dataesr/scientific-paragraphs-categorization huggingface dataset:
A similar genetic history seems evident in the Italian Duroc breed (which, however, had a larger N e ; Table  S3 ), reflecting deeper parental relatedness and consistent with an original strong bottleneck that occurred at the beginning of the 1990' when the heavy pig selection programme was defined and differentiated the Italian Duroc breed from other Duroc lines  (Bosi & Russo 2004). Breeds that experienced recent admixtures had, in general, a low nROH and as a proportion, had a higher frequency of short-medium ROHs than long ROHs, with high N e. This group included the two breeds that had nROH less than 30, S ROH less than 300. 00 Mb and N e greater than 55, i. e. Nero Siciliano and Sarda, for which the ROH-derived landscape was in agreement with the large variability observed in candidate gene markers and SNP chip data  (Mu ñoz et al.
The scarcity of methods using divisive algorithms led us to focus on them. A number of splitting procedures were designed in the past, the oldest one being by  Williams and Lambert (1959)  is said to be monothetic in the sense that object sets are split according to the values of only one variable. Another approach using all variables simultaneously is said to be polythetic, it has the advantage to only depend on inter object distances or dissimilarities. The method of  Macnaughton-Smith et al. (1964)  combine the advantages to be divisive, polythetic and computationally manageable. It is implemented in DIANA (Divisive ANAlysis) clustering algorithm available on R free software environment. In this work, we propose a new constrained Divisive Hierarchical Clustering (DHC) method named MapClust that takes into account geographical constraints and we apply it on an archaeological pottery dataset from middle Loire Valley (France).
To study the contribution of the constraint, we also present the results obtained with DIANA. The MapClust clustering method was developed in a project on medieval and modern pottery from the middle Loire Valley  (Husi dir. , 2003 (Husi dir. , , 2013)). This project, which began more than twenty years ago, is one of the first research projects at the national level to have tackled the question of the study of pottery over a long period of time (6th to 17th c. ), in a collective and systemic way, particularly in the structuring and analysis of data. This research has made possible the development of the european information network on medieval and modern ceramics named ICERAMM. The website associated with this network is built as an online database referencing typological tools and information on pottery assemblages for France and Belgium (http://iceramm.
, , 2008 (Bellanger et al. , , 2015;; 2021; Bellanger and Husi, 2012). As the pottery corpus continues to grow with the addition of new sites, a purely descriptive approach to the spatialization of the results is insufficient for a rigorous analysis of the pottery data. This is why we developed MapClust, a clustering method to deal with data that are not homogeneous in their spatial distribution and often patchy, for which traditional spatial statistics tools like kriging are inadequate. MapClust makes it possible to answer the problems of clustering and spatialization of archaeological contexts associating (i) pottery data that compose them, (ii) geographical distance between sites. This approach is essential for the construction of cultural areas, in this case pottery areas, in accordance with the distribution of data and the greater or lesser geographical proximity of the sites.
Data collection In this paper, which main aim is to illustrate the interest of the MapClust method, we have chosen only two of the numerous technical and decorative traditions contained in the 2020 data corpus. We will present here the analyses of the spatial distribution of white-beige or ochre-red pottery between the 8th and 10th c. mobilizing for this question 22 places out of the 51 recorded for the Middle Loire basin (Fig. 2 ). This chronological choice is guided by the changes that took place during this period, when light-coloured productions made in oxidising firing replace those of dark black or grey colour in reducing firing. We have chosen the technique of Minimum Vessels Count (MINVC) to quantify pottery by fabric  (Orton and Tyers, 1992). It is the quantifying technique nearest to historical reality without, for example, problems of fragmentation rates such as the number of sherds.
Multidimensional analysis of the productions of white-beige and ochre-red colour between the 8th and 10th century We consider here the same question of defining pottery areas based on the colour of the productions, but analysing simultaneously the two productions, white-beige and ochre-red. Correspondence Analysis (CA)  (Benzécri, 1973; Greenacre, 2007)  was performed on both variables to describe the structure of the dataset. We use ! " , the probability density estimation of the unique principal component of the CA as the variable of interest to compute in (Eq. 2) and obtain a partition with MapClust clustering method. Average silhouette widths (top right) and WSS (bottom right). Referring to the average silhouette widths criterion, the best value correspond to the partition into 5 clusters (Fig.
White-beige productions DIANA results on white-beige dataset do not show a geographical separation of the study area (Fig. 15 ) as for the ochre-red dataset. Fig. 15. White-beige -Dendrogram obtained DIANA (4-clusters partition). The clusters are spread over large areas. It seems that DIANA method does not work properly for this type of data (Table  3 ). Table  3 : White-beige -Confusion matrix between DIANA clusters and MapClust. It yields ARI value as 0. 14 that indicates a very bad agreement between the two partitions. The ochre-red dataset show a result with the first separation on the dendrogram. Despite this, the DIANA algorithm do not help for data with strong geographical context. This and the very few results with the white-beige dataset show the necessary need of geographical constraint in the context of univariate analysis.
Discussion and conclusion The spatial analysis of artefacts, particularly pottery, is generally realized only according to the intensity of the data, with a blurred boundary from one space to another, constructed without any real statistical processing. Moreover, in our case, archaeological data are measured at a limited number of locations. As a consequence, it is not possible to use geostatistical methods. Indeed, we choose to use simple spatial indicators without additional statistical assumptions to build our proposed clustering method. MapClust brings a new perspective to the archaeological problem of determination of cultural areas using pottery since it takes into account the data to build the clusters but also the distance between sites. The application of MapClust clustering method on pottery data leads to results near similar to those already observed on an empirical study in 2013, confirming the relevance of a statistical approach applied to a dataset too large for a simple descriptive analysis.
Overall, there is great stability in the local economic areas located around the main consumption centres in the Loire area. Whether MapClust is used separately on white-beige or ochre-red dataset or with both of them, we can observe: (i) three main areas, Haut-Poitou, Touraine and Blésois-Orléanais, (ii) one or two secondary areas more on the periphery to the extreme west with Anjou and to the east with Berry. There is a strong tradition of common ochre-red manufacturing for the Blésois and Orléanais, always in the same cluster at a low level of partition (IV) of the dendrogram (Fig. 6 , 9 and 12). In the same vein, it is necessary to wait for the third partition (III) to differentiate good way to answer the question of how to construct cultural areas from a large amount of data. The interest also comes from the fact that MapClust can be used for pottery but also for many other artefact.
This methodological research is currently being pursued in a project of the French National Research Agency (ANR) entitled ModAThom for "Explanatory Model of Urban Construction of Angkor Thom". This project includes the study of an important pottery corpus, but also other artefact resulting from many excavations made in the capital of the Khmer empire in Cambodia (https://anr. fr/Projet-ANR-17-CE27-0008). In addition, MapClust has easy-to-use tools to choose the number of clusters and to characterize geographically the created clusters. It does not require a lot of practice of the R language to run, thanks in particular to a web application Shiny more intuitive for users. The choice was made to develop both approaches, classical R package and web application in order to enlarge the target audience.
INTRODUCTION Whole-genome sequencing (WGS)  (Ng and Kirkness, 2010; Shendure et al. , 2017)  has become the standard technique in clinical settings for tailoring personalized treatments  (Rehm, 2017)  and in research settings for building reference genetic databases  (Schwarze et al. , 2018; 1000 Genomes Project Consortium, 2015; Chisholm et al. , 2013). Technological advances in the last decade enabled a massive increase in the throughput of WGS methods  (Heather and Chain, 2016) , which provided the opportunity for population-scale sequencing  (Goldfeder et al. , 2017) , where a large sample from a population is sequenced for studying ancestry and complex phenotypes  (Lango Allen et al. , 2010  throughout the article  Locke et al. , 2015) , as well as rare  (Agarwala et al. , 2013; Gibson, 2012; Chen et al.
g. , in projects such as TOPMed  (Taliun et al. , 2019; TOPMed, 2016)  will provide training data for imputation methods to predict rarer variant genotypes, and this can increase the sensitivity of GWAS. Although imputation and sparse genotyping methods enable a vast decrease in genotyping costs, they are computationally very intensive and require management of large genotype panels and interpretation of the results  (Howie et al. , 2012). The imputation tasks can be outsourced to third parties, such as the Michigan Imputation Server, where users upload the genotypes (as a Variant Call Format, VCF, file) to a server that performs imputation internally using a large computing system. The imputed genotypes are then sent back to the user. However, there are major privacy  (Naveed et al. , 2015)  and data security  (Berger and Cho, 2019)  concerns over using these services, since the genotype data are analyzed in plaintext format where any adversary who has access to the third party's computer can view, copy, or even modify the genotype data.
The public key is used to encrypt the genotype data into ciphertext, i. e. , random-looking data that contain the genotype data in a secure form. It is mathematically provable (i. e. , equivalent to the hardness of solving the ring learning with errors, or RLWE, problem,  Lyubashevsky et al. , 2010)  that the encrypted genotypes cannot be decrypted into plaintext genotype data by a third party without the private key, which is in the possession of only the researcher. Even if an unauthorized third party copies the encrypted data without authorization (e. g. , hacking, stolen hard drives), they cannot gain any information from the data as they are essentially random noise without the private key. The security (and privacy) of the genotype data are therefore guaranteed, as long as the private key is not compromised.
The security guarantee of the imputation methods is based on the fact that genotype data are encrypted in transit, during analysis, and at rest. The only plaintext data that are transmitted to the untrusted entity are the locations of the variants, i. e. , the chromosomes and positions of the variants. Since the variant locations are publicly known for genotyping arrays, they should not leak any information. However, when the genotyping is performed by sequencing-based methods, the variant positions may leak information, as we discuss more in the next sections. The encrypted genotypes are sent through a channel to the imputation service. The channel does not have to be secure against an eavesdropper because the genotype data are encrypted by the researcher. However, secure channels should be authenticated to prevent malicious man-in-the-middle attacks  (Gangan, 2015).
The encrypted genotypes are received by the imputation service, an honest-but-curious entity, i. e. , they will receive the data legitimately and extract all the private information they can from the data. However, a privacy breach is impossible as the data are always encrypted when they are in the possession of the imputation service. Hence, the only reasonable action for the secure imputation server is to perform the genotype imputation and to return the data to the researcher. It is possible that the imputation server acts maliciously and intentionally returns bad-quality data to the researcher using badly calibrated models. However, it is economically or academically reasonable to assume that this is unlikely, since it would be easy to detect this behavior on the researcher's side and to advertise the malicious or low quality of the service to other researchers.
Genotype imputation models We provide five approaches implemented by four different teams. For simplicity of description, we refer to the teams as Chimera, EPFL, SNU, and UTHealth-Microsoft Research (UTMSR) (see STAR Methods). Among these, CKKS is used in three different approaches (EPFL-CKKS, SNU-CKKS, and UTMSR-CKKS), and BFV and TFHE are each utilized by separate approaches (UTMSR-BFV and Chimera-TFHE, respectively). The teams independently developed and trained the plaintext imputation models using the reference genotype panel dataset. For each target variant, the tag variants in the vicinity of the target variant are used for imputing the target variant, i. e. , the tag variants in the vicinity are used as features in the imputation models. The chimera team trained a logistic regression model and the EPFL team trained a multinomial logistic regression model.
Overall, these results indicate that secure imputation models can provide genotype imputations comparable with their non-secure counterparts. To test the performance of the methods on rare variants, we focused on the 117,904 variants whose minor allele frequency (MAF) is between 0. 5% and 5%. These variants represent harder to impute variants since they are much less represented compared with the common variants. The results show that the vicinity-based approaches that our methods use show a clear decrease in performance compared with the HMM-based approaches (Figure  3G ). This is expected since our approaches depend heavily on the existence of well-represented training datasets. In the rare variants, however, the number of training examples for the non-reference genotypes goes as low as 1 or 2 examples over 1,000 individuals.
We hope that our study can provide a reference for the development of privacy-aware and fully secure approaches that employ HE. Second, the amount of genomic data have increased several orders of magnitude in recent years. This provides enormous genotype databases where we can train the imputation models and test them in detail before implementing them in secure evaluation frameworks. Another significant development is the recent formation of genomic privacy communities and alliances, i. e. , Global Alliance for Genomic Health (GA4GH), where researchers build interdisciplinary approaches for developing privacy-aware methods. For example, our international study stemmed from the 2019 iDASH Genomic Privacy Challenge. We firmly believe that these communities will help bring together further interdisciplinary collaborations for the development of secure genomic analysis methods.
Nevertheless, even with the training, our results show that the secure imputation framework can train and evaluate in run times comparable with plaintext (non-secure) methods. In the future, we expect many optimizations can be introduced to the models we presented. For example, we foresee that the linear model training can be replaced with more complex feature selection and training methods. Deep neural networks are potential candidates for imputation tasks, as they can be trained for learning the complex haplotype patterns to provide better imputation accuracy  (Das et al. , 2018). With the introduction of the graphical processing units (GPUs) on the cloud, these models can be trained and evaluated securely and efficiently. It is, however, important to be thorough about the security of the data because, as we mentioned before, even the number of untyped target variants that the researcher sends to the server can leak some information about the datasets.
We are hoping that our codebase can provide a central role in the development of a community (similar to dynverse (dynverse, n. d. ) or TAPE  (TAPE, n. d. 2019; Rao et al. , 2019)  repositories for trajectory inference and protein embedding, respectively) where users can use the developed methods and datasets for uniform benchmarking of their new imputation methods. technical support to set up the computational environment for unified evaluation. X. J. is CPRIT Scholar in Cancer Research (RR180012), and he was sup RLWE assumption. More precisely, each tag variant is first encoded as a polynomial with its coefficients, and the encoded plaintext is encrypted into a ciphertext using the underlying HE scheme. The plaintext polynomial in the BFV scheme is separated from an error polynomial (inserted for security), whereas the plaintext polynomial in the CKKS scheme embraces the error.
Then Equation 2 is homomorphically evaluated on the encrypted genotype data by using the plain weight parameters. We exploit parallel computation on multiple individual data, and hence it enables us to obtain the predicted genotype estimates over different samples at a time. Our experimental results indicate that the linear model with 32 tag variants as features for each target variant shows the most balanced performance in terms of timing and imputation accuracy in the current testing dataset (see Table  S8  and Figure S5 ). Our protocols achieve at least a 128-bit security level from the HE standardization workshop paper  (Albrecht et al. , 2018). We defer the complete details to the ''UTHealth-Microsoft Research team solution'' section in the supplementary document.
EPFL-CKKS EPFL uses a multinomial logistic regression model with d À 1 neighboring coefficients and 1 intercept variable for each target variant, with three classes {0,1,2}. The plaintext model is trained using the scikit-learn python library. The input variants are represented as values {0,1,2}. There is no pre-processing applied to the training data. For a target position j, the predicted probabilities for each class label are given by: ;. ; z ðp;j;,Þ dÀ1 g are sent encrypted and packed to the server, using the CKKS homomorphic cryptosystem, and the exponents in Equation 3 are computed homomorphically. The client decrypts the result and can obtain the label probabilities and hard predictions for each position. For the prediction, we use several numbers of regression coefficients, ranging from 8 to 64; as this number increases, both the obtained accuracy and the computational complexity increase (see Table  S6 ).
SNU-CKKS The SNU team applies one-hidden layer neural network for the genotype imputation. The model is obtained from Tensorflow module in plain (unencrypted) state, and the inference phase is progressed in encrypted stated for given test SNP data encrypted by the CKKS HE scheme. We encode each ternary SNP data into a 3-dimensional binary vector, i. e. , 0/ð1; 0; 0Þ, 1/ð0; 1; 0Þ and 2/ ð0; 0; 1Þ. For better performance in terms of both accuracy and speed, we utilize an inherent property that each target SNP is mostly.
D. K. , S. H. and J. H. C. were supported by the Institute for Information & Communications Technology Promotion (IITP) Grant through the Korean Government (MSIT), (Development and Library Implementation of Fully Homomorphic Machine Learning Algorithms supporting Neural Network Learning over Encrypted Data), under Grant 2020-0-00840. M. K. was supported by the Settlement Research Fund (No. 1. 200109. 01) of UNIST (Ulsan National Institute of Science & Technology) and Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2020-0-01336, Artificial Intelligence graduate school support [UNIST]).
Variant and genotype datasets All the tag and target variant loci, and the genotypes are collected from the public resources. We downloaded the Illumina Duo 1M version 3 variant loci from the array's specification at the Illumina web site (https://support. illumina. com/downloads/human1m-duo_v3-0_product_files. html). The file was parsed to extract the variants on chromosome 22, which yielded 17,777 variants. We did not use the CNVs and indels while filtering the variants and we focused only on the single nucleotide polymorphims (SNPs). We then intersected these variants with the 1000 Genomes variants on chromosome 22 to identify the array variants that are detected by the 1000 Genomes Project. We identified 16,184 variants from this intersection. This variant set represents the tag variants that are used to perform the imputation.
html Source Data for Figures 1, 2, 3, 4, and 5 and supplemental information This work https://doi. org/10. 5281/zenodo. 4947832 Software and algorithms R Statistical Computing Platform The R Foundation https://www. r-project. org/ Source Code and Documentation for Secure Imputation Models This work https://doi. org/10. 5281/zenodo. 4948000 Source Code for generating Figures 1, 2, 3, 4, and 5 and the Figures S1-S8 This work https://doi. org/10. 5281/zenodo. 4947832.
We set the number of the adjacent tag SNPs as a pre-determined parameter d, and run experiments on various choices of the parameter (d = 8k for 1%k%9). As a result, we check that d = 40 shows the best accuracy in terms of micro-AUC. Since the running time of computing genotype score grows linear to d, the fastest result is obtained at d = 8. We refer the intermediate value d = 24 to the most balanced choice in terms of accuracy and speed. The security of the utilized CKKS scheme relies on the hardness of solving the RLWE problem with ternary (signed binary) secret. For the security estimation, we applied the LWE estimator  (Albrecht et al. , 2015) , a sage module that computes the computational costs of state-of-art (R)LWE attack algorithms. The script for the security estimation is attached as a figure in the ''SNU team solution'' section in the supplementary document.
Methods MOBY was modeled in the SimulO program as shown in Fig. 1. The model consists of several stacked cylinders, some above the water, some below, along with the three arms sticking out from the central buoy. The full angle acceptance of the radiance collectors in MOBY is 0. 5°, however MOBY is not a fixed platform and moves slightly during the measurement period. The typical integration time for the upwelling measurements is 30 s to 1 min. Statistically there is a 2°variation in the pointing of MOBY around the average measurement direction during this integration time. Thus while the acceptance angle at any one moment is 0. 5°, during the measurement MOBY is sampling a much larger range of angles. To account for this, the acceptance angle of the radiance detectors in the SimulO runs were opened up to 2°.