Matter and dark matter in galaxies represent two main components linked by the gravitational interaction. Collisions of galaxies may create an offset between the centers of mass of these components. Ignoring internal dynamics of particles in the dark matter halo and Keplerian rotations of matter in the galaxy, we focus on possible relative oscillations of the matter in the dark matter halo. This two-fluid model is somewhat similar to the ``giant dipole resonances'' in nuclei. We estimate possible amplitude and frequency of such oscillations assuming that the offset of the centers of mass is small as compared with the size of the galaxy. Such oscillations, if exist, should manifest themselves in anomalies of velocities of stars in the galaxy, such as the density waves and runaway stars which have orbit periods in resonance with oscillations.

A permutation $π$ is said to avoid a chain $(σ:τ)$ of patterns if $π$ avoids $σ$ and $π^2$ avoids $τ.$ In this paper, we define a notion of pattern avoidance for compositions of positive integers and use that idea to enumerate permutations of length $n$ that avoid the chain $(312,321:σ)$ for any pattern $σ\in \bigcup_{m\geq 1} S_m$. We also enumerate those permutations that avoid the chain $(312,4321:σ)$ for any $σ\in S_3.$

Large-scale multi-objective optimization problems (LSMOPs) remain challenging due to the high-dimensional decision spaces, complex variable interactions, and limited function evaluation budgets, which make it difficult to balance the convergence, diversity, and stability. Existing two-archive evolutionary algorithms can alleviate the conflict between convergence and diversity, but they often underuse archive reliability and problem-structure information, leading to inefficient search, incomplete front coverage, and late-stage archive drift. To address these issues, this paper proposes TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm. Archive trustworthiness is defined by integrating evolutionary progress with convergence-archive maturity, and is used to coordinate variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. TRUST-TAEA is evaluated on the LSMOP benchmark suite with 500--5000 decision variables and 2, 3-objectives. Experimental results show that TRUST-TAEA achieves superior and highly competitive performance in terms of convergence, diversity, and stability. A three-objective day-ahead scheduling case of a grid-connected microgrid further demonstrates its practical applicability, where TRUST-TAEA obtains the best IGD$^+$ value and generates a feasible dispatch strategy balancing cost, emissions, and grid-power fluctuation.

Quiver skew braces or skew bracoids are equivalent to braided groupoids, that is, groupoids with a constraint of abelianity. They are the quiver-theoretic version of skew braces, an increasingly studied structure lying in the intersection of group and ring theory. In this paper, we define ideals and quotients for quiver skew braces, with respect to two notions of morphisms. Following the track of a previous work of ours (2025), we define a classical semidirect product à la Brown, and a categorical semidirect product à la Bourn and Janelidze, for the category of quiver skew braces. It is known that connected groupoids can be expressed as the datum of a group of loops and a set of vertices. We demonstrate how no such decomposition holds for quiver skew braces, which makes their theory richer than the theory of groupoids.

The homogeneity scale, $R_{\rm H}$, offers a fundamental test of the Cosmological Principle, yet it has not yet been measured with 21cm intensity mapping surveys. A key limitation for such a measurement is the telescope beam, which artificially smooths the observed signal. We quantify this effect using the two-point correlation function and the correlation dimension, $\mathcal{D}_2(r)$, to model how beam convolution suppresses intrinsic clustering. For any given redshift $z$, we identify a maximum beam width, $σ_{\rm max}(z)$, beyond which the homogeneity scale cannot be recovered. This limit defines an inaccessible region in the $σ\times z$ parameter space, where $R_{\rm H}$ is erased by beam smoothing. Applying this framework to several current and upcoming radio telescopes, we assess their ability to probe $R_{\rm H}$. Our results provide the first quantitative forecast of the instrumental requirements for measuring the cosmic homogeneity scale with 21cm IM, and establish a theoretical basis for future observational applications.

Losses are ubiquitous in physics and are usually regarded as harmful in quantum information processing. Here, we propose a loss-induced scheme to achieve nonreciprocity and nonreciprocal entanglement in a superconducting platform, where two remote superconducting transmon qubits are connected via two lossy auxiliary cavities. The nonreciprocity in our scheme originates from interference between multiple lossy coupling paths. The coherent phases associated with the qubit-resonator couplings reverse sign under propagation reversal, while the loss-induced phases remain direction independent. Their combined effect leads to different interference conditions in the opposite directions, resulting in unequal effective couplings. We show that this loss-induced scheme can generate nonreciprocal quantum entanglement, indicating that loss can be utilized as a resource. Moreover, the tunability of nonreciprocity and nonreciprocal entanglement in our scheme can be manipulated by the relative phase induced by loss, allowing to tailor both reciprocal and nonreciprocal behaviors. Our results establish a direct link between engineered loss and nonreciprocal entanglement in quantum information processing and offer potential applications in scalable quantum networks.

We prove, for every horizon \(N\ge 3\), the existence of the strengthened low-rank performance-estimation certificate proposed by Grimmer, Shu, and Wang for the Drori--Teboulle constant-step gradient-descent bound. For each \(N\ge 3\), let \(ρ_N\in(0,1)\) be determined by \(ρ_N^{2N}(2Nρ_N+2N+1)=1\). We show that the GSW certificate equations admit positive vectors \(a,b,c,d\) satisfying all residual equations. The proof proceeds through a reduced residual system in the variables \(d\), a simplex existence argument for a positive reduced zero, a terminal residual completion identity, and a tail-square convolution argument proving the cumulative margins that force \(b>0\) and then \(a>0\). Consequently, the GSW low-rank PEP certificate exists for every \(N\ge 3\) and yields the Drori--Teboulle upper bound. We also include the one-dimensional quadratic and Huber lower-bound examples for nonnegative steps, while the quadratic example excludes negative constant steps from being optimal. Together these prove the Drori--Teboulle minimax constant-stepsize value over all real constant steps for every \(N\ge 3\).

This article analyzes the feasibility of having a second synchrotron in Latin America, to be located, in principle, in a city within the Greater Caribbean region but open to all the continent. It is shown that an initiative of this sort is compatible with the economies of the region and would require a marginal increase of the current regional investment in science, which is broadly below that of other regions of the world, with peaks of low financing precisely in the Greater Caribbean. The project is not only feasible, but, beyond its purely scientific interest. it would have an impact for the development of cities in the region. The article is mainly focused to analyze this impact from the social, economic, and political point of view. It is shown that the return of the investment would have its break-even point long before the end of the expected lifetime of the infrastructure, and that through a system of smaller accelerators, that would be part of the same project, the benefit would not concentrate on the country hosting the facility. These smaller facilities could contribute to the national development as possible nuclei of cities of knowledge, project which belongs to the priority of some countries/cities of the region.

It is well known that a strictly massless spin-$3/2$ particle can interact consistently only within supergravity. Recently, positivity arguments have shown that an effective field theory of a massive Majorana spin-$3/2$ particle admits a smooth $m \to 0$ limit only if a graviton is present and the four-fermion contact interactions are tuned to the values dictated by $\mathcal{N}=1$ supergravity. In this work, we investigate how this limit is approached at finite mass. Assuming that the graviton $t$-channel pole can be discarded, we derive non-forward, tree-level dispersive bounds on massive spin-3/2 contact operators and determine the region of effective couplings consistent with unitarity and analyticity. For sufficiently small $m$, we find that the allowed parameter space forms a bounded, Planck-suppressed neighbourhood of the supergravity point, defined by the supergravity values of the four-fermion couplings. The supergravity point lies on the boundary of this region. In the regime $m \ll M_{\rm Pl}$, the volume of the allowed region scales parametrically as \[ \mathrm{Vol} \sim \frac{m^{6}}{M_{\rm Pl}^{6}} \, , \] and shrinks to zero as $m \to 0$, smoothly reproducing the massless-limit results. The allowed region becomes unbounded when mass approaches the Planck scale. We further analyze the effect of including additional light scalar and pseudo-scalar degrees of freedom, motivated by the Polonyi model, and find that their couplings are also bounded in a way similar to the contact couplings and that it doesn't enlarge the allowed contact coupling space.

We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural networks (QNNs) by computing their effective dimension, a capacity measure grounded in a proven generalization-error bound, and compare them with classical artificial neural networks (ANNs) of equivalent trainable-parameter count. Supervised binary classification tasks are used to benchmark performance across photonic and superconducting QNNs, both of which exhibit superior converged (lower) cross-entropy loss and (higher) prediction accuracy relative to matched-parameter ANNs. For a nonlinearly separable task, our photonic QNN with a single pair of trainable parameters successfully converged (loss 0.04 and accuracy 100%), whereas the equivalent ANN failed to learn the decision boundary, saturating at random-guessing performance. We simulate photonic quantum circuits, training them on the XOR problem and a two-class Iris subset using gradient-free optimization, and assess their robustness to sampling errors under realistic noise processes including photon loss and phase-shifter imperfections. Circuits with comparatively high effective dimension were deployed remotely on a six-qubit photonic quantum processor, achieving classification accuracies of up to 100% in both online and offline learning settings. Notably, even the simplest QNN deployed, with just two trainable parameters, successfully solved tasks that classically require ANNs with at least quadruple the number of parameters, suggesting an emergent algorithmic advantage. Overall, these results demonstrate a clear proof-of-principle that gate-based QNNs can be realized and trained effectively on current photonic hardware, providing proof of algorithmic advantage on a gate-based photonic QNN.

The persistent challenge of creating stable de Sitter vacua within string theory undermines the observational validity of the $Λ$ cold dark matter (CDM) model. This difficulty suggests that the concordance model of cosmology, characterized by a constant dark energy $Λ$, may reside in the swampland of inconsistent quantum gravity theories rather than the string landscape of consistent ones. Recent observational data, particularly from the Dark Energy Spectroscopic Instrument (DESI), have significantly challenged $Λ$CDM cosmology. Specifically, the combination of DESI baryon acoustic oscillation measurements with cosmological surveys seem to indicate a preference for a dynamic, time-evolving dark energy rather than a constant, with roughly 10\% reduction in density over the last several billion years. This review summarizes significant advancements made over the past two years in linking DESI findings to string-inspired scenarios.

The KMOC (Kosower-Maybee-O'Connell) formalism establishes a bridge between quantum scattering amplitudes and classical observables in gravitational systems. In this work, we show how the weak-field limits of the four classical black hole metrics - Schwarzschild, Kerr, Reissner-Nordstrom, and Kerr-Newman - can be reproduced within this formalism. Starting from three-point amplitudes with exponential spin structure for both gravitational and electromagnetic interactions, we compute four-point scattering amplitudes and extract the momentum impulse via the KMOC formula. Matching these results with geodesic motion in a general metric allows us to reconstruct the metric components to leading order in G, a, and Q^2. For the Kerr-Newman case, we include interference terms between gravitational and electromagnetic interactions, which produce a Q^2 a/r^3 contribution to g_{tϕ} that does not appear in the Kerr or Reissner-Nordstrom weak-field limits separately. Our results are consistent with those of arXiv:1907.00431 [hep-th], where the Kerr-Newman metric is derived from minimal coupling amplitudes using the KMOC formalism arXiv:1908.04342 [hep-th]. All results are verified through their consistency with the well-known full metrics, though we emphasize that the KMOC formalism as applied here reproduces only the weak-field expansions, not the complete non-linear solutions.

We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use an exponent measure, an infinite-mass law that naturally arises in the analysis of multivariate extremes. Central to this framework are activation variables, which abstract the single-big-jump principle, along with additional randomization that enriches the class of eSCM laws. This formulation encompasses all possible laws of directed graphical models under the recently introduced notion of extremal conditional independence. We also identify an inherent asymmetry in eSCMs under natural assumptions, enabling the identifiability of causal directions, a central challenge in causal inference. Finally, we propose a method that utilizes this causal asymmetry and demonstrate its effectiveness in both simulated and real datasets.

Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The construction occurs in a finite periodic cube T3. Entropy production maximizing solutions with turbulent initial data are selected. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation

We propose a framework to infer the coupling strength and the natural frequency distribution in a coupled Stuart-Landau oscillator system with a large population. The inference method uses observation of linear response of a macroscopic quantity and of an oscillator. We first solve the direct problem on the response with transforming the system into the phase-amplitude equations. Solving the inverse problem, we show that the coupling strength is inferred from observation of an oscillator and the natural frequency distribution from macroscopic responses. The proposed method requires only one-dimensional observation in the two-dimensional Stuart-Landau system. Validity of the inference theory is examined by numerical simulations.

Measure-valued Pólya sequences (MVPS) are processes whose dynamics are governed by generalized Pólya urn schemes with infinitely many colors. Assuming a general reinforcement rule, exchangeable MVPSs can be viewed as extensions of Blackwell and MacQueen's Pólya sequence, which characterizes an exchangeable sequence whose directing random measure has a Dirichlet process prior distribution. Here, we show that the prior distribution of any exchangeable MVPS is a Dirichlet process mixture with respect to a latent parameter that is associated with the atoms of an emergent conditioning $σ$-algebra. As the mixing components have disjoint supports, the directing random measure can be interpreted as a random histogram with bins randomly located on these same atoms. Furthermore, we extend the basic exchangeable MVPS to include a null component in the reinforcement, which corresponds to the presence of a fixed component in the directing random measure. Finally, we examine the effects of relaxing exchangeability to conditional identity in distribution (c.i.d.) and find out that the two are equivalent for balanced MVPSs. The paper features a complementary study of some properties of probability kernels that underlies the analysis of exchangeable and c.i.d. MVPSs.

Graphene provides a canonical setting for Floquet band engineering, where circularly polarized light can dynamically open topological gaps at Dirac points and generate nonequilibrium Hall responses. Here we show that uniaxial strain and off-resonant circularly polarized light with tunable incidence angle enable a controllable route to Floquet higher-order topology in graphene. Using a strained honeycomb tight-binding model with Peierls coupling and a high-frequency expansion for the effective Floquet Hamiltonian, we find that strain drives the Dirac cones toward the Dirac-merging (semi-Dirac) critical regime, where the light-induced mass becomes strongly anisotropic. For oblique incidence, the projected drive is effectively elliptically polarized and, in combination with strain, stabilizes a phase with gapped edges but robust in-gap corner modes in finite geometries, realizing a Floquet second-order topological insulator. We characterize the phase diagram via the Chern number and a crystalline-symmetry-quantized polarization invariant. Finally, first-principles-informed tight-binding calculations corroborate the predicted topological evolution in strained graphene nanostructures. Our results identify driven strained graphene as a realistic and tunable platform for realizing and diagnosing Floquet higher-order topological phases.

In this work, we examine the problem of stationary superposition in the Bohmian amplitude phase formulation, where amplitude and phase obey coupled nonlinear equations and direct linear superposition is not generally preserved. Considering two near degenerate stationary branches, we derive a hierarchical reduction in which the mean amplitude satisfies an Ermakov Pinney equation, while the difference amplitude evolves through a forced Mathieu Hill type modulation induced by energy and stationary current differences. It is shown that energy coherence alone does not uniquely determine phase coherence, since independent stationary currents continue to enter both the modulation and phase difference equations. For weak amplitude modulation, a Wronskian based stationary branch obtained from an Ermakov Pinney solution admits a controlled amplitude phase construction, leading to an algebraic phase representation and a Jacobi Anger spectral expansion. As a result, a linear spectral structure emerges through Bessel weighted amplitude and phase modulation. Such a representation is naturally suited for modelling aperture geometries, as illustrated by rectangular and parabolic slit reductions exhibiting Fresnel type phase chirp and modulation driven sidebands. The present construction therefore provides an analytical route by which linear spectral superposition reemerges from nonlinear Bohmian amplitude phase dynamics. Keywords Bohmian mechanics; stationary superposition; amplitude and phase modulation; nonlinear superposition; Mathieu Hill equation; Fourier Bessel expansion.

The equilibrium figure of dwarf planet Haumea is studied to determine if the observed shape is compatible with a differentiated hydrostatic body. Three groups of interior models of Haumea are assumed, all with a rocky core and a volatile-rich outer shell that may contain some porosity. A third layer located between the core and the outer shell has a density suggesting partial differentiation or the presence of a large fraction of organic matter. Using the code BALEINES, which solves for the equilibrium figures of the boundaries between layers, we show that the hydrostatic models closest to the shape derived by stellar occultation approach a state of critical rotation, which translates into a pinched shape with large deviations from an ellipsoid (up to 110 km). The previous stellar occultation and light curves cannot distinguish between the ellipsoid and the pinched shape, but we predict this figure could be observable on the next stellar occultation of Haumea on May 4, 2026, if some chords are obtained in the northern or southern limbs of the shadow.

We study the propagation and emission of gravitational waves in the metric-affine formulation of the bumblebee model, where spontaneous Lorentz symmetry breaking arises from a vector field acquiring a nonvanishing vacuum expectation value. Working in the geometric-optics limit of the linearized theory, we derive the modified dispersion relation governing the graviton modes and show that it depends on the orientation of the wave vector relative to the background vector. The polarization sector is examined for timelike and spacelike configurations of the Lorentz-violating vacuum. In both cases only two independent tensor modes propagate, although their propagation properties and tensor structure depend on the orientation of the background field. We then construct the retarded Green function associated with the modified wave operator and determine the radiation-zone produced by localized sources. In the timelike configuration the Lorentz-violating effects appear through a modified propagation speed and an overall amplitude renormalization, leading to a shifted retarded time while preserving the quadrupole structure of the waveform. In contrast, the spacelike sector introduces anisotropic corrections to the quadrupole amplitude together with an additional contribution proportional to the third time derivative of the quadrupole moment. As an astrophysical application, the gravitational radiation emitted by a circular binary black hole system is evaluated, allowing observational constraints on the Lorentz-violating combination $ξb^{2}$ to be estimated using multimessenger bounds from GW170817/GRB~170817A and waveform consistency requirements from gravitational wave observations.

Most production ERC-4337 Paymasters rely on Process-Oriented Abstraction (POA): a centralized off-chain server signs each sponsorship request, acting as a potential censorship bottleneck. We propose Asset-Oriented Abstraction (AOA), encapsulating payment capability in a persistent, user-owned on-chain asset -- the Gas Card -- rather than an off-chain signing process. Following the Design Science Research (DSR) methodology, we implement SuperPaymaster on Optimism Mainnet, anchoring sponsorship validity in on-chain Soulbound Token state and deterministic policy rules, removing the off-chain signer as a validity gate. We evaluate gas costs via single-UserOp ERC-20 transfers on Optimism Mainnet (n = 50 per system). In pure L2 execution gas (txGasUsed; actualGasUsed = txGasUsed + PVG), SuperPaymaster (167,830) is lower than both evaluated POA baselines: Alchemy Gas Manager (205,951) and Pimlico ERC-20 paymaster (328,937). It still pays a ~32,000-gas on-chain verification overhead versus Alchemy, but reduces gas by 49% versus Pimlico by replacing on-chain token liquidation with an internal balance update. In total billed gas, SuperPaymaster (286,818) exceeds Alchemy (257,299) due to higher bundler PVG overhead, not paymaster architecture. Code structural analysis and on-chain Mainnet evidence confirm that sponsorship validity requires no off-chain signing server: validatePaymasterUserOp reads only on-chain state. These findings suggest that AOA can mitigate the usability-decentralization-efficiency trade-offs in gas payment.

The original description of the k-d tree recognized that rebalancing techniques, used for building an AVL or red-black tree, are not applicable to a k-d tree, because these techniques involve cyclic exchange of tree nodes that violates the invariant of the k-d tree. For this reason, a static, balanced k-d tree is often built from all of the k-dimensional data en masse. However, it is possible to build a dynamic k-d tree that self-balances when necessary after insertion or deletion of each k-dimensional datum. This article describes insertion, deletion, and rebalancing algorithms for a dynamic, self-balancing k-d tree, and measures their performance.

We present a new extended resolution clause learning (ERCL) algorithm, implemented as part of a conflict-driven clause-learning (CDCL) SAT solver, wherein new variables are dynamically introduced as definitions for {\it Dual Implication Points} (DIPs) in the implication graph constructed by the solver at runtime. DIPs are generalizations of unique implication points and can be informally viewed as a pair of dominator nodes, from the decision variable at the highest decision level to the conflict node, in an implication graph. We perform extensive experimental evaluation to establish the efficacy of our ERCL method, implemented as part of the MapleLCM SAT solver and dubbed xMapleLCM, against several leading solvers including the baseline MapleLCM, as well as CDCL solvers such as Kissat 3.1.1, CryptoMiniSat 5.11, and SBVA+CaDiCaL, the winner of SAT Competition 2023. We show that xMapleLCM outperforms these solvers on Tseitin and XORified formulas. We further compare xMapleLCM with GlucoseER, a system that implements extended resolution in a different way, and provide a detailed comparative analysis of their performance.

We present a controlled $x$-resolved numerical diagnosis of target-mass corrections (TMC) in the operator-product-expansion sum-rule approach to inelastic quarkonium--nucleon interactions, using global-fit gluon PDFs ABMP16, MSHT20, CT18 and NNPDF4.0. Applying the known hypergeometric TMC weight to native LHAPDF grids, we decompose the Mellin-moment suppression into finite $x$-windows and identify which parts of the gluon distribution drive the near-threshold cross-section reduction. PDF uncertainties are propagated to the integrated ratios $R_n$ and to the energy-dependent ratio $R_{\rm TMC}(\sqrt{s}\,)$; the factorisation-scale dependence and the sensitivity to the binding-energy parameter $ε_0$ are quantified explicitly. The cross section is computed via direct partonic convolution, bypassing the finite-moment threshold ansatz that produces unphysical exponents ($a\approx 8$-$11$ without and $28$-$32$ with TMC weights) with modern small-$x$-singular gluons.

Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the usefulness of graph states. We consider a noise model where the initial qubits undergo depolarizing noise before the application of the CZ operations that generate edges between qubits situated at the nodes of the resulting graph state. For this model we develop a method for calculating the coherent information -- a lower bound on the rate at which entanglement can be distilled, across a bipartition of the graph state. We also identify some patterns on how adding more nodes or edges affects the bipartite distillable entanglement. As an application, we find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.

Spiking neural networks (SNNs) are a promising paradigm for energy-efficient event-driven computation, but large-scale SNN execution remains challenging because sparse spike communication and synchronization can dominate runtime. Existing solutions across CPU, GPU, ASIC, and FPGA platforms offer different trade-offs between programmability, efficiency, and scalability. To address this gap, we present NeuroRing, a modular and scalable SNN accelerator based on a stream-dataflow architecture and a bidirectional ring topology, implemented in High-Level Synthesis (HLS) on FPGAs. NeuroRing supports modular single- and multi-FPGA deployment and is compatible with existing SNN workflows through integration with the NEST simulator. We evaluate NeuroRing on the cortical microcircuit benchmark and a Sudoku constraint-satisfaction workload. Results show that NeuroRing preserves the key activity statistics of the NEST reference model, achieves faster-than-real-time execution of the full-scale cortical microcircuit with a real-time factor (RTF) of 0.83, exhibits meaningful strong and weak scaling, and provides competitive energy efficiency on two programmable FPGAs. These results position NeuroRing as a flexible and scalable platform for both neuroscience simulation and broader event-driven applications.

We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph $D_{r,s,\ell}$. Using switching equivalence, we reduce the spectrum to the real parts of the two cycle gains and obtain an explicit expression of the characteristic polynomial in terms of matching polynomials of natural subgraphs. For the bipartite case, we determine the extremal gain assignments by coefficient comparison. For the non-bipartite cases, we analyze the Coulson integral kernels. Finally, the maximum-energy conditions are determined in all cases, while the minimum-energy conditions are determined except when $r$, $s$, and $\ell$ are all odd. For this remaining case, we alternatively prove sign restrictions for any improvement over $(0,0)$, and prove a Hessian criterion at the origin, which provides a sufficient condition for $(0,0)$ to fail to be an energy minimizer.

A fundamental result in 4-manifold topology asserts that any two exotic smooth structures on a simply-connected, closed 4-manifold differ by a cork twist: the operation of removing a compact, contractible, codimension-zero submanifold and regluing it by a diffeomorphism of its boundary. In this paper, we introduce the notion of a surface cork, an analogous object in the setting of smoothly embedded, closed surfaces $F$ in closed 4-manifolds $X$. This is a compact, contractible, codimension-zero submanifold intersecting $F$ in a controllable manner, whose removal and regluing via a diffeomorphism of its boundary changes the diffeomorphism type of $(X, F)$ as a pair while leaving its homeomorphism type unchanged. The way in which the surface $F$ interacts with the codimension-zero submanifold leads us to define three distinct notions of surface corks: enclosing surface corks, exterior surface corks, and transverse surface corks. We establish the existence of exterior surface corks for certain previously known examples of exotic pairs. Furthermore, we give the first explicit construction of a transverse surface cork for certain exotic families arising from Fintushel--Stern rim surgery. Notably, this transverse surface cork turns out to be diffeomorphic to a 4-ball.

Small carbon hydride cations, such as the methylidyne ion (CH$^+$), play an important role in the chemistry of the interstellar medium (ISM). They participate in gas-phase reaction networks leading to the formation of hydrocarbon species that act as precursors to more complex organic molecules. CH$^+$ is a highly reactive ion that is rapidly destroyed by H, H$_2$, and free electrons, making its excitation challenging to model. Its level populations depend not only on radiative and inelastic processes but also on chemical formation and destruction rates, a mechanism known as chemical pumping. We investigate this effect using a new set of ab initio state-resolved ro-vibrational (reactive and inelastic) collision data to model the observed CH$^+$ emission. Multiple rotational and ro-vibrational transitions of CH$^+$ detected toward the planetary nebula NGC 7027 are analyzed. The chemical structure of CH$^+$ is modeled with the CLOUDY code using updated reaction rates, providing the temperature and density structure across the nebula. A non-local thermodynamic equilibrium (NLTE) analysis is performed using CLOUDY and the single-zone RADEX code with a comprehensive set of spectroscopic and collisional data. In addition, chemical formation and destruction processes are implemented in RADEX and explored via Markov Chain Monte Carlo sampling. The CLOUDY model reproduces the observed CH$^+$ line fluxes within a factor of 1.3 on average. It indicates that rotational and ro-vibrational lines arise from physically distinct regions, primarily differing in temperature. RADEX models show that chemical pumping significantly enhances populations above ($\upsilon = 0, J = 1$), strongly increasing ro-vibrational emission, especially in the $\upsilon =2 \to 1$ band. Single-zone models remain limited, highlighting the need for full 1D modeling including all excitation processes.

Using $(10\,087 \pm 44) \times 10^6$ $J/ψ$ events collected with the BESIII detector, we perform the first amplitude analysis of the process $J/ψ\toγηπ^0$. The decay is dominated by the intermediate processes $J/ψ\toπ^0 b_1(1235)^0 \toγηπ^0$, $J/ψ\toπ^{0}ρ(1450)^0 \toγηπ^0$ and $J/ψ\toηh_1(1170) \toγηπ^0$. Contributions from $J/ψ\toγa_0(980)^0\toγηπ^0$, $J/ψ\toγa_2(1320)^0\toγηπ^0$ and $J/ψ\toγa_2(1700)^0\toγηπ^0$ are observed with a statistical significance exceeding $5σ$, constituting the first observation of radiative transitions of $J/ψ$ to isospin-triplet scalar mesons. The total branching fraction of $J/ψ\toγηπ^0$ is measured to be $(25.7\pm0.3\pm1.5)\times 10^{-6}$, where the first uncertainty is statistical and the second systematic. This result is consistent with the previous measurement, with the precision improved by more than a factor of two.