dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgments. The first author expresses his gratitude to the second and fourth authors, and the  Department of Mathematics at the University of Hawai'i at Mānoa  for their hospitality during a visit in November 2019 where part of this work was carried out. The authors would also like to thank  Robin Deeley  for pointing out a mistake in an earlier version of this paper. On behalf of all authors, the corresponding author states that there is no conflict of interest.
USA stock market These data of length 2022 from the American stock market were recorded daily from January 2nd, 1992 to December 31st, 1999. They represent the daily stock prices of the S&P 500 stock market (SPX). They are among the most closely followed stock market indices in the world and are considered as an indicator of the USA economy. They have also been recently examined by  [40]  and can be found at: (www. investing. com). On Figure  2 , we observe that the trend of the SPX daily stock price series is not constant over time. We also observe that stock prices have fallen sharply, especially in the time interval between the two vertical dashed blue lines (the period of the 1997-1998 Asian financial crisis). Denote by D t the value of the stock price for SPX index at day t, and the first difference of the logarithm of stock price, X t as X t = log (D t ) -log (D t-1 ) = log D t D t-1.
1. 6. Thanks. Many thanks are due to the persons who commented on the prior versions. Special thanks to Benjamin Wesolowski and Marco Streng, for suggesting to simply use 𝑏 = 1 in the dimension 8 attack. This significantly simplify the description of the attack in this case. (Although as noted above the general 𝑏 > 0 case is still useful for the dimension 4 attack). Thanks to the anonymous referees for numerous suggestions to improve the exposition of this paper. This work was supported by the ANR ANR-19-CE48-0008 project Ciao.
Funding information:  Jongmin Han  was supported by  Basic Science Research Program  through the  National Research Foundation of Korea (NRF)  funded by the  Ministry of Education  ( 2018R1D1A1B07042681 ). Juhee Sohn  was supported by the  NRF  grant funded by the  Korea government (MSIT)  ( 2021R1G1A1003396 ).
This approach is the most useful, both because of its accuracy (16 decimal points of importance) and the speed of its solutions and convergence; by addressing unfavorable adverse problems and stability conditions, it can also have wide applications. In this paper, we applied two approaches for the control of the boundary conditions: constant and variable. The θ-scheme method has rarely been used in the thermal field, though it is unconditionally more stable for θ∈ [0. 5, 1]. The simulation was carried out using Matlab software.
Generally, inverse problems are known problems that are more difficult to solve compared to direct problems; they may also suffer from the lack of an optimal selection, making them a complex problem. A lack of uniqueness and/or a lack of solutions, or an instability of the solution to small problems that are due to changes in the provided data (disturbance) can lead to major problems with solutions  [2]. To solve the problem of heat transfer through walls, Layal-Chahwane and al  [3]  presented an inverse method that estimated their thermal properties by adopting the limited difference method through the simspark environment program  [4]. A good agreement was found between the direct and the reverse methods  [5]. Jingbo Wang and al  [6]  studied the problems in evaluating parameters, rebuilding thermal history (including thermal flow at the borders), and rebuilding the heat source.
(B M ) jN • • • (B 2 ) jN B jN       Therefore, the gradient of the function J(Q)is given by ∇J(Q) = ( ∂ ∂q 1 J(Q), ∂ ∂q 2 J(Q),. , ∂ ∂q M J(Q),. , ∂ ∂q 2M J(Q)) T Numerical Results All computations were carried out in Matlab with about 16 significant decimal digits. In these examples, we chose:    and 18  show that the perturbations exist only in the beginning a end of the graphs. Despite the boundary conditions, they are variable. All thi strates the reliability and the power of convergence of this method. We can als the graphs are similar for exact solutions and estimation. The new method is illustrated by the following algorithm, Figure  19 :    and 18  show that the perturbations exist only in the beginning a end of the graphs. Despite the boundary conditions, they are variable.
Acknowledgements. This is a part of my PhD thesis. I would like to thank my PhD supervisors Eric Luçon and Ellen Saada for introducing this subject, for their useful advices and for their encouragement. This research has been conducted within the FP2M federation (CNRS FR 2036), and is supported by ANR-19-CE40-0024 (CHAllenges in MAthematical NEuroscience) and ANR-19-CE40-0023 (Project PERISTOCH). I would like to warmly thank two anonymous Referees for their useful and precise comments, which considerably helped to improve the paper.
In translational oncology research, the patient-derived xenograft (PDX) model and its use in mouse clinical trials (MCT) are increasingly described. This involves transplanting a human tumor into a mouse and studying its evolution during follow-up or until death. A MCT contains several PDXs in which several mice are randomized to different treatment arms. Our aim was to compare longitudinal modeling of tumor growth using mixed and joint models. Mixed and joint models were compared in a real MCT (N = 225 mice) to estimate the effect of a chemotherapy and a simulation study. Mixed models assume that death is predictable by observed tumor volumes (data missing at random, MAR) while the joint models assume that death depends on nonobserved tumor volumes (data missing not at random, MNAR). In the real dataset, of 103 deaths, 97 mice were sacrificed when reaching a predetermined tumor size (MAR data).
Joint and mixed model estimates of tumor growth slopes differed significantly [0. 24 (0. 13;0. 36)log(mm 3 )/week for mixed model vs. -0. 02 [-0. 16;0. 11] for joint model]. By disrupting the MAR process of mice deaths (inducing MNAR process), the estimate of the joint model was 0. 24 [0. 04;0. 45], close to mixed model estimation for the original dataset. The simulation results confirmed the bias in the slope estimate from the joint model. Using a MCT example, we show that joint model can provide biased estimates under MAR mechanisms of dropout. We thus recommend to carefully choose the statistical model according to nature of mice deaths. Significance: This work brings new arguments to a controversy on the correct choice of statistical modeling methods for the analysis of MCTs. We conclude that mixed models are more robust than joint models.
How to best analyze the data collected in such MCT experiments has not clearly been resolved. In the literature, several criteria have been suggested to summarize this dynamic (Supplementary Data S1): both continuous (e. g. , tumor growth inhibition, AUC ratio) or categorical [e. g. , modified RECIST (mRECIST)] criteria have been suggested  (2). However, categorization from quantitative information induces an inherent loss of information. For example, mRECIST is a summary measure of the complete kinetics of tumor growth. In the case of MCTs, it should be noted that even the suggested continuous criteria are in fact summarized measurements of tumor growth kinetics. Some authors recommend using several criteria and then critically evaluate the results obtained  (4, 5). Nevertheless, the most genuine approach is the analysis of quantitative tumor growth evaluated at different times during the follow-up.
MCT Study The MCT study was performed at OncoDesign. All experimental procedures were approved by the Ethics Committee of OncoDesign (C2EA; registration number 91) and were performed in full compliance with the ARRIVE guidelines, EU Directive 2010/63/ EU for animal experiments, and the 2013 French Regulatory Decree. All efforts were made to minimize animal suffering and to reduce the number of animals used  (11). The MCT dataset was composed of 25 PDX breast cancer models provided by the IMODI French consortium  (12). A total of 225 mice were randomized to three arms with a randomization within each PDX model. The original objective of this MCT was to estimate and compare the effect of two dose levels  The 63-day follow-up included an on-treatment period (with three administrations 7 days apart) and then no treatment from day 14 onward.
Missing Data Mechanisms In MCT, the tumor growth process is stopped by death (regardless of the cause of death) which entails a dropout and missing tumor volumes. Before applying any statistical method, it is crucial to understand the nature of the missing data as statistical models are not all robust to the same type of missing data mechanism. Two different mechanisms are to be distinguished (  15 ): (i) Missing at random (MAR): occurrence of missing data is only related to observed data (in the MCT context, some sacrifices of mice are linked to an ethical threshold of tumor volume not to be exceeded (e. g. , 1,500 mm 3 ) and tumor volumes are measured by researchers). It is a noninformative study dropout. (ii) Missing not at random (MNAR): occurrence of missing data is related to unobserved data (in MCT context, death due to natural causes).
It is an informative study dropout. In our use case, after identifying the missing data process related to deaths, an additional analysis was performed by perturbing the initial dataset to modify the missing data process. Taking into account the observed process, the data were disrupted to have a scenario with only MNAR data by making the last TV measurements unobserved before death. This was done by considering only tumor volume measurements below a threshold that is itself below the ethical threshold. The number of deaths and date of deaths were unchanged in this dataset. The objective of these analyses was to assess the robustness of the estimates provided by the mixed and joint models in the MCT framework.
Linear Mixed-effects Regression Model A linear mixed-effects regression model, such as recommended by authors  (2)  for analyses of MCT, is robust to MAR process due to death. With this type of model, the mean evolution of tumor growth is estimated using a linear regression while taking into account the correlation between the repeated tumor Mixed vs. Joint Models in Mouse Clinical Trial Analysis volumes of each mouse using mouse-specific correlated random effects on time functions. In the presence of subgroups and different treatments, it is possible to estimate the mean evolution for each subgroup and each treatment. In the case of the MCT of breast cancer treated with liposomal irinotecan, the model included a piecewise linear tumor growth trajectory (one slope on-treatment and a second slope after the end of treatment period) at the population and mouse levels as follows: Several change points were tested (3, 4, and 5 weeks post treatment initiation; Supplementary Data S2).
Simulations A simulation study was carried out to evaluate the impact of the proportion of MAR and MNAR deaths on the estimation of the parameters of mixed and joint models. In these simulations, we assumed a single group with a 28-day follow-up with several sample size of mice (300, 200, and 100). In addition, a proportion of all-cause deaths of 50% was assumed with the following MNAR and MAR distribution scenarios: 50% MNAR and 0% MAR, 40% MNAR and 10% MAR, 30% MNAR and 20% MAR, 20% MNAR and 30% MAR, 10% MNAR and 40% MAR, 0% MNAR and 40% MAR. For each scenario, 1,000 datasets were created. Tumor growth kinetics were simulated using a single slope mixed linear regression model with random intercept and slope. MNAR deaths were simulated using R programs provided by Thomadakis and colleagues  (10)  and MAR deaths using log tumor volume thresholds depending on the desired proportion of deaths, which mimic the ethical threshold of real MCTs.
Description of MCT The real MCT dataset was composed of 25 PDX breast cancer models with a total of 225 mice (between 1 to 18 measures per mice, 75% with at least 11 measures during follow-up) distributed by subtypes and doses as described in Fig. 2. It should be noted that the graphical description of the data is essential but that over time, due to the deaths of the mice, the average representation of the tumor evolution is not representative of the average tumor evolution of the initial study population because it is calculated only on survivors (i. e. , mice with low tumor growth evolution). This is an illustration of survivor bias. During the follow-up period, 103 deaths were observed and the reasons and description of deaths (Fig. 3 ) by subtypes and treatment doses are as follows:  Most deaths (88%) were related to sacrifice after reaching a too large tumor size, which is characteristic of MAR data.
1) gave very similar results to mixed models including also the PDX level correlation (two-level, AIC: 1458. 7). The estimates obtained by joint model under the assumption of MNAR dropout due to death differed substantially from those obtained by the mixed models under the assumption of MAR dropout, especially in the second period when the number of deaths was increasing (Fig. 3 ). As most of the dropouts were due to sacrifices, that is a MAR process, this illustrates the bias that can be induced by an incorrect assumption regarding the nature of the dropout mechanism. Furthermore, to confirm that this difference in estimation between the mixed model and the joint model is due to the nature of the deaths, a complementary analysis was performed by perturbating the MAR data process. In the case of MCT and a MAR missing data process on tumor growth, this process can become MNAR by artificially rendering unobserved the tumor values that gave rise to the sacrifice (considering only the tumor volume measurements at an earlier stage than the ethical threshold, 900 mm 3 for this use case).
In this case, mice have between 1 to 17 measures during follow-up and 75% of mice have at least 7 measures. However, the original date of death of each mouse has been retained. The results of these complementary analyses are presented in Fig. 4. As can be seen from the graphs when the missing data process is no longer MAR then the estimates of the joint model and the mixed model on the whole dataset are close. These results support the fact that the biased estimates provided by the joint model on the raw data are likely due to the MAR process of the missing data.
Discussion In MCTs, antitumor efficacy is evaluated by modeling tumor growth using statistical models for longitudinal data. These models must handle the early dropout induced by the death of mice to avoid survivor bias in analyses over during the follow-up, as well as a simulation study, we compared the results of two statistical modeling methods, mixed models and joint models, described in the literature for the analysis of this type of data. We showed, with the analy-sis of the real dataset and the associated complementary analysis, that the joint model can lead to biased estimates of the antitumor efficacy of a treatment in the presence of a high proportion of dropouts that were explained by the observations, that is MAR. Moreover, the additional simulation study confirmed Joint models including observations to predict death in addition to the current level of biomarker (in our use case tumor volume) have been developed to tackle this problem of biased estimation for MAR situations  (10, 17).
However, joint models are complex in terms of the number of parameters to be estimated, and it is therefore only possible to use them in the context of MCTs when there is a relatively large amount of data. Indeed, our simulation study showed higher proportions of nonconvergence of the joint models than the mixed models. The nonconvergence of the joint model observed in the simulations corresponds to the worst case. Indeed, for a real dataset, this convergence could probably be improved by specifying some parameters as example initial and/or control values of the convergence algorithm. In addition, joint models can be parametrized in various ways which can lead to misspecification of the model and biased estimates. In the context of MCT analysis, it is therefore important to record the reasons for dropouts and especially the causes of death, to inform the choice of the statistical model to be used for the analysis of this type of data in particular with many dropouts.
In the context of many dropouts due to mouse sacrifices related to too large and therefore unethical tumor size, we recommend using linear mixed models. Furthermore, in the case where in each treatment arm there are several mice from the same PDX [MCT setting as opposed to the single mouse trial (1 mouse per PDX in each treatment arm)], we recommend the use of nested random effects linear mixed models. For the additional analysis, we created a database containing only MNAR study dropouts by making the tumor growth measurements leading to death unobservable. An alternative would have been to create a database with MNAR study dropouts by randomly drawing MNAR study dropouts from the original dataset. However, in the original database, given the low number of deaths leading to MNAR study dropouts (N = 12), this strategy did not seem adequate.
35 -9. 9 55. 4 82. 7 20% MNAR 30% MAR 0. 39 -0. 01 93. 9 100. 0 0. 33 -15. 2 25. 2 80. 0 10% MNAR 40% MAR 0. 39 0. 03 93. 6 100. 0 0. 34 -12. 1 40. 1 81. 2 0% MNAR 50% MAR 0. 39 0. 06 94. 9 100. 0 0. 37 -4. 7 79. 8 85. 2 NOTE: N: sample size (number of mice) of the simulated datasets. Mean: average slope estimate of the 1,000 datasets. Bias (%): (slope estimateslope true )/slope true *100. Coverage (%): proportion of times the 95% confidence interval of the slope estimated by the model contains the true value. Convergence (%): number of times the statistical model has converged. AACRJournals. orgCancer Res Commun; 3(1) January 2023.
Acknowledgements This work was supported by the  Agence Nationale de la Recherche (ANR)  through the project  DYRAQ ANR-17-CE40-0016  and partly supported by the  IRP -CNRS  project  SPEDO  (for L. LT). J. L. acknowledges that the ICB is supported by the  EUR-EIPHI Graduate School  (Grant No. ANR-17-EURE-0002 ).
Sample collection Surveillance was performed monthly between June 2017 and May 2019. Bats were caught at the cave entrance upon emergence using Austbat three-bank harp traps (Faunatech), with traps kept open for five hours each sampling night. All animals captured during this period were sexed and recorded on data sheets. Only a subset of a maximum of 80 bats were sampled per month, whereby equal proportions of population demographics by sex and age were randomly taken for sample collection (also representing a sufficient sample size that could reliably be targeted with the available manpower over the duration of the sampling nights). During months when certain population cohorts were absent from the colony (e. g. , adult males), numbers of other cohort groups sampled were increased. Samples (blood, urine, oral and rectal swabs) were collected from R.
40  , yielding a nested amplicon of 268 bp. After analyses of nested products on a 1. 5% agarose gel (Lonza), all products of appropriate size were excised and purified with the Zymoclean™ Gel DNA Recovery Kit (Zymo Research). Purified amplicons were prepared for sequencing with the BigDye Terminator v3. 1 Cycle Sequencing Kit (Thermo Fisher Scientific) according to manufacturer's recommendations for 10 μl reactions and purified with the ethanol/EDTA/sodium acetate precipitation method. Sequencing was performed on the ABI 3500xl at the DNA Sequencing facility of the University of Pretoria. Sequences were submitted to Genbank with accession numbers: MZ547450-MZ547649.
Phylogenetic analysis Sequence manipulations and alignments were performed with CLUSTALW in the BioEdit sequence alignment editor (v7. 2. 5)  41. Sequences of relevant coronavirus species and similar reference genomes identified from BLAST analyses of sequences from this study were collected from GenBank (NCBI). Estimations of pairwise similarities were performed with p-distance analyses in MEGA v7  42. Phylogenetic analyses were performed with Bayesian phylogenetics using BEAST v. 1. 10. 4  43. CIPRES Science Gateway was used to run jModelTest2 and BEAST  44. Maximum clade credibility trees were constructed with the general time reversible (GTR) model with gamma distribution and invariant sites. Bayesian MCMC chains were set to 25,000,000 states, sampling every 2500 steps, and convergence confirmed via an effective sample size (ESS) of > 200.
All terms were included in a single model as the analytical goal was to test and compare the effects of multiple factors  49, 50. The GAMM initially fit with the restricted maximum likelihood estimation method using the mgcv package 51 in R 4. 2. 1  52  , then used these estimates to initialize Metropolis-Hastings MCMC sampling of the model posterior. Spline wiggliness was penalized to reduce to linear effects in the absence of support for nonlinear effects. Convergence and efficiency of MCMC chains were checked using the R-hat and Effective Sample Size statistics  53. Significance of nonlinear model terms was determined using Nychka criteria  54  , and reported model estimates and confidence intervals as means and 95% high-density intervals of posterior predictions. Both raw and modelestimated values of prevalence in pooled fecal samples were converted to individual-sample level using the Burrows estimator  55  , which corrects for upward bias in pooled sampling.
Coronavirus presence and diversity detected A total of 720 fecal pools and 710 rectal swabs were tested for coronavirus nucleic acid with a conventional RT-PCR assay  40. This resulted in a combined 200 positive samples, 94 from rectal samples (raw detection rate 13. 2%) and 106 from fecal pools (raw detection rate 14. 7%, corrected to 5. 2% when accounting for pooling). Modelestimated average (intercept) detection rate was 9. 6% (CI 7. 3-11. 9%) for rectal swabs, and 3. 3% (CI 2. 5-4. 1%) for fecal samples after correcting for pooling (Table  S1 ). The detection rate among rectal swabs was not statistically different from that estimated for the overall uncorrected pooled fecal samples (Table  S1 ). Datasets for samples containing coronavirus RNA are listed in supplementary dataset S1 and S2.
Recapture-directed estimates for duration of viral excretion Lastly, recapture data was used to compare detectable duration of viral excretion. For estimation of possible viral clearance or persistent infections, bats need to be frequently recaptured and tested for coronavirus RNA, preferably shortly after the initial detection of excretion. A total of 75 bats (10. 6%) from the 710 individuals sampled were recaptured. Among the recaptured bats, RNA was detected from 20 individuals. In nine recaptured bats, coronavirus RNA was detected only at their last recapture indicating bats were infected since their first capture. The remaining 11 bats represented individuals from which viral RNA was detected at their first or second capture, though not at subsequent captures (Fig. 5 ), which may be used to estimate possible viral clearance times.
Acknowledgements This work was financially supported in part by the  National Research Foundation (NRF) of South Africa : the  DSI-NRF South African  Research Chair held by WM Grant No. 98339  (as well as postdoctoral fellowship funding). The  NRF  is also thanked for funding the equipment based at the  DNA Sanger sequencing facility  in the  Faculty of Natural and Agricultural Sciences, University of Pretoria  (UID:78566) that was used to generate Sanger sequencing data presented in this work. The financial assistance of the  National Research Foundation (NRF)  towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. The research was also funded by the  Poliomyelitis Research Foundation  research Grant  19/09  awarded to  Marike Geldenhuys.