We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain defined by a level-set function. The full-order discretisations employ a cut finite element method (Cutfem) with Nitsche boundary conditions and ghost-penalty stabilization. Three complementary estimators are proposed: (i) Deim approximation quality indicators for the stiffness matrix and force vector, which are constant in the number of Pod modes, (ii) dual-norm residual estimators in both plain and Jacobi-preconditioned form, and (iii) a Pod tail-energy indicator. A rigorous theoretical framework is established, comprising a uniform coercivity result for the Cutfem bilinear form, an active-dof residual bound that accounts for ghost-penalty degrees of freedom, a combined a posteriori bound, and sharp effectivity analysis for the residual estimators. The key theoretical finding is that the large observed effectivity indices are explained by ghost-penalty degree-of-freedom inflation, and that restricting the residual to active degrees of freedom is predicted to reduce effectivity. Numerical experiments on a parametric ellipse domain with semi-axes confirm the theoretical predictions, achieve significant online speedup, and demonstrate algebraic convergence of the true error alongside exponential decay of the residual estimators.

We develop a resurgent approach to the problem of unique continuation of mock theta functions across their natural boundary. The starting point is the representation of the associated Mordell-Appell integrals as Laplace transforms of resurgent functions, which serve as the primary analytic objects. By rotating the Laplace contour by $π$, i.e. onto the Stokes line, one obtains, in all known cases, the mock-modular relations between the Mordell-Appell integrals and the corresponding unary series in $\hat q=e^{-πi τ}$ and $\hat q_1=e^{-πi (-1/τ)}$. We then prove that these relations admit a unique solution on the $q$-side, expressed in terms of $q=e^{πi τ}$ and $q_1=e^{πi (-1/τ)}$, with coefficients determined by the corresponding Mordell-Appell integrals. This yields a canonical continuation across the natural boundary, given by a resurgent extension of the classical principle of permanence of relations, and singles out a distinguished family of mock theta functions in each group. We present a complete analysis for the order 3 and 5 cases (mf3 and mf5). The method extends naturally to higher orders; a general theory will appear in a separate paper.

Practical quantum advantage is expected to depend on fault-tolerant quantum computing, although the architectural overhead needed to support fault tolerance is still extremely high. Prior FTQC designs generally emphasize either fast logical-qubit accessibility at the cost of significant qubit overhead, or high logical-qubit density at the cost of added workload latency. We propose an architecture that balances these competing objectives by placing surface-code patches around an ancilla-centric region, which yields nearly uniform ancilla access for all data qubits. Building on this design, we introduce a new workload-driven placement method that uses the $T$-gate profile of an application to determine an effective floorplan. We further provide a reconfigurable optimization for reducing the latency of $Y$-gate measurements on a per-workload basis. To improve flexibility, we also study concurrent execution of multiple programs on the same architecture. Numerical evaluation indicates that our approach keeps cycles per instruction near the optimal regime while reducing the number of required data tiles by up to $\sim21\%$, and achieves up to $\sim90\%$ efficiency when running 10 programs concurrently.

In this paper, we investigate the quasinormal modes of two covariant effective black holes characterized by the quantum parameter $ζ$, charge $Q$, and cosmological constant $Λ$, under the scalar perturbation. By employing the pseudo-spectral method, we numerically calculate the quasinormal frequencies and analyze the influence of $ζ$ on the spectra with respect to $Q$. Our results demonstrate that while the quantum parameter $ζ$ significantly modifies the quasinormal frequency spectrum, the non-monotonic behavior and overtone outbursts persist. Notably, the impact of quantum gravity on the overtone outbursts is not merely limited to enhancement or suppression; instead, it introduces additional spectral features. Furthermore, a comprehensive analysis of the full quasinormal mode spectrum reveals rich interactions between complex and purely imaginary modes, including damping-rate crossings and merging-splitting behavior. These phenomena typically accompany overtone outbursts in near-extremal regimes, suggesting a potential connection between mode interactions and overtone outbursts. This work emphasizes the necessity of analyzing the full quasinormal frequency spectrum rather than focussing solely on fundamental modes, and provides novel insights into its underlying spectral structures.

We designed and implemented InvestChat, a multimodal tablet-based application that supports stock market exploration with multiple coordinated views and an LLM-powered chat. We evaluated the application with 12 novice investors. Our findings suggest that combining natural language, touch, and pen input during stock market exploration facilitates user engagement. Participants leveraged the modalities in complementary ways, enjoying the freedom of choice and finding natural language most effective.

We present an approach for enhancing non-playable characters (NPCs) in games by combining large language models (LLMs) with computer vision to provide contextual awareness of their surroundings. Conventional NPCs typically rely on pre-scripted dialogue and lack spatial understanding, which limits their responsiveness to player actions and reduces overall immersion. Our method addresses these limitations by capturing panoramic images of an NPC's environment and applying semantic segmentation to identify objects and their spatial positions. The extracted information is used to generate a structured JSON representation of the environment, combining object locations derived from segmentation with additional scene graph data within the NPC's bounding sphere, encoded as directional vectors. This representation is provided as input to the LLM, enabling NPCs to incorporate spatial knowledge into player interactions. As a result, NPCs can dynamically reference nearby objects, landmarks, and environmental features, leading to more believable and engaging gameplay. We describe the technical implementation of the system and evaluate it in two stages. First, an expert interview was conducted to gather feedback and identify areas for improvement. After integrating these refinements, a user study was performed, showing that participants preferred the context-aware NPCs over a non-context-aware baseline, confirming the effectiveness of the proposed approach.

Model transformations are central to MDE, but formal verification is difficult because mainstream transformation languages are undecidable. DSLTrans was designed to be Turing-incomplete to improve verifiability, yet earlier verification based on path-condition enumeration still suffered exponential blow-up and did not scale to realistic cases. We present a tractable verification workflow for DSLTrans and formalize when it is complete. The method combines three contributions: (i) a Cutoff Theorem proving that bounded model checking is complete for a precise DSLTrans fragment and positive existence/traceability properties, turning an infinite search into a finite computable bound; (ii) composable, soundness-preserving optimizations (per-class bounds, CEGAR-based fragment verification, and trace-aware dependency analysis) that reduce SMT encoding size; and (iii) a Z3-based implementation evaluated on realistic transformations from the ATL Zoo and related benchmarks. On 29 concrete transformations and 899 properties spanning compiler lowering, schema translation, behavioral modeling, graph mapping, and stress tests, 552 properties are proved, 345 produce concrete counterexamples (including intentional negative and boundary cases), and only 2 remain undecided within timeout. For properties beyond the tractability budget, we introduce tractability-driven refinement (precondition specialization, postcondition decomposition, and transformation instrumentation), achieving up to 112x speedup while eliminating spurious counterexamples. The workflow is supported by a web IDE and a concrete execution engine for runtime validation.

An explicit solution is derived for the Bellman inequality corresponding to minimax optimal dual control. The minimizing player determines control action as a function of past state measurements and inputs. The maximizing player selects disturbances and model parameters for the underlying linear time-invariant dynamics. The optimal minimizing policy is a dual controller that optimizes the tradeoff between exploration and exploitation. Once sufficient data has been collected, the policy becomes a deterministic certainty equivalence controller. However, when data is insufficient, the policy introduces a randomized term to improve excitation.

The multiplicity-dependent suppression of $Υ(n\mathrm{S})$ states measured by CMS in $pp$ at $\sqrt s=7\,$TeV \cite{CMS2020}, and of $ψ(2S)\big/J/ψ$ measured by LHCb at $\sqrt s=13\,$TeV \cite{LHCb2024}, is subjected to four multi-differential tests: \emph{cone isolation}, \emph{azimuthal sectors}, \emph{transverse sphericity}, and \emph{prompt vs. non-prompt}. Cone and sphericity close a \emph{scissors constraint}: the local reading of the Comover Interaction Model is in tension with the cone data, its global reading with the sphericity data. The non-prompt flatness forces the mechanism to act at early proper times. None of the considered hadronic or string-based frameworks -- CIM local or global, PYTHIA 8 MPI \cite{Sjostrand2015}, rope hadronisation \cite{Bierlich2015}, CGC \cite{Ma2015}, Trainor TCM \cite{Trainor2008} -- naturally satisfies the four constraints simultaneously in its published form. The surviving class is an early, globally correlated medium consistent with partonic degrees of freedom, co-occurring with the ALICE strangeness enhancement \cite{ALICE_SE}, the long-range ridge \cite{CMS_ridge}, and below the threshold of the partonic baryon-meson $v_2$ \cite{ALICE_v2}, in a density window compatible with the Campanini \& Ferri equation of state \cite{Campanini2011}.

In this work, we introduce a paralinguistic supervision paradigm for low-resource multilingual speech emotion recognition (LRM-SER) that leverages non-verbal vocalizations to exploit prosody-centric emotion cues. Unlike conventional SER systems that rely heavily on labeled verbal speech and suffer from poor cross-lingual transfer, our approach reformulates LRM-SER as non-verbal-to-verbal transfer, where supervision from a labeled non-verbal source domain is adapted to unlabeled verbal speech across multiple target languages. To this end, we propose NOVA ARC, a geometry-aware framework that models affective structure in the Poincaré ball, discretizes paralinguistic patterns via a hyperbolic vector-quantized prosody codebook, and captures emotion intensity through a hyperbolic emotion lens. For unsupervised adaptation, NOVA-ARC performs optimal transport based prototype alignment between source emotion prototypes and target utterances, inducing soft supervision for unlabeled speech while being stabilized through consistency regularization. Experiments show that NOVA-ARC delivers the strongest performance under both non-verbal-to-verbal adaptation and the complementary verbal-to-verbal transfer setting, consistently outperforming Euclidean counterparts and strong SSL baselines. To the best of our knowledge, this work is the first to move beyond verbal-speech-centric supervision by introducing a non-verbal-to-verbal transfer paradigm for SER.

In this article, we introduce a transverse averaging operator for basic forms on a Riemannian foliation equipped with an isometric transverse Lie algebra action, under the assumption that the leaf closure space is compact. Unlike the classical averaging operator in equivariant geometry, which is defined by integration over a compact Lie group, our operator is built purely from infinitesimal transverse data and does not require any global group action. We show that it sends every closed basic form to an invariant basic form representing the same basic cohomology class. As a main application, we compute the diffeological de Rham cohomology of the homogeneous space $G/H$, where $G$ is a connected Lie group, not necessarily compact, and $H$ is a connected Lie subgroup, not necessarily closed. Let $\mathfrak g$ and $\mathfrak h$ be the Lie algebras of $G$ and $H$, respectively. Assuming that $\mathfrak g$ is of compact type and that $G/\overline{H}$ is compact, we prove that \[ H^\bullet_{dR}(G/H)\cong H^\bullet(\mathfrak g,\mathfrak h). \] If, in addition, $\mathfrak h$ is an ideal in $\mathfrak g$, then under the weaker assumption that $G/\overline{H}$ is compact, we obtain \[ H^\bullet_{dR}(G/H)\cong H^\bullet(\mathfrak g/\mathfrak h), \] without requiring $\mathfrak g$ to be of compact type.

In sixth-generation (6G) cellular networks and beyond, aerial platforms, such as uncrewed aerial vehicles (UAVs) and high-altitude platform stations (HAPS), are anticipated to play a crucial role in enhancing connectivity, expanding network coverage, and supporting advanced communication services. However, the deployment of energy-efficient onboard communication systems is essential for their widespread adoption and effectiveness. The integration of energy harvesting (EH) into aerial platforms is envisioned to be pivotal in promoting both energy and cost efficiency. In this paper, we propose a new paradigm for aerial platforms in which they can collect energy from the transmitted signals of nearby aerial platforms. The paper employs a two-tier architecture with HAPS super-macro base stations (HAPS-SMBS) system: regular HAPS-SMBS nodes serve as base stations, while a "mother" HAPS-SMBS node acts as a manager to coordinate communications between regular HAPS-SMBS and the ground station, thus enabling wireless energy transfer. Specifically, we analyze the characteristics of EH-enabled HAPS-SMBS and compare their performance with those without EH. Additionally, we derive the optimal regular HAPS-SMBS positioning to mitigate signal attenuation and power loss. Subsequently, we formulate a joint optimization problem for regular HAPS-SMBS positioning and the EH factor. We solve the problem using the iterative distance and EH factor algorithm (IDFA); however, we employ $Q$-learning to verify its effectiveness. Our findings indicate that, compared to conventional EH systems, IDFA and $Q$-learning exhibit higher data rate performance. In contrast, $Q$-learning outperforms IDFA systems in linear modelswith intensive training in approximating optimal values. Furthermore, maximizing transmit power achieves higher gains than systems without EH.

Multivariate Pearson diffusions are characterized by a linear drift and a diffusion matrix that is quadratic in the state variables. We derive closed-form expressions for the mean and covariance matrix of this class using matrix exponential integrals, and extend this framework to a broader class of nonlinear diffusions with Pearson-type multiplicative noise. The main contribution is a new parameter estimator for these nonlinear multiplicative models based on Strang splitting, which decomposes the stochastic system into a deterministic nonlinear ordinary differential equation and a multivariate Pearson diffusion. The estimator is constructed by composing their respective flows and applying a Gaussian transition approximation with exact moments from the Pearson component. We prove that the estimator is consistent and asymptotically efficient. We also introduce a new model within this class, the Student Kramers oscillator, and prove existence and uniqueness of the strong solution and of an invariant measure. We evaluate the estimator through simulation studies on this oscillator and on the multivariate Wright-Fisher diffusion from population genetics, where it outperforms the Euler-Maruyama, Gaussian approximation, and local linearization estimators. We conclude with an application to Greenland ice core data using the Student Kramers oscillator.

This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere, torus, projective plane, or Klein bottle. An extension argument based on the Tits alternative for mapping class groups then implies that every finitely generated periodic subgroup of the full homeomorphism group is finite for all surfaces outside this exceptional list, recovering and extending a theorem of Guelman and Liousse to non-orientable surfaces. For the circle, we prove that every finitely generated periodic subgroup of its homeomorphism group is finite and cyclic. We close with remarks on manifolds with boundary and open questions on the Burnside problem for hyperbolic three-manifolds and doubled handlebodies.

In this paper, we analyze the $1 \rightarrow 4$ decay channel for the production of doubly heavy quarkonium, $(b\bar{c})$ or $(c\bar{c})$, via top-quark decays, $t \to (b\bar{c}) + c + c + \bar{s}$ and $t \to (c\bar{c}) + b + c + \bar{s}$, within the framework of nonrelativistic QCD (NRQCD). The dominant contributions are considered in color-singlet S-wave states, i.e., $(b\bar{c})[^1S_0]$, $(b\bar{c})[^3S_1]$, $(c\bar{c})[^1S_0]$, and $(c\bar{c})[^3S_1]$. Our calculations show that the decay widths for $\bar{B_{c}}$, $\bar{B_{c}^{*}}$, $η_{c}$ and $J/ψ$ production are 0.2251, 0.3099, 0.0537 and 0.0555 MeV, respectively, resulting in ${\cal O}(10^{4}\text{--}10^{6})$ level of $\bar{B}_c^{(*)}$ events and ${\cal O}(10^{3}\text{--}10^{5})$ level of charmonium produced at LHC per year. In particular, we find that the dominant contribution to $η_{c}$ and $J/ψ$ production via top-quark decays arises from this decay channel proposed in this work. Moreover, this multi-body top-quark decay process can serve as a sensitive probe for validating the narrow-width approximation (NWA). Finally, we provide a detailed analysis of theoretical uncertainties and differential distributions to facilitate the corresponding experimental searches. The production of a hadron associated with three quarks contains rich physical information, providing new insights for the LHC to study $B_c$ mesons and charmonia.

We study matched and Euclidean-mismatched decoding on finite Fourier-curve constellations with tangent-space artificial noise. Each hypothesis induces a Gaussian law with symbol-dependent rank-one covariance. We derive exact Euclidean pairwise errors for arbitrary pairs and an exact Gaussian-expectation representation for matched decoding on bilaterally tangent-orthogonal pairs. For uniform even constellations, the Euclidean side yields explicit distance spectra and symbol-error bounds across all offset classes; the matched side is exact on antipodal pairs and benchmarked numerically at the full-codebook level via Monte Carlo. By isolating the detection-theoretic consequence of tangent-space artificial noise, these results clarify analytically how noise fraction and constellation density enter the mismatch behavior; secrecy-rate implications require additional channel and adversary modeling.

We analytically study the effect of backreaction from analog Hawking radiation on its entanglement entropy in the Bose-Einstein condensate (BEC). The backreaction is expected to play an essential role in the decrease of the entanglement entropy and in realizing the Page curve. Since the BEC theory has microscopic Hamiltonian and thus exhibits unitarity, it is desirable to reproduce the Page curve explicitly by using the Hamiltonian. In order to analyze this in a concrete example, we study the BEC with a step-like configuration that has been extensively studied in the literature. By using the microscopic theory, we derive an explicit form of backreaction from analog Hawking radiation. Combining it with the known results of the Bogoliubov coefficients, we analytically compute the entanglement entropy of the Hawking radiation, and show that it decreases as expected due to the backreaction for sufficiently low energy modes over a wide range of the parameter characterizing the step-like configuration.

A site-specific Type-II codebook design is proposed for downlink massive multiple-input multiple-output (MIMO) limited-feedback beamforming. The key idea is to embed a learned site-specific propagation prior into the Type-II channel state information (CSI) feedback pipeline. Specifically, the base station (BS) uses a low-overhead reference signal received power (RSRP) fingerprint collected during synchronization signal block (SSB) probing to infer a user equipment (UE)-dependent dominant beam subspace before explicit CSI acquisition. The UE then estimates and feeds back only the low-dimensional effective channel coefficients within this inferred subspace, thereby avoiding full-dimensional online subspace discovery while retaining a rich multi-beam representation capability. To analyze the proposed design and compare it with standardized feedback mechanisms, a unified subspace-projection framework is developed by jointly characterizing CSI acquisition, UE-side compression, BS-side reconstruction, and effective spectral efficiency. Under this framework, Type-I, Type-II, port-selection feedback, and the proposed scheme are interpreted as different ways of inducing a feedback representation subspace. The probing codebook and the BS-side subspace inference network are then formulated as a coupled task-oriented design problem and are optimized end-to-end by maximizing the normalized CSI-capture efficiency. Extensive simulation results demonstrate that the proposed feedback scheme achieves Type-II-comparable CSI-capture capability with substantially lower online overhead and UE-side complexity, thereby improving the effective spectral efficiency.

We compute the transmission properties of electromagnetic (EM), gravitational wave (GW), and static gravitational perturbations through geometric throats in spherically symmetric spacetimes. On the ultrastatic Ellis-Bronnikov background, decomposition of the four-dimensional Maxwell equations into vector spherical harmonics yields an effective Schrödinger problem with centrifugal barrier $V_\ell^{(\mathrm{EM})}=\ell(\ell+1)/(σ^2+r_0^2)$ peaked at the throat. For the lowest physical EM mode ($\ell=1$), frequencies below the barrier-top frequency $ω_{\max}=\sqrt{2}/r_0$ are strongly suppressed by sub-barrier tunnelling. Gravitational wave perturbations ($\ell\ge 2$) see a qualitatively similar barrier and are likewise strongly suppressed below their respective barrier-top frequencies. By contrast, the static gravitational monopole ($\ell=0$), governed by the linearised Einstein equations on the same background, satisfies the source-free conservation law $(a^2Φ')'=0$ with no potential barrier, yielding the exact solution $Φ\propto\arctan(σ/r_0)$. We extend these results to a one-parameter family of throat geometries with varying profile shapes, and to a reflected-Schwarzschild (Damour-Solodukhin-type) wormhole, demonstrating that the qualitative asymmetry\emdash strong sub-barrier suppression for all propagating radiation ($\ell\ge 1$) versus polynomial attenuation for the static monopole ($\ell=0$)\emdash is universal for static, spherically symmetric throats. Numerov integration, WKB estimates, and exact analytical solutions are compared throughout. The results establish a structural constraint-wave asymmetry arising from the multipole decomposition of the field equations, independent of the matter content sourcing the geometry, on a fixed background.

We present a set of numerical-relativity binary neutron star merger simulations incorporating muons and muonic reactions for two baseline baryonic equations-of-state. In order to investigate the possible impact of muons and muonic weak reactions, we treat neutrinos with a gray (energy-independent) truncated moments scheme and an implicit-explicit time integrator. Newly computed neutrino rates are employed within the full kinematics approach for a set of relevant reactions, and pair-processes are modeled via opacities computed using reaction kernels, that allow a consistent treatment of neutrino interaction rates. We find that equilibration between matter and radiation is successfully captured by a novel two timescales approach. Of astrophysical interest is the general agreement between our muonic and non-muonic results regarding the remnant evolution, disk and outflow properties. Average electron fractions, asymptotic velocities and temperatures are different by less than $\sim 6\%$, while the main impact of muons is a reduction in ejecta masses by at most $\sim 17\%$. Therefore, based on our findings, accounting for the presence of muons and muonic reactions might result much less severe consequences regarding nucleosynthetic yields and electromagnetic counterparts than previously reported in the literature.

We investigate the stability of ultra-compact stellar configurations in the context of an interacting vacuum component. By extending the Tolman-Oppenheimer-Volkoff equations to include a covariant energy exchange between the fluid and vacuum sectors, we examine how the classical Buchdahl stability limit is modified. We analyze two phenomenological interaction models: a coupling to the matter energy density gradient and a direct coupling to the spacetime curvature. Numerical integration reveals that while standard General Relativity predicts a central pressure divergence as the compactness approaches the Buchdahl threshold, the interaction term $Q_ν$ relaxes the pressure gradient and maintains a finite, well-behaved central pressure for proper domains of the coupling parameter. These results demonstrate that an interacting vacuum provides a physical mechanism to bypass classical geometric bounds, potentially supporting ultra-compact objects in regimes previously considered singular.

Quantum key distribution protocols based on the quantum eraser phenomenon offer an operational advantage: automatic identification of matching and mismatching encoding choices through interference, eliminating basis reconciliation. However, binary quantum eraser implementations permit an eavesdropper to recover Alice's encoded bit with $85\%$ probability. To overcome this constraint, we introduce a ternary quantum eraser protocol employing three polarization states with $120^\circ$ angular separation, transmitted in three-photon groups with randomized temporal ordering. This extension achieves enhanced security through two complementary mechanisms. First, the reduced distinguishability of symmetrically-arranged quantum states limits single-photon discrimination. Second, the combinatorial complexity of unknown photon ordering constrains multi-photon eavesdropping strategies. Security analysis against individual eavesdropping attacks within the four-dimensional path-polarization Hilbert space establishes that an eavesdropper's maximum success probability is bounded at $54\%$, substantially below the binary discrimination bound. The protocol maintains a binary-equivalent efficiency of 0.30 bits per photon, comparable to established binary QKD protocols at the sifted-rate level, while preserving the operational simplicity inherent to quantum eraser cryptography.

The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. In this chapter, we present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, we derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. We then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. The quantum description is developed using Floquet theory, where the periodically driven spin system is represented by a unitary Floquet operator acting on a $(2j+1)$-dimensional Hilbert space. Within this framework, signatures of quantum chaos such as spectral statistics, entanglement generation and recurrences are discussed. The model also admits an interpretation as a system of interacting qubits, enabling explicit few-qubit realizations and direct connections with quantum information measures through reduced density matrices and entanglement entropy. By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science.

We present a magnetic model for an antiferromagnetic compound $γ$-Mn$_3$(PO$_4$)$_2$, which was previously shown to exhibit a 1/3 magnetization plateau due to the trimer-based structure of the lattice of magnetic Mn$^{2+}$ ions with $S=5/2$. An exchange Hamiltonian that yields observed field transitions is obtained from fitting magnetization data. It is shown that both biquadratic coupling and single-ion anisotropy are necessary to be present in the magnetic model to explain multiple phase transitions in the magnetic susceptibility data. The calculated magnetic spectrum is in agreement with the low-temperature specific heat data.

Crystal structure prediction has traditionally relied on prototype-based seeding, approaches that often bias sampling toward known low-energy basins and overlook metastable polymorphs with unconventional symmetries. Here, we introduce Selective Random Structure Search (SRSS), a high-throughput, unbiased framework designed to explore the configurational space of crystalline materials across all dimensions. SRSS combines symmetry-constrained random generation with feature-based diversity selection and rapid relaxation and stability evaluation via universal machine-learning interatomic potentials (uMLIPs). Applied to diverse systems, including bulk system SiC and BaPtAs, 2D layered compounds NbSe2, and 1D nanotubes GaN, SRSS successfully recovers known ground states while revealing numerous previously unreported, dynamically stable polymorphs. Notable discoveries include complex cage-like SiC polytypes, low-energy BaPtAs polymorphs beyond experimental records, a semiconducting orthorhombic phase of 2D-NbSe2, and distinct armchair/zigzag GaN nanotubes. Crucially, the entire workflow operates efficiently on standard CPU resources without GPU acceleration, demonstrating that rigorous, hypothesis-free polymorph discovery is accessible even in resource-limited settings. SRSS thus establishes a robust, scalable platform for mapping the full landscape of crystal stability, bridging the gap between exhaustive search and computational feasibility.

The initial outpatient consultation is critical for clinical decision-making, yet it is often conducted by a single physician under time pressure, making it prone to cognitive biases and incomplete evidence capture. Although the Multi-Disciplinary Team (MDT) reduces these risks, they are costly and difficult to scale to real-time intake. We propose Aegle, a synchronous virtual MDT framework that brings MDT-level reasoning to outpatient consultations via a graph-based multi-agent architecture. Aegle formalizes the consultation state using a structured SOAP representation, separating evidence collection from diagnostic reasoning to improve traceability and bias control. An orchestrator dynamically activates specialist agents, which perform decoupled parallel reasoning and are subsequently integrated by an aggregator into a coherent clinical note. Experiments on ClinicalBench and a real-world RAPID-IPN dataset across 24 departments and 53 metrics show that Aegle consistently outperforms state-of-the-art proprietary and open-source models in documentation quality and consultation capability, while also improving final diagnosis accuracy. Our code is available at https://github.com/HovChen/Aegle.

We derive the Euler (hyperbolic) hydrodynamic limit for the directed exclusion process (DEP), a one-dimensional conservative interacting particle system that preserves particle-hole symmetry while breaking left-right symmetry. The proof relies on an explicit multi-process coupling, which guarantees a strong form of attractiveness and macroscopic stability for the particle system. Further open questions about DEP are briefly discussed.

Given a graph $F$, a Berge copy of $F$ (Berge-$F$ for short) is a hypergraph obtained by enlarging the edges arbitrarily. Győri, Salia and Zamora determined the maximum number of hyperedges in a connected $r$-uniform hypergraph on $n$ vertices containing no Berge path of length $k-1$ for all $k\geq 2r+14$ and sufficiently large $n$, and asked for the minimum $k_0$ such that this extremal number holds for all $k\geq k_0$. In this paper, we prove that the extremal number holds for all $k\geq 2r+2$ and fails for $k\le 2r+1$, thereby completely resolving the problem posed by Győri, Salia and Zamora. Moreover, we improve the result of Füredi, Kostochka and Luo, who determined the maximum number of hyperedges in a $2$-connected $n$-vertex $r$-uniform hypergraph containing no Berge cycle of length at least $k$ for all $k\geq 4r$ and sufficiently large $n$, by showing that this extremal number holds for all $k\geq 2r+2$ and fails for $k\le 2r+1$. Our approach reduces Berge-Turán problems to classical extremal graph theory problems, and applies recent work of Ai, Lei, Ning and Shi concerning the feasibility of graph parameters and the Kelmans operation.

Similar to some other two-Higgs doublet models (2HDM), the flipped 2HDM admits of a light pseudoscalar physical state whose mass can be well below 50 GeV. The fact that the pseudoscalar decays dominantly into a $b{\bar b}$ pair makes its identification at the Large Hadron Collider (LHC) difficult. Moreover, the regions of the parameter space corresponding to a light pseudoscalar tend to jeopardize perturbativity at a rather low scale. One possibility that ameliorates this problem is to postulate that the light physical state has the admixture of an SU(2) singlet field. In such a situation, however, the production mode of the pseudoscalar along with a $Z$ (which provides a useful tag) gets suppressed. We have here chosen to fall back on the QCD-driven final state, namely, one or two jets, together with an energetic squeezed $b{\bar b}$-pair. We utilize boosted di-b-jet tagging techniques and a strategy based on boosted decision trees (BDT) to analyze the signals, considering all backgrounds and likely fakes (mostly from charmed quarks). We find that, including 10\% systematics, one can expect signal significance of 5-10$σ$ with an integrated luminosity of 3 $ab^{-1}$.

Plotting the mass-density of a wide range of astronomical objects as a function of their mass reveals that the vast majority of these objects fall along a ``cohesive object sequence'' that extends all the way from asteroids to the largest stars. Trends and features within this sequence reflect fundamental astronomical processes and phenomena, including the gravitational contraction of progressively higher-mass planets and the onset of nuclear reactions within stars. Meanwhile, compact stellar remnants fall well off this sequence, reflecting their extreme natures. This type of plot is therefore useful both for showcasing the relationships and connections between a wide range of astronomical objects and for clarifying the distinctions used to identify particular types of objects.