Yiming Qian
email: yimingqian@ids.osaka-u.ac.jp

Cheikh Brahim
email: cheikh-brahim.el-vaigh@irisa.fr

El Vaigh

Yuta Nakashima

Hajime Nagahara
email: nagahara@ids.osaka-u.ac.jp

Yutaka Fujioka
email: fujioka@let.osaka-u.ac.jp

Built Year Prediction from Buddha Face with Heterogeneous Labels

Keywords: Computing methodologies → Computer vision, Neural networks, • Applied computing → Fine arts Semi-supervised Learning, KL Divergence, Deep Learning, Regression

Buddha statues are a part of human culture, especially of the Asia area, and they have been alongside human civilisation for more than 2,000 years. As history goes by, due to wars, natural disasters, and other reasons, the records that show the built years of Buddha statues went missing, which makes it an immense work for historians to estimate the built years. In this paper, we pursue the idea of building a neural network model that automatically estimates the built years of Buddha statues based only on their face images. Our model uses a loss function that consists of three terms: an MSE loss that provides the basis for built year estimation; a KL divergence-based loss that handles the samples with both an exact built year and a possible range of built years (e.g., dynasty or centuries) estimated by historians; finally a regularisation that utilises both labelled and unlabelled samples based on manifold assumption. By combining those three terms in the training process, we show that our method is able to estimate built years for given images with 37.5 years of a mean absolute error on the test set.

INTRODUCTION

Buddhism has started in India and spread all over the Asian subcontinent from India to, e.g. Japan through China. As Buddhism flourished along the centuries within several civilisations and dynasties, people started embracing the new religion, and now it is SUMAC '21, October 20, 2021, Virtual Event, China. . considered as the fourth largest religion in the world. They created their own Buddha statues, which are not only religion symbols but also art pieces that express their own culture.

The built information will help historians to connect the design of Buddha with the historical events such as dynasty change, revolution, etc. However, as history goes by, due to wars, natural disasters, and other reasons, the document that records the history of Buddha statues went missing.

It is an immense work for historians to estimate the built year of statues after the record is lost. Chemical analysis-based methods, such as radiocarbon dating [START_REF] Ervin | Radiocarbon dating: an archaeological perspective[END_REF], weathering-base dating [START_REF] Barbara | Weathering of inorganic materials: dating and other applications[END_REF], thermoluminescence dating [START_REF] Wintle | Thermoluminescence dating of sediments[END_REF], can be used to estimate Buddha statues' built years, but these methods have some drawbacks. For example, radiocarbon dating is only capable of identifying the date of organic components, which is not always the case for Buddha statues. The weathering-based method analyses the degrading of the surface due to weathering, being applicable to statues in limited environmental settings. Thermoluminescence dating is only applicable to statues made of a material that was heated during the building process, such as bronze, ceramic, or gold coating. Those methods are expensive, time consuming, and only applicable to limited situations.

In this work, we propose a method that estimates a Buddha statues built year leveraging only the image of Buddha faces. To the best of our knowledge, we are the first to address this task in an automatic manner. We use the dataset of Buddha statues presented by Renoust et al. [START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF], which, to the best of our knowledge, is the only dataset that comes with a rich set of annotations on built time, materials, etc. One major challenge in this dataset is its heterogeneous labels; that is, due to the inherent nature of cultural heritage as mentioned above, Buddha statue history can be lost, and thus some labels are completely missing or can only be roughly estimated by historians. As for their built time, many samples do not have relevant labels at all; some come with their exact built year, and the others only have more ambiguous expressions on the built time, such as the dynasty or century that they were established in.

In this paper, we are proposing a method that estimates the built year from Buddha statue's facial images using a deep learning-based model. We trained a regression model to compute the built year from the image embedding extracted with a convolutional neural network (CNN) backbone. To make full use of the heterogeneous labels, we take advantage of weakly-labelled and unlabelled images in a semi-supervised manner and devise a loss function so that labels with different ambiguities can be incorporated into training. More specifically, our loss function consists of a MSE loss to reduce an image embedding to a scalar representing the built year, a Kullback-Leibler (KL) divergence-based loss that constraints the built year values to a certain given range, and a regularisation loss designed to unleash the information hidden in the unlabelled images.

Contribution. In addition to the above mentioned new loss functions, we propose to represent the built time as Gaussian functions. This unifies the labels in different ambiguity levels and provides a way to incorporate them in our KL divergence-based loss term. We experimentally show that our method can estimate the built year with 37.5 years of mean absolute error (MAE).

PRIOR WORK

In this section, we limit the discussion to the semi-supervised learning framework (Section 2.2) and how it can be used to address the fine-grained task of Buddha statue's built year prediction (Section 2.1).

Built Year Prediction

When literature about the Buddha statue is missing, their built year can be identified using some chemical analysis-based method, which analyses the chemical components of the material. Such methods are both time consuming and material-dependent since they can only be applied for some specific materials, such as wood or stone, in most cases demanding special equipment. The recent movement of digitisation of the humanities allows to build digital scans of Buddha statues, opening the door to automatic analysis that requires data and computers.

Machine learning, or more specifically CNNs, such as ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] and VGG [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF], has been one of the main driving forces of this movement, allowing to automatically extract features from an image that give accurate representation for different kinds of entities, such as text, natural images, or art pieces. They are extensively used as off-the-shelf model in styles classification [START_REF] Bar | Classification of artistic styles using binarized features derived from a deep neural network[END_REF][START_REF] Brahim | GCNBoost: Artwork Classification by Label Propagation through a Knowledge Graph[END_REF][START_REF] Garcia | Context-aware embeddings for automatic art analysis[END_REF][START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF], authorship identification [START_REF] Ma | From part to whole: who is behind the painting?[END_REF], and artworks retrieval [START_REF] Mao | Deepart: Learning joint representations of visual arts[END_REF]. Mensink [START_REF] Mensink | The rijksmuseum challenge: Museum-centered visual recognition[END_REF] proposed a method that applies max-margin regressor to SIFT features to identify painting built years. Strezoski [START_REF] Strezoski | Omniart: a large-scale artistic benchmark[END_REF] improved this built year estimation task with a multitask learning deep learning network. Classification of various aspects of Buddha statues is addressed in [START_REF] Brahim | GCNBoost: Artwork Classification by Label Propagation through a Knowledge Graph[END_REF][START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF], but their built years are predicted in the century basis, which only gives rough ideas about their establishment. The major drawback of the traditional deep learning approach is it requires an enormous amount of labelled data during the training process. Furthermore, the past approaches require built year labels in normalized form, which often leads to quantizate the label into centuries and reformulate the prediction problem as a classification problem.

In our Buddha project, we do not have the luxury of having a large labelled dataset. To handle this situation, we start to investigate the possibility of applying semi-supervised learning to relax this labelled data shortage.

Semi-supervised Learning

Semi-supervised learning is a way to combine labelled data and large amounts of unlabelled data into the same training process. In this context, several assumptions are adopted to make the best of unlabelled data.

The most widely used one is the cluster assumption, stating that: if two samples are in the same cluster, they are likely to belong to the same class. This is a strong assumption particularly for classification problems, which allows to give pseudo labels to unlabelled samples. In this way, the labelled data and pseudo-labelled data can be used in the training process. With inclusion of pseudo-labelled data, the training data pool significantly increases, which improves the data diversity and lowers the chance of over-fitting. There are two major ways of semi-supervised learning: transductive learning [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF][START_REF] Moscovich | Minimax-optimal semisupervised regression on unknown manifolds[END_REF] and inductive learning [START_REF] Berthelot | MixMatch: A Holistic Approach to Semi-Supervised Learning[END_REF][START_REF] Li | Learning to impute: A general framework for semi-supervised learning[END_REF][START_REF] Sohn | Fix-Match: Simplifying Semi-Supervised Learning with Consistency and Confidence[END_REF][START_REF] Tarvainen | Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results[END_REF][START_REF] Zou | Confidence regularized self-training[END_REF]. Transductive learning produces labels only for unlabelled data available in the training, while the inductive learning assigns new data with a label from prediction.

The manifold assumption is another popular assumption, which is applicable for both regression and classification problems [4, 12-14, 23, 32]. It states that: the high-dimensional data lie roughly on a low-dimensional manifold, which implies that in the manifold the densely sampled regions are smoother with smaller gradient. Under this assumption, a regularizer with radial basis function kernel can be used to enforce the smoothness among label and unlabelled data [START_REF] Berikov | Solving weakly supervised regression problem using low-rank manifold regularization[END_REF].

Our paper devises a semi-supervised regression model that predicts built years with high accuracy. Furthermore, we study how unlabelled data facilitate the regression task, taking into account the manifold assumptions in the context of semi-supervised learning.

DATASET

We obtained the dataset from Renoust et al. [START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF], which consists of 7,518 scanned Buddha images from 5 different books. The retina face detection algorithm [START_REF] Deng | Retinaface: Single-stage dense face localisation in the wild[END_REF] was deployed by the authors to extract the face of statues. These face images were then aligned and resize to 112 × 112, following the same process in [START_REF] Deng | Arcface: Additive angular margin loss for deep face recognition[END_REF]. The algorithm found 4,949 Buddha face images in the dataset. Among them, only 1,887 have built time labels, while the remaining do not provide any information about their built time. The built time labels associated with respective images fall into three types: dynasty in which the statue was built, ranging from 40 years to 700 years, century, and exact year. Hereinafter, we call these labels built time collectively, while using built year whenever it pinpoints a certain year. We picked out the label with the smallest range if multiple labels are available. The distribution of the labels is as follows:

• dynasty: 320 samples • century: 316 samples • year: 1,251 samples

We randomly split the dataset into 70% (i.e., 3,464 samples) for training and 30% (i.e., 1,485 samples) for testing, where 1,340 out of 3,464 samples have built time labels in the training set and 547 out of 1,485 samples in the testing set.

Figure 2 shows some sample Buddha face images after alignment. Many of them have missing facial parts (Fig. 2 (h)). All images of the dataset were collected by scanning printed books, which often leads As mentioned previously, D L contains three types of labels, i.e., one that gives exact year of building and the others that give the range of built time (dynasty or century). We denote the corresponding sets by D Y L , D D L , and

D C L , respectively (D L = D Y L ∪ D D L ∪ D C L )
. In order to unify labels with different ambiguities, we represent the built time with Gaussian N (𝜇, 𝜎 2 ). For samples with exact built year, we use the built year as mean 𝜇 and 2.5 as standard deviation 𝜎, covering 10 years centred at the year in the 95% confidence interval. A century spans 100 years, so the mean is set to the middle of the century (i.e., 𝜇 = 1, 450 for the 15th century) and 25 years as standard deviation. For dynasties, we use the middle year of the dynasty period as 𝜇 and the quarter of the dynasty period as 𝜎, which covers the dynasty within the 95% confidence interval. Therefore, our label 𝑡 is given by a tuple 𝑡 = (𝜇 𝑡 , 𝜎 𝑡 ), which identifies a Gaussian. Figure 3 illustrates two examples Gaussian. The blue line represents the Kamakura dynasty, which starts at 1185 and lasts until 1333. The mean for this dynasty is 1259 and the standard deviation is 37. The red line is the 10th century (from 901 to 1000), where the mean and standard deviation are 950 and 25, respectively. Our model consists of a ResNet50 variant of Arcface [START_REF] Deng | Arcface: Additive angular margin loss for deep face recognition[END_REF], pretrained with 17 million human face datasets [START_REF] An | Partial FC: Training 10 Million Identities on a Single Machine[END_REF], as backbone, of which the last batch normalisation layer is connected to a fully connected layer to predict built year.

(a) (b) (c) (d) (e) (f) (g) (h) (i)
To make full use of the dataset with labelled and unlabelled images, we design a dedicated semi-supervised loss function, consisting of three terms, which are the mean squared error (MSE) loss, a KL divergence-based loss to better incorporate the different ambiguity levels, and a regularisation to make a smoother manifold with unlabelled samples.

MSE loss. The MSE loss provides basic supervision merely for samples with exact built years. Let 𝑓 (𝑥) denote our model to regress the built year from image 𝑥. Our MSE loss 𝐸 is defined as:

𝐸 = 1 |D Y L | (𝑥,𝑡 ) ∈ D Y L ∥𝑓 (𝑥) -𝜇 𝑡 ∥ 2 , (1)
where 𝜇 𝑡 is the mean of 𝑡. KL divergence-based loss. This loss utilises the different ranges of the built time labels in the dataset. Intuitively, an arbitrary pair of predicted built year must have a similar relationship (i.e., the closeness) to the ground-truth built time, which is not as straightforward as computing the distance between two samples, since the built time labels come with different ambiguities. Inspired by t-SNE [START_REF] Van Der Maaten | Visualizing data using t-SNE[END_REF], we encode such pairwise relationships into conditional probability 𝑞(𝑓 (𝑥 ′ ) | 𝑓 (𝑥)) of prediction 𝑓 (𝑥 ′ ) given 𝑓 (𝑥) (or conditional probability 𝑝 (𝑡 ′ | 𝑡) of ground-truth 𝑡 ′ given 𝑡), where (𝑥, 𝑡) and (𝑥 ′ , 𝑡 ′ ) are in D L . We enforce 𝑞 being similar to 𝑝, so that the pairwise relationships in the ground-truth built year labels are maintained in the predictions.

More specifically, for prediction, we define the conditional probability 𝑞(𝑓 (𝑥 ′ ) | 𝑓 (𝑥)) as the likelihood of 𝑓 (𝑥 ′ ) assuming that it follows 𝑁 (𝑓 (𝑥), 𝜎 2 𝑡 ), normalised over all samples in all training samples, where 𝜎 𝑡 is borrowed from the ground truth-label 𝑡 associated with 𝑥 (i.e., (𝑥, 𝑡) ∈ D L ). This can be formalised as:

𝑞(𝑓 (𝑥 ′ ) | 𝑓 (𝑥)) = 1 𝜎 𝑡 √ 2𝜋 exp - (𝑓 (𝑥 ′ )-𝑓 (𝑥)) 2 2𝜎 2 𝑡 𝑥 ′ 1 𝜎 𝑡 √ 2𝜋 exp - (𝑓 (𝑥 ′ )-𝑓 (𝑥)) 2 2𝜎 2 𝑡 . (2)
Similarly, we can define the pairwise conditional probability 𝑝 (𝑡 ′ | 𝑡) from ground-truth labels 𝑡.

𝑝 (𝑡 ′ | 𝑡) = 1 𝜎 𝑡 √ 2𝜋 exp -1 2
(𝜇 𝑡 ′ -𝜇 𝑡 ) 2 𝜎 2 𝑡 𝑡 ′ 1 𝜎 𝑡 √ 2𝜋 exp -1 2
(𝜇 𝑡 ′ -𝜇 𝑡 ) 2 𝜎 2 𝑡 . (3)
The summations in the above two equations are computed over

(𝑥 ′ , 𝑡 ′ ) ∈ D L .
Our KL divergence-based loss 𝐶 based on conditional probability 𝑞 and 𝑝 is calculated by

𝐶 = (𝑥,𝑡 ) KL(𝑝 ∥𝑞) = (𝑥,𝑡 ) (𝑥 ′ ,𝑡 ′ ) 𝑝 (𝑡 ′ | 𝑡) log 𝑝 (𝑡 ′ | 𝑡) 𝑞(𝑓 (𝑥 ′ ) | 𝑓 (𝑥)) , (4)
where (𝑥, 𝑡) and (𝑥 ′ , 𝑡 ′ ) are in D L .

Regularisation. Our regularisation loss is designed to unleash the information that is hidden in the unlabelled samples. It uses the manifold assumption, enforcing a smoother manifold by incorporating unlabelled data in the training process.

According to the manifold assumption, feature vectors from the backbone lie on a smooth low-dimensional manifold in the feature space. Berikov and Litvinenko [START_REF] Berikov | Semi-supervised regression using cluster ensemble and low-rank co-association matrix decomposition under uncertainties[END_REF] suggested that the decision function should change slowly in regions where feature vectors are densely distributed. From this assumption, the large amount of unlabelled data can help smooth the manifold and so regularise the training process. We adapted the radial basis function (RBF) [START_REF] Berikov | Semi-supervised regression using cluster ensemble and low-rank co-association matrix decomposition under uncertainties[END_REF][START_REF] Robert | Local linear semi-supervised regression[END_REF][START_REF] Zhu | Semi-supervised learning using gaussian fields and harmonic functions[END_REF] to approximate the smoothness of the manifold.

Let 𝑔(𝑥) denote feature vector 𝑣 from our backbone 𝑔, where our model 𝑓 is the composition of 𝑔 and regressor (a fully connected layer) ℎ (i.e., 𝑓 (𝑥) = ℎ(𝑔(𝑥)). Following [START_REF] Berikov | Semi-supervised regression using cluster ensemble and low-rank co-association matrix decomposition under uncertainties[END_REF], the pairwise regularisation weight 𝜙 (𝑔(𝑥), 𝑔(𝑥 ′ )) is applied between a pair of a labelled sample and an unlabelled sample, which is given by:

𝜙 (𝑔(𝑥), 𝑔(𝑥 ′ )) = exp - ∥𝑔(𝑥) -𝑔(𝑥 ′ )∥ 2 2𝑙 2 , ( 5
)
where 𝑔(𝑥) and 𝑔(𝑥 ′ ) are the output from the last batch-normalisation layer, and 𝑙 is a parameter to control the smoothness. We used 𝑙 = 0.75 based on [START_REF] Berikov | Semi-supervised regression using cluster ensemble and low-rank co-association matrix decomposition under uncertainties[END_REF]. The regularisation term 𝑅, which is the mean of the regularisation weights, is given as follows:

𝑅 = 1 |D L | |D U | 𝑥 𝑥 ′ 𝜙 (𝑔(𝑥), 𝑔(𝑥 ′ )), (6)
where the first and second summations are computed over the images 𝑥 and 𝑥 ′ in D L and D U , respectively. This term enlarges data pools used in training by 200%, allowing our model to be robust to overfitting. Overall loss function. Our overall loss function ℓ is a linear combination of three terms, given by

ℓ = 𝛼𝐿 + 𝛽𝐶 + 𝛾𝑅, (7)
where we empirically set 𝛼 to 1, 𝛽 to 15, and 𝛾 to 0.1 which scales the three terms into similar weights.

EXPERIMENTS

We report on a set of experiments conducted to assess the benefit of our model. Section 5.1 describes the state-of-the-art (SOTA) methods, along with the different baselines we evaluated. Section 5.2 gives the implementation details. Moreover, we compare our model with the baseline methods in Section 5.3. Finally, Section 5.4.2 reports and analyses the errors of our model.

Baselines

Our model was compared against the following baseline and SOTA methods. For training these baselines, we used all samples in training set, where for the ones with dynasty or century labels, the middle years were employed instead of Gaussian function-based representation.

Nearest Neighbour Search. We store feature vector 𝑔 0 (𝑥) of 𝑥 and 𝑡 for (𝑥, 𝑡) ∈ D L , where 𝑔 0 (𝑥) is the feature embedding from a ResNet50 variant of ArcFace [START_REF] Deng | Arcface: Additive angular margin loss for deep face recognition[END_REF] (the subscript 0 is to emphasise that it is the original pretrained model). For a new Buddha face image 𝑥 ′ , we compute 𝑔 0 (𝑥 ′ ) and find the nearest neighbour from the stored feature vectors in terms of the cosine similarity. The prediction by this method is given as the label 𝑡 associated with the nearest neighbour.

Gaussian Process Regression. Gaussian process regression [START_REF] Christopher | Gaussian processes for machine learning[END_REF] is a non-parametric kernel-based probabilistic model. We used 𝑔 0 as our feature extractor and MATLAB implementation with default parameters.

ResNet50 Regression w/o fine-tuning. We evaluate the same network structure as ours but without fine-tuning the backbone. The model is trained solely by our MSE loss.

Semi-supervised Deep Kernel Learning (SSDKL) [START_REF] Jean | Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance[END_REF]. SS-DKL was proposed by Jean et al. [START_REF] Jean | Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance[END_REF] and utilises the power of deep learning and Gaussian process to learn a model from both labelled and unlabelled data. Their objective is to maximise the likelihood of labelled data and at the same time minimise the predictive variance in the unlabelled data. We used their original implementation. 1 GCNBoost Regression. A GCN-based transductive semi-supervised learning classifier in [START_REF] Brahim | GCNBoost: Artwork Classification by Label Propagation through a Knowledge Graph[END_REF] is adapted to the task of built year prediction. This method requires pseudo labels for unlabelled samples, and we used our full model to compute those pseudo labels. A knowledge graph is built by connecting samples that have the same built years. We adapted the GCN to make it an output layer a single scalar representing the built year. The MSE loss term is used to train the model in an end-to-end manner.

Implementation Details

Our model and its variants were implemented on PyTorch. For training, a A100 GPU with 40G of RAM was used. The batch size was set to 256, the learning rate was set to 0.003, and Adam was used for optimisation. For the MSE loss, we standardised the built year (i.e., 𝜇's in the training set to have zero mean and unit variance). From our preliminary experiments, we found that data augmentation by only random horizontal flipping leads to the best performance; therefore, we used this in all experiments.

Results

We evaluated our method and its variants for ablation studies, as well as the baselines listed in Section 5.1. The test set of the dataset contains 1,485 samples, where 547 of them have a built time label, and 371 have an exactly built year label. Our evaluation uses only these 371 samples as it is not trivial to evaluate errors based on dynasty and century labels. We employed mean absolute error (MAE) as our error metric.

Table 1 shows the performances of all methods in comparison. Rows 1, 2, 3 and 6 are the inductive baselines. Nearest Neighbour Search (row 1) and Gaussian Process Regression (row 2) did not perform well, while ResNet50 Regression w/o fine-tuning (row 3) gave competitive performances. This implies that training with the MSE loss can benefit a lot, and our backbone provides rich cues about Buddha statues even though it is trained on human faces; yet end-to-end training helps. These results may also suggest that the relationship between the feature space and the built year space is not simple, which can support the use of our KL divergence-based loss and regularisation term.

Rows 4 and 5 are the performances of transductive baselines. GC-NBoost Regression [START_REF] Brahim | GCNBoost: Artwork Classification by Label Propagation through a Knowledge Graph[END_REF] shows a better performance when compared to SSDKL [START_REF] Jean | Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance[END_REF], but both methods did not perform as well as other methods. For SSDKL, we consider that the original feature vector obtained from our backbone did not have sufficient cues about the built years and the error accumulated in the iterations. GCNBoost Regressor suffers from the sparse connectivity between samples in the test set and those in the training set since we added edges 1 https://github.com/ermongroup/ssdkl between the samples with exactly same built years; therefore, the features cannot be well trained. Moreover, we do not have Buddha statues attributes other than the built years ones. Those attributes (if available) can improve GCNBoost accuracy as shown in [START_REF] Brahim | GCNBoost: Artwork Classification by Label Propagation through a Knowledge Graph[END_REF] as they emphasis the relationship between the nodes in GCNBoost's knowledge graph. Rows 6 to 10 show performances of our model on the ablation study over the loss terms, where "MSE", "KL", and "Reg. " stand for the MSE loss, KL divergence-based loss, and regularisation terms, respectively. The results clearly show the importance of the MSE loss term, while the KL divergence-based loss and regularisation terms provide less impact on the performance. This is quite reasonable because the MSE loss term is the only one that gives direct supervision about the built time, while the others only tell the relationships among the samples. Yet, the best performance is obtained when we combined all three terms, which implies their complementarity.

For tasks that involve cultural heritage, the availability of samples (i.e., images in our case) is a critical problem. Cultural heritages are often stored in a secure place, and very limited access is allowed. Under this circumstance, the only way to acquire images of cultural heritages is to make digital scans of their images printed in catalogues or books, as Renoust et al. did in [START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF]. The image quality is thus affected by various factors, such as the quality of captured images, the quality of printing, and the quality of digital scans. Moreover, image quality degradation due to these factors may not necessarily be distinguishable from the texture of Buddha statues themselves. This is an inherent problem that particularly rises with cultural heritage. We therefore investigated the performance of our method with respect to the image quality.

We employed Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) [START_REF] Mittal | Noreference image quality assessment in the spatial domain[END_REF] to measure the image quality. BRISQUE uses an image quality score in [0, 100], where a lower score indicates better quality. The distribution of the image quality scores in the entire dataset (including both training and test sets) is shown in Fig. 4. The correlation between the image quality scores and built year labels is -0.3021, which weakly indicates that a statue captured with a higher image quality tends to be established more recently. Example images with the highest, medium, and lowest qualities To see the impact of the image quality on our method, we plotted the relationship between the image quality score and prediction errors in Fig. 6. The figure shows that images with a higher quality (i.e., a lower score) got a lower error, and vice versa. From this, we can conclude that the image quality is an important factor to determine the prediction accuracy. The t-SNE visualisations of the feature vector extracted from both training and test sets before and after fine-tuning are shown in Figs. 8 and9, respectively. For the labelled samples, the built years (the middle years for dynasty and century labels) are colour coded. Before fine-tuning, we can see that the year is almost randomly distributed. Whereas after fine-tuning, the distribution of the samples looks to be more structured, which indicates that our loss function effectively gives supervision to the backbone based on the similarity in the feature vectors and ground-truth labels. ones with high errors tend to have more visible damage and lower image quality. The statues with high errors were built in 1091, 1047, and 1241, respectively; however, our method predicted them as 647, 578, and 640. The source of the errors can come from the low image quality; for example, image (g) looks to have block noises due to compression, while (h) and (i) are dark and blurry. This is consistent with our result in Section 5.3.

CONCLUSION

In this work, we proposed a method to estimate the built year of Buddha statues from only their face images. We faced four main challenges to solve this task: First, the images in the dataset were collected from digital scans of 5 different books, which introduced many artefacts and distortions. Second, the dataset is quite small, containing only 4,949 facial images. Third, only 30% of samples in this small dataset are labelled. Finally, this dataset contains two types of labels: exact built years and the range of built years (i.e, dynasty and centuries) estimated by historians. To overcome those challenges, we modelled the labels in the form of Gaussian functions, which provided a unified built time representation for training. We also designed a new loss function to handle Gaussian functionbased built time representation as well as unlabelled samples. Our experimental results showed that our method outperformed stateof-art methods and baselines by a significant margin. As our future work, we plan to use the different Buddha statues related information available in the dataset [START_REF] Renoust | Historical and modern features for Buddha statue classification[END_REF], such as built material, original location, which can be correlated with built time. For this, we need to handle highly heterogeneous data as the dataset has a lot of missing entries. The second direction is to collect more samples for better training.

Figure 1 :

 1 Figure 1: Distribution of built time on labelled data.

4 METHOD

 4 Our task is to estimate the built year 𝑡 of a given image 𝑥. Although the transductive paradigm may also work for our task because the number of cultural heritages merely increases, we this time choose the inductive paradigm. More specifically, we denote our labelled training set D L = {(𝑥 𝑖 , 𝑡 𝑖 ) | 𝑖 = 0, . . . , 𝐼 L } and unlabelled training set D U = {𝑥 𝑖 | 𝑖 = 0, . . . , 𝐼 U } for training, where 𝑥 𝑖 and 𝑡 𝑖 are the 𝑖th image and the corresponding label; and 𝐼 L and 𝐼 U is the numbers of samples in the labelled and unlabelled training sets, respectively.

Figure 2 :

 2 Figure 2: Some samples of Buddha face images in the dataset. (a) Amidanyorai (阿弥陀如来), (b) Seishibosatsu (勢至菩薩), (c) Mirokubutsu (弥 勒 仏), (d) Amidanyorai (阿 弥 陀 如 来), (e) Fudōmyōō (不 動 明 王) (f) Kongōrikishi (金 剛 力 士) (g) Zōchōten (増長天) (h) Jisha (侍者) (i) Zenzaidōji (善財童子).

Figure 3 :

 3 Figure 3: Two examples Gaussian to represent built times. The blue line is N (1259, 37 2 ), which represents the Kamakura dynasty (1185-1333). The red line is N (950, 25 2 ), covering the 10th century.

Figure 4 :Figure 5 :

 45 Figure 4: The distribution of image quality scores measured by BRISQUE.

Figure 6 :

 6 Figure 6: The relationship between image quality scores and prediction errors in MAE.

Figure 7 (

 7 b) shows a more scattered distribution. On the other hand, Fig.7 (c) shows a greater amount of estimation concentrated in a narrower band where its distribution shares more similarity with ground truth map.

  𝑝 (𝑡 ′ |𝑡 ), 𝑞 (𝑓 (𝑥 ′ ) |𝑓 (𝑥))

Figure 7 :Figure 8 :Figure 9 :

 789 Figure 7: Visualisation of conditional probabilities (a) 𝑝 (𝑡 ′ |𝑡), 𝑞(𝑓 (𝑥 ′ )|𝑓 (𝑥)) for (b) MSE+KL, (c) MSE+Reg., and (d) MSE+KL+Reg.

Figure 10 :

 10 Figure 10: Examples of images with low (first row), medium (second row) and high error (third row) estimation error in our test set.

Table 1 :

 1 Comparison of different methods and some variants of ours. Only 371 samples in the test set that have exact built year labels were used.

		Methods	MAE (Year)
	1	Nearest Neighbour Search	130.9 ± 9.8
	2	Gaussian Process Regression	199.9 ± 5.4
	3	ResNet50 Regression w/o fine-tuning	73.8 ± 4.0
	4	GCNBoost Regression [9]	217± 15.5
	5	SSDKL [12]	245.3± 4.0
	6	Ours (MSE)	56.2 ± 3.7
	7	Ours (KL+Reg.)	338.3 ± 33.1
	8	Ours (MSE+KL)	40.2 ± 3.62
	9	Ours (MSE+REG)	39.3 ± 3.55
	10 Ours (MSE+KL+Reg.)	37.5± 3.64


Cécile Chamayou-Robert

Carole Digiorgio
email: carole.di-giorgio@univ-amu.fr

Olivier Brack
email: olivier.brack@wanadoo.fr

Olivier Doucet
email: olivier_doucet@cotyinc.com

Cécile Chamayou

Blue Light induces DNA-damage and may contribute to chromosome aberrations in normal human skin keratinocytes

Keywords: Blue light, DNA damage, DNA repair, keratinocytes

Background: The generation of DNA damage by ultra-violet radiations (UV) is well established, and both the nature of the DNA lesions and their respective DNA-repair pathways, have largely been described. Besides UV rays, visible light constitutes a very important part of the sun spectrum where blue light is considered a significant contributor to premature aging. However, blue light-induced DNA damage has not been deeply explored yet.

Methods: In the present study, we assessed in human skin keratinocytes the DNA and Chromosome damaging activities of blue light rays (415 nm) as well as their associated DNA-repair mechanisms.

Results: Our results demonstrated that blue light induced dose-dependent DNA-damage in human keratinocytes. Both Oxidative and Cyclobutane-Pyrimidine-Dimers (CPD) DNA-lesions were generated. They were repaired through base excision repair (BER) and nucleotide excision repair (NER) pathways, respectively. Moreover, by using the Micronucleus assay we demonstrated, for the first time, that a blue wavelength exerted a clastogenic/aneugenic effect in human keratinocytes, leading to chromosome heritable aberration.

Conclusion:

We concluded that, in normal human keratinocytes, blue light creates genotoxic lesions which might accelerate or at least contribute to premature skin aging.

Introduction

Blue light (400-500nm) takes part of the visible electromagnetic spectrum. Natural sunlight blue wavelengths, which are always mixed with green, yellow and red wavelengths, have been shown to play an important role in the regulation of sleeping patterns and circadian rhythms. [START_REF] Rabstein | Differences in twenty-four-hour profiles of blue-light exposure between day and night shifts in female medical staff[END_REF] However, since the 1980s the development of light-emitting diodes (LED) without red and near infrared wavelengths, and the concomitant exponential use of digital technologies, such as flat-screen TVs, computers, tablets and smart phones, have led to a drastic increase of human exposure to blue light [START_REF] Wolf | Children's Environmental Health in the Digital Era: Understanding Early Screen Exposure as a Preventable Risk Factor for Obesity and Sleep Disorders[END_REF] and to several concerns about their possible involvement in the development of degenerative eye diseases. Moreover, the expansion of therapeutic protocols using blue light irradiation in several dental treatments and dermatologic therapies, has highlighted their potential sideeffects. [START_REF] Yoshino | Effects of blue-light irradiation during dental treatment[END_REF] The toxic and genotoxic effects of blue wavelengths have mainly been studied in the context of their therapeutic and ocular risks: they have been shown to induce cellular dysfunction and cell death in gingival fibroblasts [START_REF] Taoufik | Effect of blue light on the proliferation of human gingival fibroblast[END_REF] and lens epithelial fibroblasts [START_REF] Xie | Effects of white light-emitting diode (LED) light exposure with different Correlated Color Temperatures (CCTs) on human lens epithelial cells in culture[END_REF] , to generate sister-chromatid exchanges and endoreduplicated chromosomes in CHO cells [START_REF] Wall | Oxidative stress and endoreduplication induced by blue light exposure to CHO cells[END_REF] , and to cause deoxyribonucleic acid (DNA) strand-breaks in retinal pigment epithelial cells. [START_REF] Sparrow | DNA is a target of the photodynamic effects elicited in A2E-laden RPE by bluelight illumination[END_REF] Blue wavelengths near ultra-violet A (UVA) (400-450 nm), shown to be the most energetic visible wavelengths, have been supposed to produce the most important adverse effects in mammalian cells 8 , mainly through the extracellular and intracellular photosensitized production of Reactive Oxygen Species (ROS). [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF] However, direct interactions with DNA-bases have been also demonstrated. [START_REF] Sparrow | DNA is a target of the photodynamic effects elicited in A2E-laden RPE by bluelight illumination[END_REF] Concerning cutaneous exposure, it has been shown that blue wavelengths penetrate into the skin [START_REF] Ash | Effect of wavelength and beamwidth on penetration in light-tissue interaction using computational methods[END_REF] and induce both ROS production and cell death. [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF][START_REF] Opländer | Effects of blue light irradiation on human dermal fibroblasts[END_REF][START_REF] Vandersee | Blue-Violet light irradiation dose dependently decreases carotenoids in human skin, which indicates the generation of free radicals[END_REF] Recent studies have shown that blue light can also induce DNA damage in keratinocytes 13, 14 but the identification of the DNA lesions have been poorly studied. In the present work, we attempted to study the DNA-damaging activity of blue light (415 nm), its DNA-repair mechanisms, and its resulting chromosome damage in human skin cells. Blue light induced DNA-damage and DNA-repair were evaluated by the comet assay in human normal keratinocytes, the predominant cell type in the epidermis. [START_REF] Wischermann | Improved alkaline comet assay protocol for adherent HaCaT keratinocytes to study UVA-induced DNA damage[END_REF][START_REF] Jean | Evaluation of sunscreen protection in human melanocytes exposed to UVA or UVB irradiation using the alkaline comet assay[END_REF] Chromosome mutations resulting from unrepaired DNA double-strand breaks and chromosome segregation abnormalities were measured by the micronucleus assay. 17

Materials and methods

Chemicals and cell cultures

All reagents for cell cultures were purchased from Dutscher (Brumath, France), except bovine pituitary extract, recombinant epidermal growth factor (rEGF) and keratinocyte serum-free medium (K-SFM) which were from GIBCO-BRL (Life Technology, Cergy Pontoise, France). All chemicals for the comet and the micronucleus assays were purchased from Sigma-Aldrich (Saint Quentin Fallavier, France). Human Epidermal Keratinocytes Neonatal were purchased from ScienCell Research Laboratories. They were maintained in "Keratinocytes-SFM" medium supplemented with bovine pituitary extract (30 µg/ml) and recombinant epidermic growth factor (rEGF, 0.2 ng/ml). Cultures were performed in a 37°C humidified incubator with 5% CO2 atmosphere.

Irradiation procedure

Blue light irradiation was carried out with a Biolambda blue light irradiator (Biolambda, Sao Paulo, Brasil) equipped with 415 nm LED, at an irradiance of 8 mW/cm². Before irradiation, well covers were removed and cells were irradiated with 4.8 J/cm², 9.6 J/cm², and 14.4 J/cm² for the standard comet assay and the micronucleus assay, and 9.6 J/cm² for DNA-repair kinetics. UVA/visible irradiation was carried out with a Suntest CPS+ solar simulator (Atlas Material Testing Technology BV, Moussy le Neuf, France) equipped with a xenon arc lamp (1100 W) and special glass filters (ID65) restricting transmission of light below 290 nm and near IR-blocking filter. The irradiation intensity was fixed at 76.5 mW/cm², and cells were irradiated with 15 J/cm 2 . UVB irradiation was carried out with an UV irradiator Bio-Sun (Vilbert Lourmat, Marne la Vallée, France). The irradiator was equipped with a monochromatic UVB lamp, which delivered a calibrated computer-assisted beam of 312 nm wavelength at an irradiance of 0.91 mW/cm 2 , and cells were irradiated with 0.08 J/cm². Blue-light, UVA and UVB doses have been selected for their low impact on cell survival, as assessed by neutral red uptake assay (more than 90% cell viability as compared to the nonirradiated cells) [START_REF] Repetto | Neutral red uptake assay for the estimation of cell viability/cytotoxicity[END_REF] .

Comet assay

The standard alkaline comet assay was performed as described by Singh et al. [START_REF] Singh | A simple technique for quantitation of low levels of DNA damage in individual cells[END_REF] , and a modified protocol has been used to improve the sensitivity of the assay by the use of specific enzymes: FPG, the formamidopyrimidine DNA glycosylase, which allows detecting 8-oxoguanine and other purine oxidation products formed when cell nuclei are exposed to oxidative stress and which specifically recognizes oxidized DNA-bases to convert them into strand-breaks [START_REF] Azqueta | Enhancing the sensitivity of the comet assay as a genotoxicity test, by combining it with bacterial repair enzyme FPG[END_REF] ; T4 endonuclease V, the specific DNA-repair protein that recognizes cyclobutane pyrimidine dimers (CPD) and cleave them to form detectable strand-breaks, allows detecting the most abundant DNAlesions induced by UVB [START_REF] Lo | Differential biologic effects of CPD and 6-4PP UV-induced DNA damage on the induction of apoptosis and cell-cycle arrest[END_REF] . Briefly, cells monolayers were irradiated before trypsinization. Cells pellets were suspended in agarose and deposited onto microscope slides, then immersed in lysis solution for 90 min at 4°C. After the lysis procedure, slides were washed with BSA enzymatic buffer and treated with T4 endonuclease V, or with FPG for 30 minutes at 37°C in a humidified chamber. Electrophoresis was then carried out for 20 minutes at 25 V and 300 mA. Finally, the slides were washed with 0.4 M Tris buffer (pH 7.5), dehydrated in 100% methanol and dried for 12 hours at room temperature. Each slide was stained with 50µl of 2 µg/ml ethidium bromide and examined at 250X Magnification using a BX53-RFL fluorescence microscope (Olympus Optical Co., Tokyo, Japan) equipped with a U-MWG2 dichroic mirror (band-pass filter, 510-550 nm; long-pass filter, 590 nm) and a UPLFLN 20x objective. Image analysis was performed using the Komet software (version 6.0 Andor Technology, Belfast, Northern Ireland). A total of 50 randomly selected cells were analyzed per slide using Fenestra Komet 6.0 image analysis software (Andor Technology, Belfast, Northern Ireland). DNA damage was expressed as the Olive Tail Moment (OTM; arbitrary units); 100 OTM values were determined for each sample, 50 from each of two separate slides/sample. The 100 calculated OTM values by sample were distributed into 40 classes between the minimal and the maximal values: each class interval corresponded to 1.4 OTM arbitrary units. A non-linear regression analysis was performed on the OTM distribution frequencies by using a  2 function with TableCurve 2D software (version 5.0; Jandel Scientific Software, San Rafael, CA). The calculated degrees of freedom (n) for this function were quantitative measures of the DNA damage for a sample. [START_REF] Bauer | The distribution of the tail moment in single cell gel electrophoresis (comet assay) obeys a chi-square (χ2) not a gaussian distribution[END_REF] The n was termed  2 OTM and was used as the sole parameter for assessing levels of DNA damage. The significance of the differences between  2 OTM values of non-irradiated and irradiated cells was analysed using Student's t-test. The percentage of DNA-damage (% DNAdamage) was determined as follows:

% 𝐷𝑁𝐴 -𝑑𝑎𝑚𝑎𝑔𝑒 = [ (χ 2 𝑂𝑇𝑀 𝑇𝑋 -χ 2 𝑂𝑇𝑀 𝐶0 ) (χ 2 𝑂𝑇𝑀 𝑇0 -χ 2 𝑂𝑇𝑀 𝐶0 ) ] 𝒙𝟏𝟎𝟎  2 OTMTX:  2 OTM of irradiated cells at each incubation time  2 OTMCO:  2 OTM of non-irradiated cells  2 OTMT0:  2 OTM of irradiated cells at T=0

Micronucleus assay

The micronucleus assay was performed according to the cytokinesis-blocked standard method. [START_REF] Fenech | Intra and inter-laboratory variation in the scoring of micronuclei and nucleoplasmic bridges in binucleated human lymphocytes. Results of an international slide-scoring exercise by the HUMN project[END_REF][START_REF] Snijders | Micronucleus Formation in Human Keratinocytes is Dependent on Radiation Quality and Tissue Architecture[END_REF] Keratinocytes were cultured for 24 hours in tissue culture chambers. Culture medium was replaced by sterile PBS and cells were submitted to irradiation. After irradiation, cells were grown in complete culture medium containing 3 µg/ml of cytochalasin B for 48-hour. Cells were fixed with methanol and stained with 10% Giemsa for 30 minutes. Micronuclei analysis was performed under a microscope at x1000 magnification. The rates of micronuclei were evaluated for the presence of independent nuclear core entities in a total amount of 5,000 binucleated cells. Micronuclei were identified as small nuclei well differentiated from cell nucleus, stained in the same manner and having a diameter less than one third of that of the cell nucleus. Micronuclei rates obtained for different exposure conditions were compared to the negative control by a Chi-squared test of independence in contingency tables.

Results

Blue-light dose-dependent DNA-damage

Figure 1 displays examples of intact and damaged nuclei observed with fluorescent microscope for the comet assay. Figure 2 displays Olive Tail Moment (OTM) distributions and the corresponding  2 OTM in human keratinocytes irradiated with blue light at different irradiation times. Nuclei appeared as condensed spherical spots with low levels of single-strand breaks in non-irradiated cells (OTM median = 0.32 - 2 OTM = 2.06 ± 0.03).

In irradiated cells, nuclei appeared as the shape of a comet, with a small tail formed by the migration of DNA fragments from the nucleus towards the anode. Blue light-irradiation generated a dose-dependent increase of DNA-damage: a significant photo-induced DNA-damage was obtained from an irradiation dose of 9.6 J/cm² (OTM median = 2.21 - 2 OTM = 2.43 ± 0.26, P<0.001).

Blue-light oxidative DNA-damage and CPD-lesions

In blue-light irradiated cells, a significant dose-dependent increase of tail moment (OTM and  2 OTM) was observed from the lowest exposure dose of 4.8 J/cm² (Figure 2), with FPG (median = 3.55 - 2 OTM = 2.99 ± 0.11) or T4 endo V (median = 2.66 - 2 OTM = 2.94 ± 0.12). Cleavage of oxidized bases and base-dimers by FPG and T4 endo V respectively resulted in a strong enhancement of the tail moment, indicating that blue light generated both oxidative DNA-damage and CPD-lesions.

DNA-repair kinetic of oxidative DNA-damage and CPD-lesions

An immediate time-dependent decrease of DNA-lesions could be observed in all the irradiated cells, indicating the rapid involvement of DNA-repair mechanisms after irradiation (Figure 3). Oxidative DNA-lesions, detected through the cleavage of oxidized-bases into apurinic sites by FPG, were totally repaired after a 60-minute incubation period for UVA/visible light irradiation, and after a 40-minute incubation period for blue light irradiation. The repair of CPD-lesions, identified through the cleavage of glycosyl and phosphodiester bonds by T4 Endo V, was slower. A consistent decrease of CPD-lesions could be observed during the first 6 hours after irradiation. Then DNA-repair was less efficient and, after 24 hours, the percentage of unrepaired CPD reached 13% in blue light exposed cells and 40% in UVB-exposed cells.

Mutagenic impact of blue light irradiation

Micronuclei appeared as small nuclear inclusions in the cytoplasm of interphase cells (Figure 4), with diameters varying between 1% and 9% of the cell diameter. In blue light irradiated cells, a dose-dependent increase of micronucleated cell levels could be observed (Table I). Induction of micronucleated cell was not significant for the irradiation doses of 4.8 and 9.6 J/cm² (mean = 9.80 ± 0.84‰ -median = 9.90‰ and mean = 12.60 ± 2.07‰median = 12.00‰ respectively), but it became significant for the irradiation dose of 14.4 J/cm² (mean = 18.60 ± 2.07‰ -median = 19‰), suggesting that some blue light induced DNA-lesions turned into unrepaired doublestrand breaks, leading to stable and heritable chromosomal damages.

Discussion

In the present study, the alkaline comet assay and the micronucleus assay were used to characterize the genotoxic impact of blue light in skin cells and to evaluate the cellular response to blue light induced DNAdamage. Irradiation by 415 nm wavelength, from the exposure dose of 9,6 J/cm², clearly induced dosedependent DNA-damage in human keratinocytes and confirmed previously published data observed in both skin and retinal epithelial cells. [START_REF] Sparrow | DNA is a target of the photodynamic effects elicited in A2E-laden RPE by bluelight illumination[END_REF][START_REF] Dong | Blue light disrupts the circadian rhythm and creates damage in skin cells[END_REF] DNA-lesions were significantly enhanced in the presence of FPG, suggesting that blue light induced oxidative DNA-damage. This data was consistent with previously published studies which established that blue wavelengths could interact with intracellular porphyrins and flavoproteins to generate reactive oxygen species (ROS) [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF][START_REF] Godley | Blue Light Induces Mitochondrial DNA Damage and Free Radical Production in Epithelial Cells[END_REF][START_REF] Omata | Intraand extracellular reactive oxygen species generated by blue light[END_REF] such as superoxide, nitric oxide and peroxynitrite. [START_REF] Opländer | Mechanism and biological relevance of blue-light (420-453 nm)-induced nonenzymatic nitric oxide generation from photolabile nitric oxide derivates in human skin in vitro and in vivo[END_REF] In UVA-irradiated cells, the indirect formation of oxidized DNA bases through excited chromophores is considered the main genotoxic mechanism leading to the formation of 8-oxo-guanine and in a lower extend, DNA strand breaks and oxidized pyrimidines. [START_REF] Pfeifer | UV wavelength-dependent DNA damage and human non-melanoma and melanoma skin cancer[END_REF][START_REF] Tewari | UVA1 induces cyclobutane pyrimidine dimers but not 6-4 photoproducts in human skin in vivo[END_REF] We could suppose that blue-light may induce oxidative DNA-damage according to the same mechanisms as UVA, through an indirect oxidative process. Surprisingly, DNA-lesions were significantly increased in the presence of T4 endo V, suggesting that blue light could also induce CPD-lesions. CPD-lesions are mainly due to high-energy photons, which are directly absorbed by DNA bases, and allow the formation of covalent bonds between two adjacent pyrimidines. [START_REF] Douki | Individual determination of the yield of the main UV-induced dimeric pyrimidine photoproducts in DNA suggests a high mutagenicity of CC photolesions[END_REF][START_REF] Mitchell | Effects of cytosine methylation on pyrimidine dimer formation in DNA[END_REF] They have been shown the predominant DNA-damage induced by UVB. Since UVA are not directly absorbed by the pyrimidine bases of DNA, the formation of CPD has long been considered negligible during UVA exposure. However, various recent studies have established that the majority of lesions induced on DNA by UVA are T-T type CPD. [START_REF] Douki | Individual determination of the yield of the main UV-induced dimeric pyrimidine photoproducts in DNA suggests a high mutagenicity of CC photolesions[END_REF][START_REF] Mouret | Cyclobutane pyrimidine dimers are predominant DNA lesions in whole human skin exposed to UVA radiation[END_REF] These lesions would derive from a Type I photosensitization mechanism, due to an energy transfer from a cell chromophore to the DNA rather than a direct excitation, as it is the case for UVB-induced CPD. [START_REF] Douki | Bipyrimidine photoproducts rather than oxidative lesions are the main type of DNA damage involved in the genotoxic effect of solar UVA radiation[END_REF] The CPD lesions observed in the present study suggested that, similarly to UVA, blue wavelengths may oxidize cellular targets to induce T-T dimers. Two DNA-repair kinetics were obtained in human keratinocytes irradiated with blue light. In FPG-treated nuclei, a rapid decrease of oxidative DNA-damage could be observed within the first 40 minutes post-irradiation. This DNA-repair kinetic was consistent with previously published data concerning UVA-induced oxidative DNAdamage: oxidized bases are rapidly eliminated by the Base Excision Repair (BER) and, after one hour, almost all the DNA-lesions are repaired. [START_REF] Cadet | Oxidative DNA damage & repair: An introduction[END_REF] In T4 Endo V-treated nuclei, the decrease of blue light induced DNA-damage was slower, and 18% of the CPD-lesions remained unrepaired after 24 hours. This DNA-repair kinetic rate was consistent with previously published data observed in UVB-irradiated cells, suggesting the involvement of the Nucleotide Excision Repair (NER), intended to remove a wide range of DNA distorting lesions, such as CPD and 6-4 photoproducts, through a mechanism more complex than BER.

Results observed with the micronucleus assay demonstrated for the first time that a blue light could exert a clastogenic/aneugenic effect in human keratinocytes, leading to heritable chromosome aberrations. Micronuclei are defined as chromosome fragments or whole chromosomes, which have been lost during cell mitosis, and form individual nuclear particles in the cytoplasm of daughter cells. [START_REF] Fenech | Intra and inter-laboratory variation in the scoring of micronuclei and nucleoplasmic bridges in binucleated human lymphocytes. Results of an international slide-scoring exercise by the HUMN project[END_REF] In the present study, it was not possible to selectively differentiate whole chromosomes and chromosome fragments since no FISHtechnique was applied. However, the diameter of micronuclei has been proposed as an indicator of a clastogenic or aneugenic activity, acentric chromosome fragments being characterized by diameters lower than 25% of cell diameter. [START_REF] Tinwell | Micronucleus morphology as a means to distinguish aneugens and clastogens in the mouse bone marrow micronucleus assay[END_REF] In cells exposed to genotoxic compounds or radiations, it has been shown that a strong proportion of micronuclei arises from clastogenic events, through unrepaired double-strand DNA-breaks. [START_REF] Fenech | Molecular mechanisms of micronucleus, nucleoplasmic bridge and nuclear bud formation in mammalian and human cells[END_REF] Our results confirmed this hypothesis, since almost all the micronuclei diameters observed in UVA, UVB and blue light irradiated cells were lower than 10% of the cell diameter. A great variety of mechanisms may transform the different DNA-lesions into acentric chromosome fragments, particularly when DNA-damage exceeds the DNArepair capacities. [START_REF] Fenech | Molecular mechanisms of micronucleus, nucleoplasmic bridge and nuclear bud formation in mammalian and human cells[END_REF] Oxidative DNA-lesions, such as 8-oxodeoxyguanosine, when they are in proximity or on opposite DNA-strands, may generate double-strand breaks through simultaneous excision-repair mechanisms of the BER repair pathway. Similarly, simultaneous excision events, related to the NER repair pathway, involved in the removal of DNA-lesions such as pyrimidine dimers, may also produce double strand-breaks. The presence of micronuclei in binucleated human keratinocytes may be considered a severe DNA damage since genes present in the extranuclear DNA-fragments are under-expressed or over-expressed, resulting in important phenotypic modifications. In survival cells, chromosome abnormalities are probably transmitted from parent cells to daughter cells, leading to chromosome rearrangement and instability. [START_REF] Hintzsche | Fate of micronuclei and micronucleated cells[END_REF] The cellular impact of blue light is being increasingly investigated. But conversely, with well documented damage described on the cornea, the consequences of blue light exposure to human skin cell DNA are less predictable and have not been deeply explored yet. Results observed in the present study suggested that a single 415 nm exposure generates both oxidized DNA-bases and CPD that may turn into heritable chromosome aberrations. Moreover, human exposure to visible light, and thus to blue light, during the daily activities of life is permanent (outside, inside, behind a window), while exposure to UVA is limited to outdoor activities during the daylight. Low-dose cumulative exposures to blue light could thus induce deleterious effects that contribute to premature skin-ageing. Further in vitro and in vivo studies are necessary to investigate the genotoxic potential of blue-light and to evaluate its impact in pre-cancer skin-lesions. As interindividual variations have been shown to play an important role in human carcinogenesis through variations in intracellular oxidative/antioxidative balance or in DNA-repair pathways, experiments should be anticipated in extended cell or skin samples. [START_REF] Panel | Individual Photosensitivity of Human Skin and UVA-Induced Pyrimidine Dimers in DNA[END_REF] In addition, experiments should be proposed to evaluate the cumulative genotoxic effects of low dose repeated blue-light irradiations to better mimic the long-term human exposure.

Conflict of interest

None declared.

FIGURE 1 .

 1 FIGURE 1. Examples of intact and damaged nuclei observed with fluorescent microscope for the comet assay

FIGURE 3 .

 3 FIGURE 3. DNA repair kinetics on keratinocytes exposed to UVA/visible, UVB, and blue light (mean ± SD, n = 4 independent experiments)

FIGURE 4 .

 4 FIGURE 4. Examples of binucleated keratinocytes with micronuclei

TABLE 1 .

 1 Mutagenic impact of UVA/visible, UVB, and blue light in human keratinocytes by the micronucleus assay


David Schmoranzer

Sumit Kumar

Sébastien Triqueneaux

Xiao Liu

Thomas Metcalf

Glenn Jernigan

Eddy Collin

Andrew Fefferman
email: andrew.fefferman@neel.cnrs.fr

A 10 mK hermetic cell for eliminating parasitic heating in cryogen-free dilution refrigerators

Keywords: parasitic heating, thermal decoupling, cryogen-free dilution refrigerator, hermetic shield, mechanical resonators, nanoelectronic devices

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In many cases, cryogen-free (dry) dilution refrigerators greatly increase the efficiency of low temperature research. The elimination of the helium bath allows for much more experimental space than in conventional (wet) dilution refrigerators as well as completely automated operation. However, in some cases, special measures are required to isolate the experiment from vibrations produced by the cryocooler of the dry fridge [START_REF] Pelliccione | Design of a scanning gate microscope for mesoscopic electron systems in a cryogen-free dilution refrigerator[END_REF][START_REF] Kalra | Vibration-induced electrical noise in a cryogen-free dilution refrigerator: Characterization, mitigation, and impact on qubit coherence[END_REF][START_REF] Schmoranzer | Cryogenic broadband vibration measurement on a cryogen-free dilution refrigerator[END_REF]. Furthermore, Schmoranzer et al. previously reported that sample heating due to environmental sources is more significant in dry fridges than in wet fridges [START_REF] Schmoranzer | Observations on thermal coupling of silicon oscillators in cryogen-free dilution refrigerators[END_REF]. Vibrations were ruled out as the cause of heating. It was speculated that the excess heating was related to the absence of a hermetic shield at 4 kelvin (IVC) in the dry fridge, which leads to additional stray photons or residual helium gas at the mixing chamber plate.

Several previous works reported deleterious effects of stray infrared light in the sample space. In experiments involving superconducting cavities and qubits, stray light is a significant source of non-equilibrium quasiparticles. For example, Barends et al. reported an increase in the quality factor of aluminum microwave cavities from 10 5 to 10 6 upon improving the shielding of the sample from "typical" to multistage [START_REF] Barends | Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits[END_REF]. These measurements were made in an electronic adiabatic demagnetization refrigerator. The optimal shielding configuration was a box-in-a-box design with a black coating: While a substantial decrease in resonator Q was observed when warming the 4 K stage in the case of typical shielding, no dependence on 4 K stage temperature was observed in the case of optimal shielding. The latter configuration also produced a significant improvement in the relaxation rate of a phase qubit. Similarly, Córcoles et al. reported an increase in the relaxation time of a superconducting qubit after embedding its package in ECCOSORB absorptive epoxy [START_REF] Córcoles | Protecting superconducting qubits from radiation[END_REF]. In this case, the sample was attached to the mixing chamber plate of a dry dilution refrigerator. These effects are not limited to qubit measurements. Bradley et al. cooled a Coulomb blockade thermometer (CBT) nanoelectronic device below 5 mK via on-chip magnetic cooling in a dry dilution refrigerator. In their detailed thermal model of the cooling process, it was speculated that a parasitic heat leak into the CBT resulted from non-equilibrium photons in the environment [START_REF] Bradley | On-chip magnetic 10 cooling of a nanoelectronic device[END_REF].

Here we present the design of a hermetic cell connected to the mixing chamber 2 plate of a dry dilution refrigerator and quantify its effectiveness in improving the thermalization of our sample, which is a mechanical resonator. We observe a significant improvement relative to a simpler shield described in [START_REF] Schmoranzer | Observations on thermal coupling of silicon oscillators in cryogen-free dilution refrigerators[END_REF] that was not vacuum tight.

Cell Design and Construction

Our hermetic cell consists of a copper tube with indium-sealed flanges at each end (Fig. 1). Ordinary copper was used for the tube and CuC2 (i.e. 3N5 purity Cu) was used for the flanges. An inner flange was welded to each end of the tube. Mating flanges were attached using 12 M3 stainless steel screws at each end. Stainless steel rings were used when closing the cell in order to minimize warping of the copper flanges (Fig. 1). We would recommend using even thicker flanges to further suppress warping at the outer part of the flange.

The bottom of the bottom flange has five M3 threaded holes used to connect the cell to the mixing chamber plate of our Bluefors LD400 cryogen-free dilution refrigerator. The opposite side of this flange, which is the vacuum side, has threaded holes used to attach the copper support structure of our mechanical oscillator. (Fig. 2). Both sides of the flange are gold plated to ensure a good thermal contact to the sample. surfaces using a manual vise-grip tool with a lever arm of approximately 15 cm. The pumping line was pinched at three nearby locations at the end of tube, with the third pinch being forceful enough to sever the tube. As a precaution, some PbSn solder was melted onto the end of the severed pumping line. The cell has been closed and thermally cycled between ambient and mK temperatures several times and remains leak-tight.

Cell Performance

The performance of the cell was quantified using a mechanical oscillator sample called a double paddle oscillator (DPO). In particular, we measured the temperature dependence of the resonance frequency of a mechanical mode of the DPO near 5 kHz down to a mixing chamber plate temperature of 10 mK. The DPO consisted of a 300 µm thick crystalline silicon substrate with a 300 nm layer of amorphous silicon deposited on top. The lateral dimensions of the oscillator were on the order of 1 cm. The inverse quality factor 1/Q and the temperature dependence of the resonance frequency of the resonator is dominated by the contribution of the thin amorphous film. Even with the amorphous layer, 1/Q remains low, ranging from 4 × 10 -8 at 10 mK to 5 × 10 -7 at 1 K. A detailed description of the oscillator and the measurement technique is given in [START_REF] Schmoranzer | Observations on thermal coupling of silicon oscillators in cryogen-free dilution refrigerators[END_REF].

Figure 3 shows the temperature dependence of the resonance frequency of the present sample (called DPO8) obtained from ringdown measurements like those shown in Fig. 1 of [START_REF] Fefferman | Elastic measurements of amorphous silicon films at mk temperatures[END_REF]. Measurements of DPO8 in four configurations are shown in Fig. 3: (1) no mixing chamber shield surrounding the DPO, (2) a simple mixing chamber shield with a ≈ 1 cm gap but no line of sight from the still shield to the DPO, (3) with all visible gaps in the simple shield closed with copper tape, and (4) the hermetic shield described above. A vertical offset was added to each of the DPO measurements so that the high temperature data overlap. The inset shows the temperature dependence of the resonance frequency of a very similar sample measured in a wet fridge. This sample was another DPO (called DPO1), also with a 300 nm layer of amorphous Si deposited wet fridge The temperature dependence of the resonance frequency of DPO8 below 50 mK strengthened as the mixing chamber shield was improved, demonstrating that the thermalization of the sample was improving. In the case of the hermetic cell, the logarithmic temperature dependence of the resonance frequency predicted by the standard tunneling model of amorphous solids [START_REF] Phillips | Two-level states in glasses[END_REF] is observed, indicating excellent sample thermalization down to 10 mK. The hermetic cell yields better thermalization of the sample than was achieved in the wet fridge, which had a hermetic seal at 4 K, a radiation shield attached to the still plate and no additional radiation shields inside the still shield.

An upper limit on the magnitude of heat required to produce the thermal decoupling observed in the absence of a mixing chamber shield is 0.2 nW [START_REF] Schmoranzer | Observations on thermal coupling of silicon oscillators in cryogen-free dilution refrigerators[END_REF].

One possibility for the origin of this heat is leakage of thermal radiation. In the absence of a mixing chamber shield, we did not observe a change in the temperature dependence of the DPO resonance frequency after the still temperature was changed from 630 to 900 mK. Thus any stray photons responsible for heating the DPO must have been radiated from surfaces warmer than the still. Indeed, when the pulse tube refrigerator was turned off, allowing the 4 K and 50 K plates to warm while the MXC and still plate temperatures were held constant, the resonance frequency of DPO8 without a hermetic shield increased (see Fig. 3 of [START_REF] Schmoranzer | Observations on thermal coupling of silicon oscillators in cryogen-free dilution refrigerators[END_REF]). The stray photons responsible for heating must then have entered the still shield through small gaps that remained despite the use of copper tape to cover any holes. In contrast, when the pulse tube was turned off with DPO8 in the hermetic cell at 10 mK, no change in the resonance frequency was observed.

Another possibility for the origin of the heating is thermal transport by residual helium gas. However, we observe no evidence of absorption of helium on the DPO, which would cause a resonance frequency shift due to mass loading.

(The effect of mass loading would dominate the elastic effect of a uniform helium layer because the shear modulus of solid helium is over 1000 times smaller than that of Si [START_REF] Fefferman | Dislocation networks in 4 he crystals[END_REF], while the density of solid helium is only about 10 times smaller than that of Si.) A monolayer of helium would cause a relative frequency shift of 5 × 10 -8 [START_REF] Rösner | Use of a double-paddle oscillator for the study of metallic films at high temperatures[END_REF], which would be easily observed (Fig. 3). Thus heating by helium gas is less likely than heating by stray photons. Superconducting qubits are sensitive not only to stray photons propagating in free space but also to an additional thermal decoupling mechanism: photons transmitted to the sample by microwave wiring. Very recently, Lane et al. constructed a hermetic 3D microwave cavity containing a transmon qubit [START_REF] Lane | A superfluid-tunable 3d transmon qubit[END_REF]. The relaxation and dephasing times of the qubit were measured with and without superfluid helium filling the microwave cavity. A photon bath temperature inside the cavity of 129 mK with superfluid and 150 mK without superfluid was inferred from the dephasing rate of the qubit. This degree of decoupling between the photon bath temperature and mixing chamber temperature is routinely observed in circuit QED experiments and is due to incomplete thermalization of microwave attenuators in the transmission lines leading to the cavity [START_REF] Yeh | Microwave attenuators for use with quantum devices below 100 mk[END_REF]. In the present work, we placed an ECCOSORB low pass filter at the 4 K stage and used superconducting coax with no additional filters between 4 K and the mixing chamber. Evidently, electronic noise transmitted by the wiring did not significantly limit the thermalization of the DPO, as demonstrated by the excellent thermalization of our sample when inside our hermetic cell. Achieving good thermalization of attenuators and circulators at mK temperature remains a challenge in the field of quantum electronics.

In conclusion, we have demonstrated much better sample thermalization with a hermetic cell than with a simpler shield that was not leak tight. The hermetic cell allows us to cool the sample to temperatures near 10 mK. The design incorporates a simple pinch seal instead of requiring the installation of an additional pumping line in the cryostat. A shield of this design would be effective in the protection of many types of devices from heating by stray photons or residual helium, which is especially significant in dry dilution refrigerators.

  The top flange has four holes for coaxial feedthroughs and a central spout in which a copper pumping tube was brazed. The coaxial feedthroughs were double ended hermetic SMA bulkhead adaptors manufactured by Huber and Suhner (34 SMA-50-0-3/111 N). They were adapted for low temperature use by replacing the elastomer gasket with an indium ring. The pumping line was a 50 cm long copper capillary tube with 2 mm outer diameter and 0.8 mm inner diameter. After closing the cell, it was connected to a helium leak detector and pumped for two days with a turbomolecular pump. No leak was detected when spraying the indium joints and the SMA feedthroughs with helium. The hermetic cell was then sealed by pinching the pumping line between two cylindrical 3

Figure 1 :

 1 Figure 1: Assembly drawing of the hermetic cell. The inset shows a cross-sectional detail of one of the indium-sealed flanges. The indicated 0.6 mm gap prevents interference of the flanges due to warping when compressing the indium ring.

Figure 2 :

 2 Figure 2: The gold plated copper support structure of the mechanical resonator samples is screwed to the gold plated top surface of the bottom flange of the hermetic cell. The copper sheet in front of the upper mechanical resonator protects this fragile device from breakage during assembly of the cell. Another sheet that protects the lower mechanical resonator has been removed for the photo.

Figure 3 :

 3 Figure 3: Relative frequency shift of one mode of a single crystal Si mechanical resonator with a 300 nm thick amorphous Si film deposited at room temperature. The labels correspond to different shield configurations (see text). Warming and cooling curves are shown for each shield configuration. For the measurements with the hermetic cell the temperature was varied slowly enough to eliminate the hysteresis visible in the other measurements. The inset shows the relative frequency shift of another mechanical resonator of the same type measured in a wet fridge.

We thank Gilles Pont for valuable technical advice. We acknowledge support from the ERC StG grant UNIGLASS No. 714692 and ERC CoG grant ULT-NEMS No. 647917 and from the US Office of Naval Research. The research leading to these results has received funding from the European Unions Horizon 2020 Research and Innovation Programme, under Grant Agreement no 824109, the European Microkelvin Platform (EMP).