Black hole perturbation theory for Kerr black holes is best studied in the Newman Penrose Formalism, in which gravitational waves are described as perturbations in the Weyl scalars $psi_0$ and $psi_4$, with the governing equation being the well-known
Teukolsky equation. Near infinity and near horizon, $psi_4$ is dominated by the component that corresponds to waves propagating towards the positive radial direction, while $psi_0$ is dominated by the component that corresponds to waves that propagate towards the negative radial direction. Since gravitational-wave detectors measure out-going waves at infinity, research has been mainly focused on $psi_4$, leaving $psi_0$ less studied. But the scenario is reversed in the near horizon region where the in-going-wave boundary condition needs to be imposed. Thus, the near horizon phenomena, e.g., tidal heating and gravitational-wave echoes from Extremely Compact Objects (ECOs), require computing $psi_0$. In this work, we explicitly calculate the source term for the $psi_0$ Teukolsky equation due to a point particle plunging into a Kerr black hole. We highlight the need to regularize the solution of the $psi_0$ Teukolsky equation obtained using Greens function techniques. We suggest a regularization scheme for this purpose and go on to compute the $psi_0$ waveform close to a Schwarzschild horizon for two types of trajectories of the in-falling particle. We compare the $psi_0$ waveform calculated directly from the Teukolsky equation with the $psi_0$ waveform obtained by using the Starobinsky-Teukolsky identity on $psi_4$. We also compute the out-going echo waveform near infinity, using the near-horizon $psi_0$ computed directly from the Teukolsky equation and the Boltzmann boundary condition on the ECO surface. We show that this echo is quantitatively different (stronger) than the echo obtained using previous prescriptions. (abridged)
Image-to-image translation plays a vital role in tackling various medical imaging tasks such as attenuation correction, motion correction, undersampled reconstruction, and denoising. Generative adversarial networks have been shown to achieve the stat
e-of-the-art in generating high fidelity images for these tasks. However, the state-of-the-art GAN-based frameworks do not estimate the uncertainty in the predictions made by the network that is essential for making informed medical decisions and subsequent revision by medical experts and has recently been shown to improve the performance and interpretability of the model. In this work, we propose an uncertainty-guided progressive learning scheme for image-to-image translation. By incorporating aleatoric uncertainty as attention maps for GANs trained in a progressive manner, we generate images of increasing fidelity progressively. We demonstrate the efficacy of our model on three challenging medical image translation tasks, including PET to CT translation, undersampled MRI reconstruction, and MRI motion artefact correction. Our model generalizes well in three different tasks and improves performance over state of the art under full-supervision and weak-supervision with limited data. Code is released here: https://github.com/ExplainableML/UncerGuidedI2I
Using gravitational wave observations to search for deviations from general relativity in the strong-gravity regime has become an important research direction. Chern Simons (CS) gravity is one of the most frequently studied parity-violating models of
strong gravity. It is known that the Kerr black-hole is not a solution for CS gravity. At the same time, the only rotating solution available in the literature for dynamical CS (dCS) gravity is the slow-rotating case most accurately known to quadratic order in spin. In this work, for the slow-rotating case (accurate to first order in spin), we derive the linear perturbation equations governing the metric and the dCS field accurate to linear order in spin and quadratic order in the CS coupling parameter ($alpha$) and obtain the quasi-normal mode (QNM) frequencies. After confirming the recent results of Wagle et al. (2021), we find an additional contribution to the eigenfrequency correction at the leading perturbative order of $alpha^2$. Unlike Wagle et al., we also find corrections to frequencies in the polar sector. We compute these extra corrections by evaluating the expectation values of the perturbative potential on unperturbed QNM wavefunctions along a contour deformed into the complex-$r$ plane. For $alpha=0.1 M^2$, we obtain the ratio of the imaginary parts of the dCS correction to the GR correction in the first QNM frequency (in the polar sector) to be $0.263$ implying significant change. For the $(2,2)-$mode, the dCS corrections make the imaginary part of the first QNM of the fundamental mode less negative, thereby decreasing the decay rate. Our results, along with future gravitational wave observations, can be used to test for dCS gravity and further constrain the CS coupling parameters. [abridged]
Explaining the decision of a multi-modal decision-maker requires to determine the evidence from both modalities. Recent advances in XAI provide explanations for models trained on still images. However, when it comes to modeling multiple sensory modal
ities in a dynamic world, it remains underexplored how to demystify the mysterious dynamics of a complex multi-modal model. In this work, we take a crucial step forward and explore learnable explanations for audio-visual recognition. Specifically, we propose a novel space-time attention network that uncovers the synergistic dynamics of audio and visual data over both space and time. Our model is capable of predicting the audio-visual video events, while justifying its decision by localizing where the relevant visual cues appear, and when the predicted sounds occur in videos. We benchmark our model on three audio-visual video event datasets, comparing extensively to multiple recent multi-modal representation learners and intrinsic explanation models. Experimental results demonstrate the clear superior performance of our model over the existing methods on audio-visual video event recognition. Moreover, we conduct an in-depth study to analyze the explainability of our model based on robustness analysis via perturbation tests and pointing games using human annotations.
Having access to multi-modal cues (e.g. vision and audio) empowers some cognitive tasks to be done faster compared to learning from a single modality. In this work, we propose to transfer knowledge across heterogeneous modalities, even though these d
ata modalities may not be semantically correlated. Rather than directly aligning the representations of different modalities, we compose audio, image, and video representations across modalities to uncover richer multi-modal knowledge. Our main idea is to learn a compositional embedding that closes the cross-modal semantic gap and captures the task-relevant semantics, which facilitates pulling together representations across modalities by compositional contrastive learning. We establish a new, comprehensive multi-modal distillation benchmark on three video datasets: UCF101, ActivityNet, and VGGSound. Moreover, we demonstrate that our model significantly outperforms a variety of existing knowledge distillation methods in transferring audio-visual knowledge to improve video representation learning. Code is released here: https://github.com/yanbeic/CCL.
Unpaired image-to-image translation refers to learning inter-image-domain mapping in an unsupervised manner. Existing methods often learn deterministic mappings without explicitly modelling the robustness to outliers or predictive uncertainty, leadin
g to performance degradation when encountering unseen out-of-distribution (OOD) patterns at test time. To address this limitation, we propose a novel probabilistic method called Uncertainty-aware Generalized Adaptive Cycle Consistency (UGAC), which models the per-pixel residual by generalized Gaussian distribution, capable of modelling heavy-tailed distributions. We compare our model with a wide variety of state-of-the-art methods on two challenging tasks: unpaired image denoising in the natural image and unpaired modality prorogation in medical image domains. Experimental results demonstrate that our model offers superior image generation quality compared to recent methods in terms of quantitative metrics such as signal-to-noise ratio and structural similarity. Our model also exhibits stronger robustness towards OOD test data.
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wa
ve boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to in-going gravitational waves, respond to these waves, and generate out-going waves. As it also turns out, if both in-going and out-going waves exist near the horizon, the Newman Penrose (NP) quantity $psi_0$ will be numerically dominated by the in-going wave, while the NP quantity $psi_4$ will be dominated by the out-going wave. In this way, we obtain the ECO boundary condition in the form of a relation between $psi_0$ and the complex conjugate of $psi_4$, in a way that is determined by the ECOs tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame, and deduce the corresponding ECO boundary condition for Teukolsky functions. We subsequently obtain the boundary condition for $psi_4$ alone, as well as for the Sasaki-Nakamura and Detweilers functions. As it also turns out, reflection of spinning ECOs will generically mix between different $ell$ components of the perturbations fields, and be different for perturbations with different parities. We also apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and solve for the spinning ECOs quasi-normal modes.
Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using non-classical states and quantum filters, which modify both the noise and signal response. We find a novel approach to r
ealising quantum filters directly from their frequency-domain transfer functions, utilising techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show a new optical realisation of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.
The second generation of gravitational-wave detectors are being built and tuned all over the world. The detection of signals from binary black holes is beginning to fulfill the promise of gravitational-wave astronomy. In this work, we examine several
possible configurations for third-generation laser interferometers in existing km-scale facilities. We propose a set of astrophysically motivated metrics to evaluate detector performance. We measure the impact of detector design choices against these metrics, providing a quantitative cost-benefit analyses of the resulting scientific payoffs.
Exotic compact objects (ECOs) have recently become an exciting research subject, since they are speculated to have a special response to the incident gravitational waves (GWs) that leads to GW echoes. We show that energy carried by GWs can easily cau
se the event horizon to form out of a static ECO --- leaving no echo signals towards spatial infinity. To show this, we use the ingoing Vaidya spacetime and take into account the back reaction due to incoming GWs. Demanding that an ECO does not collapse into a black hole puts an upper bound on the compactness of the ECO, at the cost of less distinct echo signals for smaller compactness. The trade-off between echoes detectability and distinguishability leads to a fine tuning of ECO parameters for LIGO to find distinct echoes. We also show that an extremely compact ECO that can survive the gravitational collapse and give rise to GW echoes might have to expand its surface in a non-causal way.
