Papers

Language models can now generate symbolic music from natural-language instructions. However, existing models still struggle to satisfy multiple explicit musical constraints simultaneously. To systematically evaluate this capability, we introduce MusicConstraintBench, a benchmark of 2180 items spanning eight families of programmatically verifiable constraints. On this benchmark, Llama-3.1-70B satisfies 0.630 of single-constraint items but only 0.044 of four-constraint ones. To address this challenge, we propose MusicRLVR, which trains a language model with group relative policy optimisation (GRPO) on verifier rewards alone, needing no human annotation, reward model or music-domain supervised fine-tuning. MusicRLVR incorporates (1) a hard validation gate that rejects malformed scores, (2) graded per-family credit that, unlike a binary reward, separates partially correct outputs, and (3) an all-satisfied bonus for meeting every constraint at once. Extensive experiments show that, after 300 GRPO updates, MusicRLVR raises Qwen3-4B-Instruct-2507 from 0.160 to 0.807 on mixed constraints, outperforming Llama-3.1-70B, and generalises to unseen property combinations, out-of-range parameters and more constraints than any training prompt. The recipe transfers to Qwen3-8B, and neither trained model loses significant accuracy on general benchmarks.

Quantum circuit simulation often appears as repeated-run workloads rather than isolated circuits: variational quantum eigensolver (VQE) sweeps, noisy multishot studies, and quantum error correction (QEC) cycles revisit closely related structure across many runs. Existing simulators optimise individual executions well, but they largely ignore cross-task shared state and therefore repeat work that could be reused safely. We propose QuWARP, a planner-based workload optimiser for a bounded state of the art simulator execution surface: it performs workload-level planning over related tasks, identifies shared prefixes, and chooses when to materialize exact typed boundary artifacts for later reuse across the evaluated statevector mode, and stabilizer-hybrid mode. Its planner treats continuation legality as a narrow correctness guardrail, abstains when reuse is unprofitable, and keeps each reuse, abstention, or refusal decision auditable through EXPLAIN-style traces, meaning inspectable planner reports with provenance and realized-cost summaries. Across real world quantum application workloads QuWARP delivers 2.95x-32.84x speedups over this work's main direct per-task Qrack denominator on reuse-positive workloads. These results show workload-level reuse planning improves repeated-run simulation while keeping unsupported handoffs auditable and out of the execution path.

M. E. Zieve conjectured that a candidate datum over the sphere is realizable whenever the gcd of the parts of every branch partition is one and it satisfies the lcm condition. We prove that this conjecture reduces to its three-branch-point case. More precisely, if every Zieve-admissible triple is realizable, then every Zieve-admissible datum with at least four branch points is realizable. As already noted by Petronio, Zieve's conjecture would imply the prime-degree conjecture of Edmonds, Kulkarni, and Stong. Song, Wen, and Zhang proved the latter conjecture in a preprint posted on arXiv in September.

Let $(\mathcal X, d, \mu)$ be a space of homogeneous type and let $\rho$ be an admissible function on $\mathcal X$. In this paper, we introduce a new class of singular integral operators associated with $\rho$, including a wide range of operators arising in harmonic analysis. For such an operator $T$ and a function $b$ belonging to suitable localized $\mathrm{BMO}$ spaces associated with $\rho$, which are strictly larger than the classical space $\mathrm{BMO}(\mathcal X)$, we establish the boundedness of the commutator $[b, T]$ from the Hardy space $H^1_\rho(\mathcal X)$ into $L^{1,\infty}(\mathcal X)$, $L^1(\mathcal X)$, and $H^1_\rho(\mathcal X)$. Moreover, the boundedness of $[b,T]$ on $H^1_\rho(\mathcal X)$ is characterized by necessary and sufficient conditions. We then apply this to investigate the boundedness of commutators of singular integrals in various settings, including Schrödinger operators on stratified Lie groups and Laguerre operators of convolution type. Our results are new even for Schrödinger operators on $\mathbb R^n$.

Reliable laparoscopic video is essential for telesurgery, yet fixed-rate digital transmission can degrade abruptly under poor channel conditions. We propose LiteSC, a lightweight semantic communication framework combining a frozen pretrained extractor, a compact joint source–channel coding pair, and a receiver-adapted surgical renderer. The extractor produces a latent with approximately 97.9% fewer scalar values than the red–green–blue (RGB) input, while inference requires neither segmentation masks nor temporal reference frames. Using separate CholecSeg8k source videos for training and testing, we evaluate LiteSC over an additive white Gaussian noise (AWGN) channel at symbol signal-to-noise ratios $E_s/N_0$ from 0 to 25 dB. At a channel bandwidth ratio of $\rho=0.0208$, equivalent to 0.0208 complex channel symbols per RGB source value, peak signal-to-noise ratio (PSNR) rises from 28.7 to 31.9 dB, structural similarity index measure (SSIM) from 0.869 to 0.919, and learned perceptual image patch similarity (LPIPS) falls from 0.102 to 0.048. Against H.265 transmission protected by low-density parity-check (LDPC) coding under the same channel-symbol budget, LiteSC achieves higher SSIM and lower LPIPS, although H.265+LDPC attains a higher peak PSNR. These results show graceful laparoscopic frame reconstruction under the evaluated AWGN conditions.

In this paper we find conditions on the PT-symmetric non-self-adjoint Dirac operator L(Q) with matrix-valued coefficients Q whose entries are PT-symmetric periodic functions for which the number of gaps in the real part of its spectrum is finite.

Ethereum decentralized finance (DeFi) provides a public, time-stamped record of transaction-level event streams, but the same public symbols can create strong machine-learning shortcuts. We introduce ETH-TraceBench, a benchmark for evaluating Ethereum DeFi representations under temporal, protocol, pool/infrastructure, and symbolic shift. The raw event universe covers January 2021-December 2025 and contains 1.35 billion transactions with logs and 5.01 billion raw log rows. Model evaluation uses a fixed 911,267-instance supervised sample, training on 2021-2024, selecting models on 2025H1, and testing on 2025H2. Simple models perform strongly on the aggregate temporal test: TraceStats-GB reaches 0.953 macro-F1 and TopicEmitterHashMLP 0.959 on the canonical DEX test set. Performance drops sharply under protocol novelty, with macro-F1 of 0.794, 0.743, and 0.766 for TraceStats-GB, TopicEmitterTrace-SGD, and TopicEmitterHashMLP, while strict unseen-pool scores remain 0.927, 0.897, and 0.935. Uniswap v4 and Ekubo v1, both absent from supervised training, are materially harder than the full test. Jointly masking emitter and topic identity reduces DEX macro-F1 to 0.916 and liquidation macro-F1 to 0.774 for TopicEmitterTrace-SGD. A standard Transformer over log-index-ordered events provides no consistent advantage over a deterministic shuffle of the same events, indicating that high aggregate scores can arise without sophisticated chronological modeling. A natural-prevalence audit estimates 2025H2 DEX prevalence among logged Ethereum transactions at about 22.5%, and a deterministic 400-transaction audit finds complete agreement with task label sources and independently re-queried raw-log counts. ETH-TraceBench therefore treats difficult transfer and controlled-input conditions, rather than a single aggregate score, as the main evaluation target.

Despite impressive visual quality, state-of-the-art video diffusion models often generate content that violates real-world physical laws. While existing solutions rely on external priors or specialized data, we investigate the root cause by exploring the internal mechanisms of these models. Specifically, we present the first interpretability study on the ”motion planning” process of text-to-video diffusion models, revealing how motion trajectories form during early denoising stages. Building upon the ”first shape, then details” finding, we combine cross-attention trajectory patterns with causal head contributions to identify a specific subset of attention heads driving motion planning. Further, our self-attention analysis shows that Rotary Position Embedding (RoPE) induces excessive spatial attention decay. This causes early candidate regions to prematurely lock into physically implausible positions, suppressing reasonable trajectories in adjacent frames and triggering generation failure modes. To address this fundamental flaw, we propose a lightweight architectural modification that scales the frequency of RoPE across different denoising steps. This strategy reduces excessive attention decay, helping the model explore better candidate regions to establish coherent physical motion. Finally, training-free and training-based experiments confirm the effectiveness of our approach in enhancing the physical commonsense of generated videos.

Pilot contamination is a major challenge in cell-free massive multiple-input multiple-output (MIMO) systems, where the limited number of orthogonal pilots makes pilot reuse unavoidable. Since the pilot assignment solution space grows exponentially with the number of users, finding the global optimum becomes computationally challenging on classical computers. Recent advances in quantum computing provide a promising approach for solving such large-scale combinatorial optimization problems. In this paper, we reformulate the assignment problem as a quantum-compatible optimization problem, enabling it to be directly solved by the Quantum Approximate Optimization Algorithm (QAOA). Specifically, the pilot contamination objective and assignment constraints are incorporated into the QAOA formulation. This allows the quantum search to focus on valid pilot assignments with low contamination cost. Simulation results show that the proposed method achieves performance close to exhaustive search, demonstrating the potential of quantum-assisted optimization for pilot assignment in future wireless systems.

LiDAR-based unmanned aerial vehicle (UAV) exploration builds maps by continually selecting where to observe next. However, decisions based on the measured map provide limited foresight into spatial continuations behind occlusions, leaving potentially informative directions unrecognized. We present WOLF, a world-model-guided framework that predicts future observations to enhance autonomous exploration. In the training stage, a recurrent world model learns observation dynamics from exploration trajectories, with recurrent memory retaining the spatial context needed to interpret partial observations across successive views. Building on this context, the model combines observation history with candidate motions during exploration to predict local occupancy and visibility. To guide further sensing, a predictive frontier generation mechanism then aligns and fuses these predictions using confidence, branch agreement, and observation quality to identify promising regions. The resulting predictive frontiers join measured ones to guide geometric viewpoint selection and trajectory generation, while new scans update subsequent predictions. In simulations, our method reduces mean terminal time by 10.9% relative to EPIC in Garage at comparable coverage and increases mean coverage from 42.12% to 98.35% in Tunnel. Real-world experiments further demonstrate onboard deployment of the learned model for online inference during physical flight.

Imbalanced gradient magnitudes between the visual and language pathways of a vision-language model are often treated as a defect to be corrected. We test that premise for one family of correction, deliberately excluding adaptive, signal-driven schemes (e.g. BalGrad, OGM, PMR, CGGM), which are a mechanistically distinct class outside this study's scope. Measuring the language-to-visual gradient-norm ratio, reported in parameter-normalised form, across nine fine-tuning conditions, three seeds, and three captioning datasets spanning distinct physical domain shifts – underwater, aerial, radiological – we find imbalance magnitude varies markedly across domains with no predictable ordering. A plain learning-rate reduction cuts imbalance substantially and lands within a few BLEU points of the best method on every dataset. Staged freezing reduces the ratio on every domain yet never ranks first; a schedule-only control isolates freezing as the cause on one dataset but not the other two. Forcing the two gradient groups to equal magnitude drives per-parameter imbalance close to zero on every domain, yet is both the best result in the study and the worst placement among full fine-tuning methods, on different datasets, with identical settings. Reductions in gradient-norm ratio do not consistently predict captioning performance across domains, and how a given level of balance is reached matters as much as the level itself. As a secondary finding, a commonly reused LoRA configuration applied to BLIP silently adapts zero visual parameters; correcting it improves BLEU-4 on all three datasets.

Extending the orbital angular momentum (OAM) degree of freedom to slow electrons would open a distinct regime of low-energy electron-matter interactions. Using time-dependent density-functional theory, we demonstrate that laser-driven armchair carbon nanotubes (CNTs) can emit OAM-carrying slow electrons. A circularly polarized OAM-writing pulse promotes circumferential electronic motion and generates OAM about the tube axis; a delayed linearly polarized extraction pulse releases slow electrons carrying the injected angular momentum. We find much higher ionization yields and net emitted axial OAM in representative CNTs than in oriented CO2 and benzene under identical laser conditions. Increasing the tube diameter enhances the ionization yield and OAM substantially, and moreover, reversing the helicity of the OAM-writing pulse flips the sign of the emitted OAM. Together, these findings establish CNTs as a platform for slow-electron emission with optically controllable OAM.

Let $\Omega\subset\mathbb C^n$ be a smoothly bounded convex domain of finite type. We characterize absolute summability on its Bergman spaces and estimate approximation errors in the summing norm. For $1<p<\infty$ and $1\le q,r<\infty$, we characterize absolutely $r$-summing Carleson embeddings $A^p(\Omega)\to L^q(\mu)$ by diagonal operators formed from normalized masses on McNeal balls. For $1<p,q<\infty$ and $1\le r<\infty$, we obtain a corresponding big Hankel criterion using local $L^q$ distances to holomorphic functions, with the appropriate volume weights. Both criteria give upper and lower norm estimates. The proofs combine uniform local nuclear estimates, kernel synthesis, and an analytic decomposition at two fixed scales. Local Taylor polynomials give explicit rank and error bounds for the embeddings. These bounds transfer to general Hankel operators when $p=2$ or $q=2$. Suitable atomic embeddings have the same best approximation errors as their diagonal models, up to constants. A family of Hankel operators contains a complemented copy of the diagonal ideal and has matching approximation rates for power sequences in the Hilbert case. For positive Toeplitz operators on finite-type ellipsoids, we compute exact spectral asymptotics in three regimes, including the critical logarithmic factor and the leading constants for geometric symbols. These asymptotics give optimal approximation rates in the summing norm. Applications to composition and Volterra operators include the target endpoint $q=1$.

We describe what a typical covering of a closed 2-orbifold looks like on a small scale. Specifically, we prove that a uniformly random covering of degree n contains in expectation $\Theta(n^0)$ short closed geodesics, potentially $\Theta(n^0)$ pairs of nearby order-2 cone points, in general $\Theta(n^{\frac{1}{m}})$ cone points of order m, and with high probability no small regions with more complicated topology. This generalises many results of Magee and Puder (2023) from orientable surfaces to possibly non-orientable orbifolds, and answers some of the questions raised by Puder and Zimhoni (2024).

Understanding nonequilibrium transport and fluctuations driven by nonclassical light in nonlinear quantum optical systems is challenging. Here, we formulate a driven quantum master equation in the rotating frame combined with full counting statistics, retaining the drive-induced frequency shifts in the system-reservoir interactions and providing a unified description of drive-assisted incoherent transitions based on the rotated system dressed-basis. Applied to a Kerr resonator and a nonlinear Jaynes-Cummings model, the approach reveals pronounced multiphoton-resonant enhancement of the drive input energy current, with significant high peaks under two-photon driving compared to the single-photon case. The two-photon resonance relations are analytically obtained. Resonance structure in the nonlinear Jaynes-Cummings model nonlinearly relies on qubit-photon couplings, with additional dressed-state branches. A low-energy-state approximation attributes the resonant current enhancement to dressed-state hybridization and efficient activation of incoherent energy exchange processes. Beyond the average current, two-photon-driving induced energy exchange picture near resonance also substantially modifies the second-order current fluctuation and higher-order current cumulant, while increasing the time-normalized signal-to-noise ratio. Adding two-photon loss introduces extra incoherent photon-pair exchange pathways and further reshapes the current and its fluctuations. We hope these results may deepen interpretation of photon driving and quantum dissipation cooperatively governing nonequilibrium energy transport and fluctuations.

Vision-language-action (VLA) models have achieved strong performance in embodied manipulation, but still struggle to distinguish between changes that should preserve behavior and those that require different actions. We identify two complementary failure modes. Under task-preserving changes, where task semantics remain unchanged but scene appearance varies (e.g., style, illumination, clutter, or paraphrasing), policies often exhibit unnecessary action drift. Conversely, under semantic-breaking changes, where key task semantics such as the target object or constraint are altered, policies frequently continue following the original trajectory instead of adapting to the new task. To address these failures, we propose BAS-VLA, a task-semantic action calibration framework built on top of a frozen base VLA. BAS-VLA adopts a breaking-centered calibration core as its default path, complemented by a selective evidence-gated preserving auxiliary that corrects appearance-induced drift when task-preserving evidence is strong. Across four target-object swap tasks, BAS-VLA improves changed-task success from 2.3% to 68.5% while maintaining strong clean and semantics-preserving performance and suppressing outdated behavior. On validated style-preserving shifts, it further improves success from 42% to 70% without degrading clean performance. These results demonstrate the importance of calibrating VLA policies to remain stable when task semantics are preserved and adapt when task semantics change.

The paper studies the optical properties of assemblies of metallic prolate and oblate nanospheroids. The frequency dependences of averaged absorption and scattering cross-sections, absorption, scattering and reflection coefficients are obtained. The calculations were performed for assemblies of spheroidal particles of various metals. The difference in the results of calculating the frequency characteristics of the absorption and scattering cross-sections for assemblies of prolate and oblate spheroids manifested itself in different location and value of the maxima. A qualitative similarity of the frequency dependences of the absorption and scattering coefficients was established. It is shown that the frequency curves of assemblies of spheroids of different metals differ significantly in the location of the extrema within the range from the visible to the ultraviolet region of the spectrum

We investigate the dynamics of nonclassicality, quantified by the Wigner Yanase skew information, in generalized Jaynes Cummings (JC) and Tavis Cummings (TC) models describing light matter interactions in cavity quantum electrodynamics. We first analyze a generalized JC model consisting of a single bosonic cavity mode coupled to a spin 1 atom, focusing on the temporal evolution of nonclassicality in both the cavity field and the atomic subsystem. We then extend this framework to a generalized TC model by introducing an additional spin $1/2$ atom, enabling us to examine the influence of collective atomic degrees of freedom. The global dynamics are investigated both with and without an $XY$ spin interaction. Our results show that, under resonance conditions, the system exhibits efficient excitation exchange between the cavity field and the atomic subsystem, resulting in regular, coherent nonclassicality dynamics and enhanced field nonclassicality generation. Conversely, an increasing longitudinal magnetic field acts primarily as an effective detuning parameter rather than a direct exchange interaction. In this off resonant regime, the atom field coupling is substantially weakened, localizing excitations within the atomic subsystem. This localization suppresses coherent energy transfer to the cavity field, leading to a pronounced reduction in field nonclassicality, while the atomic subsystem retains the majority of the quantum correlations. Notably, atomic superposition states exhibit highly irregular spin dynamics, reflecting a detuning-induced redistribution of quantum correlations. These findings demonstrate that the dynamics of spin and field nonclassicality are governed primarily by interaction mediated excitation flow and resonance conditions rather than the initial energy distribution alone, ..

We investigate square-lattice skyrmion crystal states in a centrosymmetric spin model with momentum-dependent magnetic interactions, including a uniform ferromagnetic interaction, easy-axis anisotropic interactions at two orthogonal finite wave vectors, higher-harmonic wave-vector interactions, and an external magnetic field. Using simulated annealing calculations, we determine the low-temperature magnetic phase diagram as functions of magnetic field and uniform ferromagnetic interaction strength. We find that the skyrmion crystal phase is stabilized at intermediate fields when the uniform ferromagnetic interaction is weak, exhibiting a noncoplanar double-$Q$ spin texture, finite scalar spin chirality, and higher-harmonic components. Increasing the uniform ferromagnetic interaction suppresses and eventually eliminates the skyrmion crystal phase through direct first-order transitions to the fully polarized state, whereas its weakening expands the skyrmion stability region and stabilizes a single-$Q$ conical spiral phase at high fields. These results clarify the mechanisms governing the square-lattice skyrmion formation in centrosymmetric magnets.

E-commerce search requires distinguishing products that are merely related to a query from those that directly satisfy the user's shopping intent. We augment query-product pairs with structured LLM-generated query and product attributes and human-validated relevance, explanations, and centrality judgments, and evaluate these signals using a simple dual-encoder retriever and MLP re-ranker. On an augmented subset of ESCI, a human-feature oracle reaches $0.9382$ nDCG@10, while a human-free trained $Q+P$ configuration reaches $0.9258$. Synthetic approximations of the human signals reach $0.9150$ overall but provide substantial gains for difficult, low-performing queries. Ablations show that most of the oracle improvement comes from post-edited explanations and annotator comments rather than the scalar centrality feature, suggesting that LLMs are most useful for exposing and approximating structured semantic supervision rather than replacing human judgment directly.

Recent discovery of reentrant superconductivity and elevated $T_c$ in Eu-substituted infinite-layer nickelates raises a critical question concerning the nature of Eu-4$f$ states and their potential interaction with Ni-$d$ electrons. Here we combine density functional theory with the dynamical mean-field theory (DFT+DMFT) calculations to investigate the valence and magnetic properties of Eu-ions in the nickelate 112 structure, explicitly treating the Coulomb repulsion in both Ni-3$d$ and Eu-4$f$ shells. We find a three-regime evolution of the Eu-4$f$ configuration driven by its Hund's rule coupling $J_{\rm H}$. The magnetic and mixed-valence Eu ionic state inferred by experiments only occurs for moderate $J_{\rm H}$, with coexisting local moments and strongly correlated $j=7/2$ quasiparticles, in contrast to the nonmagnetic state at small $J_{\rm H}$ and the fully spin-polarized divalent state at large $J_{\rm H}$. This local-itinerant duality arises from an effectively hole-doped orbital-selective Mott state induced by the intra-4$f$ charge transfer between $j=5/2$ and $7/2$ manifolds. It not only explains the origin of the mixed-valence and local moment behaviors of the Eu-ions observed experimentally, but also predicts low-energy 4$f$ quasiparticles that may hybridize with the Ni-3$d$ electrons and contribute to the elevated $T_c$. Our work provides a basis for understanding the unusual ferromagnetic and superconducting properties of Eu-substituted infinite-layer nickelates.

This work presents the $\textit{ab initio}$ calculations of the electronic energy spectrum of the In$_{4}$CdI$_{6}$ compound. The study was conducted within the framework of density functional theory (DFT), using local density approximation (LDA) and general gradient approximation (GGA) pseudopotentials, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. The GGA approximation was implemented using the PBE and PBEsol exchange-correlation functional. Based on the electronic energy structure, the type of the minimum band gap was determined, and an analysis of the energy level dispersion for both the valence and conduction bands was performed. Furthermore, the effective masses of electrons ($\textit{m}_{c}$) and holes ($\textit{m}_{v}$) for In$_{4}$CdI$_{6}$ were established. The energy band analysis was complemented by the calculation of the density of states (DOS). Based on the electronic energy spectrum, the real and imaginary components of the dielectric function are calculated. Using the Kramers-Kronig relations, we also derive such fundamental optical functions of In$_{4}$CdI$_{6}$ as the refractive index $\textit{n}$, and the extinction coefficient $\textit{k}$.

Autonomous navigation of unmanned aerial vehicles in constrained three-dimensional environments has been a challenge in the robotics domain. The application of autonomous unmanned aerial vehicles in civil infrastructure inspection involves the use of such vehicles in bridge inspection, tunnel inspection, and structural inspection. The use of deep reinforcement learning in the autonomous navigation of unmanned aerial vehicles has been successful in constrained environments. However, the computational cost of the algorithm limits the application of the algorithm in the autonomous navigation of unmanned aerial vehicles. This paper proposes the use of the spiking neural network-based Proximal Policy Optimization algorithm in the autonomous navigation of unmanned aerial vehicles in constrained sequential environments. The proposed algorithm integrates the use of spike-based actor-critic reinforcement learning with the Proximal Policy Optimization algorithm. The proposed algorithm uses the stochastic Gaussian policy in the autonomous navigation of unmanned aerial vehicles. The proposed algorithm was implemented in the autonomous navigation of unmanned aerial vehicles in constrained 3D environments. The proposed algorithm was successful in completing 1913 episodes out of more than 3000. The proposed algorithm was successful in passing an average of 2.10 windows per episode. The proposed algorithm was successful in achieving a success rate of 63.77%. The proposed algorithm was successful in achieving success rates of more than 90% in the later stages of the algorithm.

Generative user interfaces (GenUI) promise personalized interfaces to a user's tasks and needs. However, user needs are often implicit—difficult for systems to infer and users to articulate, making it hard for users to arrive at their ideal interface. We propose Elicitive User Interfaces, a design approach to GenUI that generates elicitation techniques as part of the interface itself. Elicitive UIs adapt these techniques to the user, task, and interface to draw out user preferences. To guide the design of Elicitive UIs, we synthesize a six-axis design space that shapes how an interface elicits user preferences. Across two user studies with a design probe, we found that while Elicitive UIs surfaced preferences users had not already formed, and that responses to elicitation varied more across users than across tasks. Users developed more consistent preferences for how they wanted to be elicited, suggesting an opportunity to personalize elicitation itself.

Using density functional theory (DFT) with the ONCVVPSP pseudopotential and PBE functional, this study investigates the structural, electronic, elastic, optical, and thermoelectric properties of the trigonal LaBiO$_{3}$ perovskite oxide (space group R3c). Ground-state parameters lattice constant, volume, bulk modulus, and its pressure derivative were determined using the equation of state. Applying the Hubbard correction (GGA+U) revealed an indirect, wide band gap of 3.51 eV. Mechanical properties, including the anisotropy factor, elastic modulus, and Poisson's ratio, were calculated via the Voigt-Reuss-Hill averaging scheme. The bulk-to-shear modulus ratio identifies the trigonal phase as ductile. Additionally, Debye temperatures and sound velocities were computed. Optical characteristics (absorption coefficient, refractive index, and electron energy loss function) were evaluated across a 0-35 eV spectral range. Finally, semi-classical transport coefficients, including electrical conductivity, Seebeck coefficient, and power factor, were calculated to assess the material's thermoelectric potential.

Human-feedback alignment has made language models useful assistants and is commonly described as aligning them with humans. However, the responses people prefer from an AI need not be the responses they themselves would give. We distinguish alignment with human preferences from alignment with human behavior, and show that alignment with human preferences can make model behavior less human-like even when both preferences and responses come entirely from humans. We call this the Turing-test gap. We show that preference alignment preserves the human response distribution only under a restrictive condition, and find no consistent evidence that real human preferences satisfy it. Empirically, the loss of human-response likelihood increases with the strength of preference weighting, regardless of its direction, and the gap also appears under standard DPO. These results establish human-likeness as an explicit dimension of alignment rather than something assumed to follow from preference alignment.

We prove that every smooth Fano threefold of characteristic p>5 is quasi-F-split. Moreover, if p>11, then it is F-split.

We construct a polynomial invariant of planar curves via skein relations, which generalizes Arnold's numerical invariant $\operatorname{St}$.

Let $X$ be a smooth minimal projective variety of general type of dimension $n\geq 4$ over $\bb C$. We prove that $|\frac{n^2+n}{2}K_X|$ is base point free. This gives a new bound for the pluricanonical case of Fujita Freeness Conjecture for nef and big canonical divisors.

Ab initio calculations of cubic perovskites RGaO$_3$ (R = Ho, Er, Tm) were performed using the full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). We investigated their structural, electronic, magnetic, and optical properties in detail. In the optimized configurations, the lattice constants ranged from 3.83 to 3.85 A. The electronic band structures indicate that ErGaO$_3$ is semiconducting, whereas HoGaO$_3$ and TmGaO$_3$ exhibit half-metallic behavior, probably due to the interaction of spin-orbit coupling with the electronic states near the Fermi level. Optical response of half-metallic compounds (HoGaO$_3$,TmGaO$_3$) is strongly governed by their spin polarization electronic structure. The semiconducting spin channel absorbs ultraviolet photons, while metallic or small gap channel interacts with infrared light. This dual behavior enables spin selective optical excitation, relevant for spintronics and optoelectronics applications. These compounds show high surface reflectivity, with TmGaO$_3$ achieving a maximum reflectivity of 69%. Moreover, their optical conductivity mainly occurs at higher energies, indicating suitability for high-energy optoelectronic applications. The calculated magnetic moments suggest a robust ferromagnetic character across this series.