dataesr/scientific-paragraphs-categorization huggingface dataset:
Graphs from finite geometries Here q denotes a prime power, and ǫ ∈ {-, +}. • Graphs arising from projective geometry designs are discussed in Sect. 5. 2, along with other Steiner graphs. • Paley graphs. The vertices are the elements of F q , with q ≡ 1 mod 4; two vertices are adjacent if their difference is a nonzero square in F q ; see [8, 9. 1. 2]. • Polar space graphs. These include polar spaces for orthogonal and unitary groups, see entries O ǫ 2d (q), O 2d+1 (q), and U d (q) in [8, Table  9. 9]. Sagemath also has an implementation of polar spaces for symplectic groups (entry Sp 2d (q) in [loc. cit. ]), but we do not use them in the database, as they have the same parameters as these for orthogonal groups. • Generalised quadrangle graphs, GQ(s, t) in [8, Table  9. 9]. Apart from these appearing as polar space graphs, with s = t = q, s 2 = t = q, and s = q 2 , t = q 3 , we provide other examples, as follows.
Graphs from combinatorics • Johnson Graphs J(m, 2), see Example 2. 1. • Orthogonal Array block graphs OA(k, n). Sage is able to build a very substantial state-of-the-art collection of orthogonal arrays (often abbreviated as OA), thanks to a large implementation project undertaken in 2013/2014 by the first author in a very productive collaboration with Julian R. Abel and Vincent Delecroix. For the present work no new constructions of OAs were needed, and the link between Sage's OAs and Strongly Regular Graphs databases filled in three new entries in Andries Brouwer's database. • Steiner Graphs (intersection graphs of BIBD) -Sage can already build several families of Balanced Incomplete Block Designs (when k ≤ 5, or projective planes, or other recursive constructions and fixed-size instances).
• Pseudo-Paley and Pasechnik graphs from skew-Hadamard matrices. These are constructions due to Goethals-Seidel  [10]  and Pasechnik  [48] , constructing graphs on (4m -1) 2 vertices from skew-Hadamard matrices of order 4m. Sage builds the corresponding skew-Hadamard matrices from a small database featuring classical constructions of skew-Hadamard matrices from  [30]  and small examples from (anti)-circulant matrices  [24, 56].
Missing values Among the 1150 realizable, according to Andries Brouwer's database, parameter sets, our implementation can realize 1142. Up to taking graph complements, the list of currently missing entries is as follows. (196 90 40 42) RSHCD -(may not exist, cf. Sect. 7) (196 135 94 90) Huang, Huang and Lin  [32]  (378 116 34 36) Muzychuk S6(n = 3, d = 3)  [46]  (512 133 24 38) Godsil (q = 8, r = 3)  [23]  The fisrt entry is discussed in Sect. 7. Implementation of the remaining three entries is currently in progress.
Entries added to database during this work By linking Sage's database of Orthogonal Arrays with its database of Strongly Regular Graphs, we were able to fill in the following three values: • (196, 78, 32, 30) -can be obtained from an OA  (6, 14)  [55] • (324, 102, 36, 30) -can be obtained from an OA  (6, 18)  [1] • (324, 119, 46, 42) -can be obtained from an OA  (7, 18)   [1]  This can be seen as a by-product of making two mathematical databases, which formerly only existed in printed form, inter-operable. In our implementation, any update of the combinatorial designs databases can be beneficial for the database of strongly regular graphs. We obtained a (1024, 462, 206, 210)-graph while going through the constructions from  [50] , although this value did not appear in the online database at that time.
Acknowledgments The authors thank  Andries Brouwer ,  Eric Chen ,  Luis Disset ,  Hadi Kharaghani ,  Misha Muzychuk ,  Tim Penttila ,  John B. Polhill ,  Leonard Soicher ,  Vladimir Tonchev , and  Alfred Wasserman  for many helpful discussions and communications. The second author was partially supported by the  EU   Horizon 2020 research and innovation programme , grant agreement OpenDreamKit No  676541.
For example, Meyers et al  [251]  generates a network model to characterize the spread of SARS in Vancouver, British Columbia. They have used census data of Vancouver and using computer simulations generated a plausible contact network that reflects an urban setting. They had chosen N = 1000 households at random from the Vancouver household size distribution, which yields approximately 2600 people. Household members were given ages according to the census data of Vancouver. Kids were then assigned to schools according to school and class size distributions to occupations according to (un)employment data, to hospitals as patients and caregivers according to hospital employment and bed data, and to other public places. Within each location then random connections were created among individuals with variable probabilities at households, hospitals and schools, workplaces, and other public places.
Moreover, the research also found that, when the vaccination coverage is close to or at the level required to provide herd immunity, this effect of opinion formation (or clustering) facilitating outbreaks is the strongest. This in turn indicates that the estimated coverage level to avert an outbreak of measles may be much higher than realistic demands  [549, 576]. Quantitative characterization. Relative to the above primarily qualitative endeavors, Salathé et al. also defined a quantitative framework for the mixing patterns of vaccination behavior and opinions related to vaccinating  [580]. Based on publicly available data from Twitter, they firstly constructed a directed social network of information flow, where sentiment towards new influenza A (H1N1)-like vaccination was classified into four types: positive, negative, neutral, and irrelevant.
Indeed, contacts dynamics that affect the spreading of transmissible illnesses are those unfolding at comparable time-scale respect to the disease  [219, 652, 676, 686]. For example, the characteristics of contacts networks at the time-scale of days are relevant for the spreading of ILIs. In order to show more clearly this crucial point we will now consider a simple, yet not trivial, model of temporal human interactions. This modeling framework is based on the empirical observation that the propensity of individuals of being engaged in social acts, activity, is heterogeneous  [596]. Interestingly, such observations have been performed in a wide range of real datasets describing different types of human interactions or human dynamics ranging from conversations on Twitter to R&D alliances between firms  [596, 705].
Remarkably, this unsupervised method, returns as most relevant queries, searches associated to influenza, influenza complications, and remedies  [721]. It is important to mention that the expression reported above could be generalized to include a set of Q variables: P = ϑ 0 + i=1,n ϑ i Qi + , (254) each one associated to a different query  [724]. However, as noted in the original paper, the performance of the method was higher adding up all the signal in a signal explanatory variable  [721]. The initial results reported were extremely impressive: GFT had a mean correlation with surveillance data of about 0. 97 and was able to predict it one/two weeks ahead. It is worth thinking about this a bit more. A simple linear regression model fed with an unparalleled dataset of queries to a search engine is able to estimate with great accuracy information about the unfolding of ILI.
Clearly the methodology described is quite simple. The strength of the approach is the unique and unprecedented dataset used. For many different reasons this data cannot be easily shared. Consequently, researchers applied, extended, and improved the GFT archetype to other data streams that are instead accessible. Examples are Twitter and Wikipedia. Indeed, in both cases large samples and/or relevant complete information can been gathered via their standardized APIs. Methods using Twitter data rely on the assumption that people post tweet, information about their health status. In particular, tweets are mined in search of ILI related terms that are fed to regression models  [723] [724] [725] [726] 736]. The relevant terms are typically provided a priory or learned via machine learning techniques.
Mobile phone based methods Mobile phones are one of the most diffuse technological device. About 96% of the worldwide population has one  [755]. For billing purposes phone carriers collect call data records (CDRs) that can be mined and used to study our communications, social networks, and mobility (see Ref. [756]  for a recent review). The last two phenomena are of epidemiological relevance. In particular, contact networks estimated via CDRs can be used to characterize human interactions at large and long-term scales well beyond those accessible via participatory experiments mentioned above. Although, not all connections mediated by mobile phones are relevant for disease transmission, recent studies clearly show the possibility of inferring close proximity networks from CDRs  [757, 758]. The temporal features describing mobile phone networks are similar to those of actual closed proximity interactions  [591, 680, 681, 759].
However, CDRs can provide just contact networks integrated in time. Indeed, the empirical timestamp of each interaction is not per se relevant for disease spreading. Interestingly, also these, time-aggregated and static, networks share several statistical features with close proximity contacts. In particular, high clustering, transitivity, and assortativity have been reported  [756]. Furthermore, integrated mobile phone datasets are typically characterized by heavy-tailed distributions of contacts and weights. However, their heterogeneity are, also in this case, function of the time window used to aggregate data  [760]. From a modeling stand point, CDRs perfectly lend themselves as input and test bed for the different modeling efforts beyond the homogeneous mixing approximation discussed in Section 4.
Furthermore, they collected information, such as destination and time, about the movements of individuals made out of their primary settlement. This data has been combined with an simple epidemic transmission model based on high resolution maps of Malaria prevalence. The fusion of these two data sources allowed to define the networks of parasite movements across the country as well as source (net emitters of people and parasites) and sink (net receivers of people and parasites) regions  [762]. These results provided unprecedented lens to characterize Malaria dynamics and spreading. More importantly, they suggested a novel set of strategies for containment that targets large flows of human movements associated with high risk of importations. These encode many aspects of the complex dynamics driving the spreading and go well beyond the typical based on local transmission hot spots or routine surveillance in high-risk areas  [762].
The system is automatized and allows to process and digest incredible amount of relevant information providing comprehensive reports that are used to facilitate the detection or monitoring of public health threats across the world. The Health Map infrastructure is behind an impressive number of projects and specific applications  [769, 770]. Examples include Health Map Flu Trends in which all the different data streams are combined to provide forecasts of flu activity in the USA  [771, 772] , Dengue Map that provides real-time alerts of dengue outbreaks  [773] , or Health Map Vaccine which connects the population with vaccines  [750, 774]. As for the partecipatory survelliance systems described above, the data provided by Health Map does not provided any information about the contacts of individuals.
Future research on mean-field behavior-disease models should aim to further exploit benefits and potentialities of simple models, such as representing simple and parsimonious environments for coupling behaviordisease dynamics and allowing predictions at a high level of abstraction (e. g. population-level prevalence and coverage). As such, a first line of inquiry should use mean-field models for investigating the implications of further social, economic, or psychological theories of behavior relevant for vaccination in order to achieve a more detailed understanding of the "typically observed" behaviour (see e. g. [400] ). A second line should aim to more extensively develop the-just initiated-empirical use of mean-field models by applying them over different datasets (e. g. different countries) and different infections (e.
It will also track how these network topologies change in the face of a severe epidemic, or even how individual behaves when an intervention measure is implemented. The vibrant body of literature on digital epidemiology shows incredible potential as well as future directions and challenges. The size and heterogeneity of the datasets we will face is destined to increase dramatically. This will require the development of new algorithms and techniques to effectively collect, store and analyze large-scale epidemiological data. In particular, new approaches, specifically designed for epidemiology, will be needed to filter, classify, and model massive data streams. Cheaper and more scalable devices will be required to improve our understanding of face-to-face interactions and thus of spreading pathways.
Acknowledgements We would like to acknowledge gratefully  Lin Wang ,  Irene Sendiña-Nadal ,  Shlomo Havlin ,  Mark Newmann ,  Alessandro Vespignani ,  Yamir Moreno ,  Jesus Gómez-Gardeñes ,  Gao-xi Xiao, Ke-ke Huang, Zhi-xi Wu, Cheng-yi Xia, Gui-quan Sun ,  Jin Zhen ,  Hai-feng Zhang ,  Ming Tang ,  Da-qing Li ,  Wen-bo Du ,  Xue-long Li ,  Xin-yang Deng ,  Chao Gao ,  Yong Deng ,  Han-xin Yang ,  Marko Jusup ,  Yoh Iwasa ,  Shingo Iwami ,  Boris Podobnik ,  Lidia Braunstein , and  Bruno Goncalves  for their constructive help and discussions. We also appreciate all our other friends with whom we maintained (and are currently maintaining) interactions and discussions on the topic covered in our review. This work was supported by the  National Natural Science Foundation of China  (Grant No. 61374169 ),  Natural Science Foundation of Anhui Province  (Grant No.
* The research of E. F. leading to these results has received funding from the  European Research Council  under the European Union's  Seventh Framework Programme  ( FP7/2007-2013)/ ERC Grant Agreement 320078. The  Institute of Mathematics of the Academy of Sciences of the Czech Republic  is supported by  RVO : 67985840. † R. K. 's research has been partially funded by  Deutsche Forschungsgemeinschaft (DFG)  through grant  CRC 1114. ‡ E. Z. 's research has been supported by the  National Science Centre, Poland , grant  2014/14/M/ST1/00108  and by the fellowship  START of the Foundation for Polish Science.
2010 ). The data we use are readily available in the Finance data set contained in gmm. The estimation methods are two-step GMM and CUP-GMM with covariance matrix estimated with Bartlett and Quadratic Spectral (QS) kernels. Table  3  reports the values of J statistic for testing the validity of the restrictions (7. 4). For the two-step GMM, it is clear that the values of test statistics di er greatly across the normalizations, and are sensitive to the choice of kernels. Furthermore, the test rejects the null of correct speci cation under Normalization 2 with QS kernel, but the conclusion is reversed under Normalization 1. In the case of CUP-GMM with Bartlett kernel, though there is a small incongruity in the values of test statistics (possibly due to an optimization error), the model is not rejected under both normalizations.
Acknowledgements The authors thank  Marine Carrasco ,  Jean-Pierre Cotton ,  Russell Davidson ,  Abdeljelil Farhat ,  V. P. Godambe ,  Christian Gouriéroux ,  Stéphane Grégoir ,  Hervé Mignon ,  Denis Pelletier ,  Mohamed Taamouti ,  Pascale Valéry , three anonymous referees, and the Editor  Esfandiar Maasoumi  for several useful comments.
Acknowledgements E. S. is grateful to  Sergio Ferrara ,  Vasco Gonçalves ,  Yassen Stanev  and  Pedro Vieira  for helpful discussions. We acknowledge discussions with  Burkhard Eden  at the early stages of this project. D. C. and E. S. acknowledge partial support by the  French National Agency for Research (ANR)  under contract StrongInt ( BLANC-SIMI-4-2011 ). The work of D. C. has been supported by the " Investissements d'avenir, Labex ENIGMASS ". P. H. acknowledges support from the  STFC  Consolidated Grant  ST/L000407/1  and the  Marie Curie network GATIS  (gatis. desy. eu) of the European Union's  Seventh Framework Programme   FP7/2007-2013/ under REA Grant Agreement No 317089. J. M. D acknowledges support from  ERC  grant  648630.
This paper contributes to the existing literature in three ways: First, we measured contacts with both contact diaries and wearable proximity sensors at a scientific conference in Germany, adding another setting to the few existing datasets that allow an analysis of measurement differences and errors. Second, we investigate the potential impact of these differences on estimates of the basic reproduction number, R 0 , and contact duration. Third, we investigate the sentiments of participants towards both methods, in particular regarding practicability, privacy, participation's effects on social interaction, and the feasibility of potential future study designs.
Questionnaire on acceptability A questionnaire on demographic data (gender and age in 10-year categories) and acceptability of the two methods was also part of the diary booklet. We asked participants to rate twelve acceptability items (5 categories, for details see Fig. 3  and Additional file 1), to estimate the time needed for completing the diary, to evaluate if study participation affected their contact patterns, and to assess their own, perceived, reporting quality. Finally, we asked the participants if they deemed potential long-term population-based study designs based on wearable sensors feasible.
Data matching Diary and sensor data were matched directly when participants reported contacts including their counterpart's ID. Contact reports with a missing or unknown ID were, for sensitivity analysis, treated as discordant or matched based on plausibility. In the latter case, we created two different matched datasets, one optimizing the concordance within the diary data, the other optimizing the concordance between sensor and diary data. A necessary condition for a plausible match was in either case that a potential counterpart matches the reported demographics. For the diary-optimized dataset, a second condition for a match was that the potential counterpart reported contact to the reporting participant; for the other dataset, the second condition was that the sensors recorded contact between the reporting participant and the potential counterpart.
Resulting datasets For both self-reported and sensor-recorded data, three datasets were available for analyses: The self-reported sets consist of (i) raw data, (ii) data with matched contact reports (diary-optimized), and (iii) matched contact reports (sensor-optimized). The sensor-recorded sets consist of raw data and filtered data, using filter 1 and 2. As results for both filtered datasets were similar, we only show results for the data obtained after applying the stricter filter, i. e. , filter 2, and refer to them as filtered data.
Differences in strength between diary and sensor data We compared for each participant the strength  [31] , which is here the sum of the durations of all contacts a participant had with all its contacts partners throughout the study day, as measured by the sensors and as computed from contact diaries. The strength is considered a good indicator for a person's potential for disease transmission  [12, 32]. From the sensor data, we could derive strength point estimates. Duration in the self-reported data was a priori categorised. Hence, the diary strength of each participant was established as an interval ranging from the minimal to the maximal plausible strengths. To compute the minimal plausible strength of an individual A, we consistently assume the smallest possible durations (including 0) for all contacts in which A was involved (i.
Questionnaire For analysis of questionnaire items that required experience in keeping a contact diary (F1 to F4, Additional file 1), we considered only participants who reported contacts. To compare groups (e. g. , differences between genders or age strata), Chi 2 -or Fisher's Exact tests, when appropriate, were used for categorical variables and Wilcoxon or Kruskal-Wallis tests for continuous variables after evaluating distribution. We considered p-values < 0. 05 as significant. Analyses were conducted with STATA 12 IC (StataCorp LP) and, most of the contact data analyses, with code written for Enthought Canopy Python 2. 7. 3.
Description of contact data In total, 329 contact reports were obtained from the contact diaries, corresponding to 199 contacts: 130 contacts were noted by both parties (corresponding to 260 reports), 35 contacts were only reported by one participant (incl. 3 contacts to a participant who did not return the contact diary), and 34 contacts with unknown ID were reported (Table  1 ). Thus, crude overall concordance was 66. 3 % (130/196; denominator without the 3 contacts contacts to a participant who did not return the diary). After matching contact reports with unknown IDs with unreciprocated reports (diary-optimized matching variant), we obtained 189 contacts of which 137 were concordant (i. e. , 137 pairs of individuals reporting each a contact with the other), 25 contacts that were only reported by one participant, and 27 remaining contacts with unknown ID.
Overall, 54. 5 % (103/189) of contacts were physical and 67. 7 % (128/189) of contacts were with a well-known counterpart (see Additional file 13: Table  S1  and Additional file 13: Table  S2 ). The sensors recorded 316 contacts among the study participants, which would have resulted in 632 contact reports in the diaries if both capturing systems had assessed all contacts completely (Table  2 ). Comparing the crude survey and sensor datasets, we found 191 contact reports in the diaries (out of 329) that were also recorded by the sensors; 407 instances where the participants did not report a contact, but a contact was recorded by the sensors; 104 diary contact reports that did not match with the sensor recordings and 34 had an unknown ID. However, comparing edited survey data including matched "unknown IDs" (sensor-optimized) with filtered sensor data, we observed 219 concordant measurements, 313 instances without a diary report that were sensor-recorded, 106 reports that were not measured by the sensors, and 4 reports with a remaining unknown ID (Table  2 ).
Diary reporting probability From the diary data, we estimated the probabilities that a contact according to the diary contact definition was reported for the four different duration categories. For the matched dataset (diary-optimized), we estimated P = 72. 2 % [63. 5-81. 1 %] for durations <5 min, P = 86. 4 % [77. 3-94. 3 %] for durations 5-15 min, P = 89. 2 % [80. 6-96. 3 %] for durations 15-60 min, and P = 94. 4 % [88. 5-98. 8 %] for durations >60 min. The estimated probability for durations <5 min was significantly lower than the estimates for all three other categories (p < 0. 01); none of the other differences was statistically significant.
Differences between sensor and diary data For the filtered and matched datasets, we estimated a congruency of 33. 9 % [28. 0-40. 5 %] for <5 min; 78. 0 % [64. 7-90. 9 %] for 5-15 min; 93. 8 % [84. 4-100. 0 %] for 15-60 min. The estimated probabilities for all duration We analysed if there was a potential gender or age effect in reporting of contacts <5 min (for details see Additional file 13); however, assessing the confidence intervals of the respective proportions, none of the group comparisons revealed a significant difference. Stratified estimates for the other duration categories were not meaningful because of very wide confidence intervals. If using the reported contacts as denominator, and calculating the proportion of all reported contacts that were also detected by the sensor network, we estimated a detection probability 57.