Corrsin equations via an adaptive solver. Three initial states (Saffman–Birkhoff, Loitsiansky, Gaussian) are analyzed across Prandtl numbers from $Pr=10^{-3}$ to $1000$. The model reproduces the distinct decay paths, with Saffman–Birkhoff yielding velocity and thermal exponents $m \simeq n \simeq -1.25$, while Loitsiansky condition accelerates mechanical decay ($m \simeq -1.51$) and increases thermal persistence ($n \simeq -0.89$). The Gaussian profile induces rapid decay ($m \simeq -2.7$), approaching a critical threshold at $t \simeq 33$ initial Lyapunov times. At $Pr=1000$, the thermal microscale drops below the Kolmogorov scale, with the Batchelor constant settling around $C_B \simeq 3.5$. Calculated Kolmogorov ($C_K \simeq 1.72-1.75$) and Obukhov–Corrsin ($C_{OC} \simeq 1.8$) constants align with benchmarks. Finally, velocity and temperature increment PDFs successfully capture multi-scale intermittency and non-Gaussian statistics, matching DNS and experimental data.

Since its first observation by the ATOMKI experiment in 2018, the $\rm ^*Be$ anomaly has attracted considerable interest within the dark sector community as it may indicate the existence of a new fundamental particle with a mass of about 16.9 MeV, the $X_{17}$. However, the minimal model describing $X_{17}$ as a new vector boson is severely constrained by null results from legacy beam-dump experiments. Among these, the E141 experiment at SLAC places stringent limits on the $X_{17}$ coupling to electrons $\varepsilon_e$ in the $5.1\times10^{-5}\lesssim \varepsilon_e\lesssim1.7\times10^{-4}$ region. This excludes the possibility of a long-lived $X_{17}$, potentially in contrast with the preliminary estimate of the particle lifetime recently reported by the ATOMKI collaboration. The E141 limits commonly adopted in the literature rely on reinterpretations of the original analysis under solid but simplifying assumptions. While these studies provide a reliable estimate of the experiment's reach, they rely on approximations that were well justified when the boson mass was largely unconstrained. With the $X_{17}$ mass now confined to a narrow region by recent experimental observations, a more refined treatment of the E141 sensitivity becomes necessary. In this work, we revisit the E141 exclusion limits in the $X_{17}$ scenario by performing a dedicated reanalysis that incorporates a more accurate treatment of the experimental setup and signal prediction. We quantify the impact of these refinements on the excluded parameter space and discuss their implications for the compatibility between the E141 constraints and the vector boson interpretation of the ATOMKI anomalies.

In these notes, we extend a formalism for computing the amplitude of gravitational-waves (GWs) beyond null-geodesic propagation, as may arise in alternative theories of gravity. We derive the wavevector divergence governing the amplitude evolution in this more general setting and apply the formalism to GWs with a frequency-independent subluminal group velocity and to massive gravitons. We show that, in both cases, a naive interpretations of the resulting amplitudes can lead to significant apparent distortions. This formalism opens the door for amplitude interactions with extra degrees of freedom in the presence of dispersion.

The trade-off between noise averaging and temporal resolution fundamentally limits conventional zero-crossing frequency estimators under dynamic and noisy conditions. This paper presents an overlapped sampling-intervals zero-crossing fitting method (OS-ZFM), which introduces a structured overlapping regression framework that decouples noise averaging from temporal update rate. The method adopts a deterministic closed-form formulation, enabling a unified bias-variance analysis to characterize the statistical behavior of the estimator and clarify the role of structured data reuse. Numerical results under intensity and background noise at a signal-to-noise ratio (SNR) of 10 dB show that OS-ZFM reduces median estimation error by more than 60% compared to conventional zero-crossing fitting methods at the same temporal resolution. It further achieves up to 90% reduction relative to basic zero-crossing detection and consistently yields lower estimation errors than Hilbert-transform-based estimators. Experimental validation utilizing impact-induced transient motion measured by laser Doppler interferometry demonstrates that OS-ZFM reconstructs smooth and physically consistent trajectories with improved temporal fidelity. Owing to its low computational complexity and deterministic formulation, the proposed method enables accurate real-time frequency and acceleration tracking in resource-constrained measurement systems.

In this paper, we present a phenomenological analysis of $B_{(s)} \to \rho\rho, \rho K^\ast$ and $K^\ast K^\ast$ decays using state-of-the-art perturbative QCD (pQCD) calculations. Our study is primarily motivated by recent polarization measurements from the LHCb and Belle II collaborations, which have significantly improved the precision of polarization fractions and enabled the first full determination of polarization-dependent CP asymmetries. This work extends the comprehensive pQCD study of charmless two-body $B$ decays reported in our previous paper [Chin. Phys. C 46 (2022) 123103], with a particular focus on polarization observables, especially the CP asymmetries in each helicity state, which reflect distinct orbital angular momentum configurations between the two vector mesons. Our predictions for the branching ratios and longitudinal polarization fractions in the $B^0 \to K^{\ast 0} {\bar K}^{\ast 0}$ and $B^+ \to \rho^0 K^{\ast +}$ modes are in good agreement with the new experimental data. However, the calculated longitudinal polarization fraction for $B_s \to K^{\ast 0} {\bar K}^{\ast 0}$ is significantly larger than the LHCb measurement. Moreover, the predicted (helicity-dependent) CP asymmetries in $B^+ \to \rho^0 K^{\ast +}$ are about $30 \%$ smaller than the observed values. These discrepancies point to a rich interplay between different topological amplitudes, highlighting the need for further theoretical investigation to resolve the long-standing polarization puzzle in two-body $B$ decays into vector mesons.

A major challenge in the modelling and simulation of grain boundaries (GBs) is the conflict between the system size and computation capability, which inherently restricts the computationally accessible boundary characters. We present an algorithm to find the irreducible macroscopic representation of any given coincident-site-lattice GB character in the cubic lattice, and thus determine the irreducible size of its supercell. The algorithm is compared with the conventional orthogonal supercell and a published calculation method to assess its merits in saving computational resources. This supercell size parameter can be used to predict which GB character is relatively special across the vast 5D space, as those GBs possess small structural units are likely to exhibit particular structure-property relationships that are worthy of attention. The prediction is confirmed by examining the energy and mobility trends of aluminum mixed GBs obtained from the atomistic simulations.

Surface contamination strongly affects the intrinsic properties of nanoscale materials, making its reliable identification and quantification crucial for both accurate experimental interpretation and nanofabrication. Although scanning transmission electron microscopy can resolve contaminants at atomic resolution within nanometer-scale regions, it cannot easily provide a quantitative, large-area contamination measure. Here, we introduce a minimally destructive recoil-projectile coincidence method for ion transmission experiments that enables element-specific identification and quantification of surface contaminants with isotopic resolution. We demonstrate this approach by comparing self-supporting graphene samples prepared using either a polymethylmethacrylate (PMMA)-based or a PMMA-free transfer process. Carbon and hydrogen are identified as the dominant surface contaminants. PMMA-free transferred graphene exhibits the lowest native contamination levels. Following in-situ thermal annealing at 400 {\deg}C for 1 h, the measured carbon areal density approaches the value expected for atomically clean single-layer graphene within the experimental uncertainty, while hydrogen coverage is strongly reduced. Unlike PMMA-transferred graphene, which rapidly recontaminates after annealing, PMMA-free transferred graphene remains nearly contamination-free for at least 140 min under ultra-high vacuum conditions ($p_{\mathrm{base}} = 2 \times 10^{-8}$ mbar). Beyond graphene, the presented method establishes a quantitative characterization platform for ultrathin materials, enabling studies of surface cleanliness, adsorption, implantation and surface interaction dynamics in such systems.

Recent demonstrations of quantum computational advantage have been driven largely by sampling problems. A prominent model, boson sampling, involves sampling from the output distribution of a linear optical network. However, its classical hardness hinges on two plausible yet less-studied conjectures: the average-case hardness of approximating Gaussian permanents, and the permanent anti-concentration conjecture (PACC). The PACC is a purely mathematical assertion regarding the distributional properties of random Gaussian matrices. While the typical magnitude of the permanent has been established for discrete random matrices, the complex Gaussian case, which governs transition amplitudes in linear optical networks, has remained open. Here, we establish a weak anti-concentration bound by upper-bounding the probability that a random Gaussian permanent is superexponentially smaller than its standard deviation. Tightening this bound to an inverse-polynomial fraction would prove the original PACC. As a corollary, we establish the typical magnitude of Gaussian permanents, on par with Tao and Vu's seminal result for Bernoulli matrices. Combined with the Aaronson-Arkhipov framework, our result implies that classically simulating boson sampling to within a superexponentially small total variation distance would collapse the polynomial hierarchy, assuming the remaining conjectures hold.

We define the lift of a partial cohomological field theory with respect to a Frobenius algebra and the corresponding lift of local polyvector fields, extending the lift procedure proposed by Della Vedova, Lorenzoni, and Savoldi. This allows us to systematically produce examples of non-semisimple homogeneous partial cohomological field theories whose integrable systems possess a second Hamiltonian structure, thus confirming the conjecture of Buryak et al. on an explicit formula for the second Poisson bracket in new non-semisimple cases. Moreover we present some relations of these lift constructions with the Morimoto theory of the lift of geometric structures to the Weil bundle of infinitely near points associated to a local algebra.

Single-pixel sensing encodes a scene as a short sequence of coded measurements, and image-free methods infer the task directly from that sequence. We show that removing image reconstruction relocates the central design problem to the lift: how 1D measurements become a 2D task representation. We organize this choice as a lift spectrum from a fixed-physics inverse, through a learned static projection, to content-adaptive retrieval. These are not interchangeable forms of reconstruction: the fixed-physics route reconstructs an image consumed at inference, whereas our spatiotemporal soft-fusion (STSF) network lifts measurements directly into task features, and task-prioritized loss scheduling (TPLS) uses a separate learned reconstruction branch only as scheduled training supervision. A probe-selected recurrent encoder and a parameter-matched lift ablation identify the STSF design. In simulation, STSF+TPLS exceeds the prior image-free baseline on three datasets at 3.13% sampling (+3.2 to +9.9 pp foreground mIoU) and remains competitive down to 0.39%. The strongest clean-trained reconstruct-then-segment baseline wins without measurement noise, but measurement noise reverses the ranking: the reconstructed task input carries a 20-70x larger normalized relative perturbation than the measurements themselves. Stressed to failure, the three lift regions exhibit distinct dominant signatures–collapse, imprinting, and coarsening. STSF+TPLS transfers without fine-tuning to a real single-pixel bench, where the reversal reappears as a proof of concept; inference takes about 14 ms per mask on an RTX 4090. Within the tested fixed-acquisition regime, measurement-to-space adaptivity therefore organizes both the clean-to-noisy operating envelope and the failure a system encounters. Code and pretrained weights: https://github.com/Hanyuyuan6/STSF-TPLS.

To maximize the duration of optical downlinks with Low-Earth Orbit satellites, it is crucial to ensure the coupling into the single mode fiber of the ground terminal even at low elevations. Adaptive optics systems are designed to correct the wavefront deformation induced by atmospheric turbulence. However, at low elevations, amplitude fluctuations (or scintillation) challenge this correction. Here we propose a methodology to design a wavefront sensor that is robust to scintillation, taking the Shack-Hartmann WFS as an example. We present a slope estimator able to handle the large dynamic intensity range between subapertures. We then present an end-to-end simulation of the AO system to show the decrease in wavefront measurement error brought by a finer sampling of the pupil plane. Finally, we discuss the feasibility of such design by means of a detailed AO error budget in the case of a LEO optical downlink.

OASIS-ERIS, the Open Acquisition System for IEPE Sensors - Electrically Refined and Inter-device Synchronization, is the successor to the previously released OASIS-UROS. It is based on the Analog Devices AD7606C-18 analog-to-digital converter, offering 18-bit resolution on eight simultaneously sampled channels, and the Espressif ESP32-S3 microcontroller. The laboratory usability of OASIS-ERIS is significantly improved compared to OASIS-UROS due to the added inter-device synchronization. By physically connecting the sample clocks across devices, a truly synchronized data acquisition can be achieved with an arbitrary number of acquisition boards. Additionally, a migration of the firmware to ESP-IDF allows a major increase of the achievable sampling frequency to 100 kHz. This paper documents the hardware and software stack of OASIS-ERIS, and provides all materials necessary for reproduction. Further, the performance of OASIS-ERIS is tested against a commercial measurement system in an Experimental Modal Analysis campaign. The results show that OASIS-ERIS closely matches the performance of the commercial system, making it a viable replacement for academia and projects with tightly constrained budgets.

Interpreting the observed properties of intermediate-mass stars requires accounting for rotation, binarity, intrinsic population diversity, and measurement uncertainty. We combine these effects in population-synthesis models of 1.4-2.5 M$_{\odot}$ stars that include pulsation properties of $\delta$ Sct variables. The synthetic populations successfully reproduce the distributions of stars observed in young associations, validating the mapping between intrinsic and observed stellar properties. Using these models, we infer a semi-empirical $\delta$ Sct instability strip by matching synthetic and observed populations. The resulting instability strip is systematically hotter than widely used theoretical prescriptions, implying that $\delta$ Sct stars are on average 0.1 M$_{\odot}$ more massive than previously assumed, with 95% of the population spanning approximately 1.50-2.30 M$_{\odot}$. We then investigate the $\delta$ Sct period-luminosity relation and reproduce its recently identified second ridge with mixture models in which roughly one-third of stars have the fifth or sixth radial overtone as their dominant mode; the fraction increases in younger populations. In contrast, unresolved binarity does not account for the second ridge. Finally, we predict the population-wide distribution of asteroseismic large separations, $\Delta\nu$, finding a peak between 6 and 7 d$^{-1}$, in agreement with recent observations. We also demonstrate that $\Delta\nu$ is most reliably measured with the échelle technique, while autocorrelation methods can produce spurious detections when used in isolation. These results show that population synthesis provides a powerful framework for interpreting populations of $\delta$ Sct stars and for linking stellar evolution, pulsation, and observation.

The fractional quantum Hall effect (FQHE) is conventionally understood in terms of strongly correlated many-body states and emergent quasiparticles with fractional charge. Here, we propose a complementary phenomenological framework in which impurity-induced geometric correlations within a Landau level contribute to the organization and stability of fractional quantum Hall states. The model considers a two-dimensional electron gas coupled to a correlated distribution of ionized impurities located at a finite distance from the electronic layer. Impurity-induced overlap between displaced Landau orbitals generates coherent guiding-center correlations and an effective splitting of the Landau-level degeneracy into fractional sublevels. Within this framework, the resulting energy spectrum reproduces the principal odd-denominator fractional sequences through the interplay between guiding-center quantization and impurity-induced orbital coherence. An explicit expression for the correlation energy is obtained in terms of the magnetic length, impurity spacing, and impurity-layer separation, providing a direct connection between the proposed mechanism and experimentally controllable heterostructure parameters. The model naturally incorporates the integer quantum Hall regime as the limiting case of vanishing correlation-induced splitting. Within this geometric picture, effective fractional factors emerge from collective orbital coherence and correlation-modified guiding-center dynamics rather than being uniquely associated with independent fractionally charged quasiparticles. Although the model does not attempt to derive topological order, anyonic statistics, or many-body incompressibility, it suggests that impurity-induced geometry and guiding-center coherence may provide an additional contribution to the emergence, stability, and experimental visibility of fractional quantum Hall states.

Classical general relativity allows time travel, but Hawking [Phys. Rev. D 46, 603 (1992)] conjectured that quantum mechanics ultimately prevents it. Here we propose a feasible experiment to test Hawking's Chronology Protection Conjecture in optics. In this scheme, time travel is inherently related to lasing, and the amplified vacuum fluctuations above laser threshold establish the quantum limits of time travel

Segmentation of adjacent structures with similar intensity distributions remains a challenging problem in image analysis, particularly when object boundaries are weak or ambiguous. Under such conditions, classical variational models may suffer from degenerated image-driven forces, leading to boundary leakage or undesired merging of neighboring regions. To address these limitations, we propose a smooth phase-separation variational model based on the Cahn–Hilliard equation for weak-boundary segmentation of homogeneous-appearance structures. The proposed framework integrates softmax-based region fitting with Cahn–Hilliard phase-field regularization to maintain interface discrimination under weak image-driven forces. We further introduce a mixed $L^2-H^{-1}$ gradient flow, which preserves higher-order interfacial regularization while allowing adaptive changes of phase masses, establish the continuous energy dissipation law, and prove the existence and uniqueness of weak solutions in the natural solution class. For numerical computation, we develop a stabilized scalar auxiliary variable (SAV) scheme that is linear, FFT-based, and satisfies a modified discrete energy dissipation law. Numerical experiments on synthetic and medical images demonstrate that the proposed method effectively separates adjacent homogeneous structures across weak boundaries and achieves competitive segmentation accuracy and improved boundary localization compared with representative variational, phase-field, and deep learning methods.

Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral over infinite space by a convenient boundary integral in piecewise-homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise-constant potentials. For electromagnetic systems with piecewise-homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities.

In the present study we have assessed the effect of suction through discrete perforations on the transition of the Blasius boundary layer. In particular, the intermittency and the spectra of the streamwise velocity fluctuations, obtained using hot-wire anemometry, were used to evaluate the optimum suction, i.e., one that provides the greatest delay in transition. The displacement thickness Reynolds number at suction was varied between 1400 and 1600, while the number of rows of holes was either four or ten. The suction holes had diameter of the order of the displacement thickness of the boundary layer, a practical size from manufacturing and maintenance perspectives. As the suction strength was increased the transition front moved downstream, with the maximum delay in transition occurring at the optimum suction. When the suction was increased further, the transition front moved upstream again. The results, supported by a scaling analysis, showed that suction volume flow rate is a better indicator of the effects of suction on the transition delay than suction velocity. In particular, suction through different numbers of rows of perforations produces largely similar effects on the boundary layer transition, provided the suction volume flow rate remains the same. However, suction through fewer rows provided a slightly greater delay in transition in addition to a slightly lower optimum suction volume flow rate. The results also showed that suction applied at a lower Reynolds number provides a substantially greater transition delay but at slightly higher values of the normalized optimum suction volume flow rate.

There is broad consensus that Type Ia supernovae (SNe Ia) are the thermonuclear explosions of C/O white dwarfs (WDs) in binary systems, but their progenitors and explosion mechanisms remain uncertain. Their earliest light curves probe the outermost ejecta and provide important constraints on the explosion. We analyse the ZTF DR2 sample of SNe Ia to search for objects exhibiting early flux excess (EEx SNe Ia). We employ two complementary approaches: (i) identifying deviations from models without early excess using power-law and SALT2 fits, and (ii) comparing observations with double-detonation (DD) and companion-interaction (CI) models. The latter identify 145 and 199 candidates, respectively, although the methods disagree substantially on both the objects selected and the total number of candidates. Combining all methods, we identify 17 robust EEx SN Ia candidates, including six over-luminous events (five 91T-like and one 03fg-like). The strongest excesses reach ${\sim}10$–17% of the peak flux. The best candidates have, on average, higher stretch and preferentially occur in lower-mass, bluer host galaxies, suggesting younger stellar populations. We estimate that EEx SNe Ia comprise $\lesssim25\%$ of all SNe Ia, consistent with previous work, with over-luminous subtypes showing a higher relative incidence than normal SNe Ia. Among the DD models, the preferred solutions favour intermediate WD core masses ($1 M_{\odot}$), low shell-burning fractions ($20\%$), and heavier He-burning products ($^{56}$Ni), whereas the CI models show no clear parameter trends. Overall, we find no compelling evidence that either scenario is preferred as the origin of the observed early flux excesses.

Europe's expertise in the ethical, legal, and social aspects (ELSA) of emerging technologies is a strategic asset for the successful and sovereign development of quantum technologies. In this position paper, we argue that this expertise should become a central part of the upcoming EU Quantum Act. At a time when quantum technologies are becoming more powerful, economically relevant, and geopolitically contested, European policy should not reduce societal considerations to risk assessment and ex-post regulation. Instead, ELSA expertise can translate European values into technological practices, governance structures, and concrete policy measures, thereby supporting a development which is responsible, socially robust, and competitive. Taking inspiration from the role of concept cars, we present eight aspirational ELSA recommendations that demonstrate what a distinctly European approach to quantum technologies could offer. These recommendations include setting European policy targets as quantum moonshots, embedding European values, addressing the motivations of younger generations, strengthening international cooperation, developing applications globally and inclusively, integrating continuous technology assessment, creating shared sociotechnical repositories, and shaping a European narrative for quantum technologies. Together, we show that ELSA is not only about mitigating risks. It can also amplify benefits, increase legitimacy and societal acceptance, support economic prosperity, and contribute to a truly sovereign European quantum future.

Collisional rotational excitation is a fundamental process in many gaseous environments. The textbook hard-sphere model stipulates that high rotational excitation results from head-on collisions, leading primarily to backward scattering, whereas long-range glancing collisions in the forward direction are inefficient for rotational energy transfer. Here, we report rotational state resolved product imaging for a system with strong attractive interaction, the charge-transfer collision between spin-orbit selected Ar+(2P3/2) ions and para/ortho-H2 molecules. Surprisingly, the H2+ products are rotationally excited and dominated by forward scattering, in sharp contrast to conventional wisdom. Quantum dynamical calculations on a first-principles diabatic potential energy matrix reproduce the observations. Trajectory surface hopping analysis further reveals that rotational excitation occurs mostly with large impact parameters, and the captured complex undergoes orbiting motion owing to the strong attractive interaction between the two collision partners before they break up. This novel mechanism should be general for collisional systems featuring strong attractive interactions, which undermine the hard-sphere assumption.

We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.

We construct and analyze stationary, axisymmetric vacuum metrics obtained by magnetic Ernst inversion of Kerr-NUT with Manko-Ruiz parameter $C$ and pre-inversion twist constant $\beta$. The transformation lies in the Ehlers orbit; our contribution is the NUT-dependent geometry and the roles of $C$ and $\beta$ in its axis, horizon, singularity, and azimuthal-CTC structure. The inversion preserves the canonical Weyl radius, the signed WLP numerator $F$, and the sign of $g_{\phi\phi}$ on regular domains. At the selected pole $x=\sigma$, $C=-\sigma$, the local axis condition and conicity are controlled by $\chi_\sigma^{(\beta)}=\beta-2m(2\sigma a+3l)$. Exterior zeros of the chosen seed Ernst representative obey the exact criterion $-\beta\in\mathcal{R}_C$; for the sampled families numerical traces yield half-line ranges with closed-form corner endpoints. For $D=a^2+l^2-2alC\ne0$, $\Lambda_\beta\Sigma$ has a finite nonzero seed-ring limit. High-precision calculations find direction-independent finite limits of both quadratic Weyl invariants along the sampled rays, without establishing $C^2$-extendibility. At $\beta=0$, exterior simple Ernst zeros are found for the sampled $C=-1,0$ cases but not for $C=+1$, consistently with the computed ranges. Near one zero the Kretschmann scalar has a generic sixth-order blow-up; a numerical angular scan identifies exceptional directions of lower order. All sampled points in the regular ($g_{\phi\phi}>0$) exterior are Petrov type I. Candidate horizon locations remain those of Kerr-NUT, and the asymptotics are Levi-Civita type.

Here, we investigate the observational viability of fractional power law inflationary potentials, $V(\varphi) \propto \varphi^n$ ($n=$ 1/3, 2/5, 2/3), within the effective framework of Loop Quantum Cosmology (LQC) incorporating inverse volume corrections. By employing LQC modifications to the background dynamics and cosmological perturbation equations in the semi-classical regime, we analytically derive the scalar spectral index $n_{\rm s}$ and the tensor-to-scalar ratio $r$. These theoretical predictions are confronted with the latest high precision joint observational constraints, including ACT DR6, Planck 2018, DESI BAO, and BICEP/Keck datasets (P-ACT-LB-BK18). While steeper classical power law models are in severe tension with modern data, our results demonstrate that the inclusion of LQC inverse volume effects induces a prominent negative shift in $n_{\rm s}$. Consequently, for specific viable ranges of the quantum geometric parameters ($\sigma$ and $\delta$), the theoretical predictions are translated horizontally across the $r-n_{\rm s}$ plane. This mechanism successfully steers classically disfavored models back into the tightly constrained 68% and 95% CLs, significantly improving their consistency with precision cosmological data.

Nickelate materials exhibit rich electronic properties that can be engineered toward cuprate-like regimes through topotactic and mixed-anion chemistry. Using first-principles calculations, we investigate the newly synthesized double infinite-layer oxyfluoride La$_3$Ni$_2$O$_5$F and its evolution under chemical pressure and epitaxial strain. The calculated phonon spectrum confirms the dynamical stability of the reported double infinite-layer crystal structure. Further, we find a highly two-dimensional cuprate-like Fermi surface dominated by Ni-$d_{x^2-y^2}$ states, with a moderate rare-earth-derived self-doping yielding an effective $\sim d^{1.2}_{x^2-y^2}$ filling. These electronic features remain remarkably robust under both chemical pressure and epitaxial strain. Spin-polarized calculations further reveal an extended manifold of nearly degenerate magnetic configurations with different in-plane and out-of-plane spin arrangements. Compressive strain further enhances this magnetic frustration while leaving the underlying electronic structure largely unchanged. Our results thus identify La$_3$Ni$_2$O$_5$F as a promising cuprate analogue and establish lattice engineering as an effective strategy for fine tuning its electronic and magnetic properties.

Hair provides mammals with diverse benefits, including protection, thermoregulation, and enhanced sensory perception. Unlike tendons and teeth, which are biomineralized, hair is hypothesized to accomplish its structure-function relationship purely through keratin, a fibrous protein that provides structural integrity. Recent research showed that mechanical properties can vary substantially both within and across hair types: the whiskers of Asian elephant (Elephas maximus) exhibit a two-order-of-magnitude material stiffness reduction from base to tip, whereas elephant body hairs are nearly homogenous. Here, we demonstrate that three hierarchical structures vary significantly along the body hairs and whiskers of domestic cat (Felis catus): the layered outer keratin wall, 250-nm-diameter melanosome-like granules in the cortex, and calcium enrichment of these granules. As occasionally described for human hair, the oblong granules are arranged in longitudinal channels, potentially reinforcing the cortex; their prevalence correlates with local mechanical properties along the hair's length. Prolonged chemical treatment of body hairs removes calcium from the granules while breaking down the outer cuticle and internal cortex, hardening bases and splitting tips. Though previously assumed uniform, morphology, composition, and elemental enrichment can change along hairs, producing composite structures with functional gradients.

In this paper, we classify all six-dimensional real nilpotent Lie bialgebras of symplectic type. The Poisson structures on all of the related six-dimensional Poisson-Lie groups are obtained. Some new integrable Hamiltonian systems for which the Poisson-Lie group plays the role of a phase space and its dual Lie group plays the role of a symmetry group of the system are obtained.

High-resolution analysis and design of large-scale heterogeneous structures require accurate reduced-order models and efficient online computation. Existing multiscale methods must repeatedly construct local basis functions for different material distributions, whereas substructure-based problem-independent machine learning (PIML) methods can be limited by prescribed boundary displacement interpolation. We propose PIML-OFEM, an overlapping finite element method accelerated by problem-independent machine learning. Each substructure retains only its corner-node degrees of freedom. Oversampled numerical basis functions are constructed by solving local elasticity problems on extended domains and restricting the solutions to the target substructure, eliminating prescribed displacement interpolation on its boundary. Independently constructed local bases are blended through a partition-of-unity overlapping formulation to obtain a globally continuous displacement field. A U-Net learns the mapping from local Young's modulus distributions to numerical basis functions, replacing repeated online local solves and allowing the model to be reused across load cases and global boundary conditions. Numerical examples show close agreement with fine-scale finite element results in displacement and elemental strain energy. PIML-OFEM reduces online computational cost relative to direct finite element analysis and improves accuracy over PIML substructure models based on linear boundary interpolation. In topology optimization, the method supports stable high-resolution iterations with small filter radii and preserves fine-scale features, including local patterns resembling rank-2 microstructures. The framework provides an efficient physics-data approach for large-scale heterogeneous structural analysis and high-resolution topology optimization.