text:
\section{Introduction}

Many discoveries in astronomy have been made by identifying unexpected outliers in collected data (e.g. \citealt{Cardamone2009}, \citealt{Massey2019}).
These outliers, also referred to as anomalies or novelties, are data points that lie outside of the normal distribution of data.
In the astronomy context, we are interested in finding unknown classes of objects, objects belonging to rare classes, and individual objects of known type with anomalous properties.
As data sets increase in size, automated methods for detecting these outliers are becoming necessary.
The Sloan Digital Sky Survey (SDSS) surveyed one third of the sky and observed over 1 billion cataloged objects \citep{York2000}.
In the near future, the Rubin Observatory will observe 40 billion objects \citep{Ivezic2018}.
These present opportunities for novel discoveries in their massive data sets, as well as the need for new, automated methods to filter the data and identify anomalies.

Outlier identification has been an area of study since as early as the 19th century \citep{Edgeworth1887}.
\new{This early work was primarily focused on identifying and filtering out measurement errors and other non-interesting outliers.
While this is still a main avenue in modern work on anomaly detection, and is in fact increasingly important for today's large data sets, we have become interested using in anomaly detection for discovery.}
Recent work in astronomy along these lines has applied a range of statistical and computational techniques.
A nearest neighbors approach, often combined with a dimensionality reduction step, has been used for outlier detection in cross-matched astronomical data sets \citep{Henrion2013}.
Applications often target specific types of objects, such as using Bayesian model selection to select rare high-redshift quasars from a star-dominated population \citep{Mortlock2012}.
Another approach is Principal Component Analysis (PCA) to identify distinguishing features; for instance, \cite{Dutta2007} used PCA for anomaly detection in SDSS and 2MASS flux and surface brightness data.

Machine learning methods are being rapidly developed as approaches to anomaly detection in astronomy and other fields.
A review of anomaly detection methods and applications using deep learning is presented in \cite{Chalapathy2019}.
Unsupervised learning lends itself to this problem, as it allows for outlier identification without expert labelling of training data or introducing biases based on expected outliers.
\cite{Baron2017} use random forests to find outliers in Sloan Digital Sky Survey (SDSS) spectroscopic data.
\cite{Solarz2017} apply support vector machines to find anomalies in the Wide-field Infrared Survey Explorer (WISE) survey.
\cite{Segal2019} explore the use of apparent complexity as a feature for machine learning algorithms to better identify radio galaxies with complex morphology.
Unsupervised learning has also been applied to anomaly detection problems beyond galaxy surveys, including on supernovae data \citep{Pruzhinskaya2019} and Kepler light curves \citep{Giles2019}.
Finally, general frameworks for anomaly detection have been developed, such as the combined machine learning--human input approach of \cite{Lochner2020}.

Deep generative models present another class of approaches to anomaly detection.
These have a natural application to identifying outliers, as they are able to model complex distributions of high-dimensional data.
\new{Autoencoders have recently shown promise in this realm:
\cite{Morawski2021} apply a convolutional autoencoder (CAE) to gravitational wave data, and \cite{DAddona2021} use a disentangled CAE to find outliers in KiDS data.
Variational autoencoders (VAEs) are a natural choice for anomaly detection as they provide a direct probability measure \citep{An2015}; \cite{Villar2021} use a VAE to detect anomalous extragalactic transients.
However, vanilla CAEs are simple models that do not always reproduce the data well, and VAEs are known to suffer from constraining priors and over-regularization \citep{Ghosh2020}, limiting their application to anomaly detection.}

Another deep generative model class that is gaining popularity is generative adversarial networks (GANs), proposed by \cite{Goodfellow2014}.
GANs were first applied to anomaly detection by \cite{Schlegl2017}, in the context of medical imaging.
They demonstrate that a GAN trained on normal images can then be used to identify abnormal images.
\cite{Zenati2018} show that training an encoder simultaneously with the GAN improves testing efficiency, and they demonstrate their performance on outlier detection tasks on a range of high-dimensional data.
GANs have also been used to detect outliers in time-series data \citep{Li2018}.
Recently, \cite{Margalef-Bentabol2020} used a GAN to detect merging galaxies and compare galaxy simulations against observations.
\cite{DiMattia2019} present a survey of the application of GANs to anomaly detection and perform empirical validation of the models.

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a natural data set for anomaly detection applications \citep{Miyazaki2018}.
It is a wide-field optical survey with very good seeing, an average of 0.6 (FWHM) in the $i$-band, and a deep magnitude limit, of 26.2 given a $5\sigma$ point source detection limit.
Many interesting objects have already been identified in HSC; some have been found by machine learning algorithms, such as in the case of galaxy interaction signatures \citep{Goulding2017}, while others used more traditional selection techniques targeted to the objects of interest, such as for strong gravitational lenses \citep{Wong2018} and extended emission line objects \citep{Sun2018}.
We are interested in finding more of these types of objects, as well as galaxies with extreme colors, galaxies with extreme activity, rare quasars, and other rare or interesting objects.
In addition to these, anomaly detection will be useful for filtering out optical artifacts in HSC.

In this work, we train a GAN to identify anomalous objects in a subsample of galaxies with HSC imaging.
We then characterize the anomalous images with a new convolutional autoencoder-based approach, and identify a set of scientifically interesting anomalies.
\new{We also compare the GAN-detected anomalies to those found with a simple CAE approach.}
This paper is organized as follows.
In Section~\ref{sec:data}, we detail the galaxy image data set used in our application.
We describe our WGAN model, approach to anomaly score assignment, technique for characterization, \new{and CAE model} in Section~\ref{sec:model}.
In Section~\ref{sec:results} we discuss our results and show anomalous galaxies identified with our framework.
We present a summary and our conclusions in Section~\ref{sec:conclusions}.
\new{A follow-up spectroscopic analysis of one of our GAN-detected anomalies is described in Appendix~\ref{sec:bluedot}.}

\section{Data}
\label{sec:data}

\subsection{Hyper Suprime-Cam Survey}

We use data from the Hyper Suprime-Cam Subaru Strategic Program \citep{Aihara2018a}.
The wide-field optical survey is imaged with the Subaru Telescope and has been ongoing since March 2014, with the first public data release in 2018 \citep{Aihara2018b}.
HSC provides extremely high sensitivity and resolving power, thanks to the large 8.2 meter mirror of the Subaru Telescope; its $i$-band seeing of 0.6 (FWHM) is a large improvement from SDSS, which has a typical $i$-band seeing of 1.4.

We work with the second public data release (PDR2, \citealt{Aihara2019}), which contains over 430 million primary objects in the wide field covering 1114 deg$^2$.
Of this wide field, a 305 deg$^2$ area is observed in full-depth full-color.
The objects in this field are observed in 5 broad-band filters, \textit{grizy}, with $5\sigma$ point-source detection limits within a 2 arcsec diameter aperture of 26.2 mag in the $r$- and $i$-bands, 26.6 mag in the $g$-band, and 25.4 mag in the $z$-band.

\subsection{Selection of Sample}

The HSC data are reduced using a sophisticated data reduction pipeline \citep{Bosch2019}.
We use the force-photometry catalog for sample selection.
Using the $i$-band CModel photometry, we select objects within a magnitude range of $20.0 < i < 20.5$ for our analysis.
This choice of a thin magnitude slice allows for a more consistent sample in object size; we note that this choice is important for ease of analysis, as detection on a wide range of magnitudes runs the risk of a bias towards identifying bright objects as anomalies.
For application to larger samples, one could train separate WGANs on each slice, or carefully choose training batches to balance magnitudes; we leave this for future work.

We exclude objects flagged as having significant issues by the pipeline.
These are, in any band: cosmic rays crossing the center pixel, saturated center pixel, interpolated center pixel, source at edge of survey volume, failed flux fit.
The full query, including these cuts and the information we retain about each sample, can be found at \url{https://github.com/kstoreyf/anomalies-GAN-HSC/blob/master/prepdata/hsc_pdr2_query.sql}, and can be run through the HSC data access site at \url{https://hsc-release.mtk.nao.ac.jp/datasearch}.

\begin{figure*}
    \begin{subfigure}{.4\textwidth}
    \centering
    \includegraphics[width=1\linewidth]{sample_real}
    \caption{}
    \label{fig:real}
    \end{subfigure}
    \hspace{4em}
    \begin{subfigure}{.4\textwidth}
    \centering
    \includegraphics[width=1\linewidth]{sample_gan}
    \caption{}
    \label{fig:gen}
    \end{subfigure}
\caption{(a) A random subsample of the HSC images used for training the WGAN and identifying anomalies. (b) A random sample of images generated by the WGAN, each conditioned on a latent-space vector drawn from a random normal distribution.}
\end{figure*}

We generate cutouts of $96 \times 96$ pixels ($\sim15\times 15$ arcsec) around each object; this captures the entirety of most objects while still being a reasonable size for training the network.
We use the $gri$-bands to construct 3-color images.
This results in a sample of 942,782 objects.
A random subsample from our final training data selection is shown in Figure \ref{fig:real}.
We see the sample contains many compact objects, most of which are faraway galaxies.
The red compact sources may be high-redshift galaxies, but some of them may also be stars; low-temperature dwarfs look similar in the survey, and are not simple to filter out.
We also see some more extended galaxies, including some with clear structure including bulges and spiral arms.

We first preprocess the images to avoid issues due to the raw data range spanning multiple orders of magnitude.
We convert the flux values to RGB values using the method of \citealt{Lupton2004}, which rescales the data using the inverse hyperbolic sine function (asinh).
We use a stretch value of 0.5 and a softening parameter of 15.
This produces values from 0 to 255 for each pixel in each band, and we then normalize these image by image to between 0 and 1.
This scaling may affect the features identified by the WGAN as anomalous; for instance, it may suppress the degree of anomaly of galaxies that have extremely high or low flux in certain regions.
However, the rescaled images should largely retain the information about each object, which is sufficient for this work; we leave further exploration of the effect of flux conversions to future work.

\section{Model and Training}
\label{sec:model}

\subsection{WGAN Architecture and Training}

The standard GAN framework, introduced in \cite{Goodfellow2014}, involves a generator and a discriminator which compete against each other in a minimax game.
The discriminator $D(\bm{x})$ learns to distinguish real images $\bm{x}$ from those generated by the generator $G(\bm{z})$, where $\bm{z}$ is a vector in the generator's latent space.
The generator, in turn, learns how realistic its generated images are based on feedback from the discriminator.
The loss function to optimize is then
\begin{multline}
\mini_G \, \maxi_D \, L_{D,G} = \mathbb{E}_{\bm{x}\sim p_{\mathrm{r}}(\bm{x})}[\mathrm{log} (D(\bm{x}))] \: + \\ \mathbb{E}_{\bm{z}\sim p_{\mathrm{z}}(\bm{z})}[\mathrm{log}(1 - D(G(\bm{z})))]
\end{multline}
where $\mathbb{E}_{\bm{x}\sim p_{\mathrm{r}}(\bm{x})}$ is the expectation value over the distribution of all real images, and $\mathbb{E}_{\bm{z}\sim p_{\mathrm{z}}(\bm{z})}$ is the expectation value over random input vectors to the generator.

GANs are notorious for instability in training; balancing the generator and discriminator losses is nontrivial, and vanilla GANs can fail to find a Nash equilibrium \citep{Salimans2016}.
One improvement is to use the Wasserstein distance as a metric to compare real and generated samples.
This is a more meaningful distance measure and is smooth even when the distributions are disjoint.
Wasserstein GANs are shown to be more stable and avoid vanilla GAN issues including mode collapse \citep{Arjovsky2017}.
The WGAN formulation is qualitatively different from that of vanilla GANs in that, rather than the discriminator outputting a probability of whether the sample was drawn from the real or generated distribution, the discriminator outputs the Wasserstein distance between the probability distributions of real and generated samples.
The WGAN discriminator is often called the ``critic'' to distinguish it, though we will continue to use ``discriminator'' for clarity.

The Wasserstein distance can be approximated by
\begin{equation}
    W\left(p_{\mathrm{r}}(\bm{x}\right), p_{\mathrm{z}}(\bm{z}))
    = \text{sup}\left[ \mathbb{E}_{\bm{x}\sim p_{\mathrm{r}}(\bm{x})}[D(\bm{x})]
    - \mathbb{E}_{\bm{z}\sim p_{\mathrm{z}}(\bm{z})}[D(G(\bm{z}))]
    \right]
\end{equation}
where ``sup'' denotes the supremum over discriminator parameters.
The generator aims to minimize this distance to achieve a distribution of generated images closest to the distribution of real images.
The generator only enters into the second term, so its loss function can be defined as
\begin{equation}
    L_G
    = - \mathbb{E}_{\bm{z}\sim p_{\mathrm{z}}(\bm{z})}[D(G(\bm{z}))] ~.
\end{equation}
The discriminator aims to maximize the Wasserstein distance; its loss function can be taken as the difference between the discriminator output on the real and generated samples.
However, a discriminator with this naive loss would get ``stuck'' when the discriminator is perfect, as the gradient vanishes and the loss function cannot continue to be updated.
One approach to address this is to apply a gradient penalty (GP) to penalize the loss to avoid vanishing gradients; to implement this we add a regularization term to the loss.
The discriminator loss is then
\begin{multline}
        L_D
    = \mathbb{E}_{\bm{x}\sim p_{\mathrm{r}}(\bm{x})}[D(\bm{x})]
    - \mathbb{E}_{\bm{z}\sim p_{\mathrm{z}}(\bm{z})}[D(G(\bm{z}))]
    \: + \\ \lambda_\text{GP} \, \mathbb{E}_{{\bm{y}}\sim p_{\mathrm{y}}} [(||\nabla_\bld{y}D(\bld{y})||_2 - 1)^2]
\end{multline}
where $\bm{y} = \epsilon \bm{x} + (1-\epsilon)G(\bm{z})$ is a uniform sampling from the line between samples from the real and generated distributions (with $\epsilon$ as a mixing parameter drawn uniformly from $0\leq\epsilon\leq1$), $\lambda_\text{GP}$ is the hyperparameter controlling the strength of the regularization, and $||\cdot||_2$ is the $L_2$ norm.

For our model we use this standard formulation of a Wasserstein GAN with gradient penalty (WGAN-GP).
The implementation is in \texttt{tensorflow} and \texttt{python}, based on that by \cite{Gulrajani2017}.
The generator and the discriminator are convolutional neural networks; the generator takes as input a latent space vector of dimension 128, and outputs an image of size $96\times96\times3$ pixels where 3 is the number of color bands.
It has a depth of 4 and a sigmoid activation function.
The discriminator takes as input an image of size $96\times96\times3$ pixels and outputs a real number; it also has a depth of 4.

We train the WGAN in batches of 32 images, with 5 discriminator updates per generator update.
For the loss functions we use the parameter $\lambda_\text{GP}=10$, and maximize the losses with the Adam optimizers with hyperparameters which we tune, choosing $\alpha=10^{-4}$, $\beta_1=0.5$, and $\beta_2=0.9$, for both the discriminator and generator.
We finalize the model at around 10,000 training iterations, after which the generator and discriminator losses stabilize and no longer improve.

A random sample of images generated with this WGAN, starting from latent space vectors drawn from a normal distribution, is shown in Figure \ref{fig:gen}.
We can see that the WGAN is able to generate realistic images for less extended objects, including neighboring objects and noise properties.
It also captures the color distribution of the population well, and reproduces the general noise properties.
However, it is unable to reconstruct the finer structure of more extended objects, such as spiral arms and distinct bulges; instead it generates diffuse-looking objects that do not always represent realistic galaxies.
That said, the fact that the WGAN does not learn to generate these more structured images is in line with our application of the WGAN to anomaly detection, as this limitation is precisely due to the fact that these images are less well-represented in the data.
We quantify the ability of the WGAN to represent the training objects and the connection to anomaly detection in the next section.

\subsection{Anomaly Score Assignment}
\label{sec:sanom_assignment}

\begin{figure*}
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_-3to-1sigcomb.png}
  \caption{}
  \label{fig:recon_neg}
\end{subfigure}
\hfill
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/recons_2.5to3.5sigcomb}.png}
  \caption{}
  \label{fig:recon_3sig}
\end{subfigure}
\hfill
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_5to20sigcomb.png}
  \caption{}
  \label{fig:recon_5sig}
\end{subfigure}
\caption{The results of WGAN image reconstruction and anomaly score assignment. The top row of each panel shows the original image, the second row shows the best WGAN reconstruction, and the bottom row shows the residual between the two. The assigned anomaly score is shown at the top of each column. The images in each panel are random samples of images in the following ranges of anomaly score: (a) significantly below the mean, (b) around $3\sigma$ above the mean, (c) greater than $5\sigma$ above the mean. It is clear that higher anomaly scores are indicative of poorer WGAN reconstructions and hence larger residuals.}
\label{fig:recon}
\end{figure*}

\begin{figure*}
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_ae_-3to-1sigcomb.png}
  \caption{}
  \label{fig:recon_ae_neg}
\end{subfigure}
\hfill
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/recons_ae_2.5to3.5sigcomb}.png}
  \caption{}
  \label{fig:recon_ae_3sig}
\end{subfigure}
\hfill
\begin{subfigure}{.325\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_ae_5to20sigcomb.png}
  \caption{}
  \label{fig:recon_ae_5sig}
\end{subfigure}
\caption{\new{The results of CAE image reconstruction and anomaly score assignment. The rows are the same as in Figure~\ref{fig:recon}, and the same images are chosen. The assigned anomaly score is shown at the top of each column; note that the images are grouped by WGAN score, so the CAE scores are not consistent with the groups.}}
\label{fig:recon_ae}
\end{figure*}

The basic procedure for anomaly detection involves setting the WGAN to generate its best reconstruction of each image.
The WGAN has learned the global distribution of the data and will be better at generating ``typical'' images; therefore, we expect that a poorly reconstructed image indicates that an object is anomalous with respect to the rest of the sample.
This approach requires a quantification of how anomalous an object is and an inverse mapping from images to the WGAN's latent space.

To determine how well the WGAN reconstructs a given image and thus how anomalous it is, we set the trained network (with weights fixed after training) to find its best reconstruction of each image.
This is defined as the generator image that minimizes a loss $L$ based on the residuals between the original image and reconstructed image, in both pixel-space and feature-space.
The generator residual $L_\mathrm{gen}$ enforces a visual similarity between the images, and is defined as the pixel-wise difference between the original image $x$ and the generator-reconstructed image $G(\bm{z})$:
\begin{equation}
L_\mathrm{gen} = \Sigma_i^P \left| x_i - [G(\bm{z})]_i \right|
\end{equation}
where $i$ indexes the $P=96\times96\times3$ pixels in the image and its corresponding reconstruction.
We also use the discriminator to perform feature-matching to capture the similarity between the features of the reconstruction and the original.
The discriminator residual $L_\mathrm{disc}$ is calculated by considering the representation $d$ from the last convolutional layer, which has dimension $6\times6\times512$, and taking the difference between this representation for the real and reconstructed images:
\begin{equation}
L_\mathrm{disc} = \Sigma_j^F \left| d(\bm{x})_j - d(G(\bm{z}))_j \right|
\end{equation}
where $j$ indexes the $F$ discriminator features.
The total loss then $L_\mathrm{tot} = (1-\lambda_\mathrm{anom}) \, L_\mathrm{gen} \, + \, \lambda_\mathrm{anom} \, L_\mathrm{disc}$, where $\lambda_\mathrm{anom}$ is a weighting hyperparameter which we tune.
We choose $\lambda_\mathrm{anom}=0.3$ to balance the typical variation in raw scores between generator and discriminator residuals.
Varying this parameter results in slightly different samples of high-scoring anomalies; the importance of the generator vs. discriminator scores is investigated in Section~\ref{sec:sanom_dist}.

The inverse mapping from image to latent-space vector is typically performed with a straightforward optimization, starting from a random draw from the WGAN's latent space and optimizing to find the latent-space vector that minimizes $L$ (e.g. \citealt{Schlegl2017}).
However, this is a time-limiting step for large samples, so we propose an improvement: we first train an encoder, a standard convolutional network, on the entire training sample to make a first approximation of the latent-space vector.
This encoder simply provides a better initial guess of the latent-space location and does not significantly affect the final reconstruction.
We then start from the encoder approximation and, for each image individually, perform a basic minimization of $L$, optimizing for 10 iterations (though the score usually converges before this).
This loss value at the final iteration, $L_\mathrm{tot}^\mathrm{final}$, quantifies the degree of anomaly of the image, so we assign this to be the image's anomaly score, $s_\mathrm{WGAN} = L_\mathrm{tot}^\mathrm{final}$.
We also preserve the information about the generator and discriminator residuals, assigning associated scores $s_\mathrm{gen} = L_\mathrm{gen}^\mathrm{final}$ and $s_\mathrm{disc} = L_\mathrm{disc}^\mathrm{final}$.
Higher anomaly scores indicate more anomalous objects, while lower scores indicate objects better modeled by the WGAN; the scores are relative and meaningful only with respect to the rest of the sample.

The result of this process is shown in Figure \ref{fig:recon}.
We can see that the WGAN is able to generate realistic images; for compact objects with standard colors, it constructs images nearly identical to the original, and assigns the objects low anomaly scores (Figure \ref{fig:recon_neg}).
The model is more challenged to generate objects with rare features or colors, as in the images with scores around $3\sigma$ above the mean shown in Figure \ref{fig:recon_3sig}.
Finally, objects with optical artifacts, such as satellite streaks or contamination from nearby bright stars, have extremely high anomaly scores, as the WGAN struggles to reconstruct them (Figure \ref{fig:recon_5sig}).

\subsection{Dimensionality Reduction with a Convolutional Autoencoder}
\label{sec:cae}

A general problem with anomaly detection is to distinguish potentially interesting objects from trivial data issues.
We propose here a new approach based on Convolutional Autoencoders (CAEs) to post-process and explore identified anomalies.

We expect the residual images, the difference between the real and reconstructed images, to contain information about why the WGAN marked an object as anomalous.
(We use the absolute difference because we are restricted to positive pixel values on the RBG scale, though this does lose potentially useful information.)
However, the pixel space is very high-dimensional, and contains information less relevant to the anomalous features we are interested in, such as background noise.
We employ a CAE to reduce the dimensionality of the data and isolate the relevant information.

We train a straightforward CAE to map the pixels of the residual images to a 64-dimensional vector.
The CAE has 4 encoding and 4 decoding layers, and uses a standard MSE loss between the true and reconstructed image.
We train the CAE in batches of 30 images, and stop the training when the loss stops improving, freezing the network at 30,000 iterations.
We then use the CAE to encode each of the images into a 64-dimensional vector representation.
We confirm that the CAE maps the encoded vectors to images that are reasonable reconstructions of the originals.
This autoencoding step allows us to extract the information most relevant to the anomalous features of the image, and perform further characterization to distinguish interesting anomalies; we demonstrate this in Section~\ref{sec:cae-umap}.
As a comparison, we also train an identically constructed CAE on the pixels of the real images; the results of this are also shown in Section~\ref{sec:cae-umap}.

\subsection{Anomaly Detection with a Convolutional Autoencoder as a Benchmark}
\label{sec:cae_bench}

\new{We compare our WGAN anomaly detection approach to a simpler method using a straightforward convolutional autoencoder.
We use the trained CAE described in Section~\ref{sec:cae}.
In that section we used the CAE for the purpose of dimensionality reduction in order to characterize the WGAN-detected anomalies, and we emphasize that that application is independent from this use of the CAE as a benchmark for anomaly detection.
For this comparison, we obtain the latent space representation from the trained CAE for each of the nearly one million HSC objects, and apply the trained decoder to get the CAE-decoded image.
We then compute a CAE anomaly score $s_\mathrm{CAE}$ by computing the residual image between the original and CAE-decoded image, and then taking the sum over the residual pixel values.
This is analogous to how we compute the generator score as described in Section~\ref{sec:sanom_assignment}.}

\new{We demonstrate the CAE approach in Figure~\ref{fig:recon_ae}.
We use the same sample of images as for the WGAN approach in Figure~\ref{fig:recon} for a direct comparison (note that the groupings are now misaligned with the CAE anomaly scores, as they are grouped by WGAN score).
The CAE decoded images are generally good reproductions of the original images, but the CAE also struggles for images that are outliers with respect to the full training set, as can be seen in Figure~\ref{fig:recon_ae_5sig}.
The CAE also produces very smooth images that lack the noise properties of the real data, while the WGAN is generally good at reproducing this noise.
We use the CAE anomaly score as a benchmark, as it is an established approach that is simpler than our WGAN method, but has some similar properties.}

\section{Results}
\label{sec:results}

\subsection{Anomaly Score Distribution}
\label{sec:sanom_dist}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{score_distribution}
    \caption{Left: The distribution of anomaly scores for the $\sim$940,000 objects in our sample, for the score based on the generator pixel-wise residual $\s{gen}$ (blue dotted), the score based on the discriminator feature-matching residual $\s{disc}$ (red dashed), and the combined total score $\s{WGAN}$ (purple solid). We normalize each by their mean and standard deviation $\sigma$, so the scores shown are in terms of $\sigma$ away from the mean of the given distribution. We do not show the long tails of these for clarity; a few objects extend up to $\s{gen}=25.5\sigma$ and $\s{disc}=35.2\sigma$, and down to $\s{gen}=-4.7\sigma$ and $\s{disc}=-2.3\sigma$.
    Right: The distribution of discriminator vs. generator scores, color-coded by total anomaly score. The dashed line shows where $\s{gen}=\s{disc}$ in terms of their $\sigma$ away from the mean.}
    \label{fig:dist}
\end{figure*}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{score_distribution_ae}
    \caption{\new{Left: The distribution of anomaly scores for the $\sim$940,000 objects in our sample, for the score based on the generator pixel-wise residual $\s{gen}$ (blue dotted), and the score based on the CAE pixel-wise residual (green dot-dashed). We show the raw scores, as these are directly comparable. As in Figure~\ref{fig:dist}, we do not show the long high-score tails for clarity.
    Right: The distribution of generator vs. CAE scores, color-coded by total WGAN anomaly score. The dashed line shows where $\s{gen}=\s{CAE}$.}}
    \label{fig:dist_ae}
\end{figure*}

We compute anomaly scores for each of the $\sim$940,000 objects in our sample, using both a generator score $\s{gen}$ and a discriminator score $\s{disc}$ as described in Section~\ref{sec:sanom_assignment}.
These raw scores have very different ranges due to their definitions based on image pixel differences or feature value differences, so to compare them we show the scores by their number of standard deviations from the mean.

These distributions are shown in the left panel of Figure \ref{fig:dist}.
Recall that higher anomaly scores indicate more anomalous objects, while lower scores indicate objects that are more well-modeled by the WGAN.
We find that the distribution is skewed towards higher scores, which is expected: most typical objects are reconstructed well by the WGAN so have similar scores, while there are more ways to be anomalous than to be typical, resulting in a wider range of scores.
The high-score tail extends out to an object with $\s{disc}=35.2\sigma$, and the low-score tail extends to an object with $\s{gen}=-4.7\sigma$ (we only show the bulk of the distribution for clarity).

The right panel of Figure \ref{fig:dist} shows $\s{disc}$ vs.  $\s{gen}$ for each of the images.
As expected, we see that most objects have relatively similar generator and discriminator scores, indicating that the generator and discriminator generally agree on the degree of anomaly of the image.
That said, the distribution has significant scatter, so the pixel-residuals and feature-residuals may be picking up on different indications of anomalousness.
At high scores, there is a skew towards higher discriminator scores: anomalous objects are more likely to have a high discriminator score compared to generator score.
However, this only applies to very high-scoring objects above $\sim5\sigma$, and is likely a result of how we compute the raw scores---there is a maximum to the generator residual due to the pixel values, while discriminator scores are essentially unbounded---so we do not subscribe great significance to this.
These distributions also reflect the fact that the scores are not Gaussian distributed, but rather have a long one-sided tail towards high anomaly scores.

\new{As a comparison, we also compute the CAE anomaly scores for each of the images as described in Section~\ref{sec:cae_bench}.
These are based on the residual pixel values between the real image and the CAE decoded image, and so they are directly comparable to the generator scores.
We show the raw score distribution for both of these in the left panel of Figure~\ref{fig:dist_ae}.
The CAE scores are lower on average than the generator scores, meaning the reconstructions are generally more similar to the original image.
The right panel shows the correspondence between the generator and CAE scores for each image, and we see that the CAE scores are typically lower.
These points are color-coded by the total WGAN score; we see that there is also not much of a correlation between CAE score and WGAN score, meaning that the discriminator component of the WGAN score corresponds more with the generator score than the CAE score.}

\new{Although the CAE scores tend to be lower than the WGAN scores, we hypothesize that this is largely due to noise properties.
Looking at Figures~\ref{fig:recon} and \ref{fig:recon_ae}, the CAE reconstructions are much smoother and less noisy than the WGAN reconstructions.
The residuals for the CAE then contain the noise of the real image.
On the other hand, the WGAN reconstructions attempt to generate images with similar noise properties as the original, as the WGAN has learned the typical noise level of the training data.
However, it will not place the noise in exactly the same pixels as in the real image (given that we are limited in the optimization step to find the best reconstruction of the image in the WGAN's latent space).
The residuals for the WGAN then contain roughly double the noise values as those for the CAE, as they include the noise of the original and the reconstruction.
This contributes significantly to the generator score, pushing the score distribution to higher values compared to the CAE scores.
If this difference is mainly due to noise, then it is not very relevant to anomaly detection; the differences in scores within each definition will be more meaningful.
We investigate this in the next section by looking at high-anomaly samples based on each score definition.
We also note that in some cases the CAE does seem to produce a better reconstruction than the WGAN, but we show in the next section that even so, the WGAN discriminator score is a more useful metric for identifying interesting anomalies.}

\subsection{High-Anomaly Sample Selection}
\label{sec:anom_sample}

\begin{figure*}
\begin{subfigure}{0.33\textwidth}
  \centering
  \includegraphics[width=0.95\linewidth]{images/score_effect_gen_ae.png}
  \caption{}
  \label{fig:score_effect_gen}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
  \centering
  \includegraphics[width=0.95\linewidth]{images/score_effect_disc_ae.png}
  \caption{}
  \label{fig:score_effect_disc}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
  \centering
  \includegraphics[width=0.95\linewidth]{images/score_effect_ae.png}
  \caption{}
  \label{fig:score_effect_ae}
\end{subfigure}

\caption{Comparison between image samples selected using various score definitions. The top panel of (a) shows a random sample with a 3$\sigma$ cut on the combined anomaly score $\s{gen}$. The lower left panel shows a sample of images that this score definition would include but $\s{disc}>3\sigma$ would miss; the lower right panel of (a) similarly shows images missed by $\s{CAE}>3\sigma$. \new{Panels (b) and (c) show the same thing for $\s{disc}$ and $\s{CAE}$}. The $\s{disc}>3\sigma$ selection shows the highest proportion of interesting anomalies, and it selects interesting images the other scores would miss; we choose this selection criterion for our high-anomaly sample for further characterization.}
\label{fig:score_effect}
\end{figure*}

We investigate the role of the generator and discriminator scores by looking at selections of high-scoring anomalies with different score definitions.
We also compare these to selections based on the CAE score.
Figure~\ref{fig:score_effect} shows a comparison of random samples of these definitions, based on a $3\sigma$ cutoff.
The larger samples in the top row of all panels show a selection based on $\s{gen}$, $\s{disc}$, \new{and $\s{CAE}$}.
It is clear that all of these high-scoring samples are anomalous with respect to the full sample (Figure~\ref{fig:real}), showing objects with interesting features and properties, as well as noise-dominated images and those with optical artifacts.
We can see that the generator score sample (Figure~\ref{fig:score_effect_gen}) contains many empty images and some containing optical artifacts; the majority of the images are clearly scientifically uninteresting.
The discriminator score sample (Figure~\ref{fig:score_effect_disc}) also has some noisy and saturated images, but it contains a significantly higher proportion of interesting-looking images, which we broadly consider as those that contain actual galaxies, and galaxies that are not just typical-colored, compact sources.
It also contains some objects of even higher interest, including extended galaxies with unusual structure, and compact objects with extreme colors.
\new{Looking at the CAE score sample (Figure~\ref{fig:score_effect_ae}), we see that the high CAE scores are picking up many images with high, grainy noise, as well as some optical artifacts.}

For each selection, we can ask which images are captured that other score definitions would miss with the $3\sigma$ cut; this is shown in the bottom row of each panel.
We can see that the generator score selects mostly noisy images that the other definitions miss (bottom panels of Figure~\ref{fig:score_effect_gen}).
The discriminator score definition, on the other hand, would capture a decent number interesting objects that are missed by both the generator and CAE definitions (bottom panels of Figure~\ref{fig:score_effect_disc}).
\new{The high-scoring CAE images that the other definitions miss (bottom panels of Figure~\ref{fig:score_effect_ae}) are, once again, mainly noise and otherwise uninteresting images.}

This analysis suggests that the generator score, which is based on the pixel-residual, is more attuned to selecting anomalous images due to noise or other image corruption issues, which tend to affect most of the pixels in the image \new{and lead to larger absolute differences between the real and reconstructed images}.
On the other hand, the discriminator selects images that are anomalous in feature-space, which is more flexible in selecting various types of anomalies including those that are more localized in pixel space.
This results in a set of images that have more potential to be scientifically interesting.
\new{We also investigate using the combined score for selecting this high-anomaly sample, and find that it effectively results in a mix of the generator and discriminator high-scoring samples; as we showed in Figure~\ref{fig:score_effect} that the generator score selects very few interesting objects missed by the discriminator score, we choose to not incorporate the generator score at all and just use the discriminator score.}

\new{We hypothesize that the WGAN is better suited to anomaly detection compared to the CAE due to several factors.
The first is that the WGAN is specifically intended to learn the true distribution of the input data.
Thus we should be able to better identify the objects that are outliers of that distribution.
On the other hand, the CAE is much simpler, just trained to compress and reproduce the images in a lower dimension.
Second, CAEs tend to smooth the data, as we see in our decoded images; this will wash out subtle anomalies, and in astrophysics we often care about these subtleties.
Finally, the WGAN's discriminator is particularly suited to anomaly detection, as it is trained to detect ``realistic'' images, which will look more like the bulk of the input data.
We can use the discriminator feature-space as a natural anomaly quantification, and we see that indeed it finds more interesting anomalies, while the CAE has no such quantity.}

We thus select our final high-anomaly sample with a cut on discriminator score, $\s{disc}>3\sigma$, as in the upper panel of Figure~\ref{fig:score_effect_disc}, producing a sample with 13,477 images, representing 1.4\% of the total sample.
We also show $\s{disc}$ as the relevant anomaly score in the rest of our analysis given its stronger relation with potentially interesting anomalies.
We note that the choice of using only $\s{disc}$ for our anomaly score is different than previous work, such as \cite{Schlegl2017}, \cite{Zenati2018a}, and \cite{Margalef-Bentabol2020}, which all use an anomaly score that combines the generator and discriminator losses.
Our choice may indeed miss some anomalies, but we have shown in Figure~\ref{fig:score_effect} that the choice of a $\s{disc}>3\sigma$ results in missing the least interesting objects.
We strive for purity over completeness in our high-anomaly sample, as we aim to identify scientifically interesting anomalies, which is easier with less contamination from noisy images.
We provide the full score information in our released catalog so subsequent studies may use a different selection if they so choose.

\subsection{Correlation with HSC Catalog Information}

\begin{figure*}
    \centering
    \includegraphics[width=0.8\textwidth]{images/hsc_histograms_ae.png}
    \caption{The distribution of catalog properties from the HSC pipeline for various score definitions. We compare the distribution of the full sample (solid orange) to those of high-anomaly samples selected by \new{$\s{CAE}$ (dot-dashed green)}, $\s{disc}$ (dashed red), and $\s{gen}$ (dotted blue). The properties we show are the effective radius $R_\mathrm{eff}$, ellipticity, blendedness, ratio of aperature to CModel flux $i_\mathrm{aper}/i_\mathrm{CModel}$, $g-r$ color, and $r-i$ color. The grey line in the blendedness panel indicates the typical threshold for filtering out highly blended objects.}
    \label{fig:hsc_hist}
\end{figure*}

In order to further explore the results of our anomaly detection process, we compare the objects in various samples with derived properties from the HSC catalog.
This acts as a validation step to understand the information that our anomaly detection approach might be using to make its assignments, \new{as well as to} determine if it is picking up on information beyond that in the catalog.
Figure~\ref{fig:hsc_hist} shows the normalized distributions of selected galaxy properties for the full sample and the $3\sigma$-anomaly samples, selected with each of the score definitions discussed previously.

We first look at the spatial extendedness of the object.
We use the effective radius $R_\mathrm{eff}$ of the exponential component from the best-fit CModel result.
It indicates the intrinsic extendedness of an object after taking PSF convolution into account.
Among the different size measurements provided in HSC database, it is the most stable and robust measure of size.
Objects with $R_\mathrm{eff}<1''$ are very compact, while those with $R_\mathrm{eff}>5''$ are quite extended (recall that the sizes of cutouts are $15 \times 15$ arcsec).
Among the objects with $R_\mathrm{eff}>5''$, we notice a population of problematic objects that do not appear to be that extended and also have faint $r$- and $g$-band magnitude; we believe that these are due to bad deblending processes.
From the figure, we see that most of the objects in the full sample are compact, with a median of $R_\mathrm{eff}\sim0.5''$.
In comparison, the generator and discriminator $3\sigma$ anomaly samples contain a majority of extended objects; the discriminator-selected sample has a median $R_\mathrm{eff}\sim2.5''$.
This shows that the WGAN tends to find high-$R_\mathrm{eff}$ objects to be more anomalous, as these high values encompass both bad deblends and actual extended galaxies.
The latter makes sense as extended objects are more resolved and can show more complex details, such as interesting galactic structure.
That said, these high-anomaly samples still contain significant numbers of compact objects, showing that the WGAN is able to detect interesting compact objects and is not simply flagging all extended objects as anomalous and all compact ones as boring.
\new{We note some small but interesting differences between the generator and discriminator samples:} the generator selects many objects with unrealistically high radii, while the discriminator tends towards intermediate-extended objects.
\new{We also show the distribution of high-CAE score objects, and we find that it separates into two populations: one of compact objects like the bulk of the full sample, and the other of very large radius objects that are likely bad deblends.
This latter peak is very similar to (and even more extreme than) that feature in the generator sample distribution.}
This supports our finding that the generator \new{and the CAE} are attuned to optical artifacts which do not have meaningful radii, while the discriminator more often finds actual galaxies with interesting properties.

We next examine the ellipticity $e$ of objects using the exponential components of the CModel flux.
Here 0 means circular and 1 means highly elliptical.
We note that this is for both extended and compact objects, and ellipticity may be less meaningful for the latter.
In the full sample, objects skew towards small ellipticity.
While the full population has a higher fraction of objects in the $0.05 < e < 0.3$ bin, the anomaly samples show an excess of very low ellipticity objects at $e < 0.05$.
\new{Interestingly, the CAE sample has the highest excess, perhaps due to having a higher proportion of compact objects.}
The anomaly samples also tend to pick up more highly elliptical ($e>0.9$) objects.
Such high ellipticity is rarely physical; it is often due to poor fits on corrupted images.

We look at the blendedness of the objects, which describes the contamination of one object by the light from other close objects.
It is computed from the $i$-band flux fits, as described in \citep{Bosch2019}.
A blendedness of 0 indicates an isolated object, while a value near 1 indicates a very blended object.
A very small number of objects are assigned unphysical negative blendedness scores; we do not show these, but they do contain a higher proportion of anomalies.
We see that in the full sample, for the vast majority of objects, their photometry is not affected by image blends.
For the anomaly samples, most images also have low blendedness values, showing that the anomaly detector is finding interesting isolated objects and not just identifying blends.
That said, the anomaly samples do also show a significantly higher fraction of highly blended objects compared to the full sample.
This is expected due to the low representation of blended objects in the data, as well as the correlation between objects with larger angular size and higher blendedness.
The grey line at $10^{-0.375}$ shows the cutoff suggested for eliminating blends \citep{Mandelbaum2018}; 4.6\% of all of the objects in our full sample are above this threshold, while 32\% of the objects in the high discriminator score sample are above it.
Interestingly, the discriminator selects for more of the highly blended objects than the generator \new{and CAE}, suggesting that many of these are actual overlapping objects and not just artifacts, as we know that the discriminator flags fewer artifacts as anomalous compared to the \new{other scores}.

The ratio between the aperture flux and CModel flux $\log_{10} (i_{\rm Aper}/i_{\rm CModel})$ is another interesting diagnosis of photometry.
It has been used as an empirical indicator for problematic objects due to bad deblending processes.
Figure \ref{fig:hsc_hist} only shows the $i$-band, but the distribution is very similar for the other bands.
The aperture flux is computed in a small $2''$ aperture on images convolved with kernels matched to a common FWHM-1.2 arcsec PSF across all five bands, to homogenize the flux measurements across the bands; the CModel flux takes into account the emission from the entire image.
Thus a low ratio means that the object is very large, or that there is a strong color gradient; it may also indicate that there is an issue with the CModel fit, for instance due to poor deblending.
We see that most objects in the full sample have a ratio near one, with a skew towards smaller ratios as expected from the flux definitions.
The $3\sigma$ anomaly samples show a markedly different distribution, with many objects having very small ratios.
This makes sense as we have seen that our anomaly detector selects for both extended objects and deblending errors.
\new{The generator-selected sample shows a large proportion of very small ratio objects: 56\% of the high generator score images have a $\log_{10} (i_{\rm Aper}/i_{\rm CModel}) < -1.0$, compared to 40\% of discriminator score images, 36\% of CAE score images, and 4.8\% of the full sample.
This aligns with the generator's tendency to flag optical artifacts that likely have poor deblends, and shows that this metric is particularly useful for understanding the types of images that our anomaly detectors are selecting.}

Finally, we look at the color distributions for both $g-r$ and $r-i$ color, based on the CModel flux fits.
We see that the high-anomaly samples are significantly bluer (lower $g-r$) than the full sample.
There is less of a difference for $r-i$ color, but the anomalies do skew towards bluer colors (lower $r-i$).
This may be because of the relationship between color and angular size: galaxies with larger $R_\mathrm{eff}$ tend to be bluer, and larger objects are disproportionately anomalous in our sample, as we have seen in the $R_\mathrm{eff}$ distribution.
In both cases, we also see a longer tail into the red end of the color distribution, indicating that the anomalous sample contains more extreme color images on both ends; this makes sense as both interesting objects and problematic photometry would exhibit extreme colors.
We see little difference in the distributions for the \new{discriminator and generator $3\sigma$ samples}, suggesting that they are capturing similar proportions of objects of each color.
\new{The CAE $3\sigma$ score distribution is more similar to the full distribution, as we have seen in the previous panels, indicating that it is not picking up on as many outlying images as the WGAN.}

We also note that there is a strong correlation between objects near bright stars and their anomaly score.
For our initial selection we performed a basic cut on objects near foreground stars, but this still left significant potentially contaminated regions.
Applying a more aggressive bright star mask, we see that 44.6\% of objects in our discriminator-defined high-anomaly sample fall within the mask, compared to only 8.5\% of objects in the full sample (this newer mask can be found at \url{https://hsc-release.mtk.nao.ac.jp/doc/index.php/bright-star-masks-2}).
For increased purity, we could apply this mask, though we would risk losing some potentially interesting anomalies; in fact, these regions are often excluded due to the amount of artifacts, but a filter based on anomaly score could make this data usable.
For this work we do not apply this mask but note that it may be useful depending on the downstream application.
\new{Additionally, future HSC data releases that are in preperation will have more sophisticated data reduction and filtering, and will allow anomaly detectors to better learn interesting anomalies.}

This comparison of the distributions of catalog properties elucidates the types of images that the WGAN generator and discriminator, \new{and in comparison the CAE}, find to be anomalous.
\new{The high anomaly score samples generally have significantly different distributions of properties compared to the full sample}.
\new{In particular, the objects with high anomaly scores tend to have more extreme properties, including} both potentially interesting and unphysical properties.
\new{We also observe that the CAE- and generator- selected high-scoring samples have relatively similar distributions to each other for many of the properties, more so than the discriminator-selected sample, confirming the tendency of the CAE and generator to select more for noisy images and optical artifacts.}
\new{Further,} we found that there is a significant number of objects with non-extreme catalog properties but that are found to be highly anomalous; this validates that the anomaly detectors are incorporating more or higher-order information in determining the degree of anomaly of an image, \new{so these anomaly samples could not be constructed with simple cuts on pipeline data}.
Our anomaly scores could be used in combination with the catalog to further filter out noisy and uninteresting images or to pick out specific types of anomalies.

\subsection{Autoencoder Results Visualized with UMAP Embedding}
\label{sec:cae-umap}

\begin{figure*}
\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/umap_gri_100k_lambda0.3_reals}.png}
  \caption{Embedding with original image pixels.}
  \label{fig:umap_100k_reals}
\end{subfigure}
\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/umap_gri_100k_lambda0.3_resids}.png}
  \caption{Embedding with residual image pixels.}
  \label{fig:umap_100k_resids}
\end{subfigure}

\vspace{1em}

\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/umap_gri_100k_lambda0.3_reals_auto}.png}
  \caption{Embedding with autoencoded original images.}
  \label{fig:umap_100k_reals_auto}
\end{subfigure}
\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{{images/umap_gri_100k_lambda0.3_resids_auto}.png}
  \caption{Embedding with autoencoded residual images.}
  \label{fig:umap_100k_resids_auto}
\end{subfigure}

\caption{The anomalies in our sample visualized with a UMAP in two dimensions, with different features used for the UMAP embedding. The choice of autoencoded residual images (lower right) produces a UMAP distribution that is most strongly correlated with anomaly score.}
\label{fig:umap_100k}
\end{figure*}

We visualize the image distribution with a Uniform Manifold Approximation and Projection (UMAP, \citealt{McInnes2018}), a dimensionality reduction algorithm that maps the objects into a 2D representation.
This is useful for understanding the global properties of the distribution, and exploring the types of objects in the sample through their clustering UMAP-space.
We perform a UMAP embedding on a 100,000-object subsample of our data set, and look at the correlation between the UMAP and our WGAN-assigned anomaly scores.

We first perform an embedding directly on the 3-color image pixels; this is shown in Figure~\ref{fig:umap_100k_reals}.
There is a general trend with anomaly score, as well as significant structure in the distribution.
We next embed the residual image pixel values between the original images and the WGAN reconstruction, as we expect the residuals to contain information about the magnitude and type of anomaly; this is shown in Figure~\ref{fig:umap_100k_resids}.
We see an increased amount of structure, including a windy filamentary structure composed of lower-scoring objects, with the high-scoring objects somewhat clustered towards the center of the distribution.
The detailed structures of the low-scoring objects in these UMAPs suggest that the embeddings are dominated by less interesting pixel-level features.

In order to address this, we use a convolutional autoencoder (CAE) to reduce the dimensionality of these images, as described in Section~\ref{sec:cae}.
\new{We emphasize that while we use the same CAE for this application as we did for assigning CAE anomaly scores, as described in Section~\ref{sec:cae_bench}, here we use it for a totally different purpose: to aid in characterizing the anomalies found by the WGAN discriminator.}
The CAE finds a 64-dimensional latent-space representation of each original image, and separately of each residual image; these are much more compressed than the 27,648 dimensions of the images ($96 \times 96$ pixels in 3 color bands).

We first apply the UMAP to embed these autoencoded low-dimensional representations of the original images; this is shown in Figure~\ref{fig:umap_100k_reals_auto}.
We see that there is now a more coherent cluster containing most of the low-scoring anomalies, though there are high-scoring objects scattered throughout the distribution.
Finally, we show the result of embedding the autoencoded residual images in Figure~\ref{fig:umap_100k_resids_auto}.
We obtain a coherent distribution with a very clear gradient in anomaly score.
This indicates that the CAE applied to the residual images is extracting information that is the most relevant to the WGAN-assigned anomaly score, as compared to the image pixels or the original images.
This provides support that our CAE technique, combined with our WGAN approach to anomaly detection, is useful for consolidating the information in the galaxy images relevant to their anomalousness.
In the next section, we show that this is useful for the further characterization of the high-anomaly sample to detect scientifically interesting anomalies.

\subsection{Characterization of Anomalies with the WGAN, CAE, and UMAP}

\begin{figure*}
\begin{subfigure}{0.68\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/umap_3sigd_auto_resids_boxes.png}
  \vspace{-2em}
  \caption{}
  \label{fig:umap_3sig_boxes}
\end{subfigure}

\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_box_magenta.png}
  \caption{}
  \label{fig:recons_magenta}
\end{subfigure}
\hspace{2em}
\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{recons_box_blue}
  \caption{}
  \label{fig:recons_blue}
\end{subfigure}

\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{recons_box_red}
  \caption{}
  \label{fig:recons_red}
\end{subfigure}
\hspace{2em}
\begin{subfigure}{.48\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{images/recons_box_limegreen.png}
  \caption{}
  \label{fig:recons_green}
\end{subfigure}

\vspace{0cm}
\caption{A visualization of our anomaly characterization method with our WGAN-based anomaly scores and autoencoded residual images. Panel (a) shows a UMAP embedding of all anomalies with  $\s{disc}>3\sigma$ above the mean, color-coded by anomaly score. Panels (b)-(e) show a random selection of galaxies in each of UMAP regions enclosed by the box of the corresponding color in panel (a). It is clear that different regions of the UMAP correspond to different types of anomalies, including both \new{interesting objects (as in (b) and (c)) and corrupted images (as in (d) and (e)).}}
\label{fig:boxes}
\end{figure*}

We use our WGAN-based anomaly score and our autoencoded residual images to explore and characterize the anomalous objects in our data set.
We perform a UMAP embedding of the autoencoded residuals for just the objects in our high-anomaly sample, as defined in Section~\ref{sec:sanom_dist}, as we are now interested in identifying the scientifically interesting anomalies among the high-scoring objects.
This is shown in Figure~\ref{fig:umap_3sig_boxes}.
The distribution shows a clear correlation with $\s{disc}$, with high-score structures around the edges of the distribution, while objects just passing the $3\sigma$ threshold are more evenly located in the center of the distribution.

In exploring the objects in this distribution, we find that the distribution reflects similarities in the objects and their residuals.
We demonstrate this by showing galaxies located in various regions of the UMAP, indicated by the colored boxes on Figure~\ref{fig:umap_3sig_boxes}.
Panels (b)-(e) of Figure~\ref{fig:boxes} show a random selection of galaxies from each of the boxes of the corresponding color.
The differences in the regions are clear visually.
Figure~\ref{fig:recons_magenta} shows images from the central region of the UMAP, which contain mostly extended galaxies with diffuse emission and little structure.
The residuals show large empty regions where the WGAN succeeded in reproducing the extended emission, with noise and background or foreground sources around the edges.
The nearness of these images in UMAP-space demonstrates that our approach successfully isolating the anomalous features and clustering based on these.
The images in Figure~\ref{fig:recons_blue} correspond to the edge of a high-scoring arm of the UMAP.
They all exhibit a strong blue-green color: some of these are due to noise, but others are bright blue sources that may be extreme star-forming regions.
We can see that the WGAN has difficulty reconstructing these complicated structures, and while it captures some of the blue color the reconstructions are dominated by diffuse yellow emission, which is more represented in the data.
We note that the attempted reconstructions are quite similar to each other, likely because there is only a small region of the WGAN's latent space that can produce images resembling these as they are far from typical training set images.
In addition to characterizing types of interesting anomalies, the UMAP is useful for separating out optical artifacts.
Figure~\ref{fig:recons_red} shows objects in a cluster far from the rest of the distribution, which contain red streaks aligned in the same direction, possibly due to satellites or other corruptions.
The WGAN struggles to reconstruct these; it attempts to line up multiple compact sources to approximate the line, as it was trained on majority compact sources, so the residuals all display similar features corresponding to gaps in the line.
The images in Figure~\ref{fig:recons_green}, from the cluster at the bottom of the UMAP, have bright green features due to corruption from nearby bright stars or passing satellites.
The WGAN reproduced the central object well but was unable to reconstruct the green features, as most of the data set does not contain these.

These sets of galaxies with distinct anomalous features demonstrate how our WGAN-based approach, combined with the CAE-enabled UMAP distribution, provides a useful way of characterizing anomalies.
We are able to disentangle anomalies that scored highly due to noise or saturation, such as those in panels (d) and (e), from those with a high score due to unusual galaxy morphology or color, such as in panels (b) and (c).
This indicates that our approach could be used to robustly filter out bad images at the pipeline level, in addition to identifying scientifically interesting anomalies in post-processing.
We built a custom visualization tool to interactively explore the UMAP space in more detail, based on a similar tool by \cite{Reis2021}; it can be accessed at \url{https://weirdgalaxi.es}.
We used this tool to perform a search for scientifically interesting anomalies; the results of this search are described in Section~\ref{sec:interesting}.

\subsection{Identified Interesting Anomalies}
\label{sec:interesting}

\begin{figure*}
\vspace{0cm}
\begin{subfigure}{.35\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{anomalies_bluesf}
  \caption{Galaxies with extreme, blue star formation.}
  \label{fig:anom_bluesf}
\end{subfigure}
\hspace{2em}
\begin{subfigure}{.35\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{anomalies_purple}
  \caption{Galaxies with purple active regions.}
  \label{fig:anom_purple}
\end{subfigure}
\vspace{1em}

\begin{subfigure}{.35\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{anomalies_mergers}
  \caption{Galaxy mergers or potential mergers.}
  \label{fig:anom_mergers}
\end{subfigure}
\hspace{2em}
\begin{subfigure}{.35\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{anomalies_tidal}
  \caption{Galaxies with tidal features.}
  \label{fig:anom_tidal}
\end{subfigure}

\vspace{1em}

\begin{subfigure}{.35\textwidth}
  \centering
  \includegraphics[width=1\linewidth]{anomalies_other}
  \caption{Images containing other potentially interesting anomalies.}
  \label{fig:anom_other}
\end{subfigure}
\vspace{0cm}
\caption{A selection of the interesting anomalies with scientific potential detected using our method.}
\label{fig:anomalies}
\end{figure*}

Using our approach combining WGAN-based anomaly scores and CAE-enabled characterization, we find a number of potentially scientifically interesting galaxy images.
A categorized selection of these is shown in Figure~\ref{fig:anomalies}.
We note that these categories were assigned by hand, and do not correlate very clearly with regions in UMAP-space; the identification and categorization required a decent amount of visual inspection using our interactive visualization tool.
That said, some of these objects do cluster in the UMAP, and in fact we found some of these objects by looking nearby previously identified images in the category of interest.

Figure~\ref{fig:anom_bluesf} shows galaxies with regions of intense blue emission, some more diffuse and some in discrete clumps; these indicate extreme star formation.
In fact, some of these objects have already been identified and followed up in the literature; for example, the leftmost and center image in the top row are part of MCG+00-25-010, a blue compact dwarf system that was found to have a metal-poor stellar population that powers extreme nebular emission \citep{Senchyna2017}.
We also find several extended galaxies with discrete intensely purple regions, shown in Figure~\ref{fig:anom_purple}.
This indicates strong emission in the $i$-band (red), which is from the H$\alpha$ line, as well as the $g$-band (blue), which could be H$\beta$ or [OIII] 4959 and 5007 lines; thus in certain redshift ranges, the purple regions would suggest star formation activity.
Figure~\ref{fig:anom_mergers} shows potential galaxy mergers, including one possible triple merger.
We also detect many galaxies with tidal features due to gravitational interactions; a sample of these are shown in Figure~\ref{fig:anom_tidal}.
Finally, Figure~\ref{fig:anom_other} shows other anomalous images with potential scientific interest, including arcs of extended emission, a strangely shaped cluster of discrete sources, and bright compact blue and white objects in extended sources.
This last sample demonstrates the potential of our approach to identify ``unknown unknowns,'' which a more targeted anomaly detection method would likely have missed.

\new{All of the objects shown here were found in our $\s{disc} > 3\sigma$ sample.
Of these 45 images, only 11 of them were in the $\s{gen} > 3\sigma$ sample, and only 2 of them were in the $\s{CAE} > 3\sigma$ sample.
This confirms that the WGAN discriminator is well suited to finding interesting anomalies that other methods, especially the simpler CAE approach, cannot.
While it is likely that those samples would have contained some number of interesting anomalies that this discriminator sample does not, we showed in Figure~\ref{fig:score_effect} that more would be lost than gained in those cases.}

We performed follow-up spectroscopic observations of several of these objects to determine if they are indeed scientifically interesting.
\new{Our findings on one of these objects is presented in Appendix~\ref{sec:bluedot}.}

\section{Summary \& Conclusions}
\label{sec:conclusions}

In this work, we presented an approach combining a WGAN, CAE, and UMAP to detect anomalous images, and applied it to a sample of $\sim$940,000 objects in the Hyper Suprime-Cam survey.
We train a WGAN on the full data set in order to model the overall distribution of the data.
Data that are not well represented in the WGAN's latent space are identified as more anomalous with respect to the data set as a whole.
We quantify the degree of anomaly by setting the WGAN to find the closest representation of each object in its latent space and reconstruct the image.
We then assign scores based on the residuals between the original and the reconstruction, both the pixel-wise residual with the generator and a feature residual with the penultimate layer of the WGAN discriminator.

We found that the discriminator is more adept at identifying interesting anomalous images, while the generator tends to identify images that are anomalous due to noise or other optical artifacts.
\new{We compare the WGAN-based scores to a simpler anomaly detection method using a convolutional autoencoder (CAE).
We find that, while the CAE reconstructions have smaller residuals from the original images than the WGAN reconstructions, they are less indicative of interesting anomalies compared to the WGAN discriminator score.
This is likely due to the CAE producing smooth, noiseless reconstructions, and the WGAN discriminator's ability to model the true data distribution.}
We thus select a high-anomaly sample based on the WGAN discriminator scores to investigate in more detail, with a $\s{disc}>3\sigma$ cut resulting in 13,477 objects.

One of the main difficulties with anomaly detection is determining which anomalies are scientifically interesting.
To address this, we augment our WGAN-based anomaly detection approach with a novel characterization method based on a CAE and a UMAP.
We use the CAE to reduce the dimensionality of the residual images, and use these lower-dimensional representations with a UMAP embedding to further cluster objects with high anomaly scores.

Using our approach, we identify numerous interesting anomalies with scientific potential, including galaxy mergers and galaxies with extreme star-forming regions.
\new{Of the 45 interesting anomalies we show from the WGAN discriminator score sample, only 2 would have been found with the CAE anomaly scores.}
We perform follow-up observations on some of these objects, and detail our findings on one of these.
The object is a compact blue source in a region of extended emission, which we find to likely be a metal-poor star-forming dwarf galaxy with unusual asymmetric emission lines, which we conclude is due to a spatially offset, extremely blue HII region.
This confirmed the scientific interest of an object detected with our approach, and demonstrates the potential for a synergy between machine-assisted anomaly detection methods and detailed observational follow-up.

We have publicly released a catalog of our full data set with our WGAN-assigned anomaly scores, together with our custom visualization tool for further exploring this data.
Our approach is flexible and can be applied to other data sets and data types.
The combination of the WGAN and CAE for unsupervised anomaly detection is scalable, reproducible, and removes spontaneity from the discovery process, making it ideal for extracting novel science from the increasingly large surveys of the coming decade.

\section*{Acknowledgements}

We gratefully acknowledge the Kavli Summer Program in Astrophysics for seeding this project; the initial work was completed at the 2019 program at the University of California, Santa Cruz.
This work was funded by the Kavli Foundation, the National Science Foundation, and UC Santa Cruz.
\new{N.R.'s work at Argonne National Laboratory was supported under the U.S. Department of Energy contract DE-AC02-06CH11357.}
K.S.F., A.L. and Y.L. are grateful for valuable insights on the interpretation of galaxy observations from Jenny Greene, Erin Kado-Fong, Kevin Bundy, Masami Ouchi, Kimihiko Nakajima, Yuki Isobe, Yi Xu, and Aaron Romanowsky.
K.S.F. also thanks Dezso Ribli, Lorenzo Zanisi, Itamar Reis, and the Flatiron Astrodata Group at the Center for Computational Astrophysics for helpful discussions.
This material is based upon work supported by the National Science Foundation under Grant No. 1714610.
\new{We also thank the anonymous reviewer for very helpful comments.}

\section*{Data Availability}

The data underlying this article are available via the Hyper Suprime-Cam CAS Data Search tool at \url{https://hsc-release.mtk.nao.ac.jp/datasearch}.
The SQL query used to obtain the data set in this work is available at \url{https://github.com/kstoreyf/anomalies-GAN-HSC/blob/master/prepdata/hsc_pdr2_query.sql}.
A subset of the derived data, including anomaly scores for all the images, is available at \url{https://github.com/kstoreyf/anomalies-GAN-HSC}, along with the code used to process the data; the full data sets are available upon request.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


text:
Q: Пустые массивы в java, проверка на пустоту В одном из заданий в курсе было написать программу, которая принимает массив целых чисел в аргументы метода и возвращает массив с наименьшим и наибольшим числом. Но также было условие, что если входной массив пустой, то возвращать должно два нуля. В примерах: getStatistic({}) == {0, 0}. Вопрос такой: что использовать для проверки массива на эту "пустоту", чтобы при введении пустого массива при вызове метода возвращались нули?
С числами всё супер, но когда массив пустой, то выдаёт ошибку ArrayIndexOutOfBoundsException, что вроде бы логично, ведь массив пустой, но я всё равно не понимаю, что можно добавить или изменить в этом коде, чтобы условие с пустыми массивами было выполнено. Хелпаните, пожалуйста.
P.S. Насколько помню я, пустой массив - тот, где задано количество обьектов в нём, но не проинициализировано их, все обьекты равны нулю. Поправьте, если я путаю, пожалуйста.
public static int[] getStatistic(int[] results) {
    int max = results[0];
    int min = results[0];
    for (int i = 0; i < results.length; i++) {
        if (results[i] < min) {
            min = results[i];
        }
        if (results[i] > max) {
            max = results[i];
        }
    }
    int[] array = {
        min,
        max
    };
    return array;
}

A: Если массив пустой, то он не содержит некоторое число неиниц. объектов, он вообще ничего не содержит. Пример: {}
Чтобы проверить массив на пустоту, можно сравнить его длину с нулём. Для этого мы используем метод массива length, возвращающий число объектов массива.
...
if (results.length == 0) {
    return new int[] {0, 0}; // быстрое объявление массива
}
...

A: public static int[] getStatistic(int[] results) {
  int max = 0;
  int min = 0;
  for (int i = 0; i < results.length; i++) {
    if (i == 0) {
      min = result[i];
      max = result[i];
    } else {
      if (results[i] < min) {
        min = results[i];
      }
      if (results[i] > max) {
        max = results[i];
      }
    }
  }
  int[] array = {
    min,
    max
  };
  return array;
}

A: В существующем коде следовало изменить инициализацию минимума/максимума и добавить проверку на первый элемент массива.
Тогда цикл for не будет выполняться для пустого массива, так как не выполнится строгое условие i < 0:
public static int[] getStatistic(int[] results) {
    int max = 0;
    int min = 0;
    for (int i = 0; i < results.length; i++) {
        if (results[i] < min || i == 0) {
            min = results[i];
        }
        if (results[i] > max || i == 0) {
            max = results[i];
        }
    }
    return new int[]{min, max};
}

redpajama_set_name: RedPajamaStackExchange


So what is your verdict? I am buying a pour-over this week and would love your input. Thanks!
The KitchenAid machine did well for an automatic drip brewer. If you only usually make a couple mugs at a time and don't mind manually making your coffee, then I suggest the Chemex. I use mine almost every day. If you're used to making more mugs at a time or would prefer something with less manual work, I felt the KitchenAid did a good job. I hope this helps.


text:
Home>Farm Business>Business
Bayer settles false ad lawsuits
TAGS: Bayer
The settlement has nothing to do with ongoing negotiations over cancer lawsuits.
Bloomberg | Mar 30, 2020
By Jef Feeley
Bayer AG agreed to pay $39.5 million to settle allegations that its Monsanto unit ran misleading ads about the controversial Roundup weedkiller and its potential health risks to humans and animals.
As part of the deal, language will be removed from Roundup Weed and Grass Killer's label saying that glyphosate -- the product's active ingredient -- only affects an enzyme found in plants. Consumers alleged that the chemical attacks an enzyme found in humans and some animals.
The settlement comes as Bayer is feverishly working to resolve more than 13,000 lawsuits blaming exposure to glyphosate in Roundup for cancer in users. The company denies glyphosate causes cancer.
After losing three cancer trials in California that resulted in combined damages of $191 million, Bayer agreed to postpone the next round of Roundup trials to provide more time for negotiations. At least a half-dozen trials scheduled to start in the first quarter of this year have been put on hold. Bayer is appealing jurors' Roundup verdicts against the company.
Bayer shares fell under siege after the company acquired Monsanto in June 2018, losing as much as 47% of their value as trial losses mounted and new cases multiplied. The stock price began edging up again with the prospect of a settlement drawing closer, yet such an agreement might still cost Bayer $10 billion to $12 billion, according analysts at Bloomberg Intelligence.
Chris Loder, a U.S.-based spokesman for Bayer, based in Leverkusen, Germany said the settlement had nothing to do with ongoing negotiations over the cancer suits. "The parties continue to mediate in good faith," in hopes of settling those suits, he added.
The proposed class-action, filed in federal court in Kansas City, Missouri, zeroed in on advertising for Roundup Weed & Grass Killer, used by gardeners to eradicate weeds in flower beds and patios. Consumers alleged glyphosate targeted an enzyme in humans and animals that bolsters the immune system, digestion and brain function. They disputed Monsanto's claims that glyphosate only impacted plants.
The case is Jones v. Monsanto Co., 19-cv-102, U.S. District Court, Western District of Missouri (Kansas City).
To contact the reporter on this story:
Jef Feeley in Wilmington, Delaware at jfeeley@bloomberg.net
To contact the editors responsible for this story:
David Glovin at dglovin@bloomberg.net
Peter Blumberg, Anthony Lin
© 2020 Bloomberg L.P.

redpajama_set_name: RedPajamaCommonCrawl


text:
Forrest "Dutch" Kissinger
Col. (ret) Forrest "Dutch" Kissinger, enlisted in the Air Force at 18 years old in 1949 as an aircraft mechanic. Three years later he was given the opportunity to become a pilot during the Korean War when the Air Force needed to surge and grow its pilot population.
"I had to take a test, and if I passed the test they would let me be a pilot," Forrest said. "If I didn't pass then my enlistment was up, and I would go home. Well, thirty-one years and three months later, I had a great career and retired as a full bird colonel."
X Corps, a force led by U.S. Maj. Gen. Edward M. Almond, stages an audacious amphibious landing at Inch'ŏn, some 150 miles behind enemy lines. The plan, conceived by UN commander Gen. Douglas MacArthur, is an unqualified success; 10 days later Seoul is liberated.


text:
Brad A. Johnson
Restaurant Photography
Hotel & Resort Photography
Brad A Johnson
Drink of the Week: The Bilbao at Fellow, Los Angeles
At Fellow in Los Angeles, The Bilboa is a modern riff on a gin martini made with rosemary-lemon-infused vermouth. It is herbal and citrusy and floral and fresh yet also surprisingly viscous and creamy, making it extremely enjoyable to sip.
Hotel Review: Downtown LA Proper
The Downtown LA Proper is the fourth outpost of Kelly Wearstler and Brad Korzan's Proper Hotel brand. (The first debuted in San Francisco in 2017, followed by Santa Monica and Austin.)…
Food Photographer of the Year Exhibition at the Royal Photographic Society in Bristol, England
Update – Review: Acre, Farm-to-Table in San Jose del Cabo, Mexico
A lot has changed at Acre in San Jose del Cabo since I originally visited and fell in love with this restaurant five years ago. But many things also remain the same. The restaurant still sits in the middle of a dusty, 25 acre farm on the outskirts of town, accessible by a meandering dirt road...
Where to Eat in Los Cabos, Mexico: The Restaurants Redefining Baja Cuisine
Mexican cuisine in Los Cabos has for decades been defined by steak and lobster. If not for the accompanying margaritas and periodic mariachi, one might have easily forgotten they were in Mexico. But that's changing. These are the restaurants redefining what it means to eat Mexican food in Los Cabos.
Hotel Review: Nobu, Los Cabos, Mexico
Nobu Hotel is a vibe, not a place. Opened in 2019 on the sparsely developed Pacific cape of Cabo San Lucas, this 200-room outpost is a sexy mashup of Japanese and Mexican motifs with a soundtrack straight out of Ibiza.
How to Make the Red Snapper a la Talla from Tamarindos Los Cabos
Step 1, Catch a red snapper. Step 2, Build a fire in your wood-burning oven and pour yourself a mezcal...
Hotel Review: The Cape, Los Cabos, Mexico
Thompson Hotels' first foray into Mexico, The Cape Hotel opened several years ago at the southern edge of the tourist corridor that connects Cabo San Lucas on the south with San Jose del Cabo to the north. This is where the Pacific merges with the Sea of Cortés. A bargain for Los Cabos, this is a fun, sexy hotel.
Photo of the Week: Los Cabos, Mexico
How to Make Sangrita, Mexico City Style
Mexico City ranks among the world's greatest destinations for dining. And one of my favorite things about dining in Mexico City is sangrita. Not to be confused with the wine-based…
Writer. Photographer. Traveler. Restaurant Critic.


Pics press save link to store the graphics to your pc. These are ready for down load, if you like and wish to grab it, simply click save logo on the page, and it'll be immediately downloaded to your laptop.
Pics I'm hoping you may like it. This image over will be labelled using.


text:
Marcelin Dally (born 13 August 1962) is a former Côte d'Ivoire hurdler. He graduated from the University of Paris Nanterre and holds an Engineer-Master in Management.

He won the silver medal at the 1988 African Championships and with the African team won the 1992 IAAF World Cup in Havana, Cuba, finishing sixth in the final on 110m hurdles. His personal best time was 13.86 seconds, achieved in July 1992 in Argentan, France. This is the national record of Côte d'Ivoire. He also holds the national record on 60m hurdles, 7.98, achieved in Nogent-sur-Oise, France, on 12 February 1994.

He managed the reform of UNESCO's intergovernmental committee for sport, overseeing the Ministerial platform (MINEPS) and served in the field as Regional Adviser in sport policy for Africa.

Currently, he is performing as Executive Officer of the International Convention Against-Doping in Sport, the global public authority regulation (targeting governments) which purports to protect values, ethics principles and integrity.

References

External links

1962 births
Living people
Ivorian male hurdlers

redpajama_set_name: RedPajamaWikipedia


Attention makeup lovers: this is one event you won't want to miss.
MAC brand ambassador and makeup artist Nicole 'Pinky' Thompson is hosting an exclusive book launch, and you can head along.
Held at The Masters Institute of Creative Education, Pinky will be talking all things beauty while recreating a look from her new book.
You'll receive a signed copy of the book, as well as complimentary drinks on arrival – the hallmark of every good event.


All-Star Asphalt and Sealcoating, Inc.
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ARE YOU USING THE RIGHT VALVE?
There are two main types of valves for passenger cars and vans.
The valves are designed for different maximum pressures!
Rubber valves are available in two versions: the standard rubber valve, which can cope with a pressure of max 450 kPa, and the high-pressure rubber valve, which can cope with max 700 kPa.
The metal valve can take a pressure of max. 1400 kPa.
If the vehicle has a recommended tyre pressure close to 450 kPa or more, there is a risk that the vehicle owner will fill them to a higher pressure. Tyre pressure also goes up when the tyre gets hot.
In these cases, a standard rubber valve should not be used, but instead a high-pressure valve or metal valve should be chosen.
This problem is not uncommon on mobile homes and caravans!
We strongly recommend using a metal valve at speeds over 210 km/h. There is a high risk of rubber valves bending at high speeds, with ensuing air leakage.


Casuals converting to permanent employment - can it be done?
The Fair Work Commission reviews modern awards every 4 years to make sure the awards continue to provide a fair and minimum safety net to employees.
In the most recent review, the Fair Work Commission decided that all awards should provide a right for casual employees to convert to part-time or full-time permanent employment in some circumstances. Some awards already contain a casual conversion clause, but not all.
Whilst the changes aren't set in stone, employees should be aware that, very soon, they may be able to make this request (if not already, depending on the award). Employers should begin planning now for the potential impact of these changes.
In what circumstances can casual employees request to be made permanent?
The Commission has developed a model casual conversion clause which it proposes to include in 85 modern awards (which do not currently contain a similar right to casual employees).
Have worked over the 12 months a pattern of hours on an ongoing basis, without significant difference, which could continue to be performed in accordance with the full-time or part-time employment provisions of the relevant award.
Employers should be aware that even if the conversion clause is not invoked, employing someone on a regular and systemic pattern can still be deemed a part-time employment arrangement even if the parties are treating it as a casual employment. This is particularly relevant in the event of dismissal.
The model clause also requires the employer to provide all casual employees (whether they become eligible for conversion or not) with a copy of the casual conversion clause within the first 12 months after their initial engagement.
Can an employer refuse a request for conversion to permanent?
If you have questions regarding casual and permanent employment or any employment law issues, please don't hesitate to contact me.


Are a family run company, All roofing team members are trained to ensure a professional roofing service.
SV Roofing & Renovation Ltd offer free Quotations, are fully insured, guarantee all work, uniformed staff, supply of photographic evidence of works undertaken.
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We take on all roof related projects, so if you can't see something above, please email us to ask.
By calling SV Roofing & Renovation you are on the way to securing your roof for years to come and also ensuring the well-being of your property in the midst of some of the most turbulent weather the United Kingdom has seen for years. It shouldn't be a case of 'let's put it off until next year!'. Sometimes when it comes to the weather, tomorrow is late enough. call us on 0800 193 2474 or 07704 939866 or email us at [email protected] to discuss your requirements, make an appointment and receive a free, no-obligation quote. Based in Kent we cover a wide area including: South London, London and Essex.


text:
Alicja Maria Zając (born 26 June 1953) is a Polish politician. She was elected to the Senate of Poland (10th term) representing the constituency of Krosno.

References

Living people
1953 births
Place of birth missing (living people)
20th-century Polish politicians
21st-century Polish politicians
20th-century Polish women politicians
21st-century Polish women politicians
Members of the Senate of Poland 2019–2023
Women members of the Senate of Poland


text:
Single Parent Families Struggle Alone – But Also Struggle in Similar Ways
If you are a single parent, or if you are considering supporting a single parent family, please know this is one of the most meaningful things you can do. Below are some of the real challenges of life as a single parent in America today.
Resource Management: This can be anything from finances to childcare to food. Stretching the dollar to cover normal daily needs–and dare I say desires/wants-of self & family. If finances are not the challenge, single parents must make the most of time to pay the attention required to meet children's needs (like school, activities, quality communication, and care) the demands of employer(s), and expectations of extended family, while still making room for recreation and rest. There is often more month than money or time in a single parent household. When a single parent comes home from work and starts their "second job" of cooking, cleaning, homework, bill paying, project making, and grocery shopping – they have completed a solid 12-14 hour day. Normally, social connectedness, and self-care suffer tremendously. Self Care – if you do not take care of yourself with proper nutrition, rest, exercise and spiritual food – you cannot possibly be balanced enough to take care of others and make sound and healthy decisions alongside having sound and healthy reactions to life's more challenging moments. A single parent must remember to ASK FOR HELP. There is no replacement for investigating and learning the community resources and unapologetically putting them in place as an active part of their home. This can be like recreation centers, libraries, coupon groups, babysitting exchanges, the church, and so on. maintain a work life balance.
Social Networking: Because time and money is stretched, it is difficult to build a support network, but it is a MUST. Many single parents have mentioned that they struggle with loneliness and isolation. Often, the dynamics of dating are so challenging that people choose to stick to themselves. Many adults do not want to date a full time single parent and share attention with the children or bother to try and "blend" a family. This type of rejection is often met with heartache and brings about low self-esteem. I believe a sound solution is to surround oneself with other FAMILIES. You are not a single – you are a FAMILY. Our first priority as a family is to its members. Our activities as "grown ups" like dating, girls/guys night out, trips to the salon, etc can be supported by the circle of families to which we belong. In turn, we can offer the same.
Making up for the missing Parts: Many single parents try to play both parent roles. If there are any moms like me, the lack of interest in baiting a fishhook or tying knots with the boy scouts must be met a neutral role model of the opposite parent that is trustworthy and consistent who will commit to this type of relationship on an ongoing and long term basis. Additionally, it is very difficult to balance the demands of work fully when your child needs you at school or at home. Overtime crushes more than the clock for a single parent– it crushes our ability to give our hearts in full connection with our child–and then crushes them. A single parent needs a network – this can be with neighbors, school, church, family – whatever circle is safe, consistent, and reflective of good & sound ethics that support the parent and the children and is at the ready for life's unexpected moments.
Guilt /Shame/Self Worth: Many single parents feel guilty and some even ashamed of having to ask more of their children than in terms of sacrifice and household operations. Often, "letting a kid be a kid" is a rare privilege. Single parents carry guilt about this at times, or overcompensate with tough love, which can be good–or build walls, depending on how it is approached and presented. Making choices about what we can do and cannot do as it relates to time and money adds to the guilt that parents carry regarding their situation. However, single parents MUST build each other up. They MUST commit to a positive and productive perspective for their kid's sakes.
Anxiety/Fear: Single parents are often faced with making the quality of interactions make up for the lack of quantity interactions. Most single parents, however, find themselves in what I call "survival mode" emotionally, financially, or physically. They are in a stance of fight or flight rather than in a place where decisions can be made based on patient, thoughtful, well strategized, and intentional efforts. Hearts that filled with grief, guilt, shame, anxiety and fear are however leading homes and families all across America. It is VERY IMPORTANT that we recognize this and develop healthy alternative habits. AWARENESS is step one – ACKNOWLEGEMENT of this reality and a plan to replace unhealthy perspectives with positive and productive perspectives and reactions is a commitment we must make and apply starting today.
Single Parent Children Struggle Also
Many children in single parent families face their own challenges:
Countless studies show that children in single parent households are under a lot more stress. When the stress accumulates it can lead to problems in school and behavioral issues. So what are single parenting's effects on a child's mentality overall?
Effects on Your Child's Emotional Health – When a single parent argues with the other parent in front of the child, this can lead to stress in the child. It is especially problematic when the parents try to get the child to take sides or deliver critical messages to the other parent through the child. The conflicts between parents and single parenting's effects on a child's mentality can lead to the child's inability to grow an attachment with either parent. This lack of an emotional attachment can lead to feelings of insecurity in the child.
The Effects of Abandonment on a Child's Mentality – When discussing single parenting's effects on a child's mentality, it is important to note the effect abandonment can have. Abandonment refers to when a parent leaves the household and cuts of all contact. Feelings of abandonment can lead a child to question his or her own self-worth. The remaining parent must help the child cope with the other parent's absence so the child doesn't develop low self-esteem. Abandoned children also tend to have trust issues and bottle up their emotions rather than express them freely.
The Effects of Constant Moving on Children – Single parents move around more often usually because they face more economic hardship and must move around frequently in order to find more affordable places to live. This frequent moving is another one of single parenting's negative effects on a child's mentality. Each time children move they have to leave behind their neighborhood friends and the transition is even more difficult when they change schools. The possible effects of frequent moving are a sense of isolation, depression, and anxiety.
A toxic combination of unstable schedules and unstable access to childcare leads to a pattern of serial quitting. Single parenting's effects on a child's mentality vary but due to its inherent challenges, single parenting can cause stress for both parent and child and it is the parent's responsibility to make it as least traumatic as possible. It is possible for the negative effects to be balanced out if the parents make an extra effort to provide their child with all the emotional support they need.
If you are a single parent, don't be hard on yourself. It is a fight to move forward so, keep up the pace, ask for help and use your resources! If you are a supporter of single parent families, THANK YOU!!
If you are considering supporting a single parent family, please know this is one of the most meaningful things you can do.
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WatStart is a new community initiative to help prospective entrepreneurs and very-early-stage technology companies in the Waterloo area.
WatStart creates opportunities for early-stage entrepreneurs to get together — online and in person — with each other and with local service providers to learn from each other and to receive ongoing guidance, support and encouragement.
Gary Will, who chronicles the Waterloo technology scene in his widely read Waterloo Tech Digest, has gathered together several local sponsors to produce a very attractive and potentially useful site. I write potentially because since its launch in early September, there has been very little activity on the website. The forums are practically dead, except for the occasional posting from sponsors, whose articles are either cut-and-paste copies of articles from somewhere else on the internet or cheesy bits of marketing fluff that you might expect to find as mail inserts with their bills. And none of it has anything to do with starting a company in Waterloo! The top non-sponsor poster has posted less than ten messages to the forum, and he's in Mississauga!
But enough of my complaining. My point is that the site has a lot of potential. All it lacks is some interesting content — Waterloo-related content — to get people talking.
Personally, I'd like to see WatStart succeed. It's not so much that I am interested in starting up a company in Waterloo, though I do toy with the idea from time to time, but I like living in Waterloo. I like working in Waterloo. Should I ever happen lose my current job at AMI Semiconductor, I'd like to see a thriving local high-tech industry from which I could choose another job. I think WatStart has the potential to help that happen.
All this is to say that I plan to give some attention to WatStart over the next little while: participating in discussions, asking questions, stirring the pot, trolling for conversation, teasing with flamebait, and the like. So don't say I didn't warn you.
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