“The paper derives sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable.”

“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”

“The spectrum of the system's response -- captured by the so-called logarithmic susceptibility (LS) -- enables a direct observation of characteristic features of real-time instantons.”

“Localized shear propagated way beyond immediate neighbors and suppressed cellular migratory dynamics in stiffer layers.”

“The paper's key finding is the effectiveness of the proposed framework in reducing semantic leakage to eavesdroppers without significantly degrading performance for legitimate receivers, especially through the use of adversarial perturbations.”

“The paper demonstrates that the number of physical measures varies upper semi-continuously.”

“The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior.”

“In cases V and VI, the Hamiltonian analysis yields 8 degrees of freedom, while only 6 and 5 modes are visible at linear order in perturbations, respectively. This indicates that additional modes are strongly coupled on cosmological backgrounds.”

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The article is based on research published on ArXiv, a repository for scientific preprints.”

“The paper identifies an anomalous decay pattern where excited modes decay slower than the fundamental mode when the charge coupling is large.”

“The paper reveals the formation of the Poisson spot and pronounced wavefront distortions, and finds significant discrepancies with conventional methods at high frequencies.”

“The results show that attention-based adversarial examples lead to measurable drops in evaluation performance while remaining semantically similar to the original inputs.”

“The paper describes how to construct a spanning set of linearly-independent, automatically orthogonal colour tensors for scattering amplitudes involving coloured particles transforming under arbitrary representations of any gauge theory.”

“The phenomenology of the resulting correlators presents some novel features, such as oscillations with an envelope controlled by the anomalous dimension, rather than the usual value of 3/2.”

“Responses to different perturbation types are dynamically incompatible when they occur in separate experiments... On the other hand, if both perturbation types are presented at random during the same experiment then the responses are compatible with each other and can be construed as produced by a unique underlying mechanism.”

“The paper focuses on Trustworthy Machine Learning under Distribution Shifts, aiming to expand AI's robustness, versatility, as well as its responsibility and reliability.”

“The title itself provides the core information: the subject is Van der Waals interactions, and the approach is pedagogical, using perturbation theory.”

“RobustMask successfully certifies over 20% of candidate documents within the top-10 ranking positions against adversarial perturbations affecting up to 30% of their content.”

“The paper finds that in (3+1) dimensions the scalar Love number is generically nonzero, while the Fermionic Love numbers follow a universal power-law. In (2+1) dimensions, the scalar field exhibits a logarithmic structure, and the Fermionic Love number retains a simple power-law form.”

“Our results mathematically characterize the background magnetic field exerts the stabilizing effect, and bridge the gap left by previous work with respect to the asymptotic behavior in time.”

“Technological bottlenecks can be conceptualized a bit like keystone species in ecology. Both exert disproportionate systemic influence—their removal triggers non-linear cascades rather than proportional change.”

“OLS can withstand up to $k \ll \sqrt{np}/\log n$ sample removals while remaining robust and achieving the same error rate.”

“The paper finds that PBHs can account for all or a fraction of dark matter, depending on the coupling constant and e-folds number.”

“Threshold rules produce a distinct non-mean-field universality class with β≈0.75 and a systematic failure of MF-DP dynamical scaling. We show that thresholding acts as a relevant perturbation to DP.”

“Schrödinger AI demonstrates: (a) emergent semantic manifolds that reflect human-conceived class relations without explicit supervision; (b) dynamic reasoning that adapts to changing environments, including maze navigation with real-time potential-field perturbations; and (c) exact operator generalization on modular arithmetic tasks, where the system learns group actions and composes them across sequences far beyond training length.”

“The research likely investigates methods to counteract signal distortions caused by nonlinearities in optical fibers.”

“Quantum errors can be modeled as deterministic physical terms rather than purely stochastic perturbations.”

“The paper demonstrates the reconstruction of short-range perturbations from scattering data in a linearized and finite-dimensional setting, along with a stability result.”

“GatedBias introduces structure-gated adaptation: profile-specific features combine with graph-derived binary gates to produce interpretable, per-entity biases, requiring only ${\sim}300$ trainable parameters.”

“The algorithm solves weighted MaxCut instances with up to 1000 vertices using only 10 qubits, and numerical results indicate that it consistently outperforms the Goemans-Williamson algorithm.”

“eFEONet augments the operator-learning framework with specialized enrichment basis functions that encode the asymptotic structure of layer solutions.”

“By concentrating adversarial perturbations on these positions, we achieve semantic degradation comparable to global methods while using substantially smaller budgets. More importantly, across multiple representative VLMs, such selective attacks convert 35-49% of benign outputs into harmful ones, exposing a more critical safety risk.”

“The paper introduces a private estimator for the $p_0$ model parameters and demonstrates its asymptotic properties.”

“Tokenizers provide the fundamental basis through which text is represented and processed by language models (LMs).”

“The article's focus is on acoustic gravitational waves originating from primordial curvature perturbations.”

“This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.”

“The research focuses on interpretable perturbation modeling.”

“The article's context focuses on the application of integrable perturbation theory to the defocusing nonlinear Schrödinger equation.”

“”

“The article's context indicates it originates from ArXiv, a repository for scientific preprints.”

“”

“The article's content is not available, so a specific quote cannot be provided. The focus is on the formula itself.”

“The paper introduces the CHIP algorithm.”

“”

“”

“”

“The article's focus is on image protection methods for diffusion models.”

“The article likely focuses on the sensitivity of the AI model to small changes in the input data, a crucial aspect of real-world application.”

“”