dataesr/scientific-paragraphs-categorization huggingface dataset:
[ x] = ρ-1 ∑ m=0 [x i, j ] • (2 t+κ ) m (2) With data packing, we can use the full plaintext domain in the Paillier cryptosystem and perform additions on the packed ciphertext simultaneously. Furthermore, in interactive protocols, using data packing helps reduce the bandwidth usage and the cost of decryption operations. The second technique we use to improve efficiency is using a multi-exponentiation algorithm to simultaneously perform the operations in the form of w ∏ i=1 a b i i = a b 1 1 • a b 2 2. a b w w. (3) Lim-Lee's multi-exponentiation algorithm  [Lim and Lee, 1994, Lim, 2000]  enables to perform (3) simultaneously by modifying the binary exponentiation algorithm using several precomputation techniques. In our work, we can apply multi-exponentiation for the computation of dot product (in (1)) over encrypted data thanks to Paillier.
For instance, the relevant dataset we will study in this paper are the following: • 51336 transcriptomic data of 37 patients with advanced non-small-cell lung cancer who have received chemotherapy. The survival time being known, the objective is to select the transcriptomic covariates that explain the survival outcome of the treatment, then to define the profiles of the patients who survive the treatment. A. Muller-Gueudin. Email: Aurelie. gueudin@univ-lorraine. fr arXiv:1909. 05481v1 [math. ST] 12 Sep 2019 • 54676 probes in 79 breast tumor samples. A new metastatic biomarker being known, the objective is to define patient profiles for this metastatic biomarker, and associated gene network in order to personalize the treatments. The variable of interest being known (treatment outcome or biological marker), the question is to find its link with the transcriptomic profile of the patients.
We propose a methodology, that, firstly selects and ranks the transcriptomic covariates that are the most linked with the outcome treatment, and secondly, that visualises the profiles of the selected transcriptomic covariates, for all the patients of the study. More generally, the problem to detect association between a variable of interest and many covariates has been tackled by many biologists and statisticians  [2, 3, 11, 18, 19]. A common example, coming from biology, is testing which of p genes' expression levels given in a dataset X is linked significantly with a variable Y , which we will call the variable of interest. The variable of interest may be a binary variable like an outcome of treatment or it may be a quantitative variable such as a phenotype or physiological parameter. In the two data studies of this paper, the aim of the biologist is not necessarily to detect exhaustively all the genes involved in his problem but to have a list of the most important of them in order to study their biological functions.
2. 2. 2. Step 2: Aggregation of statistical methods applied on the resulting dataset. The statistical methods proposed in this part are not fixed and can be adapted by the practitioner according to its preferred selection methods and the characteristics of the data (nature of variable of interest Y , samples' sizes and so on). The idea is the following: we choose several methods to select the pretreated covariates X. We perform L methods, then each covariate X i obtains a score S i ∈ {0, 1,. , L} that is the number of selections among the L methods. By this way, the covariates can be ranked according to their link with the outcome Y. For instance, in the examples developed in our simulation studies and in real data, Y is binary, the size of the samples are low and we choose eight different methods of selection: five different multiple testing procedures applied to the Wilcoxon test (Bonferroni, Benjamin-Hochberg, q-values, local FDR, FAMT), logistic regression penalised by Lasso, and two selections by random forests (threshold step and interpret step, see  [16] ).
Interest of our data pretreatment In order to emphasize the interest of our data pretreatment, we compare the results of a Wilcoxon test after three different data pretreatments: Procedure 1: nothing is done on the dataset X. Procedure 2: the covariates X are decorrelated, taking Y into account, with the factor analysis procedure of  [7, 15] , implemented in the R package FAMT. This gives a new dataset X † Y. Procedure 3: the 4 clusters are estimated with the procedure of  [9] , implemented in the R package ClustOfVar; then the covariates are decorrelated in each cluster, taking Y into account, with the factor analysis procedure of  [7, 15] , implemented in the R package FAMT. This gives a new dataset X * Y obtained by the concatenation of the decorrelated clusters. Remark: our data pretreatment is the Procedure 3.
We have supposed that the number of clusters is known. If that is not the case, the user can choose its own number of clusters by using the graphical tools of the ClustOfVar procedure (plots of the dendrogram). Our objective is to find out the differently expressed covariates in the two groups (groups Y = 0 and Y = 1) with sample sizes n 2 = 30. For this, we perform Wilcoxon tests on each of the p pretreated covariates of the dataset (that is X for Procedure 1, X † Y for Procedure 2, X * Y for Procedure 3), given a three sets of p p-values. For each of these procedures, the selected covariates are those with p-values lower than 0. 05. We compare these procedures on N = 100 runs of (X, Y ). For the comparison, we count the number of influential covariates that are correctly detected (this number is noted TP, for True Positive), this indicator gives an idea of the sensibility of the test after the procedure.
05). After this filtering we obtained a dataset with n = 37 patients and p = 6810 covariates. In the pretreatment step, we found that the p = 6810 covariates are decomposed in 3 independent group of covariates. In a first time, the biological question was to find the genes which can explain a survival time greater or lower than 12 months. We then consider a binary response variable Y : Y = 1 for the 24 patients whose survival time is lower than 12 months and Y = 0 for the 13 patients whose survival time is greater than 12 months. The response variable being binary, we first applied the selection method presented in Section 2. 2. 2. Moreover, as the survival time was known for all the 37 patients without any censoring, we also apply our method on the same dataset (6810 covariates) but here, Y is the survival time.
The table 2 is a little disappointing, because regression and classification do not select the same covariates. Whatever, among the covariates with a C-score (score in the classification case) equal to 7, there is only one with a R-score (score in the regression case) lower than 4 (equal to 0!). But these two analyses are not looking for the same kind of link with the covariates. Moreover, these two approaches give two tools to detect influential covariates. We can combine these two approaches and consider the covariates that are selected by at least one approach, or consider the covariates that are selected by both of them. In the Figure  5 , we show the heatmap of the selected covariates which have a classification score and a regression score greater than five. For the visualisation of the results, we then build an heatmap obtained thanks to the R package heatmaply after co-clustering of the survival times (on the x-axis) and of the covariates (on the y-axis) with the function hclust (Figure  5 ).
Biological network involving ERα36 in breast cancer ERα36 is a variant of the oestrogen receptor α encoded by the ESR1 locus and expressed only in humans  [33]. ERα36 expression and activity have been mainly studied in vitro and in vivo in the context of breast cancer. However, due to the lack of comprehensive transcriptomic data that include ERα36, only sparse information is available on factors that could act up-and downstream ERα36 in biological networks. Our challenge from a statistical point of view was to explain the ERα36 expression variation obtained in a small number of breast tumors from a large number of potential explanatory variables that correspond to the 54676 transcriptomic probes. For this, we analysed the biological network involving ERα36 through the use of 4 sets of Affymetrix transcriptomic data obtained from breast tumors of different molecular subtypes: the triple negative (noted TN), ERa66+, PR+ and PR-datasets (details are provided in Section D of the Appendix).
The analysis was performed in three steps (Figure  6 ). Step 1, clinical data completion. These 4 transcriptomic datasets were completed by the measurement of ERα36 expression level in each tumor. Biological details are given in Section D of the Appendix. Step 2a, statistical analysis. To explain the ERα36 expression variation obtained in a small number of tumors from a large number of potential explanatory variables, we used the R package armada, in its regression version (as in Section 4. 1 where Y is quantitative), that allowed to select, among the 54676 initial probes, a few hundreds of genes whose expression is supposed to be correlated to that of ERα36 (ARMADA score ≥ 1). We obtained four lists of respectively 711, 277, 319 and 369 probes correlated to the expression of ERα36 in the TN, ERa66+, PR+ and PR-groups.
Step 2b, functional analysis. From these four lists of transcriptomic probes, we carried out a functional analysis using the MSigDB database (GSEA). In particular, we looked for transcription factors and microRNAs involved in the regulation of the majority of genes from the different lists (TN, ERa66+, PR+ and PR-). The results indicated that four transcription factors: NFAT, FOXO4, SP1 and LEF-1, were common regulators and could therefore be mediators of the ERα36 effect in all breast tumor subtypes. Interestingly, a study by  [1]  has shown that these transcription factors FOXO4, SP1 and LEF-1 are transcriptional hallmarks characteristic of cancer cells and associated to the Wnt signaling pathway (involved in metastasis and maintenance of cancer stem cells). Regarding the analysis of microRNAs, the results indicated that the majority of the genes whose expression correlated to ERα36 one in the TN set were regulated by the microRNAs: hsa-miR-106B, hsa-miR21 and hsa-miR-29A, listed as oncogenic microRNAs involved in metastatic processes, survival and self-sufficiency in growth factors of mammary tumors  [20].
The final goal of our study was to identify the molecular signatures accounting for the ERα36 expression level in the four different sets of tumors. These signatures were identified thanks to the R package heatmaply after co-clustering of the ERα36 expression (on the x-axis) and of the covariates (on the y-axis) with the function hclust. For each of the four tumor datasets, a heatmap was built which accounted for the expression level of the genes correlated to ERα36. Thanks to the associated dendogram, different classes of tumors were defined and characterized by both the level of ERα36 expression and an associated molecular signature. The Figure  8  illustrates the results for the study on the dataset ERa66+: two classes of tumors were identified, called ERα36 ++ and ERα36 -. Taken together, the armada package helped to cluster patients which breast tumor highly express ERα36 and associated genes.
Conclusion and perspectives We have proposed a new methodology which is able to select the covariates (here the genes) that are linked with a variable of interest (here the treatment of an outcome or a biological marker). The method is of particular interest in the high dimensional case and when the covariates are correlated. The algorithms corresponding to this method are available through the R package armada. After this selection obtained with our method, it is then easy to visualise the selected genes (or probes) for all the patients, and to classify the genetic profiles of patients with respect to their treatment outcome or biological marker. In the study of the treatment by chemotherapy in the advanced nonsmall-cell lung cancer, we have identify three types of genetic profiles defined with two clusters of genes.
A. 2. Interest of our data pretreatment In order to emphasize the interest of our data pretreatment, we compare the results of a Wilcoxon test after three different data pretreatments: Procedure 1: nothing is done on the dataset X. Procedure 2: the covariates X are decorrelated, taking Y into account, with the factor analysis procedure of  [7, 15] , implemented in the R package FAMT. This gives a new dataset X † Y. Procedure 3: the 4 clusters are estimated with the procedure of  [9] , implemented in the R package ClustOfVar; then the covariates are decorrelated in each cluster, taking Y into account, with the factor analysis procedure of  [7, 15] , implemented in the R package FAMT. This gives a new dataset X * Y obtained by the concatenation of the decorrelated clusters. Remark: our data pretreatment is the Procedure 3.
1 comes from Transgene team thanks to B. Bastien. T. Boukhobza, H. Dumond and C. Thiebaut conducted the biological study of Section 4. 2 and performed the functional analysis that follows the covariates selection with armada. S. Cairo and O. Déas ; XenTech, Genopole, 91000 Evry (France) provided the TN dataset; A. De Reynies, I. Bieche and J. Métral from the Carte d'Identité des Tumeurs program provided the access to transcriptomic raw data and biological samples (ERa66+, PR+, PR-datasets). The statistical methodology has been developed by A. Gégout-Petit and A. Muller-Gueudin, and thanks to Y. Shi and H. Chakir during their Master internships.
the TN dataset corresponding to Affymetrix transcriptomic comprehensive data from 17 patients derived xenografts (PDX) breast tumors was extracted from the Xentech TM database with the permission of Olivier Déas and Stefano Cairo (MTA CXT-295 Xentech SAS/University of Lorraine ; [24]). • the 3 other datasets (46 tumors ER66+, 29 tumors PR+, 16 tumors PR-) were part of those from the Carte d'Identité des Tumeurs Program (CIT) from the Ligue Nationale Contre le Cancer described in [17]. Transcriptomic raw data were kindly provided by Aurélien De Reynies and Jacqueline Métral. One microgram of cDNAs from each tumor sample gathered at the Oncogenetics laboratory, INSERM U735, Institut Curie-Hôpital-Centre René Huguenin, St Cloud, France was also kindly provided by Ivan Bieche to measure ERα36 expression.
As illustrated in the third line of Table  1  below, reducing from O(t 2 ) to O(t) enables to reduce the r-wise independence parameter from r = O(t 3 ) down to r = O(t 2 ); the number of input random bits is then now decreased from Õ(t 4 ) to Õ(t 3 ) with the trivial construction (and from O(t 3+ε ) to O(t 2+ε ) with expander graphs). Our technique is as follows. The authors of [IKL + 13] obtain = O(t 2 ) by performing a mask locality refreshing at the end of each ISW multiplication gadget. Instead we modify the ISW multiplication by performing a series of internal locality refreshing. For this we consider successive i × i ISW submatrices and perform a mask refreshing after the processing of each submatrix; these internal mask refreshing enable to bring the locality down to = O(t). We have also performed a formal verification of our new algorithms, using the CheckMasks tool  [Cor18] , for both the locality and the security properties; we provide the source code in  [Cor19a].
Concrete Implementation We have implemented our constructions for AES in C, on a 44 MHz ARM-Cortex M3 processor. The processor is used in a wide variety of products such as passports, bank cards, SIM cards, secure elements, etc. The embedded TRNG module can run in parallel of the CPU, but it is relatively slow: according to our measurements on emulator, it outputs 32 bits of random in approximately 6000 cycles. Our results, obtained by running the code on emulator, are given in Table  10 , and are compared with the classical Rivain-Prouff countermeasure. We see that the most efficient countermeasure is the SecMultFLR algorithm with multiple PRGs, using the 3-wise independent PRG. For n = 3 and n = 4 we obtain a 52% and 61% speedup respectively, compared to Rivain-Prouff. We provide the source code in  [Cor19b].
Method: The target population is independent seniors aged 60 years and over. To follow this population, the 6 domains of intrinsic capacity are systematically monitored with pre-established tools proposed by WHO especially STEP 1 which has been adapted in digital form to make remote and large-scale monitoring possible. Two tools were developed: the ICOPE MONITOR, an application, and the BOTFRAIL, a conversational robot. Both are connected to the Gerontopole frailty database. STEP 1 is performed every 4-6 months by professionals or seniors themselves. If a deterioration in one or more domains of intrinsic capacity is identified, an alert is generated by an algorithm which allows health professionals to quickly intervene. The operational implementation of the INSPIRE ICOPE-CARE program in Occitania is done by the network of Territorial Teams of Aging and Prevention of Dependency (ETVPD) which have more than 2,200 members composed of professionals in the medical, medico-social and social sectors.
Thus, two tools were developed by the Toulouse Gerontopole: a) the ICOPE MONITOR, an application, which is an adapted version of the ICOPE WHO application, accessible via smartphone or tablet; and b) the BOTFRAIL, an internet conversational robot, accessible via computer, smartphone or tablet. These two complementary tools can be used in two modes: professional mode and self-assessment mode for the senior or his/her caregiver. Both are connected to the pre-existing Gerontopole frailty database created in 2016 to collect medical and sociodemographic data from frail older people who received a face to face standardized gerontological assessment in the Occitania region. Data from more than 6,000 patients in 180 different health centers have already been collected since 2017. The database complies with all French and European regulations in terms of health data security.
The authorization of the French "National Commission for Data Protection" was granted on April 13, 2017 (Ref. Nb. MMS/OSS/NDT171027, authorization request Nb. 19141154). These tools may be used by everyone. However, in the context of the INSPIRE ICOPE-CARE program, during the first (face to face) STEP 1 screening, the professional collects the senior's oral consent to keep his/her data in the frailty database as well as to monitor his/her intrinsic capacity regularly. If the assessment is normal, lifestyle advice is provided by the professional who also trains the senior or his family/caregiver to use the tools in «self-assessment» mode.
Remote screening of STEP 1 -ongoing monitoring The ongoing screening of intrinsic capacity deficits is based on a remote monitoring system. After having been taught by health professionals how to use the ICOPE MONITOR app and/ or BOTFRAIL tool, seniors are invited to continuously use the STEP 1 every 4-6 months. If the senior cannot carry out the self-assessment, a professional will intervene every 6 months to perform the STEP 1 follow-up. STEP 1 data collected using the ICOPE MONITOR application or BOTFRAIL every 4 to 6 months are transmitted to the Gerontopole frailty database. If a deterioration in one or more domains of intrinsic capacity is identified during monitoring, an alert is generated by an algorithm. During the first deployment phase of the project, the management and processing of these alerts is carried out by the experienced nurses of the Gerontopole in collaboration with the primary care providers [General Practitioners (GP) and nurses].
STEP 4 -Ensure a referral pathway and monitoring of the care plan with links to specialized geriatric care As mentioned above, monitoring consists of the repetition every 4-6 months of STEP 1, either by self-assessment or with the help of a family member or professional caregiver. Digital medicine used in the INSPIRE ICOPE-CARE program makes it possible to simultaneously monitor large populations regardless of where they live and the extent of local medical resources and can also ensure the implementation and follow up of the personalized care plan proposed in STEP 3. Thus, digital medicine allows to focus the action of the health professionals on those who need and when they Remote support from the reference center: specialized unit / GP, specialized unit / nurse. Note. The follow-up is always digital (self-assessment / caregiver or nurse support).
Since January 2019, these nurses have used the STEP 1 tool for all their patients; to date (March 2020), around 950 seniors have been assessed. Some preliminary data on step 1 in 755 subjects showed that mean age was 80. 9 ± 7. 3 years, 67. 3% were female (n=298) and 699 (92. 6%) had at least one domain of intrinsic capacity affected. Table  2  shows the results of the STEP 1 evaluations. The nurses especially those trained on frailty assessment in the framework of cooperation protocol (more than 160 nurses) are also involved. Since January 2020, the Gerontopole has organized several training courses on the use of STEP 1 and ICOPE. To date, 94 nurses have been trained and 240 are registered for the next sessions. An agreement was signed between the Toulouse University Hospital and the Occitania Regional Health Agency to pay nurses 15 euros for this evaluation.
Pharmacists: In collaboration with the regional union of pharmacists and the pharmacy unit of Toulouse University Hospital, volunteer pharmacists and 6th year pharmacy students are also trained on the ICOPE program. To date (March 2020), 65 pharmacists have been trained and approximately 80 are registered for the next training sessions. The STEP 1 will be performed in the pharmacies by the pharmacists and in the event of an abnormal STEP 1, the pharmacist will direct the patient to his/her GP. Institutions: A partnership is set up with CEDIP (CEntre D'Information et de Prévention -Agirc-Arrco), which is a complementary pension fund in France, to carry out STEP 1 for their beneficiaries. To date (March 2020), more than 300 seniors have been assessed. An analysis made on 207 subjects with usable data showed that mean age was 70.
The Inspire Program was supported by grants from the Region Occitanie/Pyrénées-Méditerranée (Reference number: 1901175), the European Regional Development Fund (ERDF) (Project number: MP0022856), ARS «Agence Régional de Santé d'Occitanie» and the Inspire Chairs of Excellence funded by: Alzheimer Prevention in Occitania and Catalonia (APOC), EDENIS, KORIAN, Pfizer, Pierre-Fabre, Fondation Avenir Cogfrail Grant. Potential Conflicts of Interest: The authors declare that they have no conflict of interest for the present paper. Acknowledgements: The authors thank all the health professionals participating in the INSPIRE ICOPE CARE Program especially Cendrine Blazy and Dr Marie Dominique Medou from Occitania Regional Health Agency and all the members of the Gerontopole "Hospital of the walls" care unit (Augusto S, Bouchon L, Cazes MC, Da Costa F, Poly M, Vaysset S) and all the members of the Occitania Territorial Teams of Aging and Prevention of Dependency.
Ethical standards: The INSPIRE protocol has been approved by the French Ethical Committee located in Rennes (CPP Ouest V) in October 2019. This research has been registered on the site http://clinicaltrials. gov (ID NCT04224038). In the INSPIRE ICOPE-CARE program, all the senior's data are collected in the Gerontopole Frailty database. This database complies with all French and European regulations in terms of health data security. The authorization of the French "National Commission for Data Protection" was granted on April 13, 2017 (Ref. Nb. MMS/OSS/ NDT171027, authorization request Nb. 19141154). During the first (face to face) STEP 1 screening, the professional collects the.