Rayleigh-Taylor instability (RTI) is of fundamental importance in fields such as inertial confinement fusion and supernova explosions, and its evolution is commonly described by potential--flow theory and buoyancy--drag models. However, both types of models struggle to accurately capture the overshoot behavior of bubble and spike velocities, as well as the subsequent reacceleration stage. To address these limitations, we develop a physics-constrained, data-driven framework based on the integral formulation of Sparse Identification of Nonlinear Dynamics (SINDy), which extracts low-dimensional dynamical equations for bubble and spike evolution directly from data. By introducing the nondimensional initial amplitude $A_0 = kη_0$ as an explicit parameter, we identify distinct dynamical equations for the bubble and the spike based on data spanning multiple Atwood numbers and initial amplitudes. The resulting low-dimensional dynamical equations not only reproduce the overshoot behavior of the velocity with good accuracy, but also capture the reacceleration stage well, while maintaining high predictive accuracy at unseen values of the wavenumber, acceleration, and Atwood number. This work provides a physics-constrained, data-driven framework complementary to conventional potential-flow and buoyancy--drag models, accurately describing the dynamical evolution of the bubble and spike at high Atwood numbers, and provides a new perspective for directly extracting the dynamical equations of interfacial instabilities from data.
Personalized neural audio watermarking systems embed user-specific payloads into audio to trace the user associated with a leaked or misused copy. Existing evaluations mainly assume access to a single personalized copy, but real-world distribution may expose multiple copies of the same recording. We find that simple sample-wise averaging breaks traceability: averaging only two copies produces tracing-failure rates of 87.7-99.7% across the five systems while largely preserving audio quality. Decoder outputs show distinct responses to coalition payload composition across systems, with high majority agreement in TimbreWM but substantially lower agreement in WMCodec. In a more sophisticated payload-aware setting, mixture weighting can further steer the decoder toward a selected nonmember, achieving a target success rate of 92.3% in TimbreWM. Preliminary confidence screening rejects many collusion-induced assignments while retaining most valid single-copy outputs. Code and results are available at https://github.com/Silwan5z/neural-audio-watermark-collusion-attack. This work highlights multi-copy traceability as an additional evaluation dimension for personalized neural audio watermarking alongside conventional single-copy robustness.
Separating touching nuclei requires local boundary detail, while cell type classification requires broader morphological context. These requirements also vary with the surrounding tissue environment. We propose the Tissue-Conditioned Adaptive Cross-Branch Interaction Network (TCINet), a single-stage model with Task-Specific Feature Adapters (TSFA) and Tissue-Conditioned Task-Aware Cross-Branch Interaction (TC-TACBI). TSFA produces branch-specific features at skip connections, and TC-TACBI controls three asymmetric paths among nucleus-presence (NP), horizontal-vertical (HV), and nucleus-type (NT) branches using predicted tissue probabilities. On PanNuke under standard three-fold cross-validation, TCINet achieves multiclass and binary panoptic quality scores of 0.519 and 0.692, respectively. Zero-shot tests on MoNuSeg yield a detection F1 score of 0.876. On PanNuke fold 0, adding TC-TACBI increases mPQ from 0.505 to 0.525. Code is available at https://github.com/celestial1321/TCINet.