dataesr/scientific-paragraphs-categorization huggingface dataset:
ACKNOWLEDGMENTS We thank many colleagues who asked good questions at several talks and posters given on this work; see, for instance, refs  81, 82   (i) Θ(t)µ = µ, for all t ∈ R. (ii) The basic probability measure P is the marginal on (Ω, F ) of µ, i. e. µ(E × X) = P(E) for any E ∈ F. It is known that any probability measure µ on (Ω × X, F × B) possesses a disintegration or factorization  35  , given by a function (ω, B) → µ ω (B) from Ω × B into the interval [0, 1] such that: (i) For any B ∈ B, µ ω is F -measurable; (ii) there exists a measurable set Ω ′ in Ω such that P(Ω ′ ) = 1 and µ ω is a probability measure on (X, B) for all ω in Ω ′ ; and (iii) for all f in L 1 µ (Ω × X) we have Ω×X f (ω, x)µ(dω, dx) = Ω X f (ω, x)µ ω (dx) P(dω). (C2) The disintegration µ ω is unique P-almost surely and it is also called a sample measure; see Young  69.
As discussed in Section II, BraMAH is a tpological data analysis approach that does not fall into the category of PH methods. The PH approach focuses on how connectivity properties of a point cloud change with respect to a parameter ǫ that is involved in the filtration rule, i. e. in the rule used to build the cell complex. PH cell complexes are parameter-dependent or multiscale, in the sense that the scale at which points are connected in the cell complex is given by the value ǫ of the filtration parameter: thus, at an ǫ = 0-scale, all points are disconnected, and they start connecting as the balls grow and intersect. The PH aim is to describe how the homologies of a cell complex so constructed are affected by the value of this parameter. BraMAH is, on the contrary, filtration-free and parameterless, in agreement with its aim, which is unambiguously identifying a branched manifold's topology from a point cloud.
The COVID-19 pandemic has led many governments to implement lockdowns. While lockdowns may help to contain the spread of the virus, they may result in substantial damage to population well-being. We use Google Trends data to test whether the lockdowns implemented in Europe and America led to changes in well-being related topic search terms. Using differences-in-differences and a regression discontinuity design to evaluate the causal effects of lockdown, we find a substantial increase in the search intensity for boredom in Europe and the US. We also found a significant increase in searches for loneliness, worry and sadness, while searches for stress, suicide and divorce on the contrary fell. Our results suggest that people's mental health may have been severely affected by the lockdown.
In this paper, we circumvent this problem by analysing data from Google Trends between January 1st 2019 and April 10th 2020 in countries that had introduced a full lockdown by the end of this period. This produces data on nine Western European countries. We also run a comparable analysis at the State level in the US. This is to our knowledge the first study to estimate the impact of lockdown on well-being related searches using Google trends data. As in previous work using Google Trends to successfully predict disease outbreaks  (Carneiro and Mylonakis (2009) ), tourism flows  (Siliverstovs and Wochner (2018) ) and trading behaviour in financial markets  (Preis et al. (2013) ), we assume that search indicators provide accurate and representative information about Google Search users' current behaviours and feelings.
Furthermore, Google search data shows aggregate measures of search activity in a location (e. g. a State or Country), and is thus less vulnerable to small-sample bias  (Baker and Fradkin (2017) ). Our main results come from a Difference-in-Difference (DiD) estimation that compares wellbeing related searches pre-and post-lockdown in 2020 to well-being related searches pre-and post-the same date in 2019, thus ensuring that seasonal changes within countries or State do not drive our findings. As set out in our pre-analysis plan (OSF; https://osf. io/4ywjc/), we submitted the thirteen following well-being related topic search terms to Google Trends: Boredom, Contentment, Divorce, Impairment, Irritability, Loneliness, Panic, Sadness, Sleep, Stress, Suicide, Well-being and Worry. We have daily data on searches for all of these.
Google Trends Data Google Trends data provides an unfiltered sample of search requests made to Google. It supplies an index for search intensity by topic over the time period requested in a geographical area. This is the number of daily searches for the specified topic divided by the maximum number of daily searches for this topic over the time period in question in that geographical area. This is scaled from zero to 100, where 100 is the day with the most searches for that topic and zero indicates that a given day did not have sufficient search volume for the specific term. A search term query on Google Trends returns searches for an exact search term, while a topic query includes related search terms (in any language). For our project, we submitted the thirteen following well-being related topic search terms to Google Trends between January 1st 2019 and April 10th 2020: Boredom, Contentment, Divorce, Impairment, Irritability, Loneliness, Panic, Sadness, Sleep, Stress, Suicide, Well-being, and Worry.
1 A related contribution is  Hamermesh (2020) , which uses data from the 2012-13 American Time Use Survey to show that happiness is correlated with both the people with whom the respondent spends time with and how this time is spent. Daily data on searches is only provided for a query period shorter than 9 months and up to 36 hours before the moment that the search request is made. Weekly data is provided for query periods between 9 months and 5 years. To obtain daily search trends between January 1st 2019 and April 10th 2020, we first downloaded daily data between January 1st and April 10th in both 2019 and 2020. As the daily data in 2019 comes from a separate request to the daily data in 2020, the scaling factors used to calculate the 0-100 score are not the same in the two periods. We therefore need to re-scale the two series so that they are comparable.
Scaling Procedure Let us denote by D i,c,2019 the number of Google daily searches for a topic on day i in country c, over the period January 1st 2019 to April 10th 2019, with an analogous number D i,c,2020 for the period January 1st 2020 to April 10th 2020. This data is obtained for each individual day i and takes on values between 0 and 100 for each day during the period considered (either January 1st 2019 to April 10th 2019, or January 1st 2020 to April 10th 2020). We cannot however directly compare the numbers from 2019 and 2020 as their denominator (the maximum number of searches during one day in the period) is not the same. A figure of 40, say, during the 2019 period may well reflect fewer searches than a figure of 35 in the 2020 period. To be able to compare these figures, we rescale the daily data for each period by the respective week search interest weights that we calculate using weekly data that is available continuously over the entire period between January 1st 2019 and April 10th 2020.
We denote by D i,c,2019-2020 the rescaled number of Google daily searches for this topic on day i in country c over the period January 1st 2019 to April 10th 2020. This is the number we wish to calculate. The following describes the calculation that allows us to obtain this figure and so make inter-day comparisons over the entire period. We first calculate the respective weekly search interest weights for all weeks between January 1st 2019 and April 10th 2020. We take the daily data from January 1st 2019 to April 10th 2019 and aggregate them to calculate the weekly average searches for the topic in country c over this period: D i,c,2019. We then carry out the same exercise for the period January 1st 2020 to April 10th 2020: D i,c,2020. From the weekly data downloaded over the entire period (i.
Sample selection We collected these data for countries that had introduced a full lockdown by the end of the period considered. This produces data on nine Western European countries: Austria, Belgium, France, Ireland, Italy, Luxembourg, Portugal, Spain and the United Kingdom. We also run a comparable analysis at the State level in the US. Appendix Figure  A1  and Appendix Table  A1  provide the date of lockdown for each of the countries and US States in our analysis. The use of Google Trends data presents a number of key advantages over survey data. First, the data are not self-reported by a sub-sample of respondents, but rather capture the impact of lockdown on the behaviours of all Google Search users. Furthermore, Google Trends data do not suffer from biases such as the observer-expectation effect or interviewer bias.
Third, Google Trends data are less vulnerable to small-sample bias. However, Google Trends data obviously have limitations. One of these is that younger individuals are relatively more likely than older individuals to use Google Search (although internet use is widespread in Europe, with 89% of EU-28 households having home internet access in 2018, from Eurostat Digital economy and society statistics). Another limitation is that we cannot look at heterogenous effects of lockdown by demographic groups, and especially on the most vulnerable populations. Our results should thus be read as the average impact of the stay-at-home orders on the health and well-being of Google Search users, rather than the effect on people with, say, pre-COVID-19 mental-health disorders.
ACKNOWLEDGEMENTS This paper was written while  Claudia Menini  was a member of the " National Group for Algebraic and Geometric Structures and their Applications " ( GNSAGA-INdAM ). She was partially supported by  MIUR  within the National Research Project  PRIN 2017. Ling Liu  was supported by the  NSF of China  (Nos. 11801515 ,  11601486 ), the  Natural Science Foundation of Zhejiang Province  (No. LY20A010003 ) and the  Foundation of Zhejiang Educational Committee  (No. Y201942625 ).
7. Automorphic vector bundles 3. 8. Coherent cohomology and Hecke operators 3. 9. Cohomological correspondences -definitions 3. 10. Cohomology and automorphic representations G. B. was supported in part by NSF postdoctoral fellowship DMS-1503047. F. C. was supported in part by NSF Grants DMS-1404620, DMS-1701703, and DMS-2001097. T. G. was supported in part by a Leverhulme Prize, EPSRC grant EP/L025485/1, ERC Starting Grant 306326, and a Royal Society Wolfson Research Merit Award. V. P was supported in part by the ANR-14-CE25-0002-01 Percolator, and the ERC-2018-COG-818856-HiCoShiVa. 1. Introduction 1. 1. Our main theorems. Let X be a smooth, projective variety of dimension m over a number field F with good reduction outside a finite set of primes S. Associated to X, one may write down a global Hasse-Weil zeta function: ζ X (s) = 1 1 -N (x) -s , where the product runs over all the closed points x of some (any) smooth proper integral model X /O F [1/S] for X.
As in the proof of Lemma 2. 4. 36, there exist Remark 2. 4. 38. Note that (using as usual that |W | = 8 distinct ideals m w such that M n ≃ ⊕ w∈W M mw , where m = (t 0 -γ 0 , t 1 -γ 1 , t 2 -γ 2 ) ⊂ k[X * (T )]. Since M n = 0, q v = 1 in k) we have that U naive v,0 = x 2 0 x 1 x 2 , and if this equals 1, then U naive v,1 = x 0 and U naive v,2 = (s 1 s 2 s 1 )x 1. Consequently we see for example that if the hypotheses of Lemma 2. 4. 36 hold then (U v,0 -1, U v,1 -α 1 , U v,2 -α 1 α 2 ) is in the support of M. 2. 5. Purity. Let K be a finite extension of Q p for some p, with residue field of order q. Following [TY07, §1], we say that a Weil-Deligne representation (W, r, N ) of W K on a vector space W over an algebraically closed field Ω which is of characteristic 0 and of the same cardinality as C is pure of weight w if there is an exhaustive and separated ascending filtration Fil i of W such that • each Fil i W is invariant under r; • if σ ∈ W K maps to Frob v(σ) K , then all eigenvalues of r(σ) on gr i W are Weil q iv(σ) -numbers; • and for all j we have N j : gr w+j W ∼ -→ gr w-j W.
Methods: Study design, setting, and participants: A nationwide cross-sectional study was performed between January 17 to March 17, 2021. Data was collected using a structured self-administered questionnaire which was distributed to a nationally representative sample of Syrian people. The questionnaire, based on a previous study, was modi ed to be suitable for Syrian society  (15) (16) (17). It was then piloted on a sample of 15 people to ensure clarity, and adjustments were made based on their feedback. Chain-referral and convenience sampling methods were employed by distributing the questionnaire in two formats: electronically as a Google Form survey via social media and messaging platforms (Facebook, Whatsapp, Twitter), and physically as hard copies to patients, their companions, and workers in public hospitals in each of Damascus, Aleppo, Homs, Tartous, Hama, and Sweida governorates.
The sample size was calculated using OpenEpi online software available at "https://www. openepi. com/SampleSize/SSPropor. htm". According to data from the United Nations, the estimated population of Syria in 2019 was about 18 million (18); based on this gure, the sample required to represent the total population was calculated to be 7336, with a con dence level of 95% and a con dence interval of 1. 14. Inclusion criteria were that the person is: (1) 18 years old or above, (2) literate, (3) a Syrian citizen living in Syria, and (4) willing to complete the questionnaire. Of the 8083 participants who responded to the questionnaire, 551 were excluded for not meeting the inclusion criteria (17 withdrew their consent to participate, 543 were not Syrians or lived outside of Syria), yielding a nal sample size of 7,531 participants.
Statistical analysis: Data from the hard copy questionnaires were entered manually by the investigators to the original Google Forms online questionnaire that was used to collect online data, after which it was exported to a Microsoft Excel spreadsheet. The raw data was then encoded in Excel to make it compatible with the statistics software. A 13 point scale was used to measure the level of commitment to IPC measures. Each individual measure was given one point, then each participant was categorized into one of three categories based on how many protective measures he/she applied: 1-Low commitment (0 -3 protective measures), 2-Moderate commitment (4 -8 protective measures) and 3-High commitment (9 -12 protective measures). We used Statistical Package for Social Sciences version 25. 0 ( SPSS Inc.
In this context, the present paper aims to analyze the general public opinion related to mask-wearing during COVID-19 by considering the tweets published in the one-year period starting from the first tweet posted regarding mask-wearing in the COVID-19 context (9 January 2020-8 January 2021). A number of 8,795,633 tweets written in English have been collected for the selected period, and stance detection using machine learning algorithms has been performed both on the entire and on the cleaned dataset. Besides collecting the COVID-19 mask dataset, annotating a subset and performing the stance detection, a series of analyses are conducted in order to connect the major events reported in the considered one-year period with the evolution of the number of tweets and the stance (in favor, against and neutral).
The chosen approach can be easily integrated into a monitoring system, which will allow the interested organizations to better observe how people's opinions changed over time regarding mask-wearing. Knowing the evolution of the opinions related to mask-wearing, different policies can be created, and various public awareness and public information campaigns can be created to support the mask adoption among the large public. The remainder of the paper is organized as follows. Section 2 provides a brief literature review structured in two parts: mask-related works in the COVID-19 context and Twitter analysis on COVID-19 data. Section 3 describes the methodology used in the paper, while Section 4 presents the COVID-19 mask dataset collection, the annotation process and the performance of the considered classification algorithms.
Section 5 presents the mask opinion dynamics in the considered period, while Section 6 connects the evolution of tweets to the major events reported in the news. The limitations of the study and discussions are provided in Section 7, while Section 8 is dedicated to conclusions and further developments. Supplementary Material accompanies the paper, consisting of collected and annotated COVID-19 mask-related datasets, along with the unigrams, bigrams and trigrams extracted for the considered period.
The authors considered data extracted for 200 countries until 9 May 2020. Based on the statistical analysis, the authors stated that in the countries not using the masks until 60 days from the start of the outbreak, the percapita mortality raised dramatically, while in the countries that have started using the masks up to 15 days of the onset, the mortality rate has been extremely low  [5]. Masks have been significantly associated with low mortality rates. The per-capita mortality increase per week in the countries making no recommendations regarding mask-wearing was approximately 55. 7%, higher than the 8. 1% recorded for the countries in which the mask-wearing recommendation was emitted by the government  [5]. Van Dyke et al. [21]  showed that after implementing the mask mandates in 24 Kansas counties, a reverse in the increasing trend of the COVID-19 incidence was observed.
Twitter Analysis on COVID-19 Data Twitter has been one of the main platforms for extracting and analyzing data related to people's opinions or feelings regarding different measures that have been taken since the coronavirus outbreak. According to Haman  [41] , since March 2020, the COVID-19 pandemic has been the dominant topic on Twitter. As a result, the scientific literature has analyzed people's opinions or emotions in relation to the COVID-19 pandemic in general or to various subjects of interest, as discussed in the following. Different emotions experienced by people on Twitter during COVID-19 have been analyzed by a series of researchers. Koh and Liew  [42]  have focused on the loneliness feeling expressed in tweets from 1 May 2020 to 1 July 2020. Three main triggers to loneliness have been considered: community impact, social distance and mental health.
The use of drugs for fighting COVID-19 based on Twitter extracted data has been analyzed in the scientific literature. Mutlu et al. [47]  have provided a set containing 14,374 tweets extracted from 11,552 unique users on Twitter in connection with the efficacy of hydroxychloroquine as a treatment for COVID-19. In the provided dataset, 47. 59% of tweets were in favor, 32. 59% of tweets were against, while 19. 81 tweets were neutral  [47]. The users' dynamics of the opinions regarding the COVID-19 vaccination in the month following the first vaccine announcement has been analyzed by Cotfas et al. [14]. The authors have considered 2,349,659 messages on Twitter regarding the COVID-19 vaccination and have concluded that most of the tweets have had a neutral stance, followed by in favor and against stances  [14].
Dataset Collection Step The tweets search has been performed using the keywords listed in Table 1  [60] , and the resulting language-specific dataset (in English) has been collected using Twitter API. As it has been assumed that the persons speaking about the inconveniences of mask-wearing or about the possible side-effects generated by mask-wearing would not wear a mask, no additional keywords have been used-other than the ones presented in Table  1. This assumption has been supported by the fact that none of the tweets in the annotated dataset that contained ideas about the presence of side effects when wearing a mask stated that the person would still use a mask for protection against COVID-19. Additionally, the set has been supplemented by adding the tweets extracted by Banda et al. [60] , selected based on the same set of keywords.
Classifiers Training and Selection Step To increase the quality of the annotated dataset, before the annotation process, the retweets and duplicated tweets have been removed, as suggested by  [61, 62]. From the remaining set, referred to in the following as cleaned dataset (in opposition to the entire dataset, which incorporates even the retweets, referred to as entire dataset), a sub-set of tweets has been extracted in a random manner. Due to the high number of tweets extracted in the one-year period considered in the analysis, the sub-set needed in the annotation process represents approximatively 1. 75% from the cleaned dataset. The annotation process has been performed by three persons, who have marked the corresponding category for each tweet in an individual file. Three categories have been considered:  in favor-all the tweets expressing positive messages regarding the use of masks during the COVID-19 pandemic with the purpose of protecting the wearer of the mask or the persons in his/her vicinity;  neutral-all the tweets referring to news related to mask-wearing, changes in the mask-wearing policies in different parts of the world or indoor/outdoor; information related to the efficiency of different types of masks; announcements related to maskselling offers; and all the tweets that do not express a clear opinion related to maskwearing;  against-all the tweets presenting a negative message regarding mask-wearing, including the refusal of wearing such a mask under all/any circumstances.
Additionally, some corrections have been made to the spelling errors and elongated words; all the letters have been transformed in lowercases; the hashtags have been unpacked. In order to perform this pre-processing step, the ekphrasis library and the Natural Language Toolkit (NLTK) library have been used along with the "re" python module  [63, 64]. Knowing that some of the classification algorithms rely on the word frequency, the Term Frequency-nverse Document Frequency (TF-IDF) has been used for reducing the weight of the most frequent words, which, in general, contain little to no information  [15]. A series of classification algorithms, such as Naive Bayes (MNB)  [65, 66] , Random Forest (RF)  [67, 68] , Support Vector Machine (SVM)  [69, 70] , Bidirectional Encoder Representations from Transformers (BERT)  [71]  and Robustly Optimized BERT Pretraining Approach (RoBERTa)  [72] , have been considered and their performance has been evaluated through the use of four of the most-well known indicators, namely Accuracy, Precision, Recall and F-score, on the purpose of selecting the best classifier for the mask dataset.
Stance Detection Step A new pre-processing step has been performed on the remaining set of tweets (the set of tweets that do not contain the annotated set). The best classification algorithm selected in the previous step has been used for stance detection. The stance detection has been performed on both the cleaned dataset and the entire dataset. As a result of the stance detection step, the considered tweets have been divided into the above-mentioned categories: in favor, neutral and against (as presented in Section 4) and their evolution is further analyzed in Section 5.