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Oct 29

Astrometric Effects of a Stochastic Gravitational Wave Background

A stochastic gravitational wave background causes the apparent positions of distant sources to fluctuate, with angular deflections of order the characteristic strain amplitude of the gravitational waves. These fluctuations may be detectable with high precision astrometry, as first suggested by Braginsky et al. in 1990. Several researchers have made order of magnitude estimates of the upper limits obtainable on the gravitational wave spectrum \Omega_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future space-based optical interferometry missions GAIA and SIM, and for VLBI interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6 quasars over a time of T ~ 1 yr with an angular accuracy of \Delta \theta ~ 10 \mu as would yield a sensitivity level of \Omega_gw ~ (\Delta \theta)^2/(N T^2 H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we take a first step toward firming up these estimates by computing in detail the statistical properties of the angular deflections caused by a stochastic background. We compute analytically the two point correlation function of the deflections on the sphere, and the spectrum as a function of frequency and angular scale. The fluctuations are concentrated at low frequencies (for a scale invariant stochastic background), and at large angular scales, starting with the quadrupole. The magnetic-type and electric-type pieces of the fluctuations have equal amounts of power.

  • 2 authors
·
Sep 21, 2010

Beyond No: Quantifying AI Over-Refusal and Emotional Attachment Boundaries

We present an open-source benchmark and evaluation framework for assessing emotional boundary handling in Large Language Models (LLMs). Using a dataset of 1156 prompts across six languages, we evaluated three leading LLMs (GPT-4o, Claude-3.5 Sonnet, and Mistral-large) on their ability to maintain appropriate emotional boundaries through pattern-matched response analysis. Our framework quantifies responses across seven key patterns: direct refusal, apology, explanation, deflection, acknowledgment, boundary setting, and emotional awareness. Results demonstrate significant variation in boundary-handling approaches, with Claude-3.5 achieving the highest overall score (8.69/10) and producing longer, more nuanced responses (86.51 words on average). We identified a substantial performance gap between English (average score 25.62) and non-English interactions (< 0.22), with English responses showing markedly higher refusal rates (43.20% vs. < 1% for non-English). Pattern analysis revealed model-specific strategies, such as Mistral's preference for deflection (4.2%) and consistently low empathy scores across all models (< 0.06). Limitations include potential oversimplification through pattern matching, lack of contextual understanding in response analysis, and binary classification of complex emotional responses. Future work should explore more nuanced scoring methods, expand language coverage, and investigate cultural variations in emotional boundary expectations. Our benchmark and methodology provide a foundation for systematic evaluation of LLM emotional intelligence and boundary-setting capabilities.

  • 2 authors
·
Feb 20 3

Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

  • 6 authors
·
May 14