At the Lagrange relative equilibrium of the three-body problem, for all values of the masses, the elliptic eigenvalues associated with vertical eigenvectors give rise to spatial quasi-periodic orbits, which become periodic in a rotating frame. In 2009, by averaging out the fast frequencies, Christian Marchal showed that these orbits, which are fixed points in the restricted average problem, form a oneparameter family connecting L 4 to L 5 . Using perturbation methods, we show the persistence of this family in the average three-body problem for nonzero masses in the limit where one mass is dominant over the other two (known as the planetary problem). We also give an analytical approximation valid for mutual inclinations less than 60 $\bullet$ . Then, using purely numerical methods, we show that this family exists in the full three-body problem (neither restricted nor average) for a wide range of masses, beyond the planetary case. We also show that the stability of its orbits evolves along the family, with inclined systems remaining stable for masses exceeding the Gascheau's value (also known as Routh's critical value). Finally, we show the impact of this family's stability on the global dynamics of the co-orbital region as well as its high instability for mutual inclinations exceeding 60 $\bullet$ .

Vector beams with spatially structured polarization and intertwined spin-orbital angular momentum (SAM-OAM) provide powerful degrees of freedom for tailoring light-matter interactions. While such structured beams are well established in the visible and infrared regimes, extending them to the extreme-ultraviolet (EUV) and soft X-ray (SXR) domains at relativistic intensities remains a major challenge. Here, we investigate the generation of higher-order harmonic vector beams driven by relativistic laser-plasma interactions. Combining theoretical analysis with three-dimensional particle-in-cell simulations, we elucidate the underlying physical mechanisms governing the transfer and conversion of polarization and orbital angular momentum during harmonic generation. We demonstrate that both the polarization topology and OAM of the emitted harmonics can be deterministically controlled by the topological charges of the driving field. Owing to the intrinsic properties of vector beams, either few-cycle driving pulses or vector polarization gating applied to multi-cycle pulses enable the production of intense isolated attosecond pulses featuring spiral wavefronts and spatially tailored polarization states. These results establish a pathway toward high-intensity structured light sources in the EUV and SXR regimes and open new opportunities for ultrafast and strong-field light-matter interaction studies with engineered angular momentum.

This study investigates the application of quantum machine learning (QML) to approximate the nonlinear component of the collision operator within the quantum lattice Boltzmann method (QLBM). To achieve this, we train a variational quantum circuit (VQC) to construct an operator $U$. When applied to the post-linear-collision quantum state $\ket{Ψ_i}$, this operator yields a final state $\ket{Ψ_f} = U\ket{Ψ_i}$ that successfully replicates the nonlinear collision dynamics derived from the Bhatnagar-Gross-Krook (BGK) approximation. Within this framework, we present two distinct architectures: the R1 model and the R2 model. The R1 model is designed for quantum simulations that involve multiple time steps without intermediate measurements, focusing on accurately capturing nonlinear dynamics in continuous evolution. In contrast, the R2 model is tailored to achieve the high-precision reconstruction of the nonlinear operator for a single time step with an unitary operator.

Relativistic nuclear collisions have emerged as a new tool for probing many-body correlations of nucleons in the ground states of atomic nuclei. Here, we investigate the connection between three-nucleon correlations inside nuclei and three-particle correlations measured in collider final states. We work within a classical rigid-rotor picture of the colliding ions, whereby correlations in the lab frame arise solely from the averaging over orientations of an intrinsic-frame nucleon density with a triaxial quadrupole deformation, characterized by Bohr parameters $β_2$ and $γ$. With a Gaussian Ansatz for the density, we derive the leading-order form of the resulting two- and three-body nucleon distributions and perform a detailed analysis of their harmonic structure. With this, we provide an analytical understanding of empirical results linking shape parameters to final-state observables, notably, the fact that the covariance of the squared elliptic flow ($v_2^2$) with the mean transverse momentum ($[p_T]$), as well as the skewness of $[p_T]$ fluctuations, are to leading order proportional to $β_2^3 \cos(3γ)$. This elucidates the connection between three-nucleon densities, nuclear triaxiality, and three-particle correlations in high-energy nuclear collisions.

This study investigates parton shower evolution incorporating both Standard Model (SM) and beyond-the-Standard-Model (BSM) radiation, focusing on the phenomenology of a massive $Z'$ boson. While traditional approaches typically assume direct $Z'$ production in the hard process, the possibility of $Z'$ production within jets, enabled by subsequent emissions in the parton shower, offers a complementary opportunity to probe new physics through jet substructure and event topology. The newly developed Herwig 7 framework supporting BSM parton showers enables efficient simulation of $Z'$ production in the logarithmically enhanced regime. Using a simple BSM benchmark, the minimal $U(1)_{B{\rm -}L}$ extension of the SM, the interplay between the SM and BSM showers is evaluated to identify kinematic features that distinguish $Z'$-induced jets from conventional signatures. BSM-radiation signatures are contrasted with SM backgrounds such as QCD, top-quark, and Drell-Yan production, identifying potential discriminants for experimental searches. Experimental sensitivity at the LHC and prospective future colliders is estimated via statistical-significance projections. We find that $Z'$ bosons produced through parton shower radiation populate non-isolated regions inside jets, providing an avenue for new-physics searches overlooked in traditional analyses.

The breakdown of Lorentz invariance, a potential signature of quantum gravity, offers a window into physics beyond general relativity. We investigate how such a violation, embodied by the Einstein-Bumblebee black hole spacetime, influences the nonlocal quantum correlations. Specifically, we study the quantum steering and Bell nonlocality between modes trapped inside and outside the event horizon of an Einstein-Bumblebee black hole. Our analysis demonstrates that quantum steering for an initially correlated state is confined to a narrow region near the event horizon, with the Lorentz-violating parameter further constraining this domain. Notably, the degree of steering asymmetry is significantly modulated by both the distance from the horizon and the Lorentz-violating parameter, with the two spatially separated regions exhibiting opposite trends. Furthermore, the Bell nonlocality measurable by an external observer strengthens with increasing distance from the black hole. These findings confirm the persistence of nonclassical correlations in a Lorentz-violating gravitational background and and offer a novel perspective on the interplay between quantum information and fundamental spacetime symmetries.

This paper examines the optimal contracts in a two-dimensional screening model where one dimension(group identity) is verifiable by agents but not falsifiable. A principal offers contracts to agents who differ in cost types and group membership. Motivated by the United States Federal policy, Work Opportunity Tax Credit, the principal receives tax benefits for hiring agents from protected groups. Under the assumption that the protected agents tend to have higher cost types, the optimal contract induces full separation across both dimensions: agents reveal the cost type and the group identity through contract choice. Furthermore, the principal is willing to hire the trait agents with a higher cost threshold than the non-trait agents, and this threshold increases with the tax credit. Conversely, when the protected agents tend to have lower cost types, the optimal design without tax credits pools groups while separating by cost type. These results demonstrate that both affirmative action and non-discrimination can be optimal depending on the cost distribution ordering across groups.

Smoke curtains are typically used in public-access buildings in connexion with ventilation effects without considering a crossed design. This paper aims to understand the fire smoke behaviour in the context of the interaction between mechanical ventilation and smoke curtains. This interaction is analysed here in the configuration of a tunnel with using numerical simulations. Initially, without the presence of fire smoke, the length of the vortex induced downstream of the curtain is determined as a function of the longitudinal velocity and the size of the curtain. It can be observed that for a sufficiently high velocity (i.e. a sufficiently high Reynolds number), the size of this vortex depends only on the height of the smoke curtain. Then, in the presence of a moderate fire heat release rate, we determined the air velocity required to prevent smoke from rising beyond a curtain measuring 1/5 the height of the tunnel. A significant reduction in this longitudinal velocity was observed in comparison to the velocity required to achieve the same level of containment without the presence of a curtain. The vortex generated by the curtain nevertheless interacts with the smoke layer, locally increasing its thickness. Lastly, this configuration is tested in the case of a medium and high fire heat release rate in a road tunnel with transverse ventilation. The work carried out suggests that the installation of smoke curtains of an appropriate size, combined with control of ventilation effects, is likely to reduce the need for them.

Wake-induced lift is a key mechanism governing the initial destabilization of bubbles rising in a chain (Atasi et al., 2023). Moore's wake model predicts limited interfacial vorticity and a relatively slender, spatially confined wake for clean spherical bubbles, suggesting that wake-mediated interactions weaken as the inter-bubble spacing increases. However, we observed pronounced large-scale lateral dispersion and strong bubble frequency dependence in controlled experiments where bubble diameter and generation frequency were independently varied, even when the inter-bubble separation exceed the characteristic wake length. A reduced-order model incorporating pairwise wake-induced interactions captured the onset of bubble chain destabilization but systematically underpredicted the subsequent emergence of large-scale dispersion. We demonstrate that bubbles rising in a chain collectively generate a mean upward liquid flow that modifies the local shear field, enhancing the lateral migration through shear-induced lift. Incorporating this self-induced weak flow into the model quantitatively reproduced both the dispersion magnitude and its frequency dependence. These results suggest that the dispersion of bubbles rising in a chain involves a two-stage mechanism, with initial chain destabilization mediated by wake interactions, followed by flow modification arising from two-way coupling between bubbles and the liquid. This collective mechanism highlights the importance of self-induced mean flow effects in continuum descriptions of bubble flows.

In two dimensions, a phase-coherent superconducting state is established via a Berezinskii-Kosterlitz-Thouless (BKT) transition, whose critical temperature $T_{\rm BKT}$ is determined by the global superfluid stiffness in uniform superconducting systems. We report that at the interface between (111)-oriented KTaO$_3$ and ferromagnetic EuO, the two-dimensional superconducting state exhibits a BKT transition relying on the direction of in-plane bias current. The highest $T_{\rm BKT}$ occurs when current is applied along one of the [11$\bar{2}$] axes of KTaO$_3$, underscoring a spontaneous breaking of the threefold lattice rotational symmetry. Such directional dependence of $T_{\rm BKT}$ is consistently reflected in the nonreciprocal signals stemming from superconducting fluctuations above the transition. We attribute this phenomenon to an interfacial phase segregation; the phase with higher $T_{\rm BKT}$ self-organizes into quasi-one-dimensional textures that stretch along one of the [11$\bar{2}$] directions. Our results point toward the emergence of exotic phases of matter beyond the description of conventional BKT physics at a superconducting interface that is subjected to ferromagnetic proximity.

Recent observations have confirmed the existence of rings around minor bodies in the outer Solar System. These objects may possess satellites as well. Here we analytically investigate the interaction between such rings and satellites. We show that the perturbations from the moons may efficiently lead to off-equatorial rings around minor bodies like trans-neptunian objects or centaurs. In particular, we derive criteria for the orbital elements under which such misaligned rings may exist. These considerations will be easily testable with the upcoming deep sky surveys.

This paper presents a quantum algorithm for solving the fractional Poisson equation \((-Δ)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system solvers to achieve exponential quantum advantage. The rational approximation represents the inverse fractional Laplacian as a weighted sum of standard resolvents, transforming the original nonlocal problem into a collection of shifted integer-order partial differential equations. These equations are consolidated into a single large linear system through a modified right-hand side construction that simplifies the quantum implementation. To enable practical implementation, we develop explicit quantum circuits via the Schrödingerization technique, which converts the non-unitary dynamics of the linear system into a higher-dimensional Schrödinger-type equation, allowing the use of standard Hamiltonian simulation. The circuit construction leverages the decomposition of shift operators to realize the discrete Laplacian and employs controlled operations to implement the select oracle. Under finite difference discretization, we provide detailed algorithmic procedures utilizing block-encoding techniques for the coefficient matrices. A comprehensive complexity analysis demonstrates that the quantum algorithm achieves a dependence on the inverse mesh size \(h^{-1}\) that is independent of the spatial dimension \(d\), in stark contrast to classical methods which suffer from exponential growth in high dimensions. This establishes an exponential quantum advantage for high-dimensional fractional problems, effectively overcoming the curse of dimensionality that limits classical approaches.

Natural genomes sometimes encode two different proteins in staggered reading frames of the same DNA sequence. Despite the prevalence of these 'overlapping genes' across the tree of life, it remains unknown whether arbitrary protein pairs can overlap, to what extent such overlaps are feasible, or what design principles govern them. Here, we study compatibility, frustration, and connectivity in the fitness landscape of overlapping genes. We computationally design sequences de novo that satisfy the dual functional constraints of two distinct protein families. The joint fitness landscape, inferred via Potts models from multiple sequence alignments, reveals a fundamental trade-off between the two proteins and provides a simple criterion for when overlap is feasible. We find widespread compatibility between protein families, with one class of reading frames markedly more permissible than others. By exploring alternative genetic codes, we find that the natural genetic code is uniquely well-suited to support overlapping genes. Constructing mutational paths between sequences, we find that sequence-diverse overlapped genes can be connected via a network of near-neutral mutations. Overall, our results suggest that protein fitness landscapes are sufficiently flexible so as to accommodate the stringent, orthogonal requirements of overlapping genes.

In their 1993 paper 'Forecasting point and continuous processes: Prequential analysis' in Test, Vovk put forward a game-theoretic definition of the Poisson process. A key assumption therein is that the rate of the Poisson process is known or specified exactly. In contrast, I replace this assumption with the less stringent -- and arguably more realistic -- one that the available information about the process takes the form of bounds on the rate rather than a single, exact value. The resulting process has properties similar to the standard, 'precise' Poisson process, albeit with an imprecise flavour to them, thus justifying the moniker 'imprecise Poisson process'.

Semantic communications (SemCom) is a promising task-oriented paradigm in which semantic features exhibit non-uniform importance. Consequently, unequal error protection (UEP), which allocates resources based on semantic importance, plays a pivotal role in maximizing system utility. However, most existing schemes adopt passive importance evaluation, which neither proactively reshapes the importance distribution nor explores its impact on UEP performance. In this paper, we propose a novel importance-ordered semantic feature restructuring (ISFR) scheme that proactively enforces a descending importance hierarchy and jointly optimizes multi-dimensional resources to improve system utility. Specifically, modules with decreasing retention probabilities and increasing distortion levels are employed, which drive the model to concentrate key semantics into front-end features and thus strengthen importance differentiation. Moreover, a joint optimization problem that jointly optimizes channel matching, feature selection, modulation schemes, and power allocation is formulated to minimize the importance-weighted total semantic distortion. To solve this non-convex problem, a hierarchical decoupling strategy is proposed, which decomposes it into four tractable subproblems. This approach leverages the ordered prior to drastically prune the search space for feature selection and modulation, while integrating greedy-based channel matching and convex power allocation. Simulation results demonstrate that the proposed ISFR scheme outperforms traditional uniform importance-based schemes under harsh channel conditions and limited resources, validating the significant robustness improvement enabled by the concentration of key semantic information.

We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by the geodesic convexity of entropy and is formulated as the response of probability distributions to optimal transport. We introduce effective Ricci curvatures $K_{\mathrm{eff}}^{(\infty)}$ and $K_{\mathrm{eff}}^{(N)}$ associated with Kullback--Leibler-type and Rényi-type entropies, corresponding respectively to the curvature-dimension conditions CD$(K,\infty)$ and CD$(K,N)$. By localizing these curvatures to finite scales using local and reference measures, we construct curvature indicators applicable to observational data. Under a local quadratic approximation, the effective curvature reduces to the Hessian of the log-density, showing that conventional Hessian-based structure classifications arise as a limiting case of the present framework. We further show that effective curvature depends on observational scale and formulate this dependence as a scale flow, distinct from Ricci flow because it describes a change of resolution rather than a time evolution of geometry. Treating curvature as a random field then extends the statistical description of density fields: curvature statistics are given by higher-order weighted integrals of the power spectrum and by spatial derivatives of the correlation function, emphasizing geometric rather than amplitude information. This framework provides a unified connection between optimal transport geometry and cosmological structure analysis, and offers a new perspective on multiscale structure and nonlinear statistics.

In Grochow and Qiao (SIAM J. Comput., 2021), the complexity class Tensor Isomorphism (TI) was introduced and isomorphism problems for groups, algebras, and polynomials were shown to be TI-complete. In this paper, we study average-case algorithms for several TI-complete problems over finite fields, including algebra isomorphism, matrix code conjugacy, and $4$-tensor isomorphism. Our main results are as follows. Over the finite field of order $q$, we devise (1) average-case polynomial-time algorithms for algebra isomorphism and matrix code conjugacy that succeed in a $1/Θ(q)$ fraction of inputs and (2) an average-case polynomial-time algorithm for the $4$-tensor isomorphism that succeeds in a $1/q^{Θ(1)}$ fraction of inputs. Prior to our work, algorithms for algebra isomorphism with rigorous average-case analyses ran in exponential time, albeit succeeding on a larger fraction of inputs (Li--Qiao, FOCS'17; Brooksbank--Li--Qiao--Wilson, ESA'20; Grochow--Qiao--Tang, STACS'21). These results reveal a finer landscape of the average-case complexities of TI-complete problems, providing guidance for cryptographic systems based on isomorphism problems. Our main technical contribution is to introduce the spectral properties of random matrices into algorithms for TI-complete problems. This leads to not only new algorithms but also new questions in random matrix theory over finite fields. To settle these questions, we need to extend both the generating function approach as in Neumann and Praeger (J. London Math. Soc., 1998) and the characteristic sum method of Gorodetsky and Rodgers (Trans. Amer. Math. Soc., 2021).

Surface-guided radiation therapy (SGRT) is now widely used for radiation-dose-free, marker-free patient positioning in modern radiotherapy. We commissioned and clinically implemented a novel SGRT system, LUNA 3D (LAP, Lueneburg, Germany), featuring browser-based operation, GPU-accelerated surface reconstruction, frame rates above 12 Hz, a large field of view, and virtual laser projection. Commissioning included tests of temperature drift, reproducibility, translational and rotational shift accuracy, gantry-related camera occlusion, agreement with cone-beam CT (CBCT), and end-to-end dosimetric performance. Results were evaluated using both an SGRT-acquired reference surface and a CT-derived external surface. Temperature drift remained below 0.4 mm on all axes. With the SGRT reference, maximum deviations were at most 0.3 mm translationally and 0.2 degrees rotationally; with the CT-derived reference, translational deviations increased to 0.8 mm, consistent with systematic bias from the reference surface. Agreement between LUNA 3D and CBCT was within 1.0 mm, and end-to-end testing showed CBCT residuals of 0.9-1.3 mm with 1.2% dosimetric deviation. All results satisfied ESTRO-ACROP guideline criteria. Clinical evaluation of 192 breast and 259 pelvic treatment datasets showed significant improvements after implementation: the breast 3D translational vector decreased by 28.7% from 7.00 +/- 4.35 mm to 4.99 +/- 2.75 mm, and the pelvic 3D rotational vector decreased by 24.0% from 2.31 +/- 0.96 degrees to 1.76 +/- 0.67 degrees (both p < 0.001). These results establish LUNA 3D as a reliable SGRT system that improves routine patient positioning accuracy.

This paper investigates the performance of a pinching-antenna (PA) system with a signal waveguide and multiple pinching antennas to serve users distributed across multiple rooms. The performance of the system is evaluated through a comparative analysis under both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes. Specifically, this paper derives closed-form expressions for the outage probability (OP) and ergodic rate (ER) in each scheme. Furthermore, asymptotic analyses are conducted to characterize the system behavior in the high signal-to-noise ratio (SNR) regime. Extensive Monte Carlo simulations are utilized to validate the accuracy of the analytical derivations. The comparative results can be summarized as follows: 1) in the downlink fixed-rate scenario, whether OMA or NOMA achieves better outage performance depends on system parameters, such as the number of users and power allocation coefficients; 2) in the uplink fixed-rate scenario, the outage performance of NOMA is inferior to that of OMA in the high-SNR regime, and the decay rate of the OP for NOMA users depends on the rate thresholds; and 3) for both uplink and downlink adaptive-rate scenarios, the rate performance comparison of the two schemes depends on system parameters in the low-SNR regime, whereas OMA generally outperforms NOMA in the high-SNR regime.

We investigate the Hausdorff dimension of level sets defined by digit growth rates in $θ$-expansions, a generalization of regular continued fractions. For any $α\geq 0$, we prove that the set \[ E_θ(α) = \left\{ x \in [0, θ] \setminus \mathbb{Q} : \lim_{n \to {+}\infty} \frac{L_{n,θ}(x) \log n \log \log n}{S_{n,θ}(x) - L_{n,θ}(x)} = α\right\} \] has full Hausdorff dimension. This extends previous work of Zhang and {Lü} (2016) on regular continued fractions to the broader framework of $θ$-expansions. The proof involves constructing explicit subsets with controlled digit growth and establishing dimension preservation through Hölder-continuous mappings.

Imaging is a crucial sensing function that finds wide applications in environmental reconstruction, autonomous driving, etc. However, the signal processing methods for existing radio imaging techniques, such as millimeter wave (mmWave) imaging, require high-resolution range estimation enabled by Gigahertz-level or even Terahertz-level bandwidth, and cannot be applied in 6G integrated sensing and communication (ISAC) network with Megahertz-level bandwidth. This paper proposes two novel high-resolution radio imaging schemes that can work on the 6G signals with limited bandwidth - bandwidth-independent synthetic aperture radar (BI-SAR), where the movable base station (BS) revolves along the static targets by 360 degrees; as well as bandwidth-independent inverse synthetic aperture radar (BI-ISAR), where the BS is static and the targets revolve along an axis by 360 degrees. Different from conventional SAR and ISAR counterparts that rely on range estimation, our proposed imaging schemes solely utilize Doppler information to perform imaging without any range information. The main technical challenge of our schemes lies in the anisotropic scattering functions over different directions, which hinder the coherent synthesis of the backscattered signals from all directions. We design an iterative adaptive approach-based Doppler association (IAA-DA) algorithm to tackle the above issue. Moreover, we also derive the imaging resolution to characterize the reconstruction quality. Real-world experiments are provided to show the feasibility and the effectiveness of our proposed 6G imaging schemes.

By using unramified cohomology groups, we construct a full sequence of cohomological invariants for hermitian forms of any type (orthogonal, symplectic or unitary) that can be used to detect hyperbolicity. The base central simple algebras can have arbitrary degree and the base field can have arbitrary characteristic. In the orthogonal case, we work with hermitian pairs, and we apply our construction to show that over fields of separable dimension 3, hermitian pairs over quaternion algebras with trivial classical invariants are hyperbolic. This last result extends a result of Berhuy to arbitrary characteristic.

We report the detection of a gamma-ray spectral line at approximately 1.5 GeV in three active galactic nuclei (AGN) using 17 years of Fermi-LAT observations. The sample includes both blazars (with relativistic jets directed toward Earth) and a radio galaxy (with a misaligned jet, free from significant beaming effects). The line is detected with local significances of $\sim$4.1$σ$, $\sim$3.9$σ$, and $\sim$2.8$σ$ in the individual sources. A joint likelihood analysis yields a combined test statistic TS $\simeq$ 57.77, corresponding to a significance well above 5$σ$. The line flux remains stable over the full observation period, in contrast to the variable continuum emission from the AGN. The appearance of an identical spectral feature in astrophysically distinct environments is difficult to reconcile with standard jet-based emission mechanisms. While a conventional astrophysical explanation remains elusive, the signal's characteristics are consistent with predictions for dark matter annihilation. This finding motivates further investigation into the nature of this spectral feature and its possible connection to particle dark matter.

We investigate inviscid numerical instabilities that arise in simulations of axisymmetric flow over a hypersonic sphere in an inert, calorically perfect gas at low specific heat ratio ($γ\approx 1.1$--$1.2$). We show that when the density ratio across the bow shock is high and the computational mesh is relatively coarse, numerically induced traveling-wave instabilities of the carbuncle type can develop in the shock layer near stagnation for inert gases. These instabilities, not previously documented in the literature, are noteworthy because bow shock oscillations are also observed experimentally in polyatomic gases exhibiting post-shock thermochemical relaxation. When such gases are modeled as inert with an effectively low $γ$, our results emphasize the need for caution to avoid conflating genuine physical instabilities with numerical artifacts in simulations.

Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model Hamiltonian systems by embedding their properties either in the architecture or in the loss function. However, they typically ignore that: i) a Hamiltonian carries units of energy and/or ii) that every integrable Hamiltonian admits a canonical transformation to action-angle coordinates in which the dynamics reduce to a simple rotation on an invariant torus. We propose BuSyNet, a deep learning architecture that combines these two constraints via a dimensionally-consistent, symplectic transformation. A symplectic layer maps input trajectories to lower-dimensional latent action-angle variables, which are then combined with system parameters to discover a symbolic Hamiltonian expression in units of energy. Evaluated on the harmonic oscillator and the Kepler two-body problem (in 2D and 3D), BuSyNet recovers concise, closed-form Hamiltonians that outperform state-of-the-art neural architectures in long-term prediction accuracy and stability, while maintaining interpretability.

We investigate nonequilibrium dynamics of a triad of fermionic superfluids connected via Josephson junctions, following sudden switch-on of two-body loss in one of the three superfluids. By formulating the dissipative BCS theory for the Lindblad equation, we find that the superfluid order parameter exhibits a phase rotation, thereby giving rise to three types of dc Josephson currents corresponding to different junctions. We demonstrate that, when the tunneling amplitude $V_{31}$ between superfluids without two-body loss is weak, two-step nonequilibrium dynamical phase transition (NDPT) characterized by the vanishing dc Josephson currents occurs: dissipation first induces the NDPT by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when $V_{31}$ is strong, dissipation induces the NDPT in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.

Pinching-antenna (PA) has recently attracted considerable research attention in wireless systems, realized by attaching small dielectric particles along a waveguide. Building upon which, the segmented waveguide-enabled pinching-antenna system (SWAN) has been proposed to mitigate the inter-antenna radiation problem in uplink transmissions of conventional PA systems. In this work, SWAN-assisted integrated sensing and communication (ISAC) is investigated, where a base station (BS) equipped with SWAN provides downlink communications for multiple communication users (CUs) and performs sensing for multiple targets. The dual-functional signals transmitted by the BS are radiated by the SWAN, and the echo signals reflected by the targets are captured by the SWAN and relayed to the BS for estimating the locations of the targets. We formulate a Cramér-Rao lower bound (CRLB) minimization problem to evaluate the performance of the ISAC system, where the CRLB of the location estimation is minimized under communication rate constraints. To jointly optimize the beamforming and the PA positions of the SWAN, we develop a Riemannian manifold optimization (RMO) method, where each variable is constrained on its corresponding Riemannian manifold, and a Riemannian product manifold (RPM) is constructed as the solution space. A penalty method combined with Riemannian Broyden-Fletcher-Goldfarb-Shanno (RBFGS) algorithm is applied to obtain a feasible solution. Simulation results show that the proposed SWAN-assisted ISAC system yields superior CRLB performance for target localization compared with existing schemes including the multi-waveguide-enabled pinching-antenna-assisted ISAC systems.

Project Daedalus (1973--1978), the most detailed interstellar probe design study ever conducted, specified a 9 mm beryllium erosion shield to protect the spacecraft payload during its 5.9 light-year cruise to Barnard's Star at 12% of the speed of light. This design, however, predated both the isolation of two-dimensional materials and the development of graph neural network (GNN) property predictors. Here, we systematically screen 20 candidate materials--spanning conventional aerospace metals, transition metal dichalcogenides, and ultra-high-temperature ceramics--using density functional theory (DFT) data from the JARVIS database (76,000 materials) with independent validation by the Atomistic Line Graph Neural Network (ALIGNN). We evaluate candidates across four criteria: specific mechanical stiffness (KV/rho), sputtering resistance, thermal neutron absorption cross-section, and thermodynamic stability. Our screening identifies hexagonal boron nitride (h-BN) and boron carbide (B4C) as dual-function materials offering simultaneous mechanical protection and neutron radiation shielding, and we propose a graphene/h-BN/polymer layered heterostructure shield design that achieves an estimated 47% mass reduction relative to the original beryllium specification. These findings will become immediately actionable upon the successful development of fusion pulse propulsion, which we note remains an outstanding engineering challenge.

We investigate kinematic and optical signatures of Lorentz-violation in the strong-field region of a rotating bumblebee black hole generated by a scalar-gradient bumblebee field. Through the analysis of spin precession of test gyroscopes and timelike geodesic motion in the spacetime, we find that Lorentz-violating effect suppresses the Lense-Thirring precession near the horizon, while enhancing geodetic precession in the static, spherically symmetric limit. For bound circular orbits in the equatorial plane, the Lorentz-violation leads to an increase in the periastron precession frequency. Furthermore, images of a geometrically thin accretion disk reveal that the Lorentz-violation has a negligible impact on the critical curve, but significantly shrinks the inner shadow and enhances the lensed ring. These results indicate that inner shadow measurements, combined with selected precession observables, may provide complementary probes of Lorentz-violating effects in strong-field gravity.

Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past iterations, which leads to faster and more robust convergence. However, for smooth convex problems, PBM only achieves an O(1/k) convergence rate, which is inferior to the optimal O(1/k^2) rate. To bridge this gap, we propose an accelerated proximal bundle method (APBM) that integrates Nesterov's momentum into PBM. We prove that under standard assumptions, APBM achieves the optimal O(1/k^2) convergence rate. Numerical experiments demonstrate the effectiveness of the proposed APBM.