The spherical harmonics m-mode decomposition is a powerful sky map reconstruction method suitable for radio interferometers operating in transit mode. It can be applied to various configurations, ...including dish arrays and cylinders. We describe the computation of the instrument response function, the point spread function, transfer function, the noise covariance matrix and noise power spectrum. The analysis in this paper is focused on dish arrays operating in transit mode. We show that arrays with regular spacing have more pronounced side lobes as well as structures in their noise power spectrum, compared to arrays with irregular spacing, specially in the north–south direction. A good knowledge of the noise power spectrum C
noise(ℓ) is essential for intensity mapping experiments as non-uniform C
noise(ℓ) is a potential problem for the measurement of the H i power spectrum. Different configurations have been studied to optimize the PAON-4 and Tianlai dish array layouts. We present their expected performance and their sensitivities to the 21-cm emission of the Milky Way and local extragalactic H i clumps.
Diffuse low grade gliomas are invasive and incurable brain tumors that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, ...the tumor gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient's health-related quality of life and help clinicians build personalized follow-ups, one would benefit from predictions of the time during which the tumor is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyze the tumor size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumor size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75% of the cases, in particular for all "fast-responders". The remaining 25% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalized predictions of the tumor regrowth time shortly after RT.
ABSTRACT
The Tianlai Dish Pathfinder Array is a radio interferometer designed to test techniques for 21 cm intensity mapping in the post-reionization universe as a means for measuring large-scale ...cosmic structure. It performs drift scans of the sky at constant declination. We describe the design, calibration, noise level, and stability of this instrument based on the analysis of about 5% of 6200 h of on-sky observations through 2019 October. Beam pattern determinations using drones and the transit of bright sources are in good agreement, and compatible with electromagnetic simulations. Combining all the baselines, we make maps around bright sources and show that the array behaves as expected. A few hundred hours of observations at different declinations have been used to study the array geometry and pointing imperfections, as well as the instrument noise behaviour. We show that the system temperature is below 80 K for most feed antennas and that noise fluctuations decrease as expected with integration time, at least up to a few hundred seconds. Analysis of long integrations, from 10 nights of observations of the North Celestial Pole (NCP), yielded visibilities with amplitudes of 20–30 mK, consistent with the expected signal from the NCP radio sky with ${\lt}10\,$ mK precision for 1 MHz × 1 min binning. Hi-pass filtering the spectra to remove smooth spectrum signal yields a residual consistent with zero signal at the $0.5\,$ mK level.
Aims. The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular, the matter power spectrum P(k) provides information about the ...cosmological distance evolution and the galaxy clustering. However the building of P(k) from galaxy catalogs requires a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted P(k) from other cosmological models, and for photometric surveys like the Large Synoptic Survey Telescope (LSST). The angular power spectrum Cℓ(z1,z2) between two bins located at redshift z1 and z2 contains the same information as the matter power spectrum, and is free from any cosmological assumption, but the prediction of Cℓ(z1,z2) from P(k) is a costly computation when performed precisely. Methods. The Angpow software aims at quickly and accurately computing the auto (z1 = z2) and cross (z1 ≠ z2) angular power spectra between redshift bins. We describe the developed algorithm based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Results. Angpow is flexible and can handle any user-defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the Cℓ(z1,z2) comparison with data. We emphasize that the Limber’s approximation, often used to speed up the computation, gives incorrect Cℓ values for cross-correlations.
In the near future, cosmology will enter the wide and deep galaxy survey era, enabling high-precision studies of the large-scale structure of the universe in three dimensions. To test cosmological ...models and determine their parameters accurately, it is necessary to use data with exact theoretical expectations expressed in observational parameter space (angles and redshift). The data-driven, galaxy number count fluctuations on redshift shells can be used to build correlation functions on and between shells to probe the baryonic acoustic oscillations and distance-redshift distortions, as well as gravitational lensing and other relativistic effects. To obtain a numerical estimation of from a cosmological model, it is typical to use either a closed form derived from a tripolar spherical expansion or to compute the power spectrum and perform a Legendre polynomial expansion. Here, we present a new derivation of a closed form using the spherical harmonic expansion and proceeding to an infinite sum over multipoles thanks to an addition theorem. We demonstrate that this new expression is perfectly compatible with the existing closed forms but is simpler to establish and manipulate. We provide formulas for the leading density and redshift-space contributions, but also show how Doppler-like and lensing terms can be easily included in this formalism. We have implemented and made publicly available software for computing those correlations efficiently, without any Limber approximation, and validated this software with the CLASSgal code. It is available at https://gitlab.in2p3.fr/campagne/AngPow.
This paper aims to explore the evolution of image denoising in a pedagological way. We briefly review classical methods such as Fourier analysis and wavelet bases, highlighting the challenges they ...faced until the emergence of neural networks, notably the U-Net, in the 2010s. The remarkable performance of these networks has been demonstrated in studies such as Kadkhodaie et al. (2024). They exhibit adaptability to various image types, including those with fixed regularity, facial images, and bedroom scenes, achieving optimal results and biased towards geometry-adaptive harmonic basis. The introduction of score diffusion has played a crucial role in image generation. In this context, denoising becomes essential as it facilitates the estimation of probability density scores. We discuss the prerequisites for genuine learning of probability densities, offering insights that extend from mathematical research to the implications of universal structures.
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