Against the backdrop of the burgeoning global low-altitude economy, countries have successively introduced a series of policies to accelerate the application and commercialization of electric vertical take-off and landing (eVTOL) aircraft. Nevertheless, purely electric eVTOLs confront constraints including limited battery energy density, high operational power requirements, and challenges associated with rapid energy replenishment, which collectively restrict their flight endurance and application scenarios. Furthermore, while eVTOL deployment is scaling up, supporting charging infrastructure and regulations remain underdeveloped. This situation presents emerging power distribution networks with new challenges in maintaining adequate electricity supply and ensuring operational continuity. To tackle these issues, following an investigation into battery energy replenishment strategies, a closed-loop supply chain-based model for eVTOL battery charging and swapping is proposed. Time-space network methods are utilized to characterize the scheduling of batteries and logistics throughout the system. Subsequently, aiming to maximize the operational revenue of the model, optimized management of battery swapping, transportation, and charging processes is implemented, facilitating coordinated operation among eVTOLs, swapping stations, and charging stations. Finally, the model is solved by Gurobi, verifying its feasibility. Simulation results further indicate that the model alleviates range anxiety for eVTOLs, offering strong support for their commercialization. Moreover, it enables coordinated scheduling between eVTOLs and the distribution network, thereby facilitating the network's gradual improvement and upgrading.

Semi-blind joint channel estimation and data detection (JCD) is a promising approach to mitigate pilot contamination in cell-free massive multiple-input multiple-output (CF-MaMIMO) networks. The effectiveness of such methods fundamentally depends on identifiability, i.e., the ability to unambiguously recover the unknown channel coefficients and transmitted data signals from the received uplink observations. In this work, we investigate the identifiability of semi-blind JCD from a large-scale system design perspective. We consider a CF-MaMIMO network in which access points (APs) and user equipments (UEs) are spatially distributed according to Poisson point processes (PPPs). The resulting network topology is modeled as bipartite random geometric graph (BRGG) that captures local connectivity induced by wireless propagation. To enable a tractable analysis, the spatially dependent graph model is approximated by a surrogate independent-edge random graph with matched degree distributions. Building on this model, we develop a recursive probabilistic analysis that characterizes the conditions under which semi-blind recovery succeeds with high probability. The proposed analysis reveals an identifiability region as a function of key system parameters, including AP and UE densities and the connectivity radius beyond which channel coefficients are assumed negligible. Monte Carlo simulations validate the predicted identifiability region and assess the accuracy of the proposed graph approximation. The proposed framework provides system level insights into how network density and connectivity affect identifiability in large-scale CF-MaMIMO systems and offers guidelines for selecting deployment parameters and pilot sequence lengths that enable reliable semi-blind recovery.

Bayesian Optimization (BO) is an effective framework for globally optimizing functions whose evaluations are expensive. It is particularly effective for optimizing functions defined over continuous domains and explicitly handles stochastic noise in evaluations. As a result, it is widely applied in areas such as hyperparameter tuning, robotics policy search, and scientific experiment design, where sample efficiency is essential. Its two-step procedure consists of model fitting followed by optimization of the acquisition function, which is often treated as a generic black-box problem despite its structured nature. In this work, we introduce KSOS-BO, a kernel-based derivative-free framework for BO acquisition optimization. KSOS-BO formulates the optimization of the acquisition function as a semidefinite program with kernel-induced representations, enabling a structured global search. Across a diverse set of benchmark functions with varying landscape properties, KSOS-BO consistently outperforms derivative-free baselines using Sobol Search, Differential Evolution, or CMA-ES to optimize the acquisition function, achieving an average regret improvement of 81.16% on 10/15 benchmarks. In particular, KSOS-BO demonstrates strong performance in highly multimodal and unimodal but ill-conditioned functions, indicating its applicability to diverse landscape structures. Despite a higher per-iteration computational cost, it converges faster in wall-clock time with an average improvement of 93.55% on 10/15 benchmarks, as it reaches high-quality solutions with fewer evaluations. Limitations include reduced effectiveness on functions with steep drops or plate-shaped regions.

The oxidation kinetics of hematite α-Fe$_2$O$_3$(0001) surfaces are vital for its applications in catalysis, environmental remediation, and industrial processes. Despite prior studies, the roles of temperature, oxygen partial pressure, and oxygen chemical potential in controlling nucleation and growth kinetics are not fully understood. Using real-time Low Energy Electron Microscopy/Diffraction (LEEM/LEED), we systematically investigate the oxidation of a reduced Fe$_3$O$_4$(111)-like surface layer to hematite under controlled conditions. We show that complete recovery of the hematite surface termination is closely linked to the nucleation and lateral growth of a two-dimensional honeycomb (H) phase. While higher temperatures accelerate nucleation, they slow lateral growth at constant oxygen pressure, indicating that oxygen supply limits the oxidation rate. Below an oxygen partial pressure threshold (~2$\times$10$^{-6}$ mbar), growth dramatically slows, underscoring the critical role of oxygen availability. Below a certain oxygen pressure threshold, the growth time rapidly increases. Our study elucidates the interplay between thermodynamics and kinetics in hematite surface oxidation, informing strategies to optimize surface properties for catalytic and industrial processes.

We prove that it is consistent that every two disjoint boldface $\mathbfΣ^1_1$ subsets of $ω_1^{ω_1}$ can be separated by a boldface $\mathbfΔ^1_1$ set. The forcing starts from $L$ and preserves CH and therefore also $ω_1^{<ω_1}=ω_1$.

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through a nonlinear coordinate transformation. Here, we derive an exact analytical expression for the network's time-dependent maximum Lyapunov exponent (MLE). We demonstrate, both numerically and analytically, that the network exhibits positive MLEs during the transients that are useful for computation. Our framework enables algebraic manipulation of transient lifetimes through network connectivity and initial conditions, providing a rigorous theoretical foundation for understanding and controlling computation with transients.

The purpose of this paper is to develop a new effective approach to higher-order mixing in the semisimple setting. We prove effective exponential mixing of all orders for partially hyperbolic algebraic actions, under a strong spectral-gap assumption. The decay rates are explicit in the Lyapunov and spectral-gap data, and the required Sobolev orders are explicit. Already at order two, our estimates require only partial Sobolev/Hölder regularity along weak stable and unstable subgroup directions, with no transverse derivatives. For representations admitting better-than-tempered decay, the resulting order-two estimate attains the optimal matrix-coefficient exponent. The proof introduces a new fractional-cohomological method in the semisimple setting. The central analytic input is a solvability theory for multiple fractional cohomological equations of Type~$II$ (sum-of-product type). These equations are solvable in a cohomology-free range governed by the spectral behavior near the edge \(0\), and the solutions satisfy estimates in partial Sobolev norms. This mechanism converts fractional solvability into order-two decay of correlations under partial regularity, and then into effective higher-order mixing, yielding a quantitative form of Rokhlin's multiple-mixing problem.

Predictive simulations and experimental design involving extreme aero-chemo-thermo-mechanical regimes require high-fidelity material representation across diverse physical states. However, data for metals, polymers, and propellants, explosives, and pyrotechnics (PEP) remain fragmented, obstructing traceability for formulators, experimentalists, and simulation engineers. This work introduces Lumina, a modular Python-based informatics framework that centralizes multiscale material data from atomistic simulation datasets to macro-scale experimental records, within a unified repository. Lumina employs a hierarchical XML-based schema and a dynamic runtime parsing mechanism to enable schema-independent parameter extraction. Beyond storage, the platform provides computational modules to visualize model fits, allowing experimentalists to optimize design of experiments (DoE) and formulators to validate chemical behaviors against benchmarks. This structured architecture serves as a high-fidelity pipeline for training machine learning models and enhancing the accuracy of predictive simulations. To streamline multi-disciplinary workflows, Lumina integrates a conversational AI assistant for intelligent material retrieval and natural language querying. By consolidating multiscale data into an extensible ecosystem, Lumina provides a scalable foundation for data-driven discovery and predictive modeling in advanced defense and aerospace engineering.

We introduce two new model comparison games that characterize separability by first-order formulas with generalized quantifiers. One is built on the Ehrenfeucht-Fraïssé game and the other is a formula-size game.

We review non-autonomous Hamiltonian systems, polynomial in two dependent variables, with the property that all of their solutions are meromorphic functions in the complex plane. These are related to known Hamiltonian systems with the Painlevé property, for which the solutions are single-valued outside a set of fixed singularities. Our systems are equivalent to them in the absence of fixed singularities, and give modified Painlevé equations otherwise. Using the geometric approach by computing the Okamoto's spaces of initial conditions for certain Hamiltonian systems with general coefficient functions, we obtain differential constraints on these functions for the systems to have only meromorphic solutions. Guided by the Newton polygon of the Hamiltonian function, we obtain all such systems with polynomial Hamiltonian of degree three, four, five, and seven, up to affine equivalence in the dependent variables, while there are none for degree six or degree higher than seven. We thus obtain a list of 12 standard polynomial Hamiltonians that can serve as reference for the Painlevé equivalence problem. This list contains also some new Hamiltonians not previously written down, such as quartic Hamiltonians for Painlevé I and II, quartic Hamiltonians for the modified Painlevé III and V equations, a quintic Hamiltonian for Painlevé IV and quintic and septic Hamiltonians for a modified Painlevé VI equation.

An edge of a graph of order $n$ is pancyclic if it lies in a cycle of every length $3,\ldots,n$. A graph of order $n$ is vertex-pancyclic if every vertex lies in a cycle of every length $3,\ldots,n$. Recently, Li and Zhan proved that every $2$-connected $[4,2]$-graph of order at least seven contains a pancyclic edge. Zhan asked whether there exists a positive integer $k$ such that every $k$-connected vertex-pancyclic graph contains a pancyclic edge. We answer this question by showing that for every positive integer $k$, there is a $k$-connected vertex-pancyclic graph containing no pancyclic edge.

This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz equation. By utilizing a weak Laplacian operator defined on a space of discontinuous functions, the proposed framework facilitates the seamless treatment of complex boundary conditions and internal interfaces. We emphasize the geometric flexibility of the LS-WG scheme on general polygonal and polyhedral partitions. Furthermore, we prove the uniqueness of the numerical solution and derive optimal-order error estimates with respect to a specifically designed discrete energy norm. Extensive numerical experiments validate the theoretical convergence rates and demonstrate the algorithm's robustness and efficiency over traditional Galerkin approaches.

Let $(M,g)$ be a Riemannian manifold. Choose a pair $(α,H)$ where $α$ is a calibration and $H$ is a calibrated distribution. Using this data we define a 1-parameter family of forms $α_\varepsilon$ and study its adiabatic limit as $\varepsilon\rightarrow 0$. We show that (i) the limit is a calibration in a generalized sense, (ii) under the usual closedness assumptions, the adiabatic calibrated submanifolds are anisotropic minimal in the classical sense defined in the calculus of variations/PDE theory. We apply this construction to $G_2$-manifolds. In this case the adiabatic calibrated condition is equivalent to a Fueter-type equation. We provide explicit examples and prove local analytic existence theorems for the adiabatic calibrated submanifolds. Applying mirror symmetry as described by the real Fourier-Mukai transform, the general picture is as follows: adiabatic limits correspond to large radius limits, $α$-calibrated (associative) submanifolds correspond to deformed Donaldson-Thomas connections, adiabatic calibrated submanifolds correspond to $G_2$-instantons.

For a complex reductive group $G$, we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular centralizer group scheme for the Langlands dual group $G^\vee$. This can be interpreted as a geometric Langlands equivalence for $\mathbb{P}^1$ with mildest wild ramification at $0$ and $\infty$.

We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary wave equation and the corresponding lab experiment proposed earlier in Eberle and Moll (2021). The investigation of the harmonic problem leads to a better reconstruction compared to the stationary one. Since we deal with real measurement data, we have to take into account, that those measurements always include measurement errors, so that we have to handle noisy data. Thus, we consider the linearized monotonicity method for noisy data and introduce a modified version of this method. Based on this, we reconstruct the inclusions numerically.

This work advocates the benefit of high resolution spectroscopic monitoring in the study of transients (local group transients given the available collecting power). As an exemplary analysis, we focus on the optical transient NGC300OT2008-1. Searching the ESO archives, we found a low resolution (LR, FORS) and a high resolution (HR, UVES) spectrum that were separated by only one day with no changes between them. The independent analysis of the FORS and UVES spectra show that in the LR spectrum we can securely identify only a small sample of lines and miss the correct characterization of the ejecta energetics which remain at the level of speculation. In the HR data, we identify a larger sample of emission lines and analyze their profiles suggestive of a complex geometry and ejecta dynamics whose inferences are simply impossible in LR spectra. Line profile studies are not possible with LR spectra, and may lead to potentially misleading measures. The limited information available from LR data compromises the interpretation and prevents formulating realistic physical scenarios, favoring parameter fitting to oversimplified, biased, standard models. In this occasion only one epoch was available, but monitoring is fundamental to characterize the transient evolution. The new scenario derived from the analysis of the HR spectrum cannot be confirmed or dismissed lacking a HR spectroscopic monitoring. LR and HR spectra serve different but complementary purposes. With LR one does bolometric-like studies (SED, strengthening or weakening of the major transitions), while with HR one does dynamics and precise physical characterization. HR spectroscopic monitoring on different types of transient has already shown how it serves to disentangle the various components, constrain their physical parameters, the involved energy source, and derive the ejecta dynamics.

We study asymptotic probabilities of attaining the maximum in heterogeneous Gaussian samples. In the two-group setting, the first sample has variance $1$ and size $n_1$, while the second has variance $σ^2>1$ and size $n_2$. We investigate the probability that the maximum of the standard-variance group exceeds that of the high-variance group. Using the classical extreme-value normalization for Gaussian maxima together with a second-order comparison of the centering terms, we show that this probability admits a non-degenerate limit if and only if $n_1\sim C n_2^{σ^2}(\log n_2)^{-(σ^2-1)/2}$ as $n_1,n_2\to\infty$ for some $C\in(0,\infty)$. In that regime, the limit admits an integral representation. Outside the critical regime, the comparison necessarily degenerates to $0$ or $1$. We then extend the analysis to finitely many independent Gaussian groups and obtain a generalized integral representation for the limiting winning probabilities. The results provide a complete asymptotic classification for this maximum-comparison problem

This letter proposes a network-wide coordinated optimization model to mitigate voltage unbalance (VU) by unleashing the remaining capacity of community inverter-based resources (IBRs). Existing single-sequence strategies ignore coupled capacity constraints and cause idle headroom. Meanwhile, they fail to harness the collective governance capabilities of community IBRs. To solve this discrepancy and exploit the unused potential, we developed a sequence-domain network model in dual commonly shared synchronous reference frames. Strict phase current and apparent power limits are formulated and convexified via polyhedral approximations. A quadratic objective function flexibly balances sequence capacity allocation. Simulation and experimental results validate the effectiveness of the proposed strategy.

Let $Γ$ be a minimal connected negative-definite plumbing tree with all vertices of genus zero, and let $Y_Γ$ be the oriented link of the corresponding normal complex surface singularity, equipped with its canonical contact structure $ξ_{\rm can}$. We give an explicit Legendrian surgery description of $ξ_{\rm can}$, showing that it is the unique consistent diagram-realizable contact structure on $Y_Γ$, up to isomorphism. We then derive a closed-form formula for Gompf's $θ$-invariant of $ξ_{\rm can}$ in the Seifert fibered case, expressed purely in terms of the Hirzebruch--Jung continued fraction expansions of the normalized Seifert invariants, and prove a recursive leaf-to-root formula for arbitrary plumbing trees. The Seifert formula recovers previously known formulas for lens spaces, dihedral manifolds, and small Seifert fibered spaces with complementary legs, and agrees with the Némethi--Nicolaescu expression via the classical Hirzebruch--Zagier identity. As a final application we show that $ξ_{\rm can}$ strictly minimizes $θ$ among all diagram-realizable contact structures on $Y_Γ$, and we use this to rule out symplectic rational homology ball fillings for a large class of Stein fillable contact rational homology $3$-spheres.

We study a coincidence between two enumerations governed by the same product formula, reminiscent of the Robbins numbers: the unweighted enumeration of twenty-vertex configurations on quadrangular domains with fixed west boundary, and the weighted enumeration of Gelfand-Tsetlin patterns avoiding three equal entries in a row. This coincidence naturally raises the question of whether there is a combinatorial explanation relating these two enumerations. In this paper, we provide such an explanation by constructing a probabilistic bijection between twenty-vertex configurations on quadrangular domains and Gelfand-Tsetlin patterns avoiding three equal entries in a row. Under this probabilistic bijection, the west boundary of a twenty-vertex configuration corresponds to the bottom row of Gelfand-Tsetlin patterns; in particular, the fixed boundary case corresponds to Gelfand-Tsetlin patterns with bottom row $(1, 2, \ldots, n)$. Combining this correspondence with an enumeration formula of Fischer and Schreier-Aigner for Gelfand-Tsetlin pattern avoiding three equal entries in a row with bounded entries, we obtain an enumeration formula for twenty-vertex configurations with a free west boundary.

Optimal power spectrum estimation on the largest angular scales of the cosmic microwave background relies on the Quadratic Maximum Likelihood (QML) estimator. Existing public implementations, however, each address only a subset of the problem and none combine power spectrum estimation with a self-consistent pixel-space likelihood within a single framework. We present CosmoForge, a public Python framework that unifies QML power spectrum estimation and pixel-based Gaussian likelihood evaluation for spin-0 and spin-2 fields on the sphere, with general (non-diagonal) noise covariances. The framework is split into three installable packages: CosmoCore (infrastructure), QUBE (Fisher and QML estimation), and PICSLike (pixel-space likelihood). A common interface exposes two interchangeable computation bases $-$ a harmonic basis built on the Sherman-Morrison-Woodbury identity and a direct pixel-space basis $-$ selecting whichever is cheaper for the configuration at hand. Exact algorithmic optimisations reduce the Fisher cost to $\mathcal{O}(\ell_{\rm max}^4)$ for arbitrary noise covariances, with Numba JIT compilation of the hot kernels and MPI parallelisation of the likelihood scan. CosmoForge reproduces the Planck low-$\ell$ Fortran reference implementation across both the QML and pixel-space likelihood pipelines, consistently with double-precision arithmetic. Native multipole binning and three output normalisations (deconvolved, decorrelated, window-convolved) are exposed through a single code path, and the same covariance infrastructure powers both QML estimation and likelihood evaluation. CosmoForge offers a general-purpose, modular, and validated tool for the optimal analysis of large-scale data on the sphere. It is publicly available, pip-installable, and extensible to non-CMB observables.

Strong interaction is typically assumed to dominate the pair production of heavy coloured resonances at the LHC. However, mixed QCD-QED contributions from gluon-photon ($gγ$) initial states become critical for highly charged states. This contribution scales with the square of their electric charges and maximises for particles in the fundamental colour representation. We study this effect for leptoquarks, which are colour-triplet bosons. We demonstrate that tree-level mixed QCD-QED contributions enhance their pair-production rates by up to $\sim 33\%$ for a charge-$5/3$ state, rivalling the size of next-to-leading-order QCD corrections. The asymmetric colour flow of $gγ$ fusion affects the radiation pattern, altering jet multiplicities and angular distributions. By recasting the latest ATLAS $μμjj$ search data, we find that these often-overlooked QED effects systematically strengthen mass exclusion limits, establishing a necessary precision standard for bounding highly charged coloured states.

Intelligent roadside infrastructure is a key enabler for cooperative intelligent transport systems (C-ITS), supporting vehicles equipped with automated driving systems (ADS), e.g., through enhanced environment perception. With a growing number and an expanding functional scope of roadside units, scalable and efficient operation becomes a challenge. This paper presents a cloud-native architecture for the operation of distributed roadside infrastructure based on a Kubernetes cluster spanning roadside units and a cloud server. Building on this architecture, a demand-driven orchestration approach is implemented to dynamically deploy resource-intensive services only when required. As a representative use case, a V2X-based collective perception application is deployed on-demand when a connected vehicle is nearby. The approach is validated in a real-world experiment in our test field in Aachen, demonstrating that the collective perception application starts in time for the vehicle to benefit from it. Without any demand, the application remains inactive, reducing energy consumption, channel congestion, and hardware wear. Beyond the primary evaluation, V2X recordings from the test field are analyzed to estimate the energy-saving potential of demand-driven operation. In summary, the results demonstrate the practical feasibility of cloud-native, demand-driven operation of roadside infrastructure and indicate its potential to improve scalability and (energy) efficiency in future C-ITS deployments.

We propose a Bernoulli phase-fitted (BPF) finite difference method for the Helmholtz equation on the interval $(0, L)$ with impedance boundary conditions. The scheme is derived from a complexified Scharfetter--Gummel discretization of the one-way factorization of the Helmholtz operator. It yields both a phase-fitted interior discretization and exact discrete impedance boundary closures. For the homogeneous problem, the method is exact for plane waves, so the scheme introduces neither numerical dispersion in the interior nor artificial reflection at the boundaries. For the inhomogeneous problem, we prove well-posedness, derive wavenumber-explicit stability estimates, and establish second-order consistency and convergence valid for all $kh\notinπ\mathbb Z$, where $k$ is the wavenumber and $h$ the grid size. In particular, under the fixed-resolution condition $kh\le s_0$ for some $0<s_0<π$ together with $kL\geπ$, the constants in the error bounds remain uniform with respect to the wavenumber, yielding a pollution-free convergence theory in the principal Nyquist regime. Numerical experiments confirm the theoretical analysis and show favorable performance compared with standard and dispersion-corrected finite difference methods.

We give a general method to build categories of combinatorial manifolds, i.e. categories of combinatorial objects satisfying some local property at every "point", as coreflective subcategories of categories of relational presheaves. To do this, we crucially rely on unique factorization systems, and we can interpet our technique as a way of building a model category whose cofibrant objects are exactly the combinatorial manifolds. We then illustrate the usefulness of this point of view by two applications. First we build a category of euclidean precubical sets, i.e. precubical sets that locally look like a grid (of some fixed dimension), and show that it is coreflective in the category of relational precubical sets. This is the combinatorial analog of eulidean locally ordered spaces and the blowup construction from directed topology. Secondly, we show how to give an abstract proof of Kleene's theorem from automata theory by defining "manifold automata" that behave well with respect to concatenation.

We propose a deep beamforming framework for enhancing target speaker(s) in multi-speaker environments. A deep neural network (DNN) is trained to estimate beamforming weights directly from noisy multichannel inputs while satisfying linear spatial constraints through an adaptive multi-term loss inspired by the augmented Lagrangian framework. The loss combines signal reconstruction with penalties that enforce a distortionless response toward the target and suppress the interference subspace. The model is further guided by the target relative transfer function (RTF) and the estimated interference subspace. The proposed model can direct a beam toward the target speaker while directing nulls toward the interfering sources, achieving superior overall enhancement performance compared with the classical LCMV beamformer constructed by the same estimated spatial signatures. Furthermore, compared with the LCMV beamformer, the proposed model produces more controlled sidelobes and improved background-noise attenuation.

The 2025 Bondi Beach mass-shooting was perpetrated by individuals inspired by ISIS (Islamic State) propaganda that increasingly featured anti-Semitic hate content following the October 2023 start of the Israel-Palestine war. Similar stories hold for other types of hate attacks, e.g. against Muslims on May 18, 2026. There is an urgent need to get ahead of future threats by understanding how and when a newly created piece of hate content will spread system-wide online. We present a two-species coalescence-fragmentation model with Susceptible-Infected-Recovered dynamics that incorporates the following published empirical features: (1) New pieces of hate content tend to be generated and promoted by a subset of in-built communities on less regulated platforms. (2) These `hate' communities create links (hyperlinks) with each other and with non-hate communities across all platforms to form dynamically evolving clusters (i.e. coalescence) across which new hate content can then spread. (3) These clusters can get broken up by moderator shutdowns (i.e. fragmentation). We present numerical solutions and derive two levels of approximate mean-field theory: Effective Medium Theory (EMT) and Beyond Effective Medium Theory (BEMT). Both numerical and analytic solutions reveal that system-wide spreading is governed by re-entrant threshold phases: as the fraction of hate communities varies, the system can transition from spreading to no-spreading and back to spreading. The derived analytic formulae give explicit insight into how these phase boundaries might be manipulated to prevent system-wide spreading. More broadly, the re-entrant phase behavior warns that policies which steadily reduce the number of hate communities can initially succeed but then backfire if pushed further, suggesting that blanket requirements for platforms to simply do `more' are over-simplistic.

We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This result extends Cuntz's classical decomposition for the Cuntz algebras $\mathcal{O}_n$ and reveals an implicit symmetric structure within Cuntz--Pimsner algebras. By exploiting this structure, we characterize the simplicity of these algebras and classify ideals, tracial weights, and KMS weights for generalized quasi-free flows. Our findings recover and refine seminal results in the literature, including those by Kitamura, Schweizer, and Laca--Neshveyev. By combining our main results with the Hao--Ng isomorphism, we study quasi-free actions on $\mathcal{O}_n$. We confirm a recent question on isometrically shift-absorption posed by Izumi on compact groups. We also identify a new dichotomy for the group $G:=\mathbb{R} \times {\rm SU}(2)$: in contrast to flows, the crossed product of a quasi-free action of $G$ on $\mathcal{O}_n$ is either non-simple or purely infinite simple.

This paper is concerned with ground states of the defocusing nonlinear Schrödinger equation with a point interaction, \[ \mathrm{i} \partial_t ψ= -Δ_αψ+ ψ|ψ|^{p - 2} \quad \text{in} \quad \mathbb{R} \times \mathbb{R}^N, \] where $- Δ_α$ denotes the Laplacian of point interaction centered at the origin with inverse s-wave scattering length $- 2 (N - 1) πα$ and we suppose that either (i) $N = 2$, $α\in \mathbb{R}$ and $p > 2$ or (ii) $N = 3$, $α< 0$ and $2 < p < 3$. At sufficiently small masses, (i) we prove that this equation admits ground states, (ii) we obtain some qualitative properties of ground states and (iii) we obtain some results relating ground states with critical points of the associated action functional.

The inherent spin-orbit interaction of electrons inevitably couples spin to the orbital angular momentum (OAM), posing a fundamental challenge to spin-free orbital transport. Here, we propose a novel strategy to achieve spin-decoupled OAM states in crystalline solids. Using angle-resolved photoemission spectroscopy (ARPES), we resolve well-isolated s-orbital bands in a chiral Te crystal, clearly separated from the p-orbital manifold. Combined circular dichroism ARPES and first-principles calculations reveal that these bands host OAM arising exclusively from interatomic hopping, with no intra-atomic contribution. Spin-resolved ARPES further confirms the absence of SAM, providing decisive evidence of spin-free OAM states. These findings establish the existence of OAM without spin polarization in crystalline solids and highlight the essential role of inter-atomic OAM. This work provides a general framework for designing spinless OAM states, opening an opportunity toward pure orbital currents for orbitronics.