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L. V. E. Koopmans

Publications and source records attributed to L. V. E. Koopmans.

At least 37 records · Page 2Linked to original sources

Using Convolutional Neural Networks to Search for Strongly Lensed Quasars in KiDS DR5

Gravitationally strongly lensed quasars (SL-QSO) offer invaluable insights into cosmological and astrophysical phenomena. With the data from ongoing and next-generation surveys, thousands of SL-QSO systems can be discovered expectedly, leading to unprecedented opportunities. However, the challenge lies in identifying SL-QSO from enormous datasets with high recall and purity in an automated and efficient manner. Hence, we developed a program based on a Convolutional Neural Network (CNN) for finding SL-QSO from large-scale surveys and applied it to the Kilo-degree Survey Data Release 5 (KiDS DR5). Our approach involves three key stages: firstly, we pre-selected ten million bright objects (with $r$-band $\tt{MAG\_AUTO} < 22$), excluding stars from the dataset; secondly, we established realistic training and test sets to train and fine-tune the CNN, resulting in the identification of 4195 machine candidates, and the false positive rate (FPR) of $\sim$1/2000 and recall of 0.8125 evaluated by using the real test set containing 16 confirmed lensed quasars; thirdly, human inspections were performed for further selections, and then 272 SL-QSO candidates were eventually found in total, including 16 high-score, 118 median-score, and 138 lower-score candidates, separately. Removing the systems already confirmed or identified in other papers, we end up with 229 SL-QSO candidates, including 7 high-score, 95 median-score, and 127 lower-score candidates, and the corresponding catalog is publicly available online. We have also included an excellent quad candidate in the appendix, discovered serendipitously during the fine-tuning process of the CNN.

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Beyond the horizon: Quantifying the full sky foreground wedge in the cylindrical power spectrum

One of the main obstacles preventing the detection of the redshifted 21-cm signal from neutral hydrogen in the early Universe is the astrophysical foreground emission, which is several orders of magnitude brighter than the signal. The foregrounds, due to their smooth spectra, are expected to predominantly occupy a region in the cylindrical power spectrum known as the foreground wedge. However, the conventional equations describing the extent of the foreground wedge are derived under a flat-sky approximation. This assumption breaks down for tracking wide-field instruments, thus rendering these equations inapplicable in these situations. In this paper, we derive equations for the full sky foreground wedge and show that the foregrounds can potentially extend far beyond what the conventional equations suggest. We also derive the equations that describe a specific bright source in the cylindrical power spectrum space. The validity of both sets of equations is tested against numerical simulations. Many current and upcoming interferometers (e.g., LOFAR, NenuFAR, MWA, SKA) are wide-field phase-tracking instruments. These equations give us new insights into the nature of foreground contamination in the cylindrical power spectra estimated using wide-field instruments. Additionally, they allow us to accurately associate features in the power spectrum to foregrounds or instrumental effects. The equations are also important for correctly selecting the "EoR window" for foreground avoidance analyses, and for planning 21-cm observations. In future analyses, it is recommended to use these updated horizon lines to indicate the foreground wedge in the cylindrical power spectrum accurately. The new equations for generating the updated wedge lines are made available in a Python library, pslines.

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Euclid: Searches for strong gravitational lenses using convolutional neural nets in Early Release Observations of the Perseus field

The Euclid Wide Survey (EWS) is predicted to find approximately 170 000 galaxy-galaxy strong lenses from its lifetime observation of 14 000 deg^2 of the sky. Detecting this many lenses by visual inspection with professional astronomers and citizen scientists alone is infeasible. Machine learning algorithms, particularly convolutional neural networks (CNNs), have been used as an automated method of detecting strong lenses, and have proven fruitful in finding galaxy-galaxy strong lens candidates. We identify the major challenge to be the automatic detection of galaxy-galaxy strong lenses while simultaneously maintaining a low false positive rate. One aim of this research is to have a quantified starting point on the achieved purity and completeness with our current version of CNN-based detection pipelines for the VIS images of EWS. We select all sources with VIS IE < 23 mag from the Euclid Early Release Observation imaging of the Perseus field. We apply a range of CNN architectures to detect strong lenses in these cutouts. All our networks perform extremely well on simulated data sets and their respective validation sets. However, when applied to real Euclid imaging, the highest lens purity is just 11%. Among all our networks, the false positives are typically identifiable by human volunteers as, for example, spiral galaxies, multiple sources, and artefacts, implying that improvements are still possible, perhaps via a second, more interpretable lens selection filtering stage. There is currently no alternative to human classification of CNN-selected lens candidates. Given the expected 10^5 lensing systems in Euclid, this implies 10^6 objects for human classification, which while very large is not in principle intractable and not without precedent.

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Assessing the impact of two independent direction-dependent calibration algorithms on the LOFAR 21-cm signal power spectrum

Detecting the 21-cm signal from the Epoch of Reionisation (EoR) is challenging due to the strong astrophysical foregrounds, ionospheric effects, radio frequency interference and instrumental effects. Understanding and calibrating these effects are crucial for the detection. In this work, we introduce a newly developed direction-dependent (DD) calibration algorithm DDECAL and compare its performance with an existing algorithm, SAGECAL, in the context of the LOFAR-EoR 21-cm power spectrum experiment. In our data set, the North Celestial Pole (NCP) and its flanking fields were observed simultaneously. We analyse the NCP and one of its flanking fields. The NCP field is calibrated by the standard pipeline, using SAGECAL with an extensive sky model and 122 directions, and the flanking field is calibrated by DDECAL and SAGECAL with a simpler sky model and 22 directions. Additionally, two strategies are used for subtracting Cassiopeia A and Cygnus A. The results show that DDECAL performs better at subtracting sources in the primary beam region due to the application of a beam model, while SAGECAL performs better at subtracting Cassiopeia A and Cygnus A. This indicates that including a beam model during DD calibration significantly improves the performance. The benefit is obvious in the primary beam region. We also compare the 21-cm power spectra on two different fields. The results show that the flanking field produces better upper limits compared to the NCP in this particular observation. Despite the minor differences between DDECAL and SAGECAL due to the beam application, we find that the two algorithms yield comparable 21-cm power spectra on the LOFAR-EoR data after foreground removal. Hence, the current LOFAR-EoR 21-cm power spectrum limits are not likely to depend on the DD calibration method.

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Galaxy-Galaxy Strong Lensing with U-Net (GGSL-UNet). I. Extracting 2-Dimensional Information from Multi-Band Images in Ground and Space Observations

We present a novel deep learning method to separately extract the two-dimensional flux information of the foreground galaxy (deflector) and background system (source) of Galaxy-Galaxy Strong Lensing events using U-Net (GGSL-Unet for short). In particular, the segmentation of the source image is found to enhance the performance of the lens modeling, especially for ground-based images. By combining mock lens foreground+background components with real sky survey noise to train the GGSL-Unet, we show it can correctly model the input image noise and extract the lens signal. However, the most important result of this work is that the GGSL-UNet can accurately reconstruct real ground-based lensing systems from the Kilo Degree Survey (KiDS) in one second. We also test the GGSL-UNet on space-based (HST) lenses from BELLS GALLERY, and obtain comparable accuracy of standard lens modeling tools. Finally, we calculate the magnitudes from the reconstructed deflector and source images and use this to derive photometric redshifts (photo-z), with the photo-z of the deflector well consistent with spectroscopic ones. This first work, demonstrates the great potential of the generative network for lens finding, image denoising, source segmentation, and decomposing and modeling of strong lensing systems. For the upcoming ground- and space-based surveys, the GGSL-UNet can provide high-quality images as well as geometry and redshift information for precise lens modeling, in combination with classical MCMC modeling for best accuracy in the galaxy-galaxy strong lensing analysis.

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Ionospheric contributions to the excess power in high-redshift 21-cm power-spectrum observations with LOFAR

The turbulent ionosphere causes phase shifts to incoming radio waves on a broad range of temporal and spatial scales. When an interferometer is not sufficiently calibrated for the direction-dependent ionospheric effects, the time-varying phase shifts can cause the signal to decorrelate. The ionosphere's influence over various spatiotemporal scales introduces a baseline-dependent effect on the interferometric array. We study the impact of baseline-dependent decorrelation on high-redshift observations with the Low Frequency Array (LOFAR). Datasets with a range of ionospheric corruptions are simulated using a thin-screen ionosphere model, and calibrated using the state-of-the-art LOFAR Epoch of Reionisation pipeline. For the first time ever, we show the ionospheric impact on various stages of the calibration process including an analysis of the transfer of gain errors from longer to shorter baselines using realistic end-to-end simulations. We find that direction-dependent calibration for source subtraction leaves excess power of up to two orders of magnitude above the thermal noise at the largest spectral scales in the cylindrically averaged auto-power spectrum under normal ionospheric conditions. However, we demonstrate that this excess power can be removed through Gaussian process regression, leaving no excess power above the ten per cent level for a $5~$km diffractive scale. We conclude that ionospheric errors, in the absence of interactions with other aggravating effects, do not constitute a dominant component in the excess power observed in LOFAR Epoch of Reionisation observations of the North Celestial Pole. Future work should therefore focus on less spectrally smooth effects, such as beam modelling errors.

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The impact of lossy data compression on the power spectrum of the high redshift 21-cm signal with LOFAR

Current radio interferometers output multi-petabyte-scale volumes of data per year making the storage, transfer, and processing of this data a sizeable challenge. This challenge is expected to grow with the next-generation telescopes such as the Square Kilometre Array. Lossy compression of interferometric data post-correlation can abate this challenge. However, since high-redshift 21-cm studies impose strict precision requirements, the impact of such lossy data compression on the 21-cm signal power spectrum statistic should be understood. We apply Dysco visibility compression, a technique to normalize and quantize specifically designed for radio interferometric data. We establish the level of the compression noise in the power spectrum in comparison to the thermal noise as well as its coherency behavior. Finally, for optimal compression results, we compare the compression noise obtained from different compression settings to a nominal 21-cm signal power. From a single night of observation, we find that the noise introduced due to the compression is more than five orders of magnitude lower than the thermal noise level in the power spectrum. The noise does not affect calibration. The compression noise shows no correlation with the sky signal and has no measurable coherent component. The level of compression error in the power spectrum ultimately depends on the compression settings. Dysco visibility compression is found to be of insignificant concern for 21-cm power spectrum studies. Hence, data volumes can be safely reduced by factors of $\sim 4$ and with insignificant bias to the final power spectrum. Data from SKA-low will likely be compressible by the same factor as LOFAR, owing to the similarities of the two instruments. The same technique can be used to compress data from other telescopes, but a small adjustment of the compression parameters might be required.

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Time-Delay Cosmography: Measuring the Hubble Constant and other cosmological parameters with strong gravitational lensing

Multiply lensed sources experience a relative time delay in the arrival of photons. This effect can be used to measure absolute distances and the Hubble constant ($H_0$) and is known as time-delay cosmography. The methodology is independent of the local distance ladder and early-universe physics and provides a precise and competitive measurement of $H_0$. With upcoming observatories, time-delay cosmography can provide a 1% precision measurement of $H_0$ and can decisively shed light on the current reported 'Hubble tension'. This paper presents the theoretical background and the current techniques applied for time-delay cosmographic studies and the measurement of the Hubble constant. The paper describes the challenges and systematics in the different components of the analysis and strategies to mitigate them. The current measurements are discussed in context and the opportunities with the anticipated data sets in the future are laid out.

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First upper limits on the 21 cm signal power spectrum from cosmic dawn from one night of observations with NenuFAR

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nançay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of $z$ = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10-85 MHz frequency range, currently under construction at the Nançay Radio Observatory in France. It is a phased array instrument with a very dense uv coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the uv plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2$σ$ upper limit of $2.4\times 10^7$ $\text{mK}^{2}$ at $z$ = 20.3 and $k$ = 0.041 $h\,\text{cMpc}^{-1}$. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future.

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Object classification with Convolutional Neural Networks: from KiDS to Euclid

Large-scale imaging surveys have grown about 1000 times faster than the number of astronomers in the last 3 decades. Using Artificial Intelligence instead of astronomer's brains for interpretative tasks allows astronomers to keep up with the data. We give a progress report on using Convolutional Neural Networks (CNNs) to classify three classes of rare objects (galaxy mergers, strong gravitational lenses and asteroids) in the Kilo-Degree Survey (KiDS) and the Euclid Survey.

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Transient RFI environment of LOFAR-LBA at 72-75 MHz: Impact on ultra-widefield AARTFAAC Cosmic Explorer observations of the redshifted 21-cm signal

Measurement of the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn (CD) and Epoch of Reionisation (EoR) promises to unveil a wealth of information about the astrophysical processes during the first billion years of evolution of the universe. The AARTFAAC Cosmic Explorer (ACE) utilises the AARTFAAC wide-field imager of LOFAR to measure the power spectrum of the intensity fluctuations of the redshifted 21-cm signal from the CD at z~18. The RFI from various sources contaminates the observed data and it is crucial to exclude the RFI-affected data in the analysis for reliable detection. In this work, we investigate the impact of non-ground-based transient RFI using cross-power spectra and cross-coherence metrics to assess the correlation of RFI over time and investigate the level of impact of transient RFI on the ACE 21-cm power spectrum estimation. We detected moving sky-based transient RFI sources that cross the field of view within a few minutes and appear to be mainly from aeroplane communication beacons at the location of the LOFAR core in the 72-75 MHz band, by inspecting filtered images. This transient RFI is mostly uncorrelated over time and is only expected to dominate over the thermal noise for an extremely deep integration time of 3000 hours or more with a hypothetical instrument that is sky temperature dominated at 75 MHz. We find no visible correlation over different k-modes in Fourier space in the presence of noise for realistic thermal noise scenarios. We conclude that the sky-based transient RFI from aeroplanes, satellites and meteorites at present does not pose a significant concern for the ACE analyses at the current level of sensitivity and after integrating over the available 500 hours of observed data. However, it is crucial to mitigate or filter such transient RFI for more sensitive experiments aiming for significantly deeper integration.

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Follow-up radio observations of the $τ$ Boötis exoplanetary system: Preliminary results from NenuFAR

Studying the magnetic fields of exoplanets will provide valuable information about their interior structures, atmospheric properties (escape and dynamics), and potential habitability. One of the most promising methods to detect exoplanetary magnetic fields is to study their auroral radio emission. However, there are no confirmed detections of an exoplanet in the radio despite decades of searching. Recently, Turner et al. 2021 reported a tentative detection of circularly polarized bursty emission from the $τ$ Boo exoplanetary system using LOFAR low-frequency beamformed observations. The likely source of this emission was presumed to be from the $τ$ Boo planetary system and a possible explanation is radio emission from the exoplanet $τ$ Boo b, produced via the cyclotron maser mechanism. Assuming the emission is from the planet, Turner et al. 2021 found that the derived planetary magnetic field is compatible with theoretical predictions. The need to confirm this tentative detection is critical as a conclusive detection would have broad implications for exoplanetary science. In this study, we performed a follow-up campaign on the $τ$ Boo system using the newly commissioned NenuFAR telescope in 2020. We do not detect any bursty emission in the NenuFAR observations. There are many different degenerate explanations for our non-detection. For example, the original bursty signal may have been caused by an unknown instrumental systematic. Alternatively, the planetary emission from $τ$ Boo b is variable. As planetary radio emission is triggered by the interaction of the planetary magnetosphere with the magnetized stellar wind, the expected intensity of the planetary radio emission varies greatly with stellar rotation and along the stellar magnetic cycle. More observations are needed to fully understand the mystery of the possible variability of the $τ$ Boo b radio emission.

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A novel radio imaging method for physical spectral index modelling

We present a new method, called "forced-spectrum fitting", for physically-based spectral modelling of radio sources during deconvolution. This improves upon current common deconvolution fitting methods, which often produce inaccurate spectra. Our method uses any pre-existing spectral index map to assign spectral indices to each model component cleaned during the multi-frequency deconvolution of WSClean, where the pre-determined spectrum is fitted. The component magnitude is evaluated by performing a modified weighted linear least-squares fit. We test this method on a simulated LOFAR-HBA observation of the 3C196 QSO and a real LOFAR-HBA observation of the 4C+55.16 FRI galaxy. We compare the results from the forced-spectrum fitting with traditional joined-channel deconvolution using polynomial fitting. Because no prior spectral information was available for 4C+55.16, we demonstrate a method for extracting spectral indices in the observed frequency band using "clustering". The models generated by the forced-spectrum fitting are used to improve the calibration of the datasets. The final residuals are comparable to existing multi-frequency deconvolution methods, but the output model agrees with the provided spectral index map, embedding correct spectral information. While forced-spectrum fitting does not solve the determination of the spectral information itself, it enables the construction of accurate multi-frequency models that can be used for wide-band calibration and subtraction.

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Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses. II.Observational constraints on the sub-galactic matter power spectrum

Stringent observational constraints on the sub-galactic matter power spectrum would allow one to distinguish between the concordance $Λ$CDM and the various alternative dark-matter models that predict significantly different properties of mass structure in galactic haloes. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to probe the sub-galactic mass structure in lens galaxies beyond the Local Group. Here, we demonstrate the first application of a novel methodology to observationally constrain the sub-galactic matter power spectrum in the inner regions of massive elliptical lens galaxies on 1-10 kpc scales from the power spectrum of surface-brightness anomalies in highly magnified galaxy-scale Einstein rings and gravitational arcs. The pilot application of our approach to Hubble Space Telescope (HST/WFC3/F390W) observations of the SLACS lens system SDSS J0252+0039 allows us to place the following observational constraints (at the 99 per cent confidence level) on the dimensionless convergence power spectrum $Δ^{2}_{δκ}$ and the standard deviation in the aperture mass $σ_{\rm AM}$: $Δ^{2}_{δκ}<1$ ($σ_{\rm AM}< 0.8 \times 10^8 M_\odot$) on 0.5-kpc scale, $Δ^{2}_{δκ}<0.1$ ($σ_{\rm AM}< 1 \times 10^8 M_\odot$) on 1-kpc scale and $Δ^{2}_{δκ}<0.01$ ($σ_{\rm AM}< 3 \times 10^8 M_\odot$) on 3-kpc scale. These first upper-limit constraints still considerably exceed the estimated effect of CDM subhaloes. However, future analysis of a larger sample of galaxy-galaxy strong lens systems can substantially narrow down these limits and possibly rule out dark-matter models that predict a significantly higher level of density fluctuations on the critical sub-galactic scales.

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Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses. I. Power-spectrum measurement and feasibility study

While the direct detection of the dark-matter particle remains very challenging, the nature of dark matter could be possibly constrained by comparing the observed abundance and properties of small-scale sub-galactic mass structures with predictions from the phenomenological dark-matter models, such as cold, warm or hot dark matter. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to search for tiny surface-brightness anomalies in the extended lensed images (i.e. Einstein rings or gravitational arcs), induced by possible small-scale mass structures in the foreground lens galaxy. In this paper, the first in a series, we introduce and test a methodology to measure the power spectrum of such surface-brightness anomalies from high-resolution Hubble Space Telescope (HST) imaging. In particular, we focus on the observational aspects of this statistical approach, such as the most suitable observational strategy and sample selection, the choice of modelling techniques and the noise correction. We test the feasibility of the power-spectrum measurement by applying it to a sample of galaxy-galaxy strong gravitational lens systems from the Sloan Lens ACS Survey, with the most extended, bright, high-signal-to-noise-ratio lensed images, observed in the rest frame ultraviolet. In the companion paper, we present the methodology to relate the measured power spectrum to the statistical properties of the underlying small-scale mass structures in the lens galaxy and infer the first observational constraints on the sub-galactic matter power spectrum in a massive elliptical (lens) galaxy.

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Degree-Scale Galactic Radio Emission at 122 MHz around the North Celestial Pole with LOFAR-AARTFAAC

Aims: Contamination from bright diffuse Galactic thermal and non-thermal radio emission poses crucial challenges in experiments aiming to measure the 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization. If not included in calibration, this diffuse emission can severely impact the analysis and signal extraction in 21-cm experiments. We examine large-scale diffuse Galactic emission at 122~MHz, around the North Celestial Pole, using the AARTFAAC-HBA system. Methods: In this pilot project, we present the first-ever wide-field image produced with a single sub-band of the data recorded with the AARTFAAC-HBA. We demonstrate two methods: multiscale CLEAN and shapelet decomposition, to model the diffuse emission revealed in the image. We use angular power spectrum metrics to quantify different components of the emission and compare the performance of the two diffuse structure modelling approaches. Results: We observe that the point sources dominate the angular power spectrum ($\ell(\ell+1)C_{\ell}/2π\equiv Δ^2(\ell)$) of the emission in the field on scales $\ell\gtrsim 60$ ($\lesssim 3$~degree). The angular power spectrum after subtraction of compact sources is flat within $20\lesssim \ell \lesssim200$ range, suggesting that the residual power is dominated by the diffuse emission on scales $\ell\lesssim200$. The residual diffuse emission has a brightness temperature variance of $Δ^2_{\ell=180} = (145.64 \pm 13.61)~{\rm K}^2$ at 122~MHz on angular scales of 1~degree, and is consistent with a power-law following $C_{\ell}\propto \ell^{-2.0}$ in $20\lesssim \ell \lesssim200$ range. We also find that, in the current setup, the multiscale CLEAN is suitable to model the compact and diffuse structures on a wide range of angular scales, whereas the shapelet decomposition method better models the large scales, which are of the order of a few degrees and wider.

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High-quality strong lens candidates in the final Kilo Degree survey footprint

We present 97 new high-quality strong lensing candidates found in the final $\sim 350\,\rm deg^2$, that completed the full $\sim 1350\,\rm deg^2$ area of the Kilo-Degree Survey (KiDS). Together with our previous findings, the final list of high-quality candidates from KiDS sums up to 268 systems. The new sample is assembled using a new Convolutional Neural Network (CNN) classifier applied to $r$-band (best seeing) and $g,~r,~i$ color-composited images separately. This optimizes the complementarity of the morphology and color information on the identification of strong lensing candidates. We apply the new classifiers to a sample of luminous red galaxies (LRGs) and a sample of bright galaxies (BGs) and select candidates that received a high probability to be a lens from the CNN ($P_{\rm CNN}$). In particular, setting $P_{\rm CNN}>0.8$ for the LRGs, the $1$-band CNN predicts 1213 candidates, while the $3$-band classifier yields 1299 candidates, with only $\sim$30\% overlap. For the BGs, in order to minimize the false positives, we adopt a more conservative threshold, $P_{\rm CNN} >0.9$, for both CNN classifiers. This results in 3740 newly selected objects. The candidates from the two samples are visually inspected by 7 co-authors to finally select 97 "high-quality" lens candidates which received mean scores larger than 6 (on a scale from 0 to 10). We finally discuss the effect of the seeing on the accuracy of CNN classification and possible avenues to increase the efficiency of multi-band classifiers, in preparation of next-generation surveys from ground and space.

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A numerical study of 21-cm signal suppression and noise increase in direction-dependent calibration of LOFAR data

We investigate systematic effects in direction dependent gain calibration in the context of the Low-Frequency Array (LOFAR) 21-cm Epoch of Reionization (EoR) experiment. The LOFAR EoR Key Science Project aims to detect the 21-cm signal of neutral hydrogen on interferometric baselines of $50-250 λ$. We show that suppression of faint signals can effectively be avoided by calibrating these short baselines using only the longer baselines. However, this approach causes an excess variance on the short baselines due to small gain errors induced by overfitting during calibration. We apply a regularised expectation-maximisation algorithm with consensus optimisation (sagecal-co) to real data with simulated signals to show that overfitting can be largely mitigated by penalising spectrally non-smooth gain solutions during calibration. This reduces the excess power with about a factor 4 in the simulations. Our results agree with earlier theoretical analysis of this bias-variance trade off and support the gain-calibration approach to the LOFAR 21-cm signal data.

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