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We propose the $\textit{lifted linear model}$, and derive model-free prediction intervals that become tighter as the correlation between predictions and observations increases. These intervals motivate the $\textit{Lifted Coefficient of Determination}$, a model comparison criterion for arbitrary loss functions in prediction-based settings, e.g., regression, classification or counts. We extend the prediction intervals to more general error distributions, and propose a fast model-free outlier detection algorithm for regression. Finally, we illustrate the framework via numerical experiments., Comment: 14 pages, 5 figures

The high binding affinity of antibodies towards their cognate targets is key to eliciting effective immune responses, as well as to the use of antibodies as research and therapeutic tools. Here, we propose ANTIPASTI, a Convolutional Neural Network model that achieves state-of-the-art performance in the prediction of antibody binding affinity using as input a representation of antibody-antigen structures in terms of Normal Mode correlation maps derived from Elastic Network Models. This representation captures not only structural features but energetic patterns of local and global residue fluctuations. The learnt representations are interpretable: they reveal similarities of binding patterns among antibodies targeting the same antigen type, and can be used to quantify the importance of antibody regions contributing to binding affinity. Our results show the importance of the antigen imprint in the Normal Mode landscape, and the dominance of cooperative effects and long-range correlations between antibody regions to determine binding affinity.

We present STARRED, a Point Spread Function (PSF) reconstruction, two-channel deconvolution, and light curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, STARRED performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a deep sharp frame combining all data, and the photometry of all point sources in the field of view as a function of time. Of note, STARRED also provides exquisite PSF models for each data frame. We showcase three applications of STARRED in the context of the imminent LSST survey and of JWST imaging: i) the extraction of supernovae light curves and the scene representation of their host galaxy, ii) the extraction of lensed quasar light curves for time-delay cosmography, and iii) the measurement of the spectral energy distribution of globular clusters in the "Sparkler", a galaxy at redshift z=1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. STARRED is implemented in JAX, leveraging automatic differentiation and GPU acceleration. This enables rapid processing of large time-domain datasets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects., Comment: 20 pages, 11 figures, 3 Tables. Published in the Astronomical Journal

The spatial resolution of astronomical images is limited by atmospheric turbulence and diffraction in the telescope optics, resulting in blurred images. This makes it difficult to accurately measure the brightness of blended objects because the contributions from adjacent objects are mixed in a time-variable manner due to changes in the atmospheric conditions. However, this effect can be corrected by characterizing the Point Spread Function (PSF), which describes how a point source is blurred on a detector. This function can be estimated from the stars in the field of view, which provides a natural sampling of the PSF across the entire field of view. Once the PSF is estimated, it can be removed from the data through the so-called deconvolution process, leading to images of improved spatial resolution. The deconvolution operation is an ill-posed inverse problem due to noise and pixelization of the data. To solve this problem, regularization is necessary to guarantee the robustness of the solution. Regularization can take the form of a sparse prior, meaning that the recovered solution can be represented with only a few basis eigenvectors. STARRED is a Python package developed in the context of the COSMOGRAIL collaboration and applies to a vast variety of astronomical problems. It proposes to use an isotropic wavelet basis, called Starlets, to regularize the solution of the deconvolution problem. This family of wavelets has been shown to be well-suited to represent astronomical objects. STARRED provides two modules to first reconstruct the PSF, and then perform the deconvolution. It is based on two key concepts: i) the image is reconstructed in two separate channels, one for the point sources and one for the extended sources, and ii) the code relies on the deliberate choice of not completely removing the effect of the PSF, but rather bringing the image to a higher resolution.

With the onset of large-scale astronomical surveys capturing millions of images, there is an increasing need to develop fast and accurate deconvolution algorithms that generalize well to different images. A powerful and accessible deconvolution method would allow for the reconstruction of a cleaner estimation of the sky. The deconvolved images would be helpful to perform photometric measurements to help make progress in the fields of galaxy formation and evolution. We propose a new deconvolution method based on the Learnlet transform. Eventually, we investigate and compare the performance of different Unet architectures and Learnlet for image deconvolution in the astrophysical domain by following a two-step approach: a Tikhonov deconvolution with a closed-form solution, followed by post-processing with a neural network. To generate our training dataset, we extract HST cutouts from the CANDELS survey in the F606W filter (V-band) and corrupt these images to simulate their blurred-noisy versions. Our numerical results based on these simulations show a detailed comparison between the considered methods for different noise levels., Comment: 15 pages, 5 figures