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Applications · Computer Vision

Sibo He, Weiying Xie, Daixun Li, Junhao Zhong, Jiayun Tian, Yunke Wang, Leyuan Fang, Gang He, Yunsong Li

Vision-Language-Action (VLA) models have shown strong potential for robotic manipulation, yet adapting pretrained models to novel tasks typically relies on substantial task-specific demonstrations, limiting scalability. Current VLA methods mostly focus on action imitation, which ignores the richer structure contained in trajectories. In contrast, motion dynamics governing how actions evolve over time are more informative and transferable, making them better suited for few-shot adaptation. Motivated by this idea, we propose DynVLA, a few-shot adaptation system that reformulates VLA learning from action imitation to trajectory-level motion dynamics modeling. Specifically, we propose Motion Dynamics Mechanism (MDM), which distills latent physical regimes from trajectories via flow-matching inversion, yielding compact representations that capture dynamics. We further design Dynamics-Constrained Modeling (DCM). DCM projects these inferred representations onto a Dynamics Bank, which stores prior motion knowledge pretrained from diverse demonstrations. By grounding action generation in these learned priors, the system enables interpolating between existing action paradigms to represent novel dynamics modes. Experiments on 13 real-world tasks demonstrate that DynVLA outperforms existing SOTA systems by 19\% in average success rate with only 10-20 demonstrations, highlighting its adaptation capabilities in real-world scenes.

Deep Learning · Everything Else

Till Muser, Alexandra Spitzer, Matti Lassas, Maarten de Hoop, Ivan Dokmanic

We introduce Flower, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displacement field and warps the mixed input features. Motivated by physics and computational efficiency, displacements are predicted pointwise, without any spatial aggregation, and nonlocality enters *only* through sparse sampling at source coordinates, *one* per head. Stacking warps in multiscale residual blocks yields Flowers, which implement adaptive, global interactions at linear cost. We theoretically motivate this design through three complementary lenses: flow maps for conservation laws, waves in inhomogeneous media, and a kinetic-theoretic continuum limit. Flowers achieve excellent performance on a broad suite of 2D and 3D time-dependent PDE benchmarks, particularly flows and waves. A compact 17M-parameter model consistently outperforms Fourier, convolution, and attention-based baselines of similar size, while a 150M-parameter variant improves over recent transformer-based foundation models with much more parameters, data, and training compute.

Applications · Chemistry, Physics, and Earth Sciences

Lisa Schneckenreiter, Sohvi Luukkonen, Lukas Friedrich, Daniel Kuhn, Günter Klambauer

Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce **Con**trastive **G**eometric **L**earning for **U**nified Computational **D**rug D**e**sign (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for pre-defined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

Applications · Computer Vision

Mikel Zhobro, Andreas René Geist, Georg Martius

Realistic simulation is critical for applications ranging from robotics to animation. Video generation models have emerged as a way to capture real-world physics from data, but they often face challenges in maintaining spatial consistency and object permanence, relying on memory mechanisms to compensate. As a complementary direction, we present 3DGSim, a learned 3D simulator that directly learns physical interactions from multi-view RGB videos. 3DGSim adopts MVSplat to learn a latent particle-based representation of 3D scenes, a Point Transformer for the particle dynamics, a Temporal Merging module for consistent temporal aggregation, and Gaussian Splatting to produce novel view renderings. By jointly training inverse rendering and dynamics forecasting, 3DGSim embeds physical properties into point-wise latent features. This enables the model to capture diverse behaviors, from rigid and elastic to cloth-like dynamics and boundary conditions (e.g., fixed cloth corners), while producing realistic lighting effects. We show that 3DGSim can generate physically plausible results even in out of distribution cases, e.g. ground removal or multi-object interactions, despite being trained only on single-body collisions.

Deep Learning · Large Language Models

Fangchen Yu, Haiyuan Wan, Qianjia Cheng, Yuchen Zhang, Jiacheng Chen, Fujun Han, Yulun Wu, Junchi Yao, Ruilizhen Hu, Ning Ding 等

Recently, the physics reasoning capabilities of (M)LLMs have attracted growing attention. However, existing physics benchmarks suffer from two major gaps: they neither provide systematic and up-to-date coverage of physics Olympiads, nor enable direct performance comparison with humans. To bridge these gaps, we present **HiPhO**, the first benchmark dedicated to high school physics Olympiads with human-aligned evaluation. HiPhO highlights three key innovations. **(1) Comprehensive data:** it compiles 13 latest Olympiads from 2024-2025, covering both international and regional competitions and spanning mixed modalities from text-only to diagram-based problems. **(2) Professional evaluation:** it adopts official rubrics to perform fine-grained grading at both the answer and step levels, ensuring alignment with human examiners. **(3) Human-level comparison:** models are awarded gold, silver, and bronze medals based on official score thresholds, enabling direct comparison with human contestants. Our large-scale evaluation of 30 state-of-the-art (M)LLMs shows that across 13 exams, most open-source MLLMs remain at or below the bronze level, open-source LLMs demonstrate notable progress with multiple gold medals, and closed-source MLLMs achieve 6-13 gold medals, while most models still fall well short of full marks. These results underscore the substantial gap between current (M)LLMs and top human contestants, as well as the considerable room for further improvement.

Deep Learning · Everything Else

Shibing Mo, Jing Liu, Jianchu Xu, Ruilin Wu

Macro placement is a fundamental step in modern VLSI physical design, determining the solution quality of high-dimensional combinatorial optimization problems. Despite recent advancements in machine learning for spatial coordinate determination, the temporal dimension of placement sequencing remains largely governed by static heuristics. In this work, we demonstrate that the placement sequence is not merely a preprocessing step but a decisive factor in optimization, where suboptimal early decisions trigger irreversible domino effects that constrain the solution space. To harness this unexplored dimension, we propose \textbf{OrderPlace}, a novel framework that automates the discovery of macro placement strategies via proxy-guided Large Language Model (LLM) evolution. Unlike existing methods that rely on manual rules like area or connectivity, OrderPlace leverages LLMs to evolve generalizable, code-level ordering strategies—ranging from static metrics to dynamic, physics-inspired mechanisms. To mitigate the prohibitive cost of evaluating sequences, we introduce a lightweight proxy evaluation mechanism that efficiently filters candidates using a deterministic greedy probe. Experimental results on the standard ISPD 2005 benchmarks demonstrate that OrderPlace discovers novel ordering strategies. Compared with WireMask-EA and the state-of-the-art method EGPlace, OrderPlace reduces wirelength by 34.04% and 14.08%, respectively.

Applications · Chemistry, Physics, and Earth Sciences

Chenguang Wang, Zihan Zhou, LEI BAI, Tianshu Yu

Template-free retrosynthesis methods treat the task as black-box sequence generation, limiting learning efficiency, while semi-template approaches rely on rigid reaction libraries that constrain generalization. We address this gap with a key insight: atom ordering in neural representations matters. Building on this insight, we propose a structure-aware template-free framework that encodes the two-stage nature of chemical reactions as a positional inductive bias. By placing reaction center atoms at the sequence head, our method transforms implicit chemical knowledge into explicit positional patterns that the model can readily capture. The proposed RetroDiT backbone, a graph transformer with rotary position embeddings, exploits this ordering to prioritize chemically critical regions. Combined with discrete flow matching, our approach decouples training from sampling and enables generation in 20--50 steps versus 500 for prior diffusion methods. Our method achieves state-of-the-art performance on both USPTO-50k (61.2\% top-1) and the large-scale USPTO-Full (51.3\% top-1) with predicted reaction centers. With oracle centers, performance reaches 71.1\% and 63.4\% respectively, surpassing foundation models trained on 10 billion reactions while using orders of magnitude less data. Ablation studies further reveal that structural priors outperform brute-force scaling: a 280K-parameter model with proper ordering matches a 65M-parameter model without it.

Applications · Chemistry, Physics, and Earth Sciences

Lin Huang, Chengxiang Huang, Ziang Wang, Yiyue Du, Chu Wang, Haocheng Lu, Yunyang Li, Xiaoli LIU, Arthur JIANG, Jia Zhang

Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features or dense tensor products on \textit{every} edge. To overcome this, we introduce \textbf{E2Former-V2}, a scalable architecture that integrates algebraic sparsity with hardware-aware execution. We introduce \textbf{Equivariant Axis-Aligned Sparsification (EAAS)}, which leverages an $\mathrm{SO}(3)\!\rightarrow\!\mathrm{SO}(2)$ change of basis to convert dense Wigner-$6j$ tensor contractions into sparse, parity-based re-indexing operations. Building on this representation, we propose \textbf{On-the-Fly Equivariant Attention}, a fully node-centric mechanism implemented via a fused Triton kernel. By eliminating materialized edge tensors and maximizing SRAM utilization, our kernel achieves up to \textbf{20$\times$ higher TFLOPS} than standard implementations. Experiments on SPICE and OMol25 show that E2Former-V2 preserves predictive accuracy while substantially accelerating inference, demonstrating the practical feasibility of large equivariant transformers on commodity GPUs.

Applications · Chemistry, Physics, and Earth Sciences

Zhixiang Cheng, Hongxin Xiang, Mingquan Liu, Tengfei Ma, Yingzhuo Tu, Wenjie Du, Bosheng Song, Yiping Liu, xiangxiang Zeng

Precise property prediction of organic materials is pivotal for next-generation electronic and energy devices. In density functional theory (DFT), the electron density (ED) serves as the fundamental determinant of material properties. Yet, establishing it as an input modality for material property prediction has been impeded by two practical barriers: scarce large-scale ED data and the enormous computational complexity of ED representation. To bridge these gaps, we introduce VisionED, an efficient physics-informed model pre-trained on electron-density images. We curate a dataset of 2 million molecules and represent ED as multi-shot images that efficiently encode both geometric and electronic structure. VisionED is then pre-trained on 12 million multi-shot ED images via cross-scale, physics-informed pretext tasks. Empirical evaluations on photovoltaic and organic chromophore datasets show that VisionED outperforms state-of-the-art baselines by up to 27.0\%, exhibiting superior robustness under distribution shifts and data scarcity. Notably, the model generalizes to unseen device-scale applications, successfully recovering experimental trends and mixing-ratio effects in ternary blends with an average accuracy of 93\%. Moreover, relative to the previous ED point cloud, the ED image improves performance by 26.2\% with 2.6$\times$ fewer memory and 4.6$\times$ lower time. The code and data are available at https://anonymous.4open.science/r/VisionED-AC1B.

Applications · Chemistry, Physics, and Earth Sciences

Francisco Giral, Álvaro Sevillano, Ignacio Perez, Ricardo Vinuesa, Soledad Le Clainche

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization across unseen geometries, wind directions, and mesh resolutions without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Applications · Chemistry, Physics, and Earth Sciences

Lixing Zhang, Guijing Duan, Di Luo

We present a comprehensive benchmarking dataset and empirical scaling-law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many-body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural-network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establish a unified dataset-driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.

Deep Learning · Algorithms

Cédric Goemaere, Gaspard Oliviers, Rafal Bogacz, Thomas Demeester

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire minimization process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer biologically plausible, ePC numerically computes exact PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures on digital hardware and beyond.

Probabilistic Methods · Gaussian Processes

Hui Li, Huafeng Liu, Chenguang Li, Tianxiao Zhang, Yajun Yang, Liping Jing

Parametric partial differential equations (PDEs) serve as fundamental models across science and engineering, yet constructing fast and accurate surrogate models from sparse, irregularly sampled observations with reliable uncertainty quantification remains challenging. Existing approaches struggle to simultaneously handle variable observation patterns, preserve physics consistency, and provide well-calibrated predictive uncertainty. We introduce Bias-Spectrum Neural Processes (BSNP), a unified meta-learning framework that systematically integrates weak structural priors (translation equivariance, locality) with strong physical priors (governing equations and boundary conditions). BSNP addresses two critical obstacles: discretization overfitting through stochastic collocation that resamples residual evaluation points, and uncertainty collapse through mean-field enforcement that applies PDE constraints only to predictive means while preserving learned uncertainty. Comprehensive experiments on nonlinear Poisson equations, Burgers dynamics, and Navier-Stokes flows demonstrate that BSNP achieves superior accuracy and well-calibrated uncertainty quantification in sparse-data regimes.

Deep Learning · Large Language Models

Mihir Prabhudesai, Aryan Satpathy, Yangmin Li, Zheyang Qin, Nikash Bhardwaj, Amir Zadeh, Chuan Li, Katerina Fragkiadaki, Deepak Pathak

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question–answer (QA) pairs—a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack sufficient large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question–answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5–10 percentage points across different model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data.

Applications · Computer Vision

Nils Morbitzer, Jonathan Evers, Artem Savkin, Thomas Stauner, Nassir Navab, Federico Tombari, Stefano Gasperini

Forecasting the evolution of dynamic environments is crucial for autonomous agents. While generative world models have recently achieved high photorealism in 2D video synthesis, by mixing within the image plane ego-motion and environmental dynamics, they exhibit physical inconsistencies, such as morphing or vanishing objects, especially over long time horizons. In this paper, we propose FR3D, a world model that predicts a persistent 3D latent representation for future dynamic 3D reconstruction. Unlike prior works that treat the world as a sequence of image-based features, FR3D explicitly decouples the 3D evolution of the scene from the agent's trajectory, treating the inferred ego-motion as a latent proxy for action. This disentanglement resolves the ambiguities between self-motion and world-motion, ensuring geometric consistency into the future. Furthermore, we introduce a teacher-student distillation strategy that leverages the spatial "common sense" of off-the-shelf foundation models, leading to robust zero-shot generalization. Extensive experiments demonstrate FR3D's strong performance for future dynamic 3D reconstruction from monocular observations across multiple datasets, even 2 seconds into the future.

Reinforcement Learning · Multi-agent

Xuhui Kang, Sung-Wook Lee, Haolin Liu, Yuyan Wang, Yen-Ling Kuo

The ability to adapt to physical actions and constraints in an environment is crucial for embodied agents (e.g., robots) to effectively collaborate with humans. Such physically grounded human-AI collaboration must account for the increased complexity of the continuous state-action space and constrained dynamics caused by physical constraints. However, most existing collaboration benchmarks are discrete or do not consider physical attributes and constraints. To address this, we introduce Moving Out, a human-AI collaboration benchmark that resembles a wide range of collaboration modes affected by physical attributes and constraints, such as moving heavy items together and coordinating actions to move an item around a corner. Moving Out consists of two challenges and human-human interaction data to comprehensively evaluate models' abilities to adapt to diverse human behaviors and unseen physical attributes. To give embodied agents the capability to collaborate with humans under physical attributes and constraints, we propose a novel method, BASS (Behavior Augmentation, Simulation, and Selection), to enhance the diversity of agents and their understanding of the outcome of actions. We systematically compare BASS and state-of-the-art models in AI-AI and human-AI experiments, showing that BASS can effectively collaborate with both unseen AI and humans.

Applications · Time Series

Hua Wang, Xianhao Jiao, Fan Zhang

Deep forecasting models often suffer from attenuated periodic perception and entangled trend–noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Deep Learning · Large Language Models

Chenxiao Yang, Nati Srebro, Zhiyuan Li

Modern language models reason within bounded attention size, a physical constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in sequences that are contextually isolated. We prove that any computable problem admits a recursive decomposition where subtasks require only exponentially smaller active context than standard autoregressive models, and this approach strictly surpasses any single-context management approaches such as summarization. We further show that modern agentic systems are naturally suited for realizing recursion in a generalized way where arbitrary processing of contexts and workflows is allowed, and prove they can achieve the same power as recursive models, yet none can surpass it. Experimentally, we train a 3B model to learn recursive reasoning and evaluate on SAT, finding that it significantly outperforms frontier LLMs.

Deep Learning · Large Language Models

Udari Sehwag, Elaine Lau, Haniyeh Oskouie, Shayan Shabihi, Erich Liang, Andrea Toledo, Guillermo Mangialardi, Sergio Fonrouge, Ed-Yeremai Hernandez-Cardona, Paula Vergara 等

Accelerating scientific discovery requires the identification of which experiments would yield the best outcomes before committing resources to costly physical validation. While existing benchmarks evaluate LLMs on scientific knowledge and reasoning, their ability to predict experimental outcomes---a task where AI could significantly exceed human capabilities---remains largely underexplored. We introduce SciPredict, a benchmark comprising 405 tasks derived from recent empirical studies in 33 specialized sub-fields of physics, biology, and chemistry. SciPredict addresses two critical questions: (a) *can LLMs predict the outcome of scientific experiments with sufficient accuracy?* and (b) *can such predictions be reliably used in the scientific research process?* Evaluations reveal fundamental limitations on both fronts. Model accuracies are 14-26\% and human expert performance is $\approx$20\%. Although some frontier models exceed human performance model accuracy is still far below what would enable reliable experimental guidance. Even within the limited performance, models fail to distinguish reliable predictions from unreliable ones, achieving only $\approx$20\% accuracy regardless of their confidence or whether they judge outcomes as predictable without physical experimentation. Human experts, in contrast, demonstrate strong calibration: their accuracy increases from $\approx$5\% to $\approx$80\% as they deem outcomes more predictable without conducting the experiment. SciPredict establishes a rigorous framework demonstrating that superhuman performance in experimental science requires not just better predictions, but better awareness of prediction reliability. For reproducibility all our data and code are provided at https://anonymous.4open.science/r/SciPredict-AI01.

Applications · Chemistry, Physics, and Earth Sciences

In Huh, Changwook Jeong, Muhammad Alam

Data-driven dynamical system models often fail to recover the long-term structure of the underlying system, as their behavior is weakly constrained off the data manifold. Conjugacy-based approaches address this limitation by learning a diffeomorphism that pushes forward a source vector field to match observed dynamics, inheriting qualitative topology from the source. However, such methods typically presuppose that the chosen source system is topologically compatible with the target data. When this assumption is violated, the conjugacy problem becomes ill-posed, and arbitrary corrections can be traded off against diffeomorphic variation, leading to non-identifiability. We propose a framework that relaxes this assumed prior by jointly learning the diffeomorphic conjugacy together with controlled adjustments to the source dynamics via low-dimensional context modulation. Inspired by versal unfolding theory, we enforce the modulation space to be orthogonal to the worst-case orbit-tangent directions, obtained by adversarially searching over a class of parameterized diffeomorphisms. This promotes an identifiable decomposition of dynamical variation into diffeomorphic and intrinsic, topology-changing components, enabling interpretable corrections that recover the canonical structure such as normal forms and symmetries.